Marta Castilho Gomes
email: marta.gomes@ist.utl.pt

Ana Paula Barbosa-Povoa

Augusto Queiroz Novais
email: augusto.novais@ineti.pt

Marta ; Gomes

M C Gomes

A P Barbosa-Póvoa

Marta Castilho Gomes

Ana Paula Barbosa-Póvoa

A discrete time reactive scheduling model for new order insertion in job shop, make-to-order industries

Keywords: job shop scheduling, make-to-order production, integer programming, reactive scheduling job shop scheduling, make-to-order production, integer programming, reactive scheduling

A discrete time reactive scheduling model for new order insertion in job shop, make-to-order industries

Introduction

Industrial environments are dynamic in nature and disturbances in the daily operation of the plant such as machine failures, processing time delays, arrival of new orders and unavailable material may cause a predetermined schedule to become inefficient or even infeasible. Thus, in realtime, the ability to rapidly react to such unexpected events and revise the schedule in an effective way is as important as the scheduling problem itself. Starting in the 1950s, a great deal of effort has been spent developing methods to generate optimal or near-optimal production schedules. However, interest in reactive scheduling techniques, an issue of major importance in practice, intensified only in the last decade and the first review papers in the field appeared a few years ago [START_REF] Raheja | Reactive recovery of job shop schedules -A review[END_REF][START_REF] Vieira | Rescheduling manufacturing systems: a framework of strategies, policies and methods[END_REF].

A review of the literature in the discrete parts manufacturing field shows that most approaches are either heuristic or based on artificial intelligence (AI) techniques. Examples of the first kind of approach are the work of [START_REF] Jain | Production scheduling/rescheduling in flexible manufacturing[END_REF], [START_REF] Fang | A rolling horizon job shop rescheduling strategy in the dynamic environment[END_REF], [START_REF] Rangsaritratsamee | Dynamic rescheduling that simultaneously considers efficiency and stability[END_REF], [START_REF] Li | An heuristic rescheduling algorithm for computer-based production scheduling systems[END_REF] and [START_REF] Suwa | Capability of cumulative delay based reactive scheduling for job shops with machine breakdowns[END_REF]. The first three make use of genetic algorithms, the fourth develops an heuristic algorithm that adapts ideas from MRP systems and the last one uses tabu search to generate schedules. [START_REF] Smith | Reactive scheduling systems[END_REF], [START_REF] Goldman | A constraint-based scheduler for batch manufacturing[END_REF], [START_REF] Sun | A dynamic reactive scheduling mechanism for responding to changes of production orders and manufacturing resources[END_REF] and [START_REF] Wong | Integrated process planning and scheduling/rescheduling -an agent-based approach[END_REF] are examples of AI-based reactive scheduling systems described in the literature. The work of [START_REF] Liao | Daily scheduling for R&D semiconductor fabrication[END_REF] is an example of a mathematical programming formulation for reactive scheduling. They present a scheduling tool (with rescheduling capabilities) for the semiconductor industry, based on an integer programming formulation. However, the model is solved by an approximate, near-optimal solution method based on Lagrangian relaxation and network flow techniques; optimal solution was not attempted.

The following lines review recent examples of reactive scheduling approaches based on mathematical programming formulations for the process industries. [START_REF] Roslöf | An MILP-based reordering algorithm for complex industrial scheduling and resheduling[END_REF][START_REF] Roslöf | Solving a large-scale industrial scheduling problem using MILP combined with a heuristic procedure[END_REF] present a Mixed Integer Linear Programming (MILP) based algorithm that can be used in different instances: to improve an existing non-optimal schedule, to reschedule jobs in the case of changed operational parameters or to insert newly arrived jobs in a production program. [START_REF] Méndez | Dynamic scheduling in multiproduct batch plants[END_REF] introduce a MILP formulation for reactive scheduling of multiproduct batch plants. The approach allows multiple rescheduling operations at the same time: insertion of new order arrivals, reassignment of existing batches to alternative units due to equipment failures and the reordering and time-shifting of old batches at the current processing sequences. [START_REF] Janak | Production scheduling of a largescale industrial batch plant. II. Reactive scheduling[END_REF] address reactive scheduling of a large-scale industrial polymer compounding plant based on a MILP continuous-time formulation for short-term scheduling and a rolling horizon medium-term scheduling framework. The unexpected events considered are unit shutdown and the addition or [START_REF] Ferrer-Nadal | Optimal reactive scheduling of manufacturing plants with flexible batch recipes[END_REF] present a MILP-based approach for reactive scheduling of multistage, multipurpose batch plants that incorporates the concept of recipe flexibility (some tasks are allowed to modify recipe parameters as an additional rescheduling action). Events of unit breakdown, late order arrival and the need of maintenance tasks are dealt with in the case study presented.

Contrary to these works, where features of the predetermined schedule are maintained and hence the scope of rescheduling is intentionally limited, [START_REF] Vin | A new approach for efficient rescheduling of multiproduct batch plants[END_REF] address the problem of efficient reactive scheduling in multiproduct batch plants with no constraints imposed upon rescheduling alternatives. The situations modelled are machine breakdown and rush order arrival; the objective function includes a term for profit maximization and a penalty term used to minimize the deviations from the original schedule. [START_REF] Relvas | Reactive scheduling framework for a multiproduct pipeline with inventory management[END_REF] present a similar MILP-based approach to reactive scheduling of a complex oil supply system composed of a pipeline and associated end-of-pipe tank farm. Various system perturbations that require rescheduling were modelled, including variation on clients' demands, imposition on product sequence, unpredicted pipeline stoppages and batch volume modifications.

The present paper introduces a new strategy for reactive scheduling of job shop, make-to-order industries that relies on an extension of an integer linear programming model previously developed by the authors for scheduling this type of industries [START_REF] Gomes | Optimal scheduling for flexible job shop operation[END_REF]. The problem addressed is that of inserting new orders in a predetermined schedule, which is important and challenging in order-driven industries. [START_REF] Artigues | An efficient algorithm for operation insertion in practical jobshop schedules[END_REF] is an example of other approach to this problem: the authors propose an exact polynomial algorithm to insert a job operation in an existing schedule for multiresource job shop with sequence dependent setup times. Also, [START_REF] Caricato | An online approach to dynamic rescheduling for production planning applications[END_REF] develop a constraint programming approach to insert a new order in a production plan once it has already started. This is applied to an industrial case study where production is composed of several phases each of which can be considered as an independent stage in a generic hybrid flow shop.

A commonly used classification divides mathematical programming models for scheduling into discrete and continuous time models. Discrete time models divide the scheduling horizon into a finite number of intervals with equal and predefined duration and allow the beginning and ending of operations to take place only at the boundaries of these time periods. In continuous time models there is no previous division of the scheduling horizon, and timing decisions are explicitly represented as a set of continuous variables defining the exact times at which the events take place.

The proposed approach consists of a Generalized Job Shop scheduling model of discrete type combined with a Reactive Scheduling Algorithm that uses a dynamic scheduling horizon to successively solve the model when new orders arrive. These are added from a given insertion point Ierapetritou (2000). Nevertheless, here the extent of schedule changes is controlled by defining the sets of orders that may be rescheduled and those that cannot. By differently assigning those sets, several scenarios for new order insertion may be defined, allowing the best balance between meeting the new order due dates and the disruption of the previously defined schedule to be chosen.

Numerical examples are used to illustrate and further clarify the proposed approach. Order demands of several units to be produced and processing routes through several machine groups where different operations may take place in parallel lead to schedule dimensions (in terms of the total number of operations) considerably higher than the majority of the papers reviewed above (mathematical programming approaches to reactive scheduling). Optimal solutions of the models were successfully obtained offering promising perspectives for the development of this strategy.

Problem definition

Figure 1 depicts the type of job shop manufacturing environment modelled. Orders may follow different processing routes. Each order has an associated demand (a number of discrete units to be produced) and due date. Machine groups, represented by rectangles in figure 1, consist of a few homogeneous machines that may process several units in parallel with an upper bound on the total number of units being processed simultaneously -the machine group capacity. Machine groups have buffers (depicted by circles in figure 1) where units wait for processing in the group.

Intermediate buffers have finite capacity, while input buffers of a processing route (b 1 and b 7 in figure 1), as well as stocks of finished order units (b 9 and b 10 in figure 1) are considered of infinite size. Finite buffers have to be considered when products are physically large and buffer room between successive machines is of limited capacity.

The number of units in an order can be divided into smaller sized lots which are loaded onto machine groups throughout the scheduling horizon. Setup times are assumed to be negligible and material handling facilities for the transport of products in the shop are assumed to be nonrestrictive. This means the only constraints imposed on the problem of scheduling orders are the finite capacities of the buffers and machine groups.

Given the machine group and buffer capacities, the problem modelled and solved in this paper consists in obtaining a production schedule for an initial set of orders (scheduling problem) and then adapting it to insert new orders arrived after production of the initial ones has started (reactive scheduling problem). Scheduling objectives are to finish the units of each order as close as possible to the corresponding due date and to minimize storage in intermediate buffers.

Different rescheduling policies can be studied that may go from a total reschedule of the old orders (exception made to those undergoing processing) to a non-reschedule of the old orders.

Reactive scheduling methodology

Generalized Job Shop Scheduling Model

In this section the integer programming model developed by [START_REF] Gomes | Optimal scheduling for flexible job shop operation[END_REF] for scheduling job shop, make-to-order industries is generalized with a view to application in a dynamic context.

The scheduling problem can be described generically as follows.

Given: a) a set of orders, each corresponding to a processing route and having an associated demand (number of units) and due date; b) buffer and machine group capacities; c) initial conditions, i.e. the number of units in the intermediate and final buffers at the start of the scheduling horizon as well as the units loaded onto the machine groups before the scheduling horizon; the scheduling problem for a discrete time horizon between 0 and T is solved so as to satisfy a given scheduling objective.

