Simon Emde
email: simon.emde@uni-jena.de

Nils Boysen
email: nils.boysen@uni-jena.de

Armin Scholl
email: a.scholl@wiwi.uni-jena.de

Balancing mixed-model assembly lines: A computational evaluation of objectives to smoothen workload

Keywords: workload smoothing Mixed-model assembly lines, assembly line balancing, sequencing, workload smoothing

Mixed-model assembly lines are widely used in a range of production settings, such as the nal assembly of the automotive and electronics industries, where they are applied to mass-produce standardized commodities. One of the greatest challenges when installing and reconguring these lines is the vast product variety modern mixed-model assembly lines have to cope with.

Traditionally, product variety is bypassed during mid-term assembly line balancing by applying a joint precedence graph, which represents an (articial) average model and serves as the input data for a single model assembly line balancing procedure. However, this procedure might lead to considerable variations in the station times, so that serious sequencing problems emerge and work overload threatens. To avoid these diculties dierent extensions of assembly line balancing for workload smoothing, i.e., horizontal balancing, have been introduced in the literature.

The paper on hand presents a multitude of known and yet unknown objectives for workload smoothing and systematically tests these measures in a comprehensive computational study. The results suggest that workload smoothing is an essential task in mixed-model assembly lines and that some (of the newly introduced) objectives are superior to others.

Assembly lines are production systems in which parts are added to a product sequentially by employing a transportation system (usually a conveyor belt) which moves the workpieces successively through productive units, called stations. They are applied to mass-produce standardized commodities, e.g., in the automotive and electronics industries. While single model lines were the norm in the early days of industrial manufacturing, nowadays multi-skilled workers and automated tool-swaps enable the assembly of a multitude of dierent variants of a common base product in consecutive cycles with negligible setup cost and time. How far exibility in these mixed-model assembly lines has progressed can be seen by looking at the number of options oered by today's car manufacturers, amounting to up to 10 32 dierent models produced on the same assembly line [START_REF] Meyr | Supply chain planning in the German automotive industry[END_REF].

Mixed-model assembly lines require the solution of two major planning tasks (see [START_REF] Meyr | Supply chain planning in the German automotive industry[END_REF] and Boysen et al. (2007a) for surveys on the complete hierarchy of line planning):

• Whenever an assembly line is initially installed or recongured, the assembly line balancing (ALB) problem is to be solved, which partitions the assembly work among the stations while regarding precedence constraints among tasks and a common cycle time with respect to some objective. To cope with multiple models to be produced on the line a joint precedence graph representing an (articial) average model is introduced, which serves as the input data for a single model ALB procedure (see [START_REF] Boysen | Assembly line balancing: Joint precedence graphs under high product variety[END_REF].

• Additionally, a short-term sequencing problem is to be solved, which decides on the succession of models to be launched down the line during a day or production shift.

Due to the fact that tasks can take diering amounts of time depending on which model they are performed on, the sum of operating times of the tasks assigned to a station can uctuate greatly. For example, the task mount sunroof might take longer for a model with an electrically powered sunroof compared to a model with a manually operated one, or is absent when no sunroof is required at all. If there are several models with electric sunroofs scheduled in a row the respective station may become overloaded. Such work overload must be compensated, e.g., by utility workers, causing additional cost [START_REF] Tsai | Mixed-model Sequencing to Minimize Utility Work and the Risk of Conveyor Stoppage[END_REF]. See [START_REF] Boysen | Sequencing mixed-model assembly lines: Survey, classication and model critique[END_REF] for a detailed survey on assembly line sequencing.

Although there is a great temporal distance between balancing and sequencing decisions, the two planning steps are anything but independent. By partitioning the workload between stations, assembly line balancing determines the station time per model. Thus, depending on the line balance dierences in a station's workload may vary to a greater or smaller extent, making it potentially impossible for a sequencing procedure to determine good model sequences. Consequently, in addition to traditional balancing objectives, e.g., the minimization of the number of stations (SALBP-1), work overload resulting from model sequencing also becomes a quality criterion for line balancing. for this interdependency, line planning needs to integrate both essential planning tasks.

In general, there exist three alternatives:

Successive Planning: In its traditional form, interdependencies between both tasks are neglected and planning is executed in two independent steps. Obviously, the resulting simplication of line planning incurs more restricted sequencing problems typically leading to higher short-term work overloads.

Simultaneous planning: The other extreme is to handle both planning tasks jointly in a simultaneous balancing and sequencing problem. Respective approaches are provided by [START_REF] Mcmullen | Using simulated annealing to solve a multiobjective assembly line balancing problem with parallel workstations[END_REF], Kim et al. (2000aKim et al. ( ,b, 2006)), [START_REF] Miltenburg | Balancing and scheduling mixed-model U-shaped production lines[END_REF], [START_REF] Sawik | Monolithic vs. hierarchical balancing and scheduling of a exible assembly line[END_REF] as well as [START_REF] Bock | Controlling mixed-model assembly lines in real-time by using distributed systems[END_REF]. However, in many settings, these approaches suer from two serious drawbacks. First, the resulting planning models contain an enormous number of decision variables and constraints, so that complexity impedes an ecient solution. Prolonged run-times of algorithms and/or a (comparatively) low solution quality are the consequences. An even more serious drawback is that both planning tasks have a completely dierent time frame. At the point in time where mid-term line balancing is executed short-term model-mixes per shift are hard to anticipate accurately. Thus it heavily depends on the forecast accuracy (and therefore the length of the planning horizon) whether a simultaneous procedure indeed increases planning quality compared to successive planning.

Anticipation: As the planning horizon of ALB is typically comparatively long, i.e., usually ranging from a few years when installing a new line (see Boysen et al., 2007a) to several months or weeks when reconguring an existing line, it seems generally more practical to decompose the total decision problem into separate yet coordinated planning steps. Respective line balancing approaches aim at anticipating the consequences on model sequencing in a more aggregated fashion instead of based on detailed model-mixes per shift. For instance, procedures known as horizontal balancing (see [START_REF] Merengo | Balancing and sequencing manual mixedmodel assembly lines[END_REF] introduce an additional objective for line balancing, which aims at smoothing the workload per station over all models. Note that a model-mix forecast is also required for such an anticipation alternative. However, merely the average model-mix over multiple sequencing periods, i.e., all shifts during the life-time of a line balance, is required and it is a well known phenomenon that aggregated forecasts are more precise than disaggregated ones (see, e.g., [START_REF] Chopra | Supply Chain Management, 3rd edition[END_REF].

It is the aim of this paper to identify suitable forms of anticipation during assembly line balancing, which are able to identify robust line balances resulting in a reduction of short-term work overloads. For this purpose, a comprehensive computational study is conducted, which, rst, determines line balances applying dierent forms of anticipation and then tests these line balances by determining the resulting work overload for dierent daily short-term model-mixes. Although some forms of anticipation have already been introduced in the literature, these alternatives have not been tested systematically, yet.

Moreover, we introduce additional forms of anticipation and investigate the inuence of product-variety as well as forecast errors.

3 For this purpose, the remainder of the paper is organized as follows. In Section 2 the dierent forms of anticipation and workload smoothing are introduced. Therefore, we review the existing literature on this topic and systematically derive novel forms of anticipation. Then, the setup of our computational study is described in detail (Section 3). Section 4 presents the results and Section 5 concludes the paper.

F

Workload smoothing

If sequencing issues are to be observed in ALB by an appropriate anticipation mechanism, two choices need to be taken: (i) an appropriate workload smoothing criterion is to be identied and (ii) the selected anticipation criterion needs to be related to the primary objective of ALB, which is usually to minimize the number of stations or workers required.

With regard to the rst choice, an objective is required which both adequately estimates the actual work overload and can be easily derived from the original input data of ALB. In the literature, dierent objectives are proposed to meet these two requirements.

Using the notation dened in Table 1, Table 2 enumerates possible objectives.

Columns A through C contain objective functions belonging to horizontal balancing, whereas the objectives of column D belong to vertical balancing according to the nomenclature of [START_REF] Merengo | Balancing and sequencing manual mixedmodel assembly lines[END_REF]. In horizontal balancing the objectives aim at a workload smoothing per station k over all models p ∈ P , so that the deviation of the actual processing time per model and station τ pk from some target station time is minimized.

Target station times are (A) the cycle time, (B) the average processing time of a model p per station and (C) the average processing time of all models per station, respectively.

In vertical balancing (Column D), the objectives aim at evenly distributing the workload among the stations, so that the average station time is to be adjusted towards the average processing time of all models per station. In each column, dierent functions can be utilized to measure the distances, which additionally can either be unweighted or weighted by the proportion of the respective product in the model-mix b p . the lexicographic case, where the most common balancing objective, the minimization of the number of stations (SALBP-1), is given top priority and workload smoothing is the secondary objective. This setting seems reasonable because, typically, due to the high level of automatization, investment cost for an assembly line are much higher than cost caused by daily work overload. Furthermore, SALBP-1 typically has many optimal solutions having the same number of stations, so that enough degrees of freedom remain to identify one of the optimal solutions which also optimizes the smoothing criterion.

4

F

p,k max{0, τ pk -Tp} (9) p,k max{0, τ pk -T } (17) k max{0, T * k -T } (25) weighted p,k max{0, bp • (τ pk -c)} (2) p,k max{0, bp • (τ pk -Tp)} (10) p,k max{0, bp • (τ pk -T )} (18) Manhattan distance unweighted p,k |τ pk -c| (3) p,k |τ pk -Tp| (11) p,k |τ pk -T | (19) k |T * k -T | (26) weighted p,k bp • |τ pk -c| (4) p,k bp • |τ pk -Tp| (12) p,k bp • |τ pk -T | (20) Euclidian distance unweighted p,k (τ pk -c) 2 (5) p,k (τ pk -Tp) 2 (13) p,k (τ pk -T ) 2 (21) k (T * k -T ) 2 (27) weighted p,k (bp • (τ pk -c)) 2 (6) p,k (bp • (τ pk -Tp)) 2 (14) p,k (bp • (τ pk -T )) 2 (22)
Since the seminal work of [START_REF] Moodie | A heuristic method of assembly line balancing for assumptions of constant or variable work element times[END_REF] several papers have been presented which deal with workload smoothing. These papers can be subdivided into two groups. The rst group provides specic line balancing procedures for a given workload smoothing criterion. The second group of workload smoothing literature deals with testing dierent smoothing criteria with regard to their ability in reducing work overload.

We summarize the rst group in Table 3, where the smoothing criterion applied (according to The multitude of dierent ALB approaches incorporating workload smoothing is an indicator of its practical relevance in real-world applications. Nonetheless, apparently only about half of the criteria of Table 2 have ever been actively researched. Also, a suitable optimization approach for a given smoothing criterion is merely one side of the coin. Moreover, the appropriateness of the dierent smoothing approaches also needs to be investigated. Up to now, this problem was merely tackled by [START_REF] Domschke | Antizipative Leistungsabstimmung bei moderner Variantenieÿfertigung[END_REF], summarized in Scholl, 1999, Ch. 3.2.2.3) and [START_REF] Bukchin | A comparative study of performance measures for throughput of a mixed model assembly line in a JIT environment[END_REF]. [START_REF] Domschke | Antizipative Leistungsabstimmung bei moderner Variantenieÿfertigung[END_REF] present a simulation study similar to our setting. The smoothing criteria (1), ( 12), ( 14), ( 15) and ( 27) from Table 2 are 3 Setup of the computational study

The basic idea of our study is to determine dierent line balances with the 28 smoothing criteria dened in Table 2. Thus, for each test instance, 28 dierent ALB solutions and an additional reference ALB solution without workload smoothing (successive planning) are determined. Then, we randomly draw dierent daily model-mixes (sequencing instances) each of which is to be solved by a mixed-model sequencing approach. The resulting work overload is our nal measure to compare the workload smoothing criteria with regard to their ability in reducing short-term work overloads. Moreover, to gain further insights we aim at comparing workload smoothing in dierent settings, namely high, medium and low product variety as well as high, medium and low forecast uncertainty, respectively.

To describe the detailed setting of our computational study, the following three sections elaborate on instance generation (Section 3.1), additional assumptions on the underlying assembly system (Section 3.2) and the applied algorithms to solve the respective optimization problems (Section 3.3).

Instance generation

Our test data is based on the 64 classic Talbot SALBP instances [START_REF] Talbot | A comparative evaluation of heuristic line balancing techniques[END_REF], which can be downloaded from http://www.assembly-line-balancing.de. On the basis of a given parameter constellation, the input data is determined as follows: Each model p ∈ P is assigned a random demand portion b p with 0 < b p < 1 and p∈P b p = 1. Then, a random task time t jp is determined for each model p and each task j ∈ V (0 ≤ t jp ≤ 2 • t j with t j being the task time of the original SALBP task) so that p∈P b p • t jp = t j ∀ j ∈ V . The station length l is equal for all stations and is set to l = 1.1 • c and the total model demand per shift is expected to be d = 200 units. Then, from the overall model-mix representative daily model-mixes have to be drawn. For this purpose, the demand vector D

= (d 1 , d 2 , . . . , d |P | ) is given by d p = b p • d • (1 + (2 • rnd(0, 1) -1) • α) ∀ p ∈ P with 0 ≤ rnd(0, 1) ≤ 1 being a
uniformly distributed random number and • representing rounding to the next integer. As a consequence, the demand for each model p in each shift is uniformly distributed, ranging from (1 -α)

• b p • d to (1 + α) • b p • d.
Each line balance is to be tested with regard to its ability to reduce work overload facing high (α = 1.0), medium (α = 0.5) and low (α = 0.1) forecast uncertainty. Moreover, multiple daily (Z = 20) model-mixes are to be tested to compute average performance, so that in total 5, 568 • 3 • 20 = 334, 080 sequencing problems are to be solved. The total run-time to solve this enormous number of optimization problems exceeded 2 months on an x86 PC with an Intel Core 2 Quad Q9550 2.8 GHz CPU, with all algorithms being implemented in Borland Delphi 2006.

Assumptions on the assembly system

To model assembly line operations and to determine the detailed work overload some assumptions on the underlying assembly system have to be introduced. From the ALB point of view, we assume an assembly system in line with the basic assumptions of SALBP (see Baybars, 1986, Becker andScholl, 2006), so that a single paced line without buers and any kind of paralleling or assignment constraints is presupposed. As the original objective of ALB, we aim at minimizing the number of stations, so that the underlying assembly system can be represented by the basic ALB problem SALBP-1.

Further assumptions on the assembly system are required to determine work overload caused by dierent model sequences. Therefore, the following additional premises hold for our hypothetical assembly system (see [START_REF] Boysen | Sequencing mixed-model assembly lines: Survey, classication and model critique[END_REF]):

• Working across the stations' boundaries is not possible (closed, non-overlapping stations).

• The constant velocity of the conveyor belt is normalized to one. • The operators return with innite velocity to the next workpiece. This is an adequate simplication whenever the conveyor speed is much slower than the walking speed of workers, as is typically the case in practice.

• Work overload is measured by the time or space necessary to complete all work in excess of the respective station's right border (without compensation).

• Work overload has no impact on the succeeding station. Thus, the model assumes that the work overload is either compensated by a utility worker or by accelerating processing velocity.

With these premises on hand, a mixed-model sequencing approach can be applied to determine a launch sequence of models which minimizes work overload. Such a mixedmodel sequencing approach schedules the models in detail at each station and cycle, by explicitly taking into account processing times, worker movements and station borders. [START_REF] Yano | Sequencing to minimize work overload in assembly lines with product options[END_REF], [START_REF] Bard | An analytic framework for sequencing mixed model assembly lines[END_REF] and [START_REF] Scholl | Pattern based vocabulary building for eectively sequencing mixed-model assembly lines[END_REF].

Applied optimization approaches

The optimization is divided into an ALB part and a sequencing part.

First, the well-known branch-and-bound procedure SALOME [START_REF] Scholl | Balancing and sequencing assembly lines, 2nd edition[END_REF]Klein, 1997, 1999) is used to determine the optimum number of stations m * for the ALB problem (SALBP-1). This solution is neither horizontally nor vertically balanced and serves as the benchmark for the improvement of the smoothing criteria. Then, to carry out the horizontal balancing, SALOME was adapted to incorporate secondary smoothing objectives. An in-depth explanation of the original algorithm would be out of the scope of this paper, so that exclusively the alterations required for workload smoothing are explained.

The general idea is to generate all feasible solutions to the ALB problem given the station count m * established in the previous step and the given cycle time c. Of these, the one with the best secondary objective value is chosen. The algorithm is a stationoriented branch-and-bound procedure, meaning that in each branching step alternative subproblems are dened by complete station loads for the next empty station. The problems are continuously subdivided, creating a multilevel enumeration tree which contains every possible solution to the given instance. In each node, a set of seven lower bounds on the number of stations is calculated and compared to the desired number of stations m * (see [START_REF] Scholl | SALOME: A Bidirectional Branch-And-Bound Procedure for Assembly Line Balancing[END_REF]. If the lower bound is greater, the node is fathomed. Of the logical tests, only the Simple Permutation Rule, the Task Time Incrementing Rule and Prexing can be used to fathom nodes (see [START_REF] Scholl | SALOME: A Bidirectional Branch-And-Bound Procedure for Assembly Line Balancing[END_REF]. All other tests that SALOME originally employs potentially eliminate branches that lead to solutions with a station count equal to m * , therefore they cannot be used here. The number of feasible line balances grows exponentially with problem size. Even SALBP-1 that the unmodied SALOME solves by nding just a single optimal solution is NP-hard; nding all solutions with m * stations can take a considerable amount of time.

It is therefore desirable to prune the enumeration tree not only with regard to capacity oriented goals but to also ignore parts of the search space where no improvement with regard to the secondary objective can be made. For this purpose, a new lower bound is proposed, whose basic idea can easily be adapted to any of the 28 smoothing criteria.