In this paper we develop a reactive scheduling strategy for the job shop problem illustrated in figure 2. The scheduling horizon is progressively shifted to take the arrival of new orders into account (dynamic scheduling horizon) and the generalized job shop scheduling model solved for successive scheduling horizons ∆T k (e.g. ∆T 1 , ∆T 2 and ∆T 3 in figure 2) such that: a) the "new orders" arrived between t (k-1) start Note that the set of orders I is divided into two sets: orders to be scheduled for the first time (I new ) and those already scheduled and that may be rescheduled (I old ). Another division of I is due to the definition of processing routes (set J). I j is the set of orders that follow processing route j, some of which may belong to I new , others to I old . M is the unordered set of machine groups while M j is the ordered set of machine groups in processing route j. This means that for each machine group m ∈ M j the model refers its preceding and succeeding elements as m-1 and m+1 respectively, which correspond to the machine groups before and after that machine group in processing route j.

Whereas the base scheduling model of [START_REF] Gomes | Optimal scheduling for flexible job shop operation[END_REF] considered constant machine groups and buffer capacities, in the generalization to the reactive scheduling context these capacities become time-dependent and parameters u imv , x im and y i are used to link successive scheduling solutions.

In terms of variables, Figure 4 illustrates the association of X and Y variables with intervals (of unit length) and that of U variables with interval limits (instants).

Until they are finished, units of order i go (even if instantaneously) through the buffers that precede the machine groups in the corresponding processing route; this is accounted for by the X imt variables. Before processing has started, units are considered to be lodging in the buffer that precedes the first machine group of the processing route. However, the stock of finished units of an order is not associated with any machine group; this is the reason why final buffers are described by a new set of variables Y it . Finally variables U imt describe the units of order i loaded onto machine group m for processing at instant t.

( ) ∑ ∑ ∑ ∑ ∈ ∈ ∈ + ∈ +           - ⋅ +         ⋅ + - ⋅ = J j I i ) i(t i i f M imt im it t i it j last Y q h X h Y Y ψ Z ∆T t 1 } { | m 1 , j j Subject to: i q X start imt = ∀ i∈ I new , m=f j : i∈ I j X imt start = 0 ∀ i∈ I new , m∈ M j |{f j }: i∈ I j Y it start = 0 ∀ i∈ I new 0 ) ( = -v t im start U v =1,…,P im ∀ i∈ I new , m∈ M j : i∈ I j im imt x X start = ∀ i∈ I old , m∈ M j : i∈ I j Y it start = y i ∀ i∈ I old imv v t im u U start = -) ( v =1,…,P im ∀ i∈ I old , m∈ M j : i∈ I j imt p t m i imt t im U U X X m i - + = - - - + ) ) ( )( 1 ( ) 1 ( 1 ∀ i∈ I, m∈ M j |{f j }: i∈ I j , t ∈ ∆T imt imt 1) im(t U X X - = + ∀ i∈ I, m=f j : i∈ I j , t ∈ ∆T ) ( ) 1 ( im p t im it t i U Y Y - + + = ∀ i∈ I, m=l j : i∈ I j , t ∈ ∆T ∑ ∑ ∑ ∈ ∈ ∈ - + = ≤ j j M m J j I i t im P t mt im c U : 1 τ τ ∀ m∈ M, t ∈ ∆T ∑ ∑ ∈ ∈ ∈ ≤ } { | : j j j f M m J j I i mt imt b X ∀ m∈ M, t ∈ ∆T ∪ {t last +1}
Variables X imt , U imt , Y it are integer.

(

) (4) (7) (6) (10) (9) (11) (12) (13) 3
(2)

(5) The objective function (1) incorporates the main decisions that influence scheduling in the make-to-order manufacturing environment modelled: to observe the order due dates and to reduce in-process inventory. Orders are composed of several units produced independently; ideally they should all be finished at the corresponding due date but it is possible to finish part of the units before and part of the units after the due date (i.e. the due date is a "soft constraint"). This is accounted for by the first term in (1). Ψ it is the earliness/tardiness penalty coefficient for order i at instant t, which is the product of the time span (regarding the due date) by the earliness/tardiness coefficients per unit of order i per time unit:

   > - ≤ - = i i i i i i d t d t g d t t d e it ) ( ) ( ψ ∀ i∈ I, t ∈ ∆T.
Y i,t+1 -Y it is the number of units of order i whose processing was finished at instant t:

) ( 1 , im p t im it t i U Y Y - = - + ∀ i, m=l j : i∈ I j , t ∈ ∆T.
The second term is the cost of keeping (uncompleted) units in intermediate buffers and the third one a penalty for the orders not fully completed at the end of the scheduling horizon (if this term was to be excluded from the objective function, the minimization of this function would imply a value of zero for the X and Y variables, i.e. no production would take place).

Equations 2 to 8 define conditions at the start of the scheduling horizon. Equation (2) states that orders in I new are released at t start and so the number of units of each order i in the first buffer of the corresponding processing route is q i . Equations ( 3) and (4) define that the intermediate and final buffers are empty and equation ( 5) guarantees that no units are loaded before the start of the scheduling horizon. Equations ( 6), ( 7) account for the orders in I old , to be rescheduled, at the start of the scheduling horizon and that may have units lodging in any buffer. Equation ( 8) accounts for the units loaded onto machine groups and still in processing.

Flow balance equations 9-11 are the "core constraints" of the model that establish the relationship between the number of units in buffers in adjacent time intervals. Equation 9 defines the number of units of an order i in an intermediate buffer between instants t and t+1 as the algebraic sum of the number of units in the buffer in the previous interval plus the number of units that the preceding machine group finished processing at instant t and hence added to the buffer minus the number of units loaded onto the next machine group at instant t, and hence were withdrawn from the buffer. This balance is different in the cases of the first buffer in a processing route (equation 10) since there is no preceding machine group, and also in the final buffer (equation 11) because there is no subsequent machine group. Note that p im , the processing time of units of order i in machine group m, is a constant: units may be considered as being processed "in parallel", Finally, the machine capacity constraints (12) ensure that the total number of units undergoing processing in a machine group between instants t and t+1 does not exceed the available capacity. In addition, buffer capacity constraints (13) limit the total number of units lodging in the buffer of a machine group, between instants t-1 and t, to the available capacity. The initial buffers of processing routes are not included in this sum since they are unlimited in size. In each iteration of the algorithm the user defines the scheduling horizon as well as the subset of "old orders" (i.e. orders already scheduled) that may be rescheduled, leaving the others unchanged or "fixed". By defining the subset of "reschedulable" old orders the extent of schedule changes is controlled by the user. Continuity between scheduling solutions for these orders is ensured by computing model parameters x im , u imv and y i . Available machine group and buffer capacities are obtained after subtracting the capacity used by the "fixed" old orders, and as a consequence are dependent on the time instant t. A detailed description of the Reactive Scheduling Algorithm is presented below. The first scheduling solution is obtained by solving the GJS model from scratch for a set of orders I and a scheduling horizon ∆T 1 defined by the user with:

Reactive Scheduling Algorithm

I new = I I old = ∅ ∆T = ∆T 1

Cycle (to be repeated):

A new scheduling solution is obtained from the last one by inserting a set of new orders. This comprises the following steps: ∀ i∈ I resch , m∈ M j : i∈ I j e2) Parameter u imv stores units whose processing in a given machine group started v time units before t k start and is still on-going: Compute machine group capacities available in ∆T k by subtracting from the total machine group capacity the units of orders in I fixed still undergoing processing:

) ( v t im imv start k U u - = v = 1,…, P im ∀ i∈ I resch ,
∑ ∑ ∑ ∈ ∈ ∩ ∈ - + = - = j fixed j M m J j I I i t im P t im m mt U c c : ) ( 1 τ τ ∀ t∈ (∆T (k-1) ∩∆T k ) c mt = c m ∀ t∈ (∆T k \∆T (k-1) ) g)
Compute buffer capacities available in ∆T k by subtracting from the total buffer capacity the units of orders in I fixed lodged in buffers:

∑ ∑ ∈ ∈ ∩ ∈ - = } { | : ) ( j j fixed j F M m J j I I i imt m mt X b b ∀ t∈ (∆T (k-1) ∩∆T k ) b mt = b m ∀ t∈ (∆T k \∆T (k-1) ) h)
Reassign sets I, I old and ∆T:

I old = I resch I = I old ∪ I new ∆T = ∆T k . i)
Solve the GJS model for I and ∆T .

j)

If k did not reach the iteration limit: go to a).

Computational study

In this section, computational results for numerical examples are presented. Example 1 (a small size job shop) is thoroughly explored in terms of results with the purpose of clarifying the reactive scheduling methodology. This includes visual representation of solutions, a powerful aid to compare and apprehend differences between rescheduling solutions. A large size job shop (example 2) is further introduced to show the capabilities of the proposed approach regarding problem size.

1 Example 1: Description

Example 1 has two processing routes depicted in figure 6. There are five machine groups in the shop; machine groups M1 and M4 are common to both processing routes. Experiments with various features of the solver to speed up the solution process showed a significant increase when the simplex dual algorithm (default setting) was replaced by the simplex primal to obtain the initial relaxed solution of the problem.

Application of the Reactive Scheduling Algorithm to example 1 consisted of scheduling old orders O1 to O7 first and then inserting new orders O8 and O9, which arrive at instant 15, henceforth called the insertion point. The GJS model is solved again and a second scheduling solution, or rescheduling solution, is obtained that schedules the new orders as well as the subset of the old ones allowed to be rescheduled. Time distribution of the order due dates is depicted in Figure 7. In Table 3, Z * stands for the optimal value of Z in the second scheduling and Z new for the contribution of new orders. While Z new can be compared between scenarios, Z * and Z resch cannot, since the number of reschedulable old orders varies. With a view to overcome this limitation, a new value of Z old is computed after the second scheduling (for ∆T = [0,60]). This value is also shown in Table 3 together with Z total , which quantifies the global rescheduling solution and is given by the sum of Z old and Z new . To further characterise the solutions, table 3 also displays the number of scheduled operations (their total and division into old and new orders), the observed changes in the first schedule (which identifies the orders actually changed) and the number of changes in the schedule. These changes may consist of new operations, removed operations or quantity changes, and are defined as follows: where U imt (schedule) and U imt (reschedule) are the values of variable U imt for the old order i in the first and second scheduling solutions, respectively.