All criteria of Table 2 aim at minimizing the deviations of station times from some target value, like the cycle time c in Column A. Relaxing the indivisibility restriction of the tasks, we can assume a perfectly smooth distribution of station times by dividing the yet unassigned workload W L p (i) for a model p on tree level i by the number of stations yet to be loaded m * -i. Since station loads cannot be any smoother than this, actual deviations from the target value can never be greater than the lower bound. For example, for criterion (1) the lower bound on tree level i is dened by:

LB(1) = p∈P i k=1 max{0, τ pk -c} + p∈P max 0, W L p (i) m * -i -c (1)
Lower bound LB(1) amounts to the sum of the cycle time exceedance that has occurred in the stations already loaded (rst term), plus the exceedance over cycle time c that would occur if the yet unassigned workload W L p (i) would be equally split among m * -i remaining stations (second term), where the average workload can be rounded up due to integer task times of ALB. The same basic idea can easily be adjusted for any other smoothing criterion.

Concerning solution quality, the original SALOME used to determine the optimal number of stations m * could solve all instances to optimality in very short time. The modied SALOME used for horizontal balancing could solve 54.89% of the instances to (proven) optimality within a given time frame of 900 CPU-seconds for ALB.

Lastly, to solve the sequencing problem, a simulated annealing algorithm similar to that proposed by [START_REF] Mcmullen | A simulated annealing approach to mixedmodel sequencing with multiple objectives on a just-in-time line[END_REF] is used. Given a total demand of d units in a given shift, the solution is represented as a sequence vector s = (s 1 , . . . , s d ) where each position s t (t = 1, . . . , d) contains the model p ∈ P to be assembled in cycle t. . The current solution is replaced by the new one if e -∆/T k > rnd(0, 1), with T k being the current temperature and 0 ≤ rnd(0, 1) ≤ 1 being a uniformly distributed random number. The initial temperature T 1 is set high enough to accept all transitions in the rst phase. Given the current temperature T k , the new temperature T k+1 is determined by [START_REF] Lundy | Convergence of an annealing algorithm[END_REF]. The epoch length L for the current temperature level is dened by

T k+1 = T k /(1 + β • T k ), β = T 1 -T F (L B -1)•T 1 •T F (Lundy
L = L B + L B • F where F = 1 -e -(f h -f l )/f h ,
f h and f l are the highest and lowest work overloads measured during the last epoch, respectively, and L B = 100 is the initial epoch length [START_REF] Cho | A robust design of simulated annealing approach for mixed-model sequencing[END_REF] [START_REF] Mcmullen | A simulated annealing approach to mixedmodel sequencing with multiple objectives on a just-in-time line[END_REF] shows that the simulated annealing algorithm nds solutions to the sequencing problem very close to the optimum (deviations are reported to be less than one percent). Another study conducted by [START_REF] Boysen | Reihenfolgeplanung bei Variantenieÿfertigung: Ein integrativer Ansatz[END_REF] testing a similar algorithm conrms these results.

Results

In order to assess the quality of the solutions obtained by the dierent smoothing objectives the improvement over successive planning is measured by

W (SC)-W (SM ) W (SC)
, where W (SC) and W (SM ) are the work overloads summarized over all Z = 20 daily modelmixes for the successive planning and the smoothing approach, respectively, averaged over all instances.

The results are listed in zero). Note that these numbers can be greater than 64 because each of the original instances was tested with three product variety and three forecast uncertainty settings, resulting in a total number of 64 • 3 • 3 = 576 instances. The values in square brackets denote the same performance measures but only for the instances that were solved to proven optimality.

The rst conclusion to be drawn is that (irrespective of the specic criterion applied)

workload smoothing considerably reduces short-term work overload compared to successive planning, where ALB disregards smoothing aspects. However, no single criterion outperforms all others with regard to all performance criteria, so that no single best criterion can be identied. In terms of improvement over the successive planning solution, smoothing criteria (1), ( 2) and (4) work best, although all criteria with the notable exception of those concerned with vertical balancing in Column D work well enough to improve balances by over or at least close to 30%, as long as a distance measure other than maximum divergence is used. Vertical balancing, while still eective, is consistently less well suited to lowering work overloads than horizontal balancing (i.e., the criteria in Columns A through C). Concerning distance measures, exceedance seems to be just a tiny bit better than Manhattan and Euclidian distances which in turn are considerably better than maximum divergence. Leaving out the latter uncompetitive distance mea- sure, the criteria of Column A outperform those of the other columns almost without exception, especially when taking into account that they found the best solution (# best) far more often than the other criteria. This also holds true when comparing the number of instances where work overload could be avoided altogether (# zero). Finally, with regard to the question whether unweighted or weighted smoothing criteria perform better no clear recommendation can be given as weighted criteria seem only slightly superior. Note that these observations are valid regardless of whether all instances or only the optimally solved ones are taken into consideration.

11 suer more from high product variety than increasing forecast errors. This is because high product variety automatically entails increasing forecast errors. When there are a lot of models which all are very unlikely to be produced during a day or shift the least bit of uncertainty can have huge eects. For instance, assume that according to the model mix a demand of 0.5 units per shift of model m is expected. This is not a very useful piece of information, since in any given shift the model will either be in demand or not, but half a unit of model m will denitely not be assembled. These rounding errors are less signicant when the expected demands per model are higher, which only happens under low product variety.

F
(a) The eects of forecast uncertainty (b) The eects of product variety less when there are lots of models to choose from than the horizontal balancing criteria (Columns A through C). This is logical, seeing that these objectives concern themselves only with average capacity demands which do not depend on the number of models. This is not the case when horizontal balancing is applied: Model-specic information is central to these objectives but grows increasingly unreliable under high variety and uncertainty.

Table 5 also allows a meaningful comparison of weighted with unweighted criteria.

Considering only the values obtained under low forecast uncertainty and low variety, regardless of column weighting is always better than not weighting, except when the maximum divergence distance measure is used, where results are ambiguous. This advantage vanishes when either forecast errors or product variety (or both) rise. All in all, while all criteria lose ground when demands become more volatile and some suer more than others, the ranking stays basically the same: in general, column A is still best, column D is still worst and they all are still a lot better than the unimproved successive planning solutions.

In conclusion, no single criterion delivers the best results in every instance. However, some clear guidelines can be given:

• as long as there is no extreme product variety, horizontal balancing is superior to vertical balancing

• among the horizontal balancing criteria, those of Column A are usually superior to the others

• minimize the maximum divergence is usually the worst distance measure

• when demands are more or less certain, i.e., there is a reduced product variety and trustworthy forecasts, it is better to weight the criteria with the expected demand portion, irrespective of which criterion is eventually chosen

• the less certain demand forecasts are, the less well horizontal balancing works All things considered, criteria (1), ( 2) and (4) work best. The average improvement over successive planning is greatest overall as well as under high product variety and forecast uncertainty. They found the best solution in the most instances and were the most successful in reducing work overload to zero. These ndings are in line with those of [START_REF] Domschke | Antizipative Leistungsabstimmung bei moderner Variantenieÿfertigung[END_REF] who found criterion (1) to clearly outperform ( 12), ( 14) and ( 15). That being said, each and every of the tested criteria was capable of greatly reducing work overloads. Taking into account that the study showed that horizontal balancing becomes increasingly dicult with rising product diversity, at some point vertical balancing might actually be a better idea. study. The results show that workload smoothing in general is always better than ignoring the interdependencies between both planning tasks when executing them successively.

Furthermore, promising smoothing criteria among the 28 investigated are identied and the impact of product variety and forecast errors is tested. However, there remain multiple challenges for future research:

• Our computational study presupposed a basic assembly line setting to identify elementary interdependencies between ALB and sequencing. However, it would be a valuable contribution to test the impact of workload smoothing in more complex settings, e.g., incorporating open station borders or parallel line segments, the impact of line stoppage or more complex primary ALB objective functions.

• Moreover, it would be interesting to compare workload smoothing with simultaneous planning. However, such a comparison requires the determination of a reliable and representative model-mix simultaneous balancing and sequencing is executed on, which remains a yet unsolved problem.

• Finally, another problem remains, when product variety reaches dimensions of modern automobile assembly lines with billions of possible models. In these dimensions of product variety there is no adequate basis for estimating future demand rates. Instead, reliable estimations can be provided only for the frequency of option occurrences over all models (option-mix), e.g., the percentage of cars equipped with air conditioning (see [START_REF] Röder | A methodology for modeling inter-company supply chains and for evaluating a method of integrated product and process documentation[END_REF]. Moreover, an ALB procedure for workload smoothing, which has to iterate through all possible models, suers from the extraordinary computational requirements in this order of magnitude.

Consequently, workload smoothing is to be altered to account for this fundamental change in information and the stations' workload is to be assigned to options.

An analogous procedure is provided by [START_REF] Boysen | Assembly line balancing: Joint precedence graphs under high product variety[END_REF] for generating joint precedence graphs.

All these challenges seem to be valuable elds of future research because workload smoothing at an early stage during ALB considerably eases and improves short-term assembly line operations.