All combinations or scenarios display a trade-off between the values of Z new and Z old : a better insertion (and hence lower values of Z new ) is obtained at the cost of a degradation of Z old . However, the magnitude of the decrease in Z new may not equal the increase in Z old and hence the quality of the global scheduling solution (assessed by Z total ). In the limit, when rescheduling of all orders is allowed (scenario 8), only orders O1 (finished at the insertion point) and O5 (close to the insertion point) are left unchanged; all other remaining orders are rescheduled. This gives rise to the best new order insertion (a 33% decrease in Z new with respect to scenario 1) but also the highest deterioration of Z old (an 88% increase). The solution is overall the best, with an improvement in Z total of 1.4%

regarding scenarios 1 to 3, but also the one displaying the most operations and schedule changes.

Scenarios 3 (rescheduling of order O7) and 5 (rescheduling of orders O4 and O7) stand out as those displaying a finer balance between new order insertion and schedule changes; the former if we want changes to be negligible and the latter when moderate changes are allowed.

Table 4 shows model performance regarding the (first) scheduling solution and the smallest and largest scenarios for rescheduling (scenarios 1 and 8). The number of variables, constraints and nonzero elements of the models are shown as well as the number of iterations and computation times.

CPU times needed to solve the models to optimality were considerably less than one second. When new orders are optimally inserted with no changes in the previous schedule (figure 12), a total of 40 operations is required to process these orders. Operations for new orders are shown in a different grey shade and pattern to differentiate from old order operations. In machine groups M1

Example 1: Visual representation of solutions

and M3 new order operations start immediately after old order operations are finished, indicating optimization of resource use; the same is not visible in the other machine groups due to processing route constraints. The number of units per operation for new orders is on average lower than for the old ones, being under 5 in several cases (for the old orders this is a multiple of 5 between 5 and 20).

In figures 13A and 13B the bar colour and pattern for new order operations is equal to that used in figure 12. Regarding the old orders, distinction is made between old order operations left unchanged and old order operations different from the initial schedule either in time allocation or number of units processed. Unchanged operations are marked with the same colour and pattern used in figure 12. Division of production into more operations with a lower unit content per operation is visible in every machine group both for old and new orders, compared with scenario 1; for new orders, the number of scheduled operations more than doubles (88 operations). Order O4 is the only exception to this operation division trend. A comparison of the time span of new order production in both scenarios shows that rescheduling of old orders allows new orders to be started earlier in all machine groups but also to be finished later in some of them. The first effect, however, is stronger since a 33% decrease in Z new is observed, and thus the overall insertion of the new orders is better in scenario 8.

Example 2: Description

A larger example is now introduced with result analysis provided in condensed form.

Figure 14 displays the job shop in schematic form, which comprises 14 machine groups and 4 processing routes. Table 5 displays the processing times and table 6 machine groups and buffer capacities. Table 7 presents the order data: due date, demand and processing route for each order.

Orders O1 to O10 are scheduled first and three new orders (O11 to O13) must be inserted in the production scheduling. The number of units to produce is 710 in total. Costs in the objective function are the same as in example 1.

Example 2: Results

A scheduling horizon of 170 time units is needed to finish production of the old orders. New orders can be scheduled from instant 40 onwards (insertion point) and a new scheduling horizon [40,240] is needed in any of the scenarios constructed to complete all orders (limits of scheduling horizon are rounded to a multiple of 10). Results and model performance are summarized in table 8.

Four scenarios were constructed for new order insertion: the extreme scenarios (no rescheduling and rescheduling of all orders allowed) and two intermediate scenarios (rescheduling of 3 and 7 orders allowed). Although the corresponding integer programming models display tenths of thousand variables and constraints, solving them to obtain (and confirm) optimal solutions took just a few seconds. The optimal value of the objective function (Z * ), number of operations scheduled and number of changes in the first schedule are also shown. Figure 15 shows division of the objective function into the Z resch and Z new terms. Allowing for a larger number of old orders to be rescheduled leads to an increase in Z resch and Z* but also a better insertion of the new orders since the corresponding Z new value decreases. On the one hand, the size of NP-hard scheduling problems for which results with exact methodologies can be obtained has been consistently increasing with the expansion of computer capacity. In the case of mixed-integer linear programming approaches, another factor adds to this effect: the development of algorithms for solving this type of models which have been incorporated into increasingly efficient software tools nowadays available to researchers as pointed out by [START_REF] Bixby | MIP: theory and practice -Closing the gap[END_REF] and [START_REF] Gupta | Flowshop scheduling research after five decades[END_REF]. On the other hand, in discrete time models scheduling constraints have only to be monitored at specific and known time points, which reduces the problem complexity and makes the model structure simpler and easier to solve, particularly when resource and inventory limitations are taken into account [START_REF] Méndez | State-of-the-art review of optimization methods for short-term scheduling of batch processes[END_REF]. In fact, the solution of the linear relaxation is generally tight to the integer solution which has a dramatic effect on the number of nodes to be solved and hence the computation time of the branch-and-bound search.

Both effects explain the fact that for example 2 the Reactive Scheduling Algorithm was able to generate the rescheduling scenarios in a few seconds although the MILP models have thousands of variables (all of discrete nature) and constraints (table 8). Response time is a critical issue for reactive scheduling since in most of the real-world industrial environments it is necessary to quickly adapt the on-going schedule after the occurrence of unexpected events.

A major disadvantage of discrete time models is that their performance depends on the time unit used. In most of the real cases processing times need to be rounded in order to avoid obtaining a very large model (which will happen if the discretisation interval used is small). In continuous time models processing times can be accurately represented because continuous variables are used for the timing decisions. A reactive scheduling approach for make-to-order industries based on a continuous time formulation has also been developed by the authors in [START_REF] Gomes | Reactive scheduling in make-to-order production systems: An optimization based approach[END_REF], Gomes, Barbosa-Póvoa andNovais (2006, 2007).

Conclusions and future work

In this paper a new strategy for reactive scheduling of job shop, make-to-order industries is Reactive Scheduling Algorithm appropriate to be included in a decision support system for scheduling job shop, make-to-order industries.

The approach is illustrated with realistic examples of a small and a large size job shop where orders have an associated due date and demand (several discrete units to be produced). In both cases, an initial schedule and different alternatives for inserting new orders were generated using commercial mathematical programming software. Optimal solutions obtained in very low CPU time show the usefulness of the proposed approach. Result analysis included computing changes to the initial schedule and, for the small size example, depicting solutions in graphical form (Gantt charts and machine load diagrams). The former is a novel aspect of this work, since measures of scheduling efficiency are well described in the scheduling literature but the impact of disruptions induced by rescheduling has seldom been addressed [START_REF] Rangsaritratsamee | Dynamic rescheduling that simultaneously considers efficiency and stability[END_REF]). Visual representation of solutions is almost absent from the scheduling literature for discrete parts manufacturing. We opted to include it since it conveys more information about a solution than numerical performance measures and therefore has a deeper impact in illustrating how the Reactive Scheduling Algorithm works.

In the future, and regarding application of this work to a specific production environment, the definition of the objective function implies determining inventory costs (of uncompleted and finished units) and penalties for failing to meet due dates, which will depend both on the product type and the client importance. The impact of the cost/penalty used for each term both on the solution generated and the computational effort should also be assessed. This sensitivity analysis would be more comprehensibly undertaken on the basis of a system that was accepted by the scientific community as a credible standard. With this work the authors aimed at the setting up of such a system, which explains their concern in adjusting the penalties for tardiness, earliness, inventory and processed orders, to values experienced and reflecting priorities of actual operating plants. On-going exploratory work suggests that given the number of criteria involved, the use of two nested optimization cycles might be preferable to the generation of Pareto curves. In which case the inner cycle would be the system as is, and the outer one the optimization of the criteria themselves, given a previous indication of the aspiration level or range for each of them.

Constant changes in production schedules induce instability, sometimes labeled "shop floor nervousness", and are undesirable in dynamic environments. Future developments of the integer programming model should therefore intensify control upon the rescheduling process such as adding constraints to limit changes in the operations previously scheduled, using different weights for old and new orders in the objective function and including a penalty term in the objective function for changes in the schedule. Inserting new orders in the production schedule is a significant problem in order-driven industries. In the future, the Reactive Scheduling Algorithm should cope List of figure captions:

(

  in time) onwards by freely rescheduling operations in the previous schedule, asin Vin and

Figure 1 .

 1 Figure 1. Manufacturing environment modelled

Figure 4 .

 4 Figure 4. Representation of the model variables.

  time is independent of the number of units that start being processed in a given machine group and time instant.

Figure 5

 5 Figure 5 depicts the reactive scheduling methodology proposed. The integer linear programming model for job shop scheduling derived above is embedded in a Reactive Scheduling Algorithm that shifts the scheduling horizon and solves the model iteratively to insert the new orders that continuously arrive at the shop.

Figure

  Figure 5: Reactive Scheduling Algorithm

  a) Increase k (k = k+1); b) Divide the set of orders I in the last iteration into sets I resch and I fixed where the former is the set of orders that can be rescheduled and the later the set of orders that remain unchanged. I = I resch ∪ I fixed c) Define a set of new orders to be inserted in the schedule, I new . d) Define a new scheduling horizon ∆T k = {t k start , t k start +1, …, t k end -1, t k end }. e) Store conditions at the start of the new scheduling horizon for orders in I resch : e1) Parameter x im stores units lodged in buffers:

  m∈ M j : i∈ I j e3) Parameter y i stores finished units:

Figure 6 .