  Objective functions for workload smoothingOnce one of the smoothing functions is selected, it needs to be related to the original objective of ALB. In principle, any coupling mechanism of multi-objective optimization can also be applied to ALB. However, in the existing assembly line literature these objectives are either put in lexicographic order or unied to a unique objective function by applying objective-specic weighting factors. The latter approach especially suers from the problem of determining suited weighting factors, which mirror the actual underlying relationship between (investment) cost of line balancing and cost caused by work overload in an adequate way. To avoid this problem, we restrict our computational study to 5

  used as a secondary objective to determine line balances. The resulting work overloads for these line balances are then calculated by a mixed-model sequencing approach for dierent daily model-mixes. As a result from their simulation setting, criterion (1) seems especially suited in avoiding work overloads. Bukchin (1998) denes a dierent simulation setting. Here, random line balances are generated for which a signicant positive correlation between the actual work overload and criterion (12) is identied. However, in contrast to these previous studies the paper on hand tests all smoothing criteria of

  According to a recent classication of model sequencing approaches provided by Boysen et al. (2009) the basic sequencing problem assumed here can be characterized by the tupel M S[ | ]. Model formulations and solution procedures for this basic mixed-model sequencing problem are provided by

  The initial solution is arbitrarily generated and neighboring solutions are reached by choosing two positions randomly and swapping the corresponding values. The dierence between the work overload of the new (W O new ) and the current (W O cur ) solution is calculated as ∆ = 100 • W Onew-W Ocur W Ocur

  . When the current temperature drops below T F = 0

Figure 1 :

 1 Figure 1: The average performance of four criteria

  Table2), the relation to the original ALB objective and the algorithmic approach are given. The abbreviations are borrowed from the ALB-classication ofBoysen et al.

	(2007b):
	HI	heuristic improvement procedure	HS	start heuristic for initial solution
	GA	genetic algorithm	TS	tabu search
	SA	simulated annealing	ACO ant colony optimization
	DP	dynamic programming	B&B branch-and-bound
	B&C branch-and-cut
	LEX lexicographic order	WF weighting factor

Table 2

 2

	and, additionally, investigates

Table 3 :

 3 An overview on workload smoothing in the literature on assembly line balancing

  model-mix, and (ii) into some representative daily model-mixes, which build the input for the related sequencing problems.ALB with the dierent smoothing criteria is to be tested in dierent settings, so that the number of models |P | is varied and product variety is dierentiated into high (|P | = 150), medium (|P | = 75) and low (|P | = 10). For each of these settings a specic line balance is to be determined, so that in total 64 • 29 • 3 = 5, 568 ALB problems have to be solved. The resulting line balances are passed over to the next step, where representative daily model-mixes are determined.

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	For each
	instance the original single-model precedence graph is taken as the joint precedence
	graph of the set of assigned product models. It is the task of instance generation to split
	each joint precedence graph (i) into its contributing models, which determine the overall
	7

Table 4 .

 4 The average improvement as explained above is labeled Imp. in the table. Additional performance measures computed for each criterion are the number of instances where the respective criterion could nd a solution with the least work overload compared to the other criteria (abbreviated by # best) and the number of instances where the respective criterion reduces work overload to zero (#

Table 4 :

 4 Average performance measures for each smoothing criterionFinally, the inuence of product variety and forecast uncertainty is to be investigated.

	Figures 1a and 1b display the impact of both factors on average improvement over
	successive planning. Both increasing product variety and forecast errors enlarge short-
	term work overload. This nding is in line with intuition because both factors increase
	the deviation between the anticipated model-mix applied in medium-term ALB and the
	daily model-mix occurring in sequencing, so that ALB increasingly operates on wrong
	data. In both gures only four selected smoothing criteria are displayed (one for each
	column in Table 2; missing criteria exhibit very similar curves). Apparently, solutions
	12

Table 5 .

 5 This table lists the reduction of work overload compared to successive

	13

Table 5 :

 5 Performance under high/low forecast errors and product variety 5 ConclusionsThe paper on hand investigates the anticipation of short-term sequencing issues by workload smoothing during medium-term line balancing. After introducing 28 dierent forms of anticipation mechanisms, all of them are tested in a comprehensive computational

	15

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


Eng. Ph.D Eleonora Bottani
email: eleonora.bottani@unipr.it

Roberto Montanari

SUPPLY CHAIN DESIGN AND COST ANALYSIS THROUGH SIMULATION

Keywords: SUPPLY CHAIN MANAGEMENT, SIMULATION, COST ANALYSIS, supply chain management, supply chain design, simulation model, economical analysis, design of experiments, Fast Moving Consumer Goods

This paper is grounded on a discrete-event simulation model, reproducing a Fast Moving Consumer Goods (FMCG) supply chain, and aims at quantitatively assessing the effects of different supply configurations on the resulting total supply chain costs and bullwhip effect. Specifically, 30 supply chain configurations are examined, stemming from the combination of several supply chain design parameters, namely number of echelons (from 3 to 5), reorder and inventory management policies (EOQ vs EOI), demand information sharing (absence vs presence of information sharing mechanisms), demand value (absence vs presence of demand "peak"), responsiveness of supply chain players. For each configuration, the total logistics costs and the resulting demand variance amplification are computed. A subsequent statistical analysis is performed on 20 representative supply chain configurations, with the aim to identify significant single and combined effects of the above parameters on the results observed.

From effects analysis, bullwhip effect and costs outcomes, 11 key results are derived, which provide useful insights and suggestions to optimize supply chain design.

The concept of Supply Chain Management (SCM) is gaining increased importance in today's economy, due to its impact on firms' competitive advantage. SCM describes the discipline of optimizing the delivery of goods, services and related information from supplier to customer, and is concerned with the effectiveness of dealing with final customer demand by the parties engaged in the provision of the product as a whole [START_REF] Cooper | Supply chain management: More than a new name for logistics[END_REF]. the FMCG supply chain (some details concerning the FMCG examined and the corresponding data are proposed in Appendix). The key results of the simulation runs and effects analysis are detailed in section 4. Concluding remarks and future research directions are finally proposed.

Literature analysis: supply chain simulation

Simulation represents one of the tools most frequently used to observe the behaviour of supply chains, in order to highlight their efficiency level and evaluate new management solutions in a relatively short time [START_REF] Iannone | Supply chain distributed simulation: An efficient architecture for multi-model synchronization[END_REF]. A main advantage of simulation models can be found in their capability to provide estimates of efficiency and effectiveness of systems and to assess the impact of changed input parameters on the resulting performance, without examining real case examples [START_REF] Harrison | Simulation modeling in organizational and management research[END_REF].

In the context of supply chain analysis, [START_REF] Persson | Performance simulation of supply chain designs[END_REF], develop a simulation model to examine a case study company. They evaluate alternative supply chain scenarios, with the aim to improve the resulting quality and costs; moreover, the authors strive to understand how quality and costs affect each other. [START_REF] Sen | Supply chain positioning strategy integration, evaluation, simulation, and optimization[END_REF], exploit simulation to examine viable supply chain positioning strategy, such as make-to-stock, make-to-order, and assemble-to-order, and explore possible integrations between those strategies, referring to a company in the electronic industry. Similarly, a simulation model is developed by [START_REF] Higuchi | Dynamic simulation of the supply chain for a short life cycle product-Lessons from the Tamagotchi case[END_REF], to investigate the bullwhip effect and boom-and-bust phenomena, in the particular context of short life cycle products. [START_REF] Chan | Simulation modeling for comparative evaluation of supply chain management strategies[END_REF], use simulation for building and testing five different supply chain models. Their main aim is to determine which supply chain models could achieve the optimal performance, in term of inventory level, order lead time, resources utilization, and transportation costs. [START_REF] Persson | The development of a dynamic supply chain analysis tool-Integration of SCOR and discrete event simulation[END_REF], developed a supply chain design tool integrating the Supply Chain Operation Reference (SCOR) methodology with discrete event simulation.

The model is particularly suitable to be used when attempting to study the supply chain from a dynamic perspective, by analyzing the effect of changes in supply chain structure on the resulting performance. [START_REF] Longo | An advanced supply chain management tool based on modeling and simulation[END_REF], develop an advanced simulation model to support supply chain management. Their research focuses on two main objectives, namely developing a flexible and efficient simulator and implementing a decision making tool for supply chain managers. Several simulation studies have also been developed with the aim to assess the impact of information sharing mechanisms on the resulting supply chain costs and performance (e.g. [START_REF] Zhang | Design and simulation of demand information sharing in a supply chain[END_REF]Lau et al., 2005;[START_REF] Zhao | Forecasting errors and the value of information sharing in a supply chain[END_REF].

However, the existing literature is often limited to the analysis of few supply chain configurations, usually referring to a two-echelon system, or specific SCM topics (e.g. information sharing, reorder policy or manufacturing strategy). Consequently, the issue of optimizing the supply chain configuration is not fully embraced in those works. A limited number of works either deal with more complex supply chains or examine multiple configurations. Among these, [START_REF] Hwarng | Modelling a complex supply chain: understanding the effect of simplified assumptions[END_REF], modelled a complex supply chain and investigate the effects of several parameters, including demand and lead time distribution, and postponement strategies, on the resulting performance. Similarly, [START_REF] Shang | Operational design of a supply chain system using the Taguchi method, response surface methodology, simulation, and optimization[END_REF], applied simulation, Taguchi method and response surface methodology to identify the 'best' operating conditions for a supply chain. They examined the following supply chain parameters: information sharing, postponement, capacity, reorder policy, lead time and supplier's reliability.