 6 Figure 6. Processing routes in example 1.

Figure 7 .

 7 Figure 7. Due dates in example 1. Orders above the time line follow processing route I, the ones below it follow processing route II.

---

  New operation: U imt (schedule) = 0 and U imt (reschedule) > 0 Removed operation: U imt (schedule) > 0 and U imt (reschedule) = 0 Quantity change: U imt (schedule), U imt (reschedule) > 0 and U imt (schedule) ≠ U imt (reschedule)

Figures 8

 8 Figures 8 to 10 display load diagrams for machine group M1, common to both processing routes, in scenarios 1, 5 and 8. A distinction is made between:

  Figure11depicts the Gantt chart for the initial schedule (old orders), figure12displays the solution after new order insertion in scenario 1 and figures 13A and 13B the solution obtained in scenario 8. Operations are represented by bars in different grey shades so as to make the distinction between adjacent machine groups clearer. Each bar displays the number of units loaded onto the machine group as well as the corresponding order (in brackets). The total number of units loaded at one time is limited by the machine group capacity.

Figure 8 .

 8 Figure 8. Capacity of machine group M1 used in scenario 1 (no orders rescheduled).

Figure 9 .

 9 Figure 9. Capacity of machine group M1 used in scenario 5 (orders O4 and O7 rescheduled).

Figure 10 .

 10 Figure 10. Capacity of machine group M1 used in scenario 8 (all orders may be rescheduled).

Figure 11 .

 11 Figure 11. Scheduling of old orders in example 1.

Figure 12 .

 12 Figure 12. Insertion of new orders without rescheduling of the old ones in example 1.

Figure 13A .

 13A Figure 13A. Insertion of new orders with full rescheduling of the old ones in example 1.

Figure 13B .

 13B Figure 13B. Insertion of new orders with full rescheduling of the old ones in example 1 (continued).

Figure 15 .

 15 Figure 15. Division of the objective function in example 2.

  presented. It combines an integer linear programming model (discrete time model) and a ReactiveScheduling Algorithm that shifts the scheduling horizon and solves the model iteratively to take account of new orders that keep arriving at the shop. Continuity between solutions is guaranteed by storing conditions in the previous solution at the start of a new scheduling horizon. When inserting new orders the extent of schedule changes is controlled by the user through definition of the subset of orders that may be rescheduled, leaving the others unchanged. Different scenarios for inserting a set of new orders in an on-going schedule can thus be constructed and compared making the

Figure 1 .

 1 Figure 1. Manufacturing environment modelled.

Figure 2 .

 2 Figure 2. Dynamic scheduling horizon for reactive scheduling.

Figure 3 .

 3 Figure 3. Scheduling horizon (discrete time treatment).

Figure 4 .

 4 Figure 4. Representation of the model variables.

Figure 5 .

 5 Figure 5. Reactive Scheduling Algorithm.

Figure 6 .

 6 Figure 6. Processing routes in example 1.

Figure 7 .

 7 Figure 7. Due dates in example 1. Orders above the time line follow processing route I, the ones below it follow processing route II.

Figure 8 .

 8 Figure 8. Capacity of machine group M1 used in scenario 1 (no orders rescheduled).

Figure 9 .

 9 Figure 9. Capacity of machine group M1 used in scenario 5 (orders O4 and O7 rescheduled).

Figure 10 .

 10 Figure 10. Capacity of machine group M1 used in scenario 8 (all orders may be rescheduled).

Figure 11 .

 11 Figure 11. Scheduling of old orders in example 1.

Figure 12 .

 12 Figure 12. Insertion of new orders without rescheduling of the old ones in example 1.

Figure 13A .

 13A Figure 13A. Insertion of new orders with full rescheduling of the old ones in example 1.

Figure 5 .Figure 6 .Figure 7 .

 567 Figure 5. Reactive Scheduling Algorithm

Figure 10 .

 10 Figure10. Capacity of machine group M1 used in scenario 8 (all orders may be rescheduled)

Figure 11 .PageFigure 12 .10

 1112 Figure 11. Scheduling of old orders in example 1

Figure 13B .Figure 15 .

 13B15 Figure 13B. Insertion of new orders with full rescheduling of the old ones in example 1 (continued)

  M1) or equal (M4) in both routes. These machine groups display a total capacity of 30 units while the other (M2, M3 and M5), assigned to only one route, can process at the most 20 units simultaneously. No more than 5 units are allowed to wait in intermediate buffers when production is running.Due dates and demand (number of units) for the set of orders to be produced, as well as the corresponding processing route, are presented in Table2. Orders O1 to O7 are scheduled first and a pair of new orders (O8 and O9) arrives requiring schedule adaptation i.e. reactive scheduling. The total number of units is 215.Parameter values g i = 20, e i = 1, h im = 0.1 and n i =10 7 for all orders i and machine groups m were used in the objective function (they are equal to the ones used in[START_REF] Gomes | Optimal scheduling for flexible job shop operation[END_REF]. A very large value for n i is used to force production of all units in the scheduling horizon and leave no uncompleted orders at the end.Both the Generalized Job Shop model and the Reactive Scheduling Algorithm were implemented in the General Algebraic Modelling System (GAMS, 1998); the GJS model was solved with CPLEX version 8.1.0 on a 3 GHz Pentium IV with 512MB of RAM running Windows XP Professional.

	times may be different (
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	14

Table 1 displays the processing times in each machine group. For machine groups common to both routes processing

Table 1 .

 1 Processing times in example 1.

Table 2 .

 2 Order data in example 1.

Table 3 .

 3 Summary of results for example 1.

Table 4 .

 4 Model performance for example 1.

Table 5 .

 5 Processing times in example 2.

Table 6 .

 6 Machine groups and buffer capacities in example 2

Table 7 .

 7 Order data in example 2

Table 8 .

 8 Summary of results for example 2

	Figure

14. Processing routes in example 2.

Table 1 .

 1 Processing times in example 1

	with other important situations in this type of industry like changes in order specifications (due date,
	demand) and order cancelling.
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	21

Table 2 .

 2 Order data in example 1

	F o r P e e r R e v i e w	O n l y
	2

Table 3 .

 3 Summary of results for example 1 : optimal value of the objective function in the second scheduling (rescheduling), where Z * = Z resch + Z new . For solution comparison, Z total must be used (Z total = Z old + Z new ). Z old , Z resch , Z new : summation of equation (1) over the set of old orders, reschedulable old orders and new orders, respectively.

	Scenario	No. of	Z * †	Z total	Z old	Z new	No. of operations	Changes in the first schedule
		reschedulable
		old orders					Total	Old orders	New orders	Changed orders	No of changes	No. of new operations	No. of removed operations	No. of quantity changes
	1	None	10960.0	14849.0	3889.0	10960.0	104	64	40	None	0	0	0	0
	2	O4	11660.0	14849.0	4549.0	10300.0	118	68	50	O4	12	8	4	0
	3	O7	12660.5	14849.0	4789.0	10060.0	105	64	41	O7	6	3	3	0
	4	O2, O6	11793.0	14848.5	3888.5	10960.0	114	64	50	O2	2	1	1	0
	5	O4, O7	13300.9	14789.4	6589.4	8200.0	122	76	46	O4, O7	34	19	7	8
	6	O3, O4, O7	13860.7	14749.2	5829.2	8920.0	134	84	50	O3, O4, O7	43	27	7	9
	7	O4, O6, O7	13502.4	14789.4	6109.4	8680.0	128	85	43	O4, O7	43	28	7	8
	8	All (O1 to O7)	14637.2	14637.2	7317.2	7320.0	141	88	53	O2, O3, O4,	64	34	10	20
										O6, O7
	† Z

*

Table 6 .

 6 Machine groups and buffer capacities in example 2

Table 7 .

 7 Order data in example 2

		Machine Machine Buffer
		group	capacity capacity
		m1	20	500
		m2	45	100
		m3	45	80
		m4	30	110
		m5	10	90
		m6	25	60
		m7	15	75
		m8	15	80
		m9	20	90
		m10	30	90
		m11	35	90
		m12	15	90
		m13	15	90
		m14	40	90
		m15	10	90
	Order Demand Due date	Processing route
	O1	60	100	I
	O2	35	50	I
	O3	30	87	I
	O4	25	22	II
	O5	25	80	II
	O6	65	60	III
	O7	40	90	III
	O8	25	50	III
	O9	85	40	IV
	O10	40	70	IV
	O11	95	70	I
	O12	85	100	III
	O13	100	90	IV

Table 8 .

 8 Summary of results for example 2 † For proven optimal solution (optimality gap = 0).

  Capacity of machine group M1 used in scenario 5(orders O4 and O7 rescheduled)

	4 F o r P e e r R e v i e w 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Time interval Fixed capacity Reschedulable old orders Insertion point Figure 8. Capacity of machine group M1 used in scenario 1 (no orders rescheduled) 40 42 44 46 48 50 52 New orders International Journal of Production Research O n l y 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 Time interval Fixed capacity Reschedulable old orders New orders Insertion point International Journal of Production Research Time interval Fixed capacity Reschedulable old orders New orders Figure 9. Page 37 of 44 Number of units 0 5 10 15 20 25 30 35 0 2 Number of units 0 5 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 O n l y 10 15 20 25 30 35 Number of units F o r P e e r R e v i e w Insertion point	54 54 54	56 56 56	58 58 58	60 60 60	Page 36 of 44
	7 8

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.uk http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.uk

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research


Jörn-Henrik Thun
email: thun@is.bwl.uni-mannheim.de

Martin Drüke
email: druekemartin@johndeere.com

André Grübner
email: andre.gruebner@henkel.com

Empowering Kanban through TPS-Principles -An Empirical Analysis of the Toyota Production System

Keywords: LEAN MANUFACTURING, TOYOTA PRODUCTION SYSTEM, EMPIRICAL Toyota Production System, just-in-time production, empirical analysis, performance

The purpose of this paper is the empirical investigation of the Toyota Production System in order to test existing relationships as they are proposed in theory. The underlying model consists of seven factors reflecting the key practices of the Toyota Production System. Using data from 188 manufacturing plants participating in the High Performance Manufacturing research project, the model's measurement characteristics were validated through confirmatory factor analysis. Path analysis of the model showed that the majority of the relationships can be confirmed. Furthermore, a comparison of mean analysis based on a conducted cluster analysis indicates that plants with a higher implementation degree of the practices of the Toyota Production System show also a higher perceived performance in terms of the key criteria of production, i.e., time, cost, quality, and flexibility.

INTRODUCTION

The Toyota Production System (TPS) can be regarded as the most popular production concept [START_REF] Black | Design rules for implementing the Toyota Production System[END_REF]. Its ground-breaking approach to implement a lean production philosophy on the shop-floor of industrial companies has revolutionized the perspective of manufacturing. Many other automotive companies adopted the practices of the TPS such as Kanban and created an equivalent production system, e.g. the HPS at the Hyundai Motor Company [START_REF] Lee | The mutation of the Toyota Production System: adapting the TPS at Hyundai Motor Company[END_REF]. The Toyota Production System bases upon the philosophy of waste elimination, which results in lean and rational production processes [START_REF] Monden | The Toyota Production System[END_REF].

Although many times the Toyota Production System is equated with just-in-time production, the very basic concept is the "reduction of cost through the elimination of waste" [START_REF] Sugimori | Toyota Production System and Kanban System -Materialization of just-in-time and respect-for-human system[END_REF]. This fact is also stressed by [START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF], who states the meaning of its primary purpose: "It's a system for the absolute elimination of waste." Using the concepts of the Toyota Production System, companies are able to eliminate waste, therefore produce efficiently and gaining a competitive advantage, which is stressed by [START_REF] Spear | Decoding the DNA of the Toyota Production System[END_REF]: "The Toyota Production System has long been hailed as the source of Toyota's outstanding performance as a manufacturer."

Considerable research has been done on the Toyota Production System, especially on the contribution of the TPS practices to manufacturing performance. One of the main drivers for the superior performance is the utilization of the just-in-time philosophy by the thorough implementation of Kanban [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF]. However, there is limited research on the interdependence of the underlying TPS practices and how they affect Kanban and which TPS practices are necessary for a successful Kanban implementation. The paper wants to close this gap by showing that Kanban enfolds its 3 full potential, if Kanban is embedded in a supportive infrastructure, which is represented by a three layer model. In this model Kanban forms the practice of the main layer, which bases upon a supportive layer of practices (factory layout, setup times and quality). These supporting practices are empowered by a layer of primary practices (multi skilled and trained workers), which is the key driver for a thorough Kanban implementation.

The paper is organized as follows. Firstly, we review the relevant literature in terms of the practices of the Toyota Production System, which constitute the three layers of the Kanban model as a foundation of the empirical analysis. Secondly, the main hypotheses for the empirical analysis are developed. Finally, we present the research design and key variables, before concluding with the analysis of the study and summary results.

LITERATURE REVIEW

Basic approaches of the Toyota Production System

The foundation of the lean philosophy is that all forms of waste have to be eliminated, as waste is defined as any activity which does not add value in the eyes of the customer. Some authors report a percentage of waste in a traditional production system of about 90 percent [START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF][START_REF] Stalk | Competing Against Time -How Time-based Competition Is Reshaping Global Market[END_REF]. Ohno identifies 7 sources of waste, which are waste of overproduction, waiting, transporting, over-processing, inventories, moving, and defective parts and products [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF]. Additionally, the waste of not making use of peoples' potential is mentioned. The following practices within the Toyota Production System strive to eliminate the sources of waste to ensure an efficient and lean production system. There are two central approaches of the Toyota Production System: just-in-time and "respect for human" system. Just-in-time is achieved through the implementation of numerous, well-known practices such as Kanban, short setup times, multi-skilled workers, etc. However, just-in-time production is just a vehicle to reach the overall goal of the total elimination of waste and, thereby, to implement lean production. Furthermore, [START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF] even points out that "the Toyota Production System is so powerful that it could squeeze water from a dry towel", which expresses the ability of TPS to eliminate waste and gain productivity in production.

The second central approach of the Toyota Production System is the "respectfor-human" system [START_REF] Sugimori | Toyota Production System and Kanban System -Materialization of just-in-time and respect-for-human system[END_REF]. All workers physical movements should add value to the product, otherwise they are considered waste. Since the workers take care of many quality problems themselves, they enjoy much broader responsibilities and authority, e.g., every worker at Toyota has the privilege, but also the duty to stop the assembly line if a problem occurs.

Practices of the Toyota Production System

Following [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF], the first aspect of the Toyota Production System is "putting a flow into the manufacturing process". In order to realize this flow, the just-in-time production concept must be regarded as the most critical aspect [START_REF] Pegels | The Toyota Production System--Lessons for American Management[END_REF]. In a just-in-time framework, the production of parts, components, etc. has to occur exactly just-in-time, i.e., not any earlier or any later. In literature there appears to be an agreement about the advantages of just-in-time production, which consist of low inventories and scrap costs, better quality, faster response to engineering changes and higher productivity [START_REF] Goyal | A Critique of the Literature on Just-in-Time Manufacturing[END_REF]. [START_REF] Sakakibara | The Impact of Just-in-Time Manufacturing and Its Infrastructure on Manufacturing Performance[END_REF], who see just-in-time as an overall organizational phenomenon, this paper concentrates on the issues that are directly linked to shop-floor operations such as setup, maintenance, etc. How such a just-in-time approach can be accomplished with respect to the production control of a manufacturing plant, can be answered with the production concept of Kanban (see for a discussion of the TPS and Kanban in the academic literature [START_REF] New | Celebrating the enigma: the continuing puzzle of the Toyota Production System[END_REF]. For Toyota, pull systems, respectively Kanban represent the ideal state of just-in-time manufacturing, because it provides the customer with what, when and the amount he or she wants [START_REF] Liker | The Toyota Way: 14 Management Principles from the World`s Greatest Manufacturer[END_REF].

With the inherent flexibility of the Kanban system, Toyota sustains its just-in-time manufacturing (Monden, 1981). [START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF] describes the basic idea of Kanban by the following analogy: "Some people imagine that Toyota has put on a smart new set of clothes, the Kanban system, so they go out and purchase the same outfit and try it on. They quickly discover that they are much too fat to wear it!" Accordingly, manufacturers must eliminate waste and make fundamental improvements in their production system before a technique such as Kanban can work efficiently. Shingo concludes that the Toyota Production System is 80 percent waste elimination, 15 percent production system, and only 5 percent Kanban [START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF].

Following the just-in-time concept, production is strictly triggered by Kanban cards so that no early or late production is allowed. This simple steering mechanism does not need a complex and therefore costly computer system for support and avoids the bureaucratic procedures of push system concepts [START_REF] Pegels | The Toyota Production System--Lessons for American Management[END_REF]. This decentralized production control system allows the parts and components to flow smoothly through a lean production facility. The pull principle as basic idea of Kanban is often illustrated by the example of a supermarket [START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF]: Supermarket customers buy what they want, when they need it. Since they take away what they need, a gap in the shelves occurs. This gap will be refilled again. The supermarket system was adopted in the machine shop at Toyota around 1953 [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF]. Also in terms of Kanban, Ohno refers to the meaning of just-in-time: "If parts arrive anytime prior to their need -not at the precise time needed -waste cannot be eliminated. By using Kanban, waste of overproduction is completely prevented" [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF].

However, if applied, Kanban reduces cost by decreasing inventories and increases on-time performance by producing parts and components with short cycle times. Accomplishing just-in-time production by using Kanban is only one step. In order to implement Kanban effectively it has to be supported by other TPS practices. This aspect is supported by Liker, who states that the TPS practices condition each other. The TPS is not a toolbox, where a company can pick the instruments that appear to be useful, but represents an approach that has to apply all TPS principles as a system in order to be effective [START_REF] Liker | The Toyota Way: 14 Management Principles from the World`s Greatest Manufacturer[END_REF]. These practices constitute a supportive and a primary layer enabling Kanban to work effectively. Furthermore, it is important to note that success necessitates the integration of the TPS practices and definitely not highly selective use of just one practice [START_REF] Towill | Exploiting the DNA of the Toyota Production System[END_REF]. A successfully working Kanban system demands an integrated infrastructure of supporting practices making Kanban more a result than an enabler of thoroughly implemented TPS practices. The highly integrated nature of Kanban can be seen as one reason why Kanban might be utilized only to a low extend. Hence, the supportive layer will be described in the following. A consequence of a smooth production flow is the production in small lots [START_REF] Sekine | One-Piece Flow -Cell Design for Transforming the Production Process[END_REF]. A lean production system strives for the ideal lot size of one. But small lots lead to many setups, which would disrupt a smooth production flow. This fact is stressed by [START_REF] Sugimori | Toyota Production System and Kanban System -Materialization of just-in-time and respect-for-human system[END_REF], who state: "…each process can produce only one piece, can convey it one at a time, …, have only one piece in stock…". [START_REF] Goyal | A Critique of the Literature on Just-in-Time Manufacturing[END_REF] strengthen this by even saying that "JIT ultimately aims at unit lot sizes and consequently aims at minimizing the setup time". Therefore, short setup times are a prerequisite.

An approach for drastically reducing setup times is introduced by Shingo commonly referred to as SMED [START_REF] Shingo | A Revolution in Manufacturing: The SMED System[END_REF][START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF]; for a critical evaluation see [START_REF] Mcintosh | A critical evaluation of Shingo's 'SMED' (Single Minute Exchange of Die) methodology[END_REF]. With SMED setups are analyzed in terms of their potential to reduce the needed setup time. In order to shorten the time that a machine has to shut down, setup process steps are differentiated into two classes: internal and external.