In this work, we exploit simulation with the aim to analyze a complex supply chain, encompassing up to 5 echelons, and apply experimental design to examine different operational conditions of the supply chain, resulting from the combination of several input parameters. As the supply chain network continues to grow in complexity, both in terms of number of levels and number of linkages, examining complex scenarios is required to derive insights for supply chain optimization. Simulations are also completed by a detailed economical analysis of the scenarios examined.

General overview

The simulation model has been developed under Simul8 TM Professional, release 12 (Visual Thinking International Inc.). The nomenclature proposed in TABLE 1 is used to describe the model and the corresponding input parameters.

INSERT TABLE 1 In this study, we adopt the representation by [START_REF] Shapiro | The impact of forecasting methods on bullwhip effect in supply chain management[END_REF], suggesting that the supply chain can be described in terms of two main processes, namely products flow and orders flow.

Accordingly, the generic i-th echelon (i=1,..N) receives orders from echelon i-1 and products (i.e. pallets) from echelon i+1, through transport activities. For each echelon, a procurement lead time L i is introduced, encompassing the time required for transports, ordering and warehousing activities. We assume deterministic lead time [START_REF] Dejonckheere | Measuring and avoiding the bullwhip effect: A control theoretic approach[END_REF], and thus order crossover phenomena [START_REF] Reizebos | Inventory order crossover[END_REF] are not considered in this study. For simplicity, we model the flow of a single product.

According to several studies in literature [START_REF] Chatfield | The Bullwhip Effect-Impact of Stochastic Lead Time, Information Quality, and Information Sharing: A Simulation Study[END_REF][START_REF] Zhang | The impact of forecasting methods on the bullwhip effect[END_REF], the number of players per echelon is set at one. Echelon 1 (i.e., the retail store) directly faces the final customer's demand, whose value at day t is d t . Customer's demand is a stochastic variable, with normal distribution N(µ;σ). Other supply chain players (except the manufacturer) forecast demand through a moving average model based on the last m observations [START_REF] Chen | Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, lead time, and information[END_REF][START_REF] Zhang | The impact of forecasting methods on the bullwhip effect[END_REF]Sun & Ren, 2005).

Each player stores product in a warehouse, whose inventory level is initially set at a defined value. This latter is assumed to be the same for all echelons considered, except echelon N, for which an infinite stock availability is hypothesised.

The supply chain configurations considered

In this section, we describe the supply chain configurations examined in this study, in terms of the following parameters: (i) number of players; (ii) reorder policy; (iii) demand information sharing mechanisms; and (iv) demand behaviour.

Number of echelons

The supply chain modelled may range from 3 (i.e. manufacturer -distributor -retail store) up to 5 echelons (i.e. manufacturer -distributor1 -distributor2 -distributor3 -retail store).

Reorder policy

Each player can place orders according to an Economic Order Quantity (EOQ) or Economic Order Interval (EOI) policy. The same reorder policy is assumed for all supply chain players.

Under EOI policy, the reorder process of echelon i can be described as follows: i.

at time t (t=1,...N days ), the i-th echelon estimates demand mean (µ t,i ) and standard deviation (σ t,i ) according to the moving average model, i.e.:

( ) ∑ ∑ - = - = - - = = t m t k 2 i , t i , k 2 i , t t m t k i , k i , t d 1 m 1 d m 1 µ σ µ (1)
where d t,i indicates the demand faced by echelon i at time t, corresponding either to the final customer's demand or to orders placed by echelon i-1, i.e.:

   - = = = - 1 ,... 2 1 1 , , N i O i d d i t t i t (2) ii.
the above values are used to compute the order-up-to level at time t (OUL t,i ), according to eq.3 [START_REF] Bottani | Quantifying the Bullwhip Effect in inventory management policies[END_REF][START_REF] Dejonckheere | Measuring and avoiding the bullwhip effect: A control theoretic approach[END_REF]:

2 , , , ) ( ) ( i t i i t i i t L t k L t OUL σ µ + ∆ + + ∆ = (3) F o r P e e r R e v i e w O n l y iii.
each ∆t, the supply chain player checks the stock available I t-1,i to decide whether to place an order. The amount of product to be ordered is derived as OUL t,i -I t-1,i . It should be noted that I t-1,i also takes into account products ordered but not yet received; iv. whenever the order is placed, the inventory level I t,i is updated based on OUL t,i .

Under EOQ policy, the reorder process of echelon i is as follows:

i. eq.1 is exploited to estimate µ t,i and σ t,i at time t;

ii. the above parameters are used to compute the value of OP t,i , based on eq.4 [START_REF] Bottani | Quantifying the Bullwhip Effect in inventory management policies[END_REF][START_REF] Dejonckheere | Measuring and avoiding the bullwhip effect: A control theoretic approach[END_REF]:

2 , , , i t i i t i i t L k L OP σ µ + = (4)
iii.

in the case I t-1,i <OP t,i , the supply chain player places an order. The quantity to be ordered Q t,i is computed starting from µ t,i , as detailed below:

h c 2 Q o i , t i , t × × = µ (5) iv.
at time t, the inventory level I t,i of echelon i is updated based on the observed demand

d t,i , i.e. i t i t i t i t Q d I I , , , 1 , + - = - (6)
As we modelled a stochastic demand, orders placed by supply chain players could always exceed the available product stock, resulting in a stock-out. Under such circumstance, orders are fulfilled by an external supplier, with infinite products availability. The overall quantity supplied by this player (Q stock-out ) is used to assess the corresponding stock-out costs. In the case the stock-out occurs at the retail store, it is assumed that the final customer buys the quantity of products available; conversely, for all the remaining players, Q stock-out,i accounts for the whole quantity ordered to echelon i. Eq.7 summarises the computation of Q stock-out,i :

F o r P e e r R e v i e w O n l y    - = = - = - - - - 1 ,... 2 1 1 , 1 , 1 , , N i O i I d Q i t i t t i t out stock (7)
Due to infinite stock availability, no stock-out may occur for the manufacturer.

Information sharing mechanisms

Point of sale (POS) data can be shared between supply chain players or only available to the retail store. Under this latter scenario, echelon i forecasts demand only based on d t,i previously defined in eq.2. Conversely, when POS data are shared, this additional information is available to all supply chain players to forecast demand. Hence, for i=1,…N-1 we have d t,i =d t in eq.2.

FIGURE 1 and FIGURE 2 show a scheme of the model structure (in terms of products, orders and information flow) respectively under absence of information sharing and when information sharing mechanisms are implemented.

INSERT FIGURE 1 AND FIGURE 2

Demand information sharing can be seen as a possible consequence of the adoption of advanced Information Technology (IT) tools for product identification and monitoring. This is, for instance, the case of Radio Frequency Identification (RFID) coupled with EPC Network [START_REF] Bottani | Economical assessment of the impact of RFID technology and EPC system on the Fast Moving Consumer Goods supply chain[END_REF].

Demand behaviour

The final customer's demand may or may not experience an increase, referred to as demand "peak", during a simulation run. In the case of non-increase, the demand mean and standard deviation are known parameters (µ and σ). When simulating an increase in demand, the demand mean and standard deviation are changed to µ'=2µ and σ'=σ at the middle of the simulation, and kept unchanged until the simulation ends.

Under the EOQ policy, the "peak" of demand involves updating Q t,i and OP t,i parameters, by exploiting eqs.4-5 with µ' and σ'. (eq.3). Moreover, the reorder interval ∆t also depends on the demand mean; in this regard, in real cases, it is expected that each supply chain echelon will modify ∆t based on µ' and σ'. In modelling this behaviour, we consider two additional scenarios, namely: a. "responsive" supply chain players [START_REF] Lowson | Quick Response: Managing the Supply Chain to Meet Customer Demand[END_REF] -∆t is updated 3 days after the demand "peak" occurred;

b. "non-responsive" supply chain players -∆t is updated 5 days after the demand "peak" occurred.

Experiments setting and outcomes

To provide a detailed investigation of the supply chain, we examine 30 different scenarios, which are obtained by combining the parameters described in the above sections, according to Design of Experiments (DoE) [START_REF] Montgomery | Applied Statistics and Probability for Engineers[END_REF]. The resulting scheme is proposed in FIGURE 3.

INSERT FIGURE 3

For each scenario, we assessed the outputs listed below (numerical values of input parameters required for the computation are detailed in section 3.4):

i. Bullwhip effect, defined as the ratio between variance of orders received by echelon N and the variance of final customer's demand, i.e.

. Under "peak" of demand, the resulting σ is analytically computed based on d t values;

ii. cost of holding stocks (C stocks ): it is computed starting from unitary cost of stocks and amount of stock available at the warehouse, i.e.: Due to infinite stock availability, such cost is not computed for the manufacturer;

iii. stock-out cost (C stock-out ): it is computed starting from the mark-up applied by each supply chain player (c i ), corresponding to the economical loss experienced, and from Q stock-out,t,i , as described by eq.9:

(9) iv. order cost (C order ): it results from unitary cost of orders c o and number of orders placed by supply chain players N orders,i (except the manufacturer), i.e.:

(10)

The number of orders is a direct outcome of the simulation run;

v. transport cost (C transport ): transport cost is assumed not to be affected by the order quantity, and to only depend upon the number of orders fulfilled. It thus results from N orders,i and unitary cost of transport (c t ), according to eq.11:

( [START_REF]EOQ-3-no_sharing-no_peak[END_REF] vi. shipping/receiving cost (C shipping/receiving ): for each echelon, this cost is derived from average number of pallets handled per year, average hourly cost of manpower (c m ) and time required to handle a pallet (t pallet ). As the model considers a player per echelon, the average number of pallets handled reflects the average customer's demand (µ), which is the same for all echelons. Hence, C shipping/receiving only depends on the number of echelons considered. In the computation, it should also be considered that the manufacturer only performs shipping activities, while the retail store only performs receiving activities.

The following formula is thus used to assess C shipping/receiving :

Input data

Input data used in the model were derived from a previous study in the field of the FMCG supply chain, performed by one of the authors. Some details concerning the data collected in the previous work and the case study features are proposed in Appendix. The reader is referred to [START_REF] Bottani | Economical assessment of the impact of RFID technology and EPC system on the Fast Moving Consumer Goods supply chain[END_REF], for a comprehensive description of the case study.

The data used for the present study are described in the following list.

• The initial value of the inventory level is set at 472 pallets for echelons 1,…N-1. Such value is derived from the average capacity of a FMCG warehouse (i.e., 500 pallets),

which is usually at 80% saturation;

• the demand distribution is characterized by µ=150 pallets/day and σ=42 pallets/day.

Those values are used under absence of demand "peak"; when "peak" of demand occurs, they are updated to µ'=300 pallets/day and σ'=59.4 pallets/day;

• the service level provided by supply chain players, corresponding to the probability to fulfil orders with the available stock, is set at 90%. Consequently, we have k=1.28 in eqs.3-4;

• the moving average interval is m=5 for distributors and m=6 for the retail store;

• L i is set at 4.5 days for all supply chain players, except the manufacturer, whose lead time is 10 days. In both cases, 0.5 days are spent for transport activities;

• h is estimated in approx 153.52 €/pallet/year, corresponding to 0.42 €/pallet/day, which is derived as the average between costs experienced by distributor and manufacturer;

• the average value of products in the FMCG context accounts for 475 €/pallet. It is supposed that each echelon applies 10% mark-up to this value, which is close to typical mark-up for food products [START_REF] Anderson | Serving the world's poor: innovation at the base of the economic pyramid[END_REF]. Hence, c i in eq.9 varies depending on the echelon considered;

• c o and c t are set at 10 €/order and 780 €/transport, respectively;

• C shipping/receiving is estimated in approx 123,187.50 €/year/echelon under absence of demand "peak" and for 185,287.50 €/year/echelon when demand "peak" is considered;

• ∆t, computed starting from the parameters described above, accounts for 5 days under absence of demand "peak", and is changed to 3 days when demand "peak" is observed.

Results and discussion

The simulation duration was set at N days =365 days. For each scenario, 25 replications were performed. This value was observed to allow reaching stabilization of the simulation outputs for echelon N. As an example of stabilization of model outputs, FIGURE 4 shows the number of orders received by echelon N under "EOQ-5-no_sharing-no_peak" scenario as a function of the number of replications.

INSERT FIGURE 4 Bullwhip effect results are detailed in TABLE 2, and graphically illustrated in FIGURE 5, in terms of standard deviation ratio (σ N /σ), instead of variance ratio, to simplify the representation. • number of supply chain echelons (factor B) -3 (low) or 5 (high);

• demand information sharing (factor C) -absence (low) or presence (high) of information sharing mechanisms;

• demand behaviour (factor D) -absence (low) or presence (high) of demand "peak";

• responsiveness (factor E) -non responsive (low) or responsive (high) supply chain players. This factor is only considered in conjunction with demand peak (D) under EOI (A) inventory management policy, according to the previous description.

Bullwhip effect results

To validate the model outcomes, the bullwhip effect values from the simulation runs were compared with those resulting from the application of the analytical approach by [START_REF] Chen | Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, lead time, and information[END_REF]. Specifically, the authors derived a lower bound for the variance amplification for echelon i, expressed as:

2 2 1 1 2 2 2 2 1 ) ( ) ( m L m L d o i k k i k k i       +       + ≥ ∑ ∑ = = σ σ (13)
1 For visualization purpose, boundaries to the high/low values of both costs and bullwhip effect were set at 12.5% of the maximum observed value. being σ 2 (o i ) the variance of orders placed by the i-th supply chain echelon, σ 2 (d) the variance of the final customer's demand, L i the procurement lead time of echelon i, and m the moving average interval. As the above formula is valid under demand information sharing and EOQ inventory management policy, we compare analytical results with simulation outcomes for the "EOQ-5-sharing-no_peak" scenario. It should be noted that in eq.13 the same value of m is assumed for all echelons, which is not the case considered in our study. Hence Bullwhip effect outcomes can be summarised in the following key results.

Result 1: other things being equal, the bullwhip effect in higher under EOI than under EOQ inventory management policy.

This result was expected; in fact, under an EOI policy, orders are placed at a defined time interval ∆t, while the quantity ordered is null in other periods. As a result, an amplification of the demand variance is observed by the supplier. This confirms a similar result by [START_REF] Jakšič | The effect of replenishment policies on the bullwhip effect: A transfer function approach[END_REF], which observed that "order-up-to" replenishment rules induce higher bullwhip effect than others inventory management policies. Outcomes from TABLE 4 also show that the impact of factor A on the resulting bullwhip effect is statistically significant at p<0.05.

Result 2: other things being equal, the bullwhip effect is greater when the number of supply chain players increase.

Again, this result was expected, as it is a direct consequence of the bullwhip effect definition (see eq.13). As can be seen from This result is known in literature [START_REF] Lee | The value of information sharing in a two-level supply chain[END_REF]Chen et al., 2004;[START_REF] Chatfield | The Bullwhip Effect-Impact of Stochastic Lead Time, Information Quality, and Information Sharing: A Simulation Study[END_REF], and should be ascribed to the possibility of supply chain players to exploit POS data, rather than orders, to forecast demand, thus reducing the resulting variability. Statistical analyses also show that demand information sharing is the factor having the highest impact on the bullwhip effect (p=0.002). FIGURE 9 also shows that 100% of scenarios experiencing high bullwhip effect are characterised by absence of information sharing mechanisms.

Interestingly, a statistically significant impact of demand information sharing mechanisms in conjunction with EOI policy, with/without high number of supply chain echelons (i.e., factors BC/factors ABC) on the resulting bullwhip effect can be observed from the results obtained.

Result 4: under some circumstances, the bullwhip effect is lower when a "peak" of demand is introduced in the supply chain.

Outcomes from TABLE 4 show that the single effect of the "peak" of demand against the bullwhip effect is not statistically significant (p>0.05); this suggests that the demand "peak", per se, does not significantly affect the observed bullwhip effect. In this regard, it can be seen from FIGURE 10 that high bullwhip effect may occur either under presence or absence of demand "peak". From the same figure, it is also interesting to note that high bullwhip effect combined with low total cost always occur under absence of demand "peak" (100% of the scenarios examined).

The combined introduction of demand "peak" and EOI inventory management policy (i.e., factors AD), as well as of demand "peak" and high number of supply chain players (i.e., factors BD), have significant impact on the resulting bullwhip effect. Specifically, outcomes in From an operational perspective, this result could be explained considering that, when an unexpected increase in demand is observed, a supply chain player tends to increase the number of orders placed. Under an EOI policy, this involves reducing the ordering interval ∆t;

consequently, a lower number of "null" orders are observed. From the computational point of view, a lower order variance emerges. This effect is particularly emphasised when N=5, as can be seen from FIGURE 7.

Result 5: under "peak" of demand, the bullwhip effect is lower if the supply chain is able to quickly react to the demand variation.

This result is evident from numerical outcomes in TABLE 2, as all "responsive" scenarios show a lower bullwhip effect than the corresponding "non responsive" ones. A reactive supply chain player is able to quickly update the reorder policy parameters (i.e., the order interval ∆t), which results in the capability to better follow the demand trend, avoiding to introduce additional variability. Nonetheless, it should be noted that no statistical evidence can be provided in this regard.

Costs analysis

Outcomes from cost analysis can be summarized in the following key points.

Result 6: the total costs observed under scenarios "EOI-5-no_sharing-peak-no_resp", "EOI-5-no_sharing-no_peak", and "EOI-5-no_sharing-peak-resp" are significantly higher than all the remaining scenarios. Result 7: other things being equal, the total costs observed are significantly higher when the number of supply chain players increase.

F

The number of supply chain echelons has the highest impact on the observed total costs of the supply chain (p=0.000). In particular, statistically significant effects of factor B are observed against all cost components considered in this study. FIGURE 7 confirms that supply chain configurations with high costs are only composed of 4 or 5 echelons.