Internal setup steps are those that can only be performed while the machine is standing still, whereas external setup steps can be done while the machine is still running. SMED tries to convert internal in external steps. By SMED, setup times have been shortened dramatically, e.g., Toyota has shortened the time for a setup of a press from more than three hours to the single-minute-range [START_REF] Pegels | The Toyota Production System--Lessons for American Management[END_REF]. On average, the reductions by SMED techniques are around 80 to 95 percent [START_REF] Shingo | A Study of the Toyota Production System From an Industrial Viewpoint[END_REF].

Kanban requires a reliable production system because the negative consequences of machine breakdowns and production disruptions cannot be compensated anymore. A reactive maintenance strategy is not appropriate any longer, because a so called firefighting strategy leads to many unexpected machine breakdowns, since machines solely receive maintenance in the case of a breakdown and not before a malfunction occurs. In 8 a lean environment, the occurrence of breakdowns cannot be accepted anymore and must be eliminated. The main purpose of preventive maintenance is to maximize overall equipment effectiveness by eliminating unexpected machine breakdowns [START_REF] Nakajima | Introduction to Total Productive Maintenance (TPM)[END_REF]. This is achieved by a scheduled maintenance programme or conditioned-based maintenance.

To enable preventive maintenance, other supportive approaches such as autonomous maintenance or training of machine operators are necessary in order to make a preventive maintenance system work effectively [START_REF] Thun | Maintaining preventive maintenance and maintenance prevention: analysing the dynamic implications of Total Productive Maintenance[END_REF], Goto, 1989a).

Especially training of machine operators is a necessity for the successful implementation of Total Productive Maintenance. Furthermore, the overall equipment effectiveness [START_REF] Dal | Overall equipment effectiveness as a measure for operational improvement[END_REF][START_REF] Ljungberg | Measurement of overall equipment effectiveness as a basis for TPM activities[END_REF] can be increased by maintenance prevention (Goto, 1989a), i.e., machines are improved during the development process.

In this paper, we focus on preventive maintenance as basic idea of Total Productive Maintenance.

The effectiveness of the Kanban system is supported by a production process structure that enables a constant and smooth flow. The layout, how the production process can be organized is illustrated with the following statement by [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF]: "In the past, lathes were located in the lathe department, and milling machines in the milling area. Now, we place a lathe, a milling machine, and a drilling machine in the actual sequence of the manufacturing processing. This way, instead of having one worker per machine, one worker oversees many machines or, more accurately, one worker operates many processes." At Toyota, such a system is called multi-process operation system. By a layout, which considers the production flow, productivity can be improved significantly [START_REF] Hyer | Cellular Manufacturing in the U.S. Industry: A Survey of Users[END_REF][START_REF] Johnson | Cellular Manufacturing at 46 User Plants: Implementation Experiences and Performance Improvements[END_REF]; [START_REF] Hyer | Reorganizing the Factory -Competing through Cellular Manufacturing[END_REF]. However, workers must be multi-skilled in order to fulfil the requirements of such a layout in terms of different operating tasks [START_REF] Huber | The Human Factor in Cellular Manufacturing[END_REF]. In a layout for smooth production flow, the system has to change from "one operator, one machine" to a system of "one operator, many machines in different processes" [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF].

In the Toyota Production System, all errors are sources of waste. Everyone in operations must beware of the meaning of quality. [START_REF] Goyal | A Critique of the Literature on Just-in-Time Manufacturing[END_REF] stress the importance of quality as the "critical element for JIT`s success". The attitude towards quality must be changed in a way that quality has to be produced originally, not checked afterwards, which is known as quality at the source. The production system should guarantee a frictionless operation. This way, the production system strives for zero defects, so that an undisturbed material flow through the production processes is possible. In order to produce quality at the source, techniques such as statistical process control are used. For the monitoring of the process quality, workers must be trained.

With a high process quality level, shorter lead times and less safety stock can be achieved.

The primary layer consists of two practices, i.e., multi-skilling and training. As setting up of the production flow is of primary interest, the Toyota Production System strives to achieve a multi-process operating system. For a machine operator on the production line, who works in a multi-process operation system, this requires the operator to become multi-skilled [START_REF] Ohno | Toyota Production System -Beyond Large-Scale Production[END_REF]. Accordingly, multi-skilled workers are a critical issue for a layout in which a worker has to operate at several different machines. Besides layout, multi-skilled workers are important for the reduction of setup times [START_REF] Jindia | Applying total employee involvement to revolving change over[END_REF]. They have to be able to accomplish the actions An overview of all layers and the particular practices is given in figure 1.

Review of empirical work

In the literature, a few empirical papers on the Toyota Production System in terms of just-in-time and Kanban exist. The interrelation between just-in-time and quality is investigated by [START_REF] Flynn | Relationship Between JIT and TQM: Practices and Performance[END_REF]. [START_REF] Forza | Work Organization in Lean Production and Traditional Plants: What are the Differences[END_REF] examines the differences between lean plants and traditional plants in terms of the work organization. A comprehensive analysis on just-in-time manufacturing is provided by [START_REF] Sakakibara | The Impact of Just-in-Time Manufacturing and Its Infrastructure on Manufacturing Performance[END_REF]. They analyze the relationship to the infrastructure and the performance. [START_REF] Nakamura | Adoption of Just-in-Time Manufacturing Methods at U.S. and Japanese Owned Plants: Some Empirical Evidence[END_REF] investigate the adoption of just-in-time manufacturing. They compare U.S. plants and Japanese owned plants. [START_REF] White | JIT Manufacturing: A Survey of Implementations in Small and Large U[END_REF] investigate the differences of the implementation of just-in-time manufacturing in small and large U.S. companies and the impact on performance. They come to the conclusion that the frequencies of the 10 JIT management practices implemented differ between the two groups of manufacturer size. [START_REF] Adler | Flexibility Versus Efficiency? A Case Study of Model Changeovers in the Toyota Production System[END_REF] [START_REF] Lewis | Lean production and sustainable competitive advantage[END_REF], in which he explores the impact of lean production principles on sustainable competitive advantage of firms. Another case study-based research on the Toyota Production System is done by van Driel and Dolfsma (2009). [START_REF] Fullerton | The production performance benefits from JIT implementation[END_REF] show performance benefits of JIT and continuous process improvement with a survey on 95 JIT-practicing firms in the U.S. An examination of the relationship between JIT and the financial performance has been done on 253 US manufacturing firms by [START_REF] Fullerton | An examination of the relationships between JIT and financial performance[END_REF]. [START_REF] Ahmad | The role of infrastructure practices in the effectiveness of JIT practices: implications for plant competitiveness[END_REF] examine empirically the role of infrastructure practices on the effectiveness of JIT practices with data based on a study of 110 plants from Japan, US, and Italy. They show that the majority of the infrastructure practices moderate the relationship between JIT practices and plant competitiveness. Matsui (2007) provides an empirical analysis of the impact of just-in-time production on competitive performance using the data of 46 Japanese manufacturing companies. Altogether it can be stated that none of the empirical studies analyze the whole package of Toyota Production System key practices, but just its singular elements.

EMPIRICAL ANALYSIS

The High Performance Manufacturing Project

The empirical analysis is based on data taken from the research project "High Performance Manufacturing". This project is an international cooperation of research groups from the U.S., Japan, Germany, Sweden, Finland, and South Korea. It is the follow up to the project "World Class Manufacturing", which was done in 1997 with the primary purpose to evaluate critical success factors in operations management (Flynn Aspects such as technology management, IT-management, quality management, or human resource management are analyzed in the manufacturing context. Furthermore, the questionnaire comprises multiple items reflecting the techniques of the Toyota Production System as they have been discussed in the earlier section so that the data can be used to construct measures corresponding to the Toyota Production System.

Research Methodology

In order to guarantee a proper translation, the international questionnaire is translated by Professors of Operations Management into the national language and is then retranslated into the original language by a different person. Afterwards, the translations are compared in order to identify potential translation problems. The plants are randomly selected from a list of plants with at least 100 employees. Data is compiled for each plant from 23 respondents from various levels in the plant hierarchy and all major functional areas. This procedure gives a transversal image of a plant and helps to avoid the key informant bias [START_REF] Sakakibara | The Impact of Just-in-Time Manufacturing and Its Infrastructure on Manufacturing Performance[END_REF] The survey is collected on a country by country basis, i.e., each research group collects the data of ca. 30 plants of the three industries automotive, electronics, and machinery separately in their particular country. The plants are defined at the three-digit Standard Industrial Classification (SIC) code level. The industries were chosen as examples of industries in transition, whose plants were expected to exhibit a wide range of variability in practices and performance [START_REF] Flynn | The World Class Manufacturing Project: A Retrospective View of Research Issues and Methodology[END_REF]. The data is then aggregated into one final international data base. The data base comprises qualitative and quantitative information, whereby the qualitative questions are intermixed in order to avoid that scale membership is readily apparent.

The estimations for the items concerning the Toyota Production System are predominantly given by the Inventory Manager, Production control manager, and three shop floor Supervisors each of which is expected to be the most knowledgeable in providing the desired information. For the empirical analysis, some plants are excluded from the data base due to missing data. The indicators used in this research were qualitative ones, measured with Likert-type scales ranging from "strongly disagree" to "strongly agree" and reflecting perceptions of managerial personnel about their topics.

The items concerning the Toyota Production System are used to create factors presenting a statistical construct for the particular subject matter like it is described in the following.

Development of a three layer Kanban Model

As the Literature Review reveals, the Toyota Production System consists of multiple practices that are connected with each other. Figure 1 All the techniques of the supportive layer as described above cannot work for themselves. They depend on other factors, which can be interpreted as the driving force of the Toyota Production System: human resources. The Toyota Production System emphasises the "respect-for-human" [START_REF] Sugimori | Toyota Production System and Kanban System -Materialization of just-in-time and respect-for-human system[END_REF]. Accordingly, a primary layer is added to the overall system which consists of two factors: multi-skilled workers and the training of workers. These people related factors training and capability to fulfil multiple tasks constitutes the primary layer that enables a production system that is controlled by a Kanban system. Note, that these two factors will not be absolutely independent from each other since both deal with a similar issue. However, in this study we analyze them separately since both practices show essential differences. The second main research hypothesis is stated as follows: Combined and properly implemented and executed, the described instruments can result in sustainable performance improvements. Short setup times lead to small lot sizes and short lead times, combined with Kanban, result in low inventories and a high fill rate. A thorough Quality Management keeps quality problems at a minimum and in combination with Total Productive Maintenance, production processes are reliable and stable. Kanban as a manufacturing execution system keeps the cost of steering the production at a minimum.

The discussed practices are influencing the key performance metrics of production time, cost, quality, and flexibility as mentioned by several authors [START_REF] Ahmad | The role of infrastructure practices in the effectiveness of JIT practices: implications for plant competitiveness[END_REF][START_REF] Groenevelt | The Just-In-Time system[END_REF][START_REF] Primrose | Evaluating the introduction of JIT[END_REF]). These competitive factors can be measured by different manufacturing performance criteria such as unit cost of manufacturing, quality of product conformance, on-time delivery performance, or flexibility to change product mix [START_REF] Ahmad | The role of infrastructure practices in the effectiveness of JIT practices: implications for plant competitiveness[END_REF]. The Toyota Production System is aiming and impacting these metrics and therefore the inner heart of production, which is the "competitive weapon" of manufacturing companies [START_REF] Skinner | Manufacturing: The formidable competitive weapon[END_REF][START_REF] Skinner | Manufacturing -missing link in corporate strategy[END_REF].

Accordingly, the question is investigated whether the plants that have implemented the Toyota Production System to a higher extend than plants with a low implementation degree show also a better performance. This aspect and the two hypothesis discussed

Analyses

The conceptual model presented in figure 1 is tested against the sample of the HPMproject. A path analytic approach is chosen to test the hypothesis 1 and 2a/b since traditional regression analyses ignore interrelations between constructs, which potentially biases the results by excluding important interdependencies from analysis [START_REF] Asher | Causal modeling[END_REF][START_REF] Bollen | Structural equations with latent variables[END_REF]. This method decomposes the empirical co-variances among the measured items and estimates path coefficients that are equivalent to standardized regression coefficients in a standard regression model. The further analysis is following a two-step approach. At first the different concepts, e.g., layout of production process, degree of multi-skilled workers, are composed, using a confirmatory factor analysis. The second step of the analysis estimates the strength of relationships between the different factors using a path model.

The seven different factors identified as key principles of the Toyota Production

System represent hypothetical constructs that are reflected in different indicator variables, i.e., a high indicator value of the usage of Kanban containers for signaling in production control is a representation of the degree of implementation of a Kanban system in the production system of a given plant. The factors are of reflective nature; they are causes of the parameter value of each indicator variable associated with a factor. Thus, the value of each indicator is a representation of each of the underlying factors. agreement between indicators and the underlying theoretical construct is reached. All factor loadings are significant with p<0.01 and show relatively high factor loadings, leading to the conclusion that good convergent validity is accomplished by the model.

Only the primary factor multi-skilling shows only low factor loadings. The measurement of this factor is associated with a higher measurement error than other factors of the model. However, all factor loadings are highly significant. Since the overall model fit also shows good explanation of the empirical data, this factor will not be discarded but further interpretation of model results have to consider the inferior measurement of this construct. To assess construct reliability Cronbach´s Alpha is calculated for each factor separately. A commonly accepted threshold value for Cronbach´s Alpha is 0.7 [START_REF] Nunnally | Psychometric Theory[END_REF]. For newly developed scales a threshold value of 0.6 can be accepted [START_REF] Sakakibara | The Impact of Just-in-Time Manufacturing and Its Infrastructure on Manufacturing Performance[END_REF]. The results depicted in table 1 show that all factors meet this standard.

INSERT TABLE 1

Table1: Confirmatory model of TPS main, supportive and primary factors Further examination of the Toyota Production System constructs has to assess the assumption that each factor is measuring a distinct empirical construct. A common criteria to assess a construct's discriminant validity are factor correlations. A high correlation between factors would indicate that they are not discriminative [START_REF] Bagozzi | Assessing Construct Validity in Organizational Research[END_REF]. The results depicted in table 2 show that some factors do correlate, partly on a relatively high level. However, since the factors presented here are part of a common production concept it cannot be expected that the factors do not correlate, since the factors are believed to be supportive in nature. The question is whether the strength of model (19.89 and 22.60). Hence, the empirical data is more accurately captured by a model that contains both constructs as separate factors.

INSERT TABLE 2 Table 2: Factor correlations

Overall structural model fit

The research hypothesis 1 and 2a/b will be tested by a structural model presented in figure 1. As method for parameter estimation, we used "unweighted least square (ULS)". In general, this method is well suited for data sets in the social sciences since ULS parameter estimation does not require multivariate normality of the data.

For the assessment of overall model quality, one common test of model fit is the chi-square value that is 978.88 with 341 degrees of freedom (p=0.00) for the presented model. However, the chi-square test does not account for model complexity. Therefore, the chi-square value should be divided by the degrees of freedom [START_REF] Jöreskog | Recent Developments in Structural Equation Modeling[END_REF]. This quotient should be equal or less than 2.5 [START_REF] Homburg | Konzeptualisierung und Operationalisierung komplexer Konstrukte[END_REF], which is not fulfilled by the model showing a value of 2.871 that could be seen as a weakness of the model. However, the usability of the chi-square test in general is limited and has been questioned in the literature [START_REF] Bentler | Significance Tests and Goodness of Fit in the Analysis of Covariance Structures[END_REF][START_REF] Bagozzi | On the Evaluation of Structural Equation Models[END_REF][START_REF] Fan | Effects of Sample Size, Estimation Methods, and Model Specification on Structural Equation Modeling Fit Indexes[END_REF]. The chi-square test is a test of exact fit between empirical data and model data although the theoretical model is only designed as an approximation of reality [START_REF] Cudeck | Cross-Validation of Covariance Structures[END_REF]. In addition, the chi-square value is sensitive to sample size effects, leading to the result that with an increasing sample size the presence of only minor deviations from the empirical covariance matrix lead to a rejection of the theoretical model [START_REF] Jöreskog | Recent Developments in Structural Equation Modeling[END_REF][START_REF] Bearden | Sample Size Effects on Chi Square and Other Statistics Used in Evaluating Causal Models[END_REF].

A more appropriate measure is the share of empirical variance that is captured by the model, here, goodness of fit indices (GFI) is considered. It is commonly accepted that the GFI and the adjusted GFI (AGFI) should exceed 0.90. This criterion is matched by the model presented here (GFI = 0.95, AGFI = 0.94). Further measures to assess overall model quality are the root mean square error of approximation (RMSEA) which should not exceed 0.10, the root mean residual (RMR<0.05) and the comparative fit index (CFI>0.90). The RMSEA value is closely matched by the model (0.09), also the CFI (0.97) indicated a reasonable fit of the model. Only the RMR (0.084) is slightly above the threshold value. Altogether the analysis of the overall model fit shows satisfactory results so that the model can be taken for further analyses.

Findings of the Structural Model

The results of the structural model are depicted in figure 2. They demonstrate a strong support for the conceptual model presented here and confirm hypothesis 1 for three out of four cases. A supportive layer of factors (layout, setup and quality) exists and fosters the implementation of a Kanban production system. The strongest link between the supportive layer and Kanban can be found in a production layout that emphasises a cellular layout of machine groupings and aims at smoothening the flow of material and products through production. Further significant support to Kanban systems is delivered by programs to shorten setup times. Of less importance is the quality focus on shop floor level. Nevertheless, the relationship is statistically significant and promotes Kanban implementation. Contrary to the theoretically assumed positive influence that preventive maintenance should have on a Kanban production system, this relationship cannot be found in the empirical data analyzed in this paper. The problems regarding discrimminant validity in terms of maintenance might be a reason for the fact that no significant influence on Kanban could be found here since this factor is not clearly separated from the people oriented factors of the primary layer. Figure 2 gives an overview of the empirical model: With regard to the primary factors and their support to factors of the supportive layer the hypothesis 2a and 2b are confirmed by the model. All four proposed relationships are highly significant and show high parameters. In order to implement a Kanban production system a strong focus should be put into upgrading and broadening of workforce skills and capabilities.

INSERT FIGURE 2

Linking TPS practices to performance

Based on the values of the described confirmatory factor analysis, a cluster analysis is performed in order to differentiate between plants that have implemented the practices of the Toyota Production System at a high, middle, or low degree. For the cluster analysis Ward's method with the squared Euklidian distance has been conducted. The grouping of the cluster analysis is confirmed by a discriminant analysis. The discriminant analysis groups the plants with regard to the cluster analysis to a degree of more than 90 percent. Accordingly, the three resulting clusters can be used for further statistical analyses. In the following, the three clusters are examined in terms of the TPS practices in order to check for consistency. The following figure depicts the mean values for the factors representing the Toyota Production System. The mean values indicate the existence of three groups with different implementation degrees of the TPS practices. The differences between the groups are on a high significant level. In the following, the three groups are investigated concerning their performance.

INSERT FIGURE 3

The mean values show differences concerning several performance criteria on a very significant level of p < 0.05. Especially, the plants which have implemented the TPS practices to a high significant degree show higher average values in terms of cost of manufacturing performance, product conformance, on time delivery, flexibility to change volume, inventory turnover, and cycle time. Accordingly, the question whether plants with a higher implementation degree of the Toyota Production System also show a better performance can be affirmed. Only for the performance criteria fast delivery and flexibility to change products mix no significant differences result. No significant differences can be observed in terms of the other two clusters, although the cluster with a medium implementation degree has almost always higher mean values in comparison

CONCLUSIONS

In this paper, we examined the Toyota Production System empirically. The results show that there exist differences between the plants participating at the "High Performance

Manufacturing"-project. The empirical analyses show that many manufacturers make use of the Toyota Production System and adopt this approach to their production area in order to "fit into their new suit".