This is an obvious result, since the increase in the number of supply chain echelons clearly involves increase in all cost components considered, due to the need of adding the cost contributions of each echelon (see eqs.8-12).

Result 8: other things being equal, the total costs observed are significantly higher under EOI than EOQ inventory management policy. As mentioned already, EOI policy usually involves a higher average stock level, as a consequence of the lower number of orders, with wider quantities. This is confirmed by statistical analyses performed, which highlight a significant impact (p=0.002) of factor A on the resulting costs of holding stocks. As order and transport costs are both computed starting from the number of orders (see eqs.11-12), the statistically significant impact of EOI inventory management policy on those cost components is a direct consequence of the number of orders placed by supply chain players under that policy.

F

As a further outcome, the combined effect of factors AB (i.e., EOI policy coupled with high number of supply chain echelons) is also found to significantly impact the total costs. Specifically, it is reasonable that factors AB substantially increase each cost component examined, since both the number of echelons and the EOI policy involve a significant increase of the cost components. This is confirmed by results in TABLE 3.

Result 9: other things being equal, the total costs observed tend to be lower when demand information sharing is introduced. However, demand information sharing has a different impact on each cost component. From TABLE 3, TABLE 4 and FIGURE 9, it can be appreciated that total costs observed are usually lower when demand information sharing mechanisms are introduced, and that the effect is statistically significant at p=0.001.

This result is a consequence of several effects. As a first point, it can be observed from TABLE 3 that costs of holding stocks are substantially lower under demand information sharing. In fact, as mentioned in result 3, the availability of POS data allows reducing the orders variability, resulting in a lower bullwhip effect and in a significant reduction of the amount of stocks required at each supply chain echelon. In this regard, a significant impact (p=0.000) of demand information sharing mechanisms on the resulting costs of holding stocks is observed in TABLE 4. Although this is a general result, it can be particularly appreciated when examining a 5echelon supply chain, where the resulting bullwhip effect is extremely high (see TABLE 2 and result 2).

Conversely, results presented in TABLE 3 indicate that stock-out costs tend to increase when demand information sharing is implemented, although the availability of POS data, per se, has no significant effect (p=0.055) on the observed stock-out costs. This result should mainly be ascribed to the way stock-out costs were modelled in our study. In fact, under demand information sharing, each supply chain player places orders based on POS data; hence, quantities ordered are usually lower than those required under unknown customer's demand, resulting in reduced average stock level. However, under stochastic demand it is always possible that demand values (and consequently orders placed) exceed the amount of stocks available; this is exacerbated when the average stock level is lower. Consequently, stock-out costs increase under demand information sharing mechanism.

Finally, demand information sharing mechanisms appear to significantly affect the observed order (p=0.003) and transport (p=0.003) costs. Looking at TABLE 3, it can be seen that, in particular, demand information sharing tends to increase the resulting order and transport costs.

In fact, the availability of POS data allows reducing the observed demand variability, allowing The combined effect of the above described cost components leads to very different results, depending on the supply chain configuration examined. More precisely, it can be seen from FIGURE 6 and TABLE 3 that costs of holding stocks are by far the most important cost component of 5-echelon supply chains. Demand information sharing thus involves a significant decrease of costs for those supply chains. An opposite situation occurs for 3-echelon supply chains. In fact, given the low number of echelons, this supply chain configuration is affected by costs of holding stocks and stock-out costs to a similar extent: such costs account for about 35% and 37% on the total costs, respectively. By amplifying the stock-out costs, information sharing leads to a slight increase of the total costs for those scenarios. Finally, 4-echelon supply chain scenarios appear to be closer to 5-echelon ones, i.e. information sharing involves decrease in the total costs; however, due to the lower number of echelons, this result is less evident.

Besides the above result, outcomes of the statistical analysis and economical assessment also

show that demand information sharing mechanisms, in conjunction with EOI policy and high number of supply chain echelons (i.e. factors ABC), appear to significantly affect the observed order (p=0.005) and transport (p=0.007) costs, and in particular tend to increase such costs. This is again a consequence of the increased number of orders placed, resulting from the reduced demand variability and corresponding decrease of quantities per order.

Result 10: other things being equal, the total costs observed increase when "peak" of demand is introduced. 10 indicate that total supply chain costs are higher when "peak" of demand is introduced, and that the impact of demand "peak" (i.e., factor D) on the observed costs is significant at p=0.012. More precisely, demand "peak" involves increase of stock-out (p=0.005), order (p=0.000), transport (p=0.000), and shipping/receiving (p=0.000) costs, resulting in substantially higher total costs.

Results in TABLE 3, TABLE 4 and FIGURE

The increase of stock-out costs was expected, since, as a consequence of demand "peak", the amount of stock available for each supply chain player is more likely to be lower than the quantity requested. Moreover, as already discussed, when a demand increase is introduced, a supply chain player tends to increase the number of orders placed, regardless of the inventory management policy applied. Hence, an increase in order costs and corresponding transport costs is observed. Finally, due to the computational procedure followed, shipping/receiving costs are amplified as a consequence of the increased quantity of pallets handled per year.

The combined effect of factors AD (i.e., demand peak and EOI inventory management policy) on the total costs, and in particular on the costs of holding stocks, is also significant. It can be observed from TABLE 3 that cost of holding stocks tends to increase under peak of demand and EOI policy. This result should be ascribed to the increased order variance caused by demand peak under EOI inventory management policy, which, in turn, involves increase in the required safety stocks for each echelon.

Similar considerations can be drawn for the combined effect of factors BD (i.e., demand "peak" coupled with high number of supply chain echelons) on the total costs. More precisely, factors BD significantly affect the resulting costs of holding stocks (p=0.000), orders (p=0.031) and transport (p=0.036). From TABLE 3, it can be seen that all the above costs components tend to be higher when examining 5-echelon supply chains under demand "peak". As previously mentioned, the higher order variance caused by demand "peak" involves increase in the required safety stocks for each supply chain echelon, resulting in a corresponding increase in their costs.

Demand "peak" also involves an increase in the number of orders placed, due to higher demand observed. Order and transport costs are thus amplified correspondingly. Result 11: other things being equal, under "peak" of demand, the total costs observed decrease if the supply chain is able to quickly react to the demand variation.

It can be seen from TABLE 4 that the combined effect of demand "peak" and responsiveness, under EOI inventory management policy (i.e., factors ADE) has a significant impact (p=0.03) on the resulting total costs observed. In fact, a quick reaction of the supply chain implies that each player updates inventory management parameters (in particular, the ∆t interval)

immediately after the demand "peak" is observed. The main outcome of such reaction is that the average stock level is quickly adapted to the new demand value, thus optimizing the overall cost of stocks. Outcomes from TABLE 4 also highlight that the combined effect of factors ADE significantly decreases the resulting stock-out (p=0.034), order (p=0.000), transport (p=0.000) and shipping/receiving (p=0.001) costs. As a result, the observed total costs decrease under this scenario.

Conclusions

Based on a discrete-event simulation model, reproducing a Fast Moving Consumer Goods (FMCG) supply chain, we have provided a quantitative assessment of the effects of different configurations on the total costs and bullwhip effect observed in the supply chain. Our analysis covers 30 possible supply chain configurations, resulting from the combination of several design parameters, such as number of echelons, reorder policy adopted, demand information sharing mechanisms, demand behaviour, and responsiveness. For each scenario, total costs and bullwhip effect were computed starting from simulation outcomes and several input parameters available in literature. Moreover, a statistical analysis of effects was performed to identify possible significant impact of single/combined supply chain design parameters on the resulting costs and demand variance amplification.

The key results of this study show that both the total logistics cost and the bullwhip effect are affected by all supply chain design parameters examined, although to a different extent. In particular, the number of supply chain echelons and the implementation of an EOI inventory management policy involve a substantial increase in the total costs and bullwhip effect, and their impact is significant at p<0.05. The presence of demand "peak" also causes an increase in the total logistics costs, although, per se, it does not significantly affect the resulting bullwhip effect. Conversely, demand information sharing mechanisms tend to reduce both the bullwhip effect and the resulting total costs, due to the significant (p=0.000) decrease in costs of holding stocks.

As the simulation model was developed using average data of the FMCG context, our results can be useful in practice to identify the optimal supply chain configuration as a function of the operating conditions. Moreover, outcomes from this study provide some insights about the supply chain cost components and their trend depending on the configuration considered.