Particularly, the analyses performed show that the training of workers has a strong influence on the Toyota Production System supporting factors preventive maintenance and quality, whereas multi-skilled workers have a strong influence on the supportive factors process-oriented shop floor layout and short setup times (However, it has to be noted that the measurement of the factor multi-skilling was not fully satisfying.

As expected from theory, the factors multi-skilling and training show a relatively high correlation.). The statistical analysis also shows a relationship between the supportive factors process-oriented shop floor layout, short setup times and quality, and the main factor of the Toyota Production System: Kanban. Therefore, the model of the Toyota Production System discussed in this paper has been proven valid with the exception of Important conclusions can be drawn from the empirical analyses. First, skills and training of the workers is the key for a successful implementation of the Toyota Production System. The supportive layer with its practices such as short setup times, layout, and quality is fulfilled by the actions of the workforce. Without the properly trained and skilled workers these practices will stay a hollow shell and they will not develop their full potential, which is again key for the core concept of the Toyota Production System Kanban.

Second, the supportive layer with quality, process-oriented layout, and short setup times forms the infrastructure for Kanban. The proper function of Kanban relies on the successful implementation of these supportive practices, since short setups, excellent quality, and a process-flow oriented layout lead to small lot sizes and a short reaction time. Surprisingly, maintenance has no significant influence on Kanban, which was not suspected, since stable processes should be a prerequisite of Kanban. One explanation could be that the companies questioned already have stable processes so that the use of autonomous or preventive maintenance is regarded as no longer important. A second explanation could be that many managers do not know about the influence of maintenance on Kanban and since they lack maintenance implementation, they do not fully deploy the advantages of Kanban, which leads to a higher number of Kanban cards in process and subsequently to higher inventories.

Thirdly, the combination of the two paragraphs leads to an important conclusion:

Since Kanban is the centre of the Toyota Production System and it is strongly influenced by the supportive factors quality, setup times and shop floor layout, which Another way of putting it is that quality, setup times and layout is the vehicle to get a functioning Toyota Production System, but the workforce is the driver.

The fourth conclusion contains a very basic, but important result: The analyses prove that plants that have implemented the practices of the Toyota Production System more thoroughly than other factories, experience better results in the key performance metrics of production: cost, cycle time, quality, and flexibility. Especially, in terms of criteria for efficiency such as manufacturing cost, high inventory turnovers or short manufacturing cycle times the TPS practices play a crucial role.

Note, that plants with a high implementation degree of the TPS practices neither show better performance in terms of fast delivery nor concerning the flexibility to change product mix. The reason for this result is quite intuitive. First, for a successful implementation of Kanban, on-time deliveries are a necessary prerequisite as an external factor of the supportive layer as well as an intended consequence of Kanban itself. Short delivery times might be counterproductive in the sense that they are realized at the cost of a lower on-time delivery ratio: The shorter the delivery times are the more difficult it will be to deliver on-time. Second, stable processes are the foundation of Kanban in order to make this production system run efficiently. Hence, many changes in the product mix are not worthwhile because they would disturb the stability of the underlying process.

The four conclusions lead to the following managerial implications: A manufacturing company should focus on the workforce first, because they must be regarded as the key for success or failure. As the analyses shows the workforce gives 25 life to the infrastructure, therefore focusing solely on TPS practices like quality, short set up times etc. and neglecting the workforce, will not achieve the desired outcome, a powerful Kanban system that supports lean just-in-time production. Hence, create the "respect-for-human" system [START_REF] Sugimori | Toyota Production System and Kanban System -Materialization of just-in-time and respect-for-human system[END_REF] as priority, since it empowers the infrastructure. Second, a manufacturer must implement the necessary infrastructure of TPS practices in its manufacturing environment, since the infrastructure is the prerequisite for a successful Kanban system. If there are TPS practices missing or only weakly established, the management should start the implementation or improvement with the shop floor layout and setup times and then focus on quality, since the first mentioned have a stronger impact on Kanban than quality. However, factory management should not neglect either one of the implication, since the analysis shows that the combination of the workforce and the supportive infrastructure is critical for the success off a Kanban system or as it is stated above, setup times and layout is the vehicle to get a functioning Toyota Production System, but the workforce is the driver.

Finally, the argument why a manufacturing company should take all this effort is quite simple: The analysis of the performance criteria cost, time, quality, and flexibility shows that a thorough implementation of TPS practices leads to a superior performance in these key manufacturing metrics, which gives a company a competitive edge over its rivals.

There are some research limitations that should be mentioned. Firstly, this study exclusively considers the automotive, electronics, and machinery industry. A generalization of the results might be critical since it cannot be ruled out that plants from other industries -not covered by the "High Performance Manufacturing" projectmight show different results concerning the TPS. This study revealed interesting results concerning Kanban and its drivers for implementation. However, there is still research needed in this area. It would be favourable to include companies from countries other than the one participating in this study. An international survey would give insights concerning the degree of implementation of the TPS in other countries or could identify the impact of cultural differences. Secondly, only respondents closely related to the production area such as the Inventory Manager, Production Control Manager, and three Shop Floor Supervisors are asked for their estimations. A comparison of these estimations with respondents from other hierarchies, e.g. shop-floor workers, or other functional areas such as human resources, logistics, etc. would be interesting since such a study could show potential distortions in terms of the perception of the advantageousness and importance of the TPS. Thirdly, a longitudinal study might be interesting with respect to the diffusion of the TPS. Such a survey would have the potential to identify certain development trends.

F

  change over times that are part of the implementation of a SMED system. The second practice in this layer is the training of machine operators. The importance of training for the functioning of just-in-time production is stressed by Sakakibara et al. (1997): "Training programs … are important in developing flexible workers … to facilitate a smooth production flow." Accordingly, training is one explicit pillar of Total Productive Maintenance. Furthermore, it is necessary to train machine operators in order to enable them to fulfil new tasks, e.g., process related quality control.

  offer a case study of model changes within Toyota Production System. They analyze the influence of the changeovers on the flexibility and the Toyota subsidiary in the U.S. Three further case studies are presented by

  al., 1997; see for the basics of the project[START_REF] Schroeder | High Performance Manufacturing -Global Perspectives[END_REF]. High performance manufacturing describes the ability of a production unit to reach continuous improvements in the manufacturing area through integration and utilization of a set of compatible management concepts. The data base contains quantitative and qualitative data from plants of the automotive, electronic, and machinery industry.

  . Responses are aggregated for each plant into one combined data set and constitute multiple indicators of insight about manufacturing related areas such as just-in-time, quality, factory layout, setups, manufacturing strategy, human resources, maintenance, etc.

Figure 1 :

 1 Figure 1: Overview of the Model

  : The ability of workers to conduct multiple tasks enables the factors of the supportive layer, esp. a cellular layout of the production process and reduction of setup times. H 1 2b: The amount of training, given to production workers enables the factors of the supportive layer, esp. preventive maintenance and assurance of high quality production.

  tested empirically in the following based on data collected within the High Performance Manufacturing project.

  lead to the conclusion that the measurement of a single factor is faulty and therefore has to be discarded if modelled as a single factor. In the literature, no commonly accepted threshold values exist, however Bagozzi et al. state that only very high factor correlation should lead to the conclusion that discriminant validity has not been achieved. As for the model presented here, two factor correlations are rather high(Multi-skilling + Training, Maintenance + Training). For these factors a test of chi-square differences is conducted to further assess discriminant construct validity. All constructs show a statistically significant increase in the overall chi-square value of the

Figure 2 :

 2 Figure 2: Results of the structural model (t-values in brackets)

Figure 3 :

 3 Figure 3: Comparison of means of the TPS-principles

  with the lowest implementation degree of the TPS. Figure4gives an overview of the mean values.

Figure 4 :

 4 Figure 4: Comparison of means of the performance criteria

  as potential reason for this the problem in terms of discrimminant validity has already been mentioned.).

  the training and skills of the workforce, the workers are the core element of the Toyota Production System and they make it a success or a failure.

  Figure3

Table 1

 1 shows the measurement of the seven factors. The validity of the factor model is assessed by convergent and discriminant validity. Convergent validity is achieved if

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		primary level	supportive level	main level
			H 1 2a	Layout	H 1 1
		Multi-Skilling 0.68	H 1 2a	Setup	H 1 1
		(26.46)		Layout	0.34
	Figure 1	o r P e e r F o r P e e r F o r P e e r F o r P e e r F o r P e e r F o r P e e r F o r P e e r F o r P e e r Maintenance Quality Training H 1 2b H 1 2b H 1 1 H 1 1 F Setup Multi-Skilling 0.70 0.20 (3.31) (5.87) (25.19) o n.s. (-0.26) r 0.83 Maintenance Training (30,68) P e Quality r e 0.10 0.49 (20.80) (3.06)	Kanban Kanba
	Figure 2		R R R R R R R R R
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					w w w w w w w w w
					O n l O n l O n l O n l O n l O n l O n l O n l O n l
					y y y y y y y y y

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			Factor correlations
		Layout	Setup	Maintenance	Quality	Multi-	Training
						skilling
	KANBAN	0.46	0.39	0.32	0.27	0.39	0.40
	Layout	1.00	0.48	0.54	0.32	0.68	0.65
	Setup		1.00	0.55	0.33	0.69	0.67
	Maintenance			1.00	0.41	0.79	0.83
	Quality				1.00	0.47	0.49
	Multi-skilling					1.00	0.96
	Table 2	All correlations are significant with p<0.01 r F o
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