Our study is grounded on the simulation of a single-product flow. To derive more general results, it would be appropriate to extend the model to include: SSt 3.89E+5 SS 3.69E+4 2.97E+4 4.51E+4 2.84E+1 3.63E+4 2.46E+4 3.05E+4 2.41E+4 5.81E+2 1.05E+4 3.09E+4 9.62E+ 1.47E+1 3.90E+ 1.44E+1 1.10E+2 9.05E+0 6.84E+3 5.79E+3 6.80E+3 Sse 9.98E+4 MS 3.69E+4 2.97E+4 4.51E+4 2.84E+1 3.63E+4 2.46E+4 3.05E+4 2.41E+4 5.81E+2 1.05E+4 3.09E+4 9.62E+ 1.47E+1 3.90E+ 1.44E+1 1.10E+2 9.05E+0 6.84E+3 5.79E+3 6.80E+3 Mse SSt 1.82E+16 SS 1.49E+15 3.07E+15 1.45E+15 7.29E+14 1.97E+15 1.11E+15 9.22E+14 8.79E+14 5.24E+14 2.23E+14 1.69E+15 3.66E+14 1.85E+14 2.88E+14 2.00E+14 1.69E+14 1.80E+14 3.65E+13 8.95E+13 3.29E+13 Sse 2.60E+15 MS 1.49E+15 3.07E+15 1.45E+15 7.29E+14 1.97E+15 1.11E+15 9.22E+14 8.79E+14 5.24E+14 2.23E+14 1.69E+15 3.66E+14 1.85E+14 2.88E+14 2.00E+14 1.69E+14 1.80E+14 3.65E+13 8.95E+13 3.29E+13 Mse 1.00E+14 F SSt 1.38E+16 SS 1.03E+15 1.89E+15 1.78E+15 2.96E+14 7.61E+14 9.21E+14 8.65E+14 8.40E+14 2.61E+14 7.59E+13 1.54E+15 2.23E+14 2.16E+14 2.03E+14 1.95E+14 1.99E+14 1.79E+14 4.10E+13 4.76E+13 2.89E+13 Sse 2.19E+15 MS 1.03E+15 1.89E+15 1.78E+15 2.96E+14 7.61E+14 9.21E+14 8.65E+14 8.40E+14 2.61E+14 7.59E+13 1.54E+15 2.23E+14 2.16E+14 2.03E+14 1.95E+14 1.99E+14 SSt 4.04E+14 SS 1.26E+13 7.30E+13 1.38E+13 3.27E+13 1.23E+14 4.66E+12 1.68E+12 7.30E+11 1.70E+13 1.40E+13 4.36E+12 8.54E+12 8.91E+11 3.63E+12 8.29E+10 9.07E+11 1.53E+10 6.77E+10 3.17E+12 1.67E+11 Sse 8.88E+13 MS 1.26E+13 7.30E+13 1.38E+13 3.27E+13 1.23E+14 4.66E+12 1.68E+12 7.30E+11 1.70E+13 1.40E+13 4.36E+12 8.54E+12 8.91E+11 3.63E+12 8.29E+10 9.07E+11 1.53E+10 6.77E+10 3.17E+12 1.67E+11 SSt 7.60E+8 SS 1.39E+8 4.91E+7 2.39E+7 1.10E+8 1.94E+8 8.02E+6 2.01E+7 6.26E+6 7.00E+7 4.37E+7 1.12E+7 6.42E+6 5.80E+6 4.35E+6 2.25E+6 4.67E+6 1.67E+6 1.53E+6 2.47E+6 3.63E+5 Sse 5.55E+7 MS 1.39E+8 4.91E+7 2.39E+7 1.10E+8 1.94E+8 8.02E+6 2.01E+7 6.26E+6 7.00E+7 4.37E+7 1.12E+7 6.42E+6 5.80E+6 4.35E+6 2.25E+6 4.67E+6 1.67E+6 1.53E+6 SSt 4.47E+12 SS 8.01E+11 3.02E+11 1.39E+11 6.29E+11 1.15E+12 4.60E+10 1.16E+11 3.64E+10 3.99E+11 2.68E+11 6.54E+10 3.82E+10 3.30E+10 2.49E+10 1.29E+10 2.64E+10 9.43E+9 9.37E+9 1.61E+10 2.24E+9 Sse 3.46E+11 MS 8.01E+11 3.02E+11 1.39E+11 6.29E+11 1.15E+12 4.60E+10 1.16E+11 3.64E+10 3.99E+11 2.68E+11 6.54E+10 3.82E+10 3.30E+10 2.49E+10 1.29E+10 2.64E+10 9.43E+9 9.37E+9 1.61E+10 SSt 6.09E+13 SS 3.09E+12 9.26E+12 4.29E+10 9.46E+12 2.29E+13 7.43E+11 4.29E+10 4.29E+10 3.09E+12 3.09E+12 4.29E+10 1.69E+12 4.29E+10 7.43E+11 4.29E+10 4.29E+10 4.29E+10 4.29E+10 7.43E+11 4.29E+10 Sse 5.69E+12 MS 3.09E+12 9.26E+12 4.29E+10 9.46E+12 2.29E+13 7.43E+11 4.29E+10 4.29E+10 3.09E+12 3.09E+12 4.29E+10 1.69E+12 4.29E+10 7.43E+11 4.29E+10 4.29E+10 4.29E+10 4.29E+10

  better follow the demand behaviour: specifically, lower quantities are ordered more frequently, with a resulting increase in the number of orders placed.

  (1) the flow of different products, with different characteristics; (2) several supply chain players per echelon; (3) leadtime stochasticity and corresponding order crossover investigation; and (4) a sensitivity analysis of model outcomes as a function of different values of the input parameters.

FIGURE 4 :

 4 FIGURE 1: qualitative scheme of the model developed under absence of information sharing.

FIGURE 7 :

 7 FIGURE 7: supply chain structure as a function of total costs and bullwhip effect.

FIGURE 8 :

 8 FIGURE 8: reorder policy as a function of total costs and bullwhip effect.

FIGURE 9 :

 9 FIGURE 9: information sharing mechanisms as a function of total costs and bullwhip effect (Note: sh = information sharing; n-sh = no information sharing).

FIGURE 10 :

 10 FIGURE 10: demand behaviour as a function of total costs and bullwhip effect.

  The same happens, under EOI policy, for the OUL t,i parameter

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	10

TABLE 3 and

 3 FIGURE 6 provide a detailed illustration of the costs resulting in the scenarios examined. Statistical analysis of outcomes was also performed, with the aim to identify and assess single and combined effects of the supply chain parameters on the simulation results. The

	procedure described by Montgomery & Runger, (2003), was followed to this extent. Outcomes,
	in terms of Sum of Squares (SS), Mean Square (MS), F-test and corresponding significance
	value (sig.) are proposed in TABLE 4. It should be noted that this analysis is limited to 20
	scenarios, resulting from the following combinations of factors:

• reorder policy (factor A) -EOQ (low) or EOI (high);

TABLE 4

 4 impact of number of factor B on the resulting bullwhip effect. FIGURE7shows that supply chains with high bullwhip effect and high total costs encompass 4 (43%) or 5 (57%) echelons, while supply chains with high bullwhip effect and low total costs are composed of 3 (50%) or 4 (50%) echelons.From TABLE 2 it can also be noted that the number of supply chain players substantially increase the bullwhip effect under absence of information sharing; conversely, under information sharing, outcomes of the simulation runs support this result to a lower extent. In this regard, focusing on TABLE 4, it can be appreciated that the combined effect of demand information sharing and number of supply chain players (i.e. factors BC) has not significant impact on the bullwhip effect. This could be explained considering that complete supply chain visibility provides, as output, substantially lower demand amplification; consequently, most of the resulting scenarios are characterised by similar values of the bullwhip effect, regardless of the number of echelons.

	, statistical analyses show a significant (p<0.05)

Outcomes of TABLE 4 also suggest that the combined implementation of EOI inventory management policy and high number of supply chain echelons (i.e., factors AB) has a significant (p<0.05) impact on the resulting bullwhip effect. As explained in result 1, under an EOI policy, several "null" orders are observed, as supply chain players place orders every ∆t. In particular, as the OUL t,i is computed according to the orders received (see eqs.1 and 3), under this scenario it is found that, due to substantial demand variance amplification, orders to echelon N are very limited in number. Conversely, quantities ordered are dramatically increased. This effect is particularly evident for high N.

TABLE 2

 2

	indicate that a lower bullwhip effect is usually observed when demand "peak" is introduced in
	the model. The same result is indicated in FIGURE 8, which shows that scenarios with high
	bullwhip effect and high total costs are mainly characterised by EOI policy (86% of the

  This result was derived from the analysis of outcomes in TABLE3. The above scenarios are all composed of 5 echelons, and operate under EOI policy and absence of information sharing. The resulting costs ranges from about 15 to 19 million €/year, while all other scenarios experience

	costs lower than 7 million €/year. It can be easily noted that the costs are almost entirely due to
	stocks, which account for 83.2% (under "EOI-5-no_sharing-peak-resp" scenario) to 86.8%
	(under "EOI-5-no_sharing-peak-no_resp" scenario) of the total costs. This result, in turn, is a
	consequence of the bullwhip effect observed, ranging from 53.24 to 108.4 in terms of σ N /σ for o r the scenarios considered (see TABLE 2), which involves high safety stock levels. In particular,
	looking at FIGURE 8 and FIGURE 9, one can see that high bullwhip effect combined with high P total costs is mainly observed under EOI policy (86% of the scenarios examined) and absence of
	e r e information sharing mechanisms (100% of the scenarios examined).
	R
	e
	v i e
	w
	O n l
	y

TABLE 1 : nomenclature used to detail the model

 1

	Parameter				Acronym			Measurement unit
	Simulation model
	Number of supply chain echelons				N (i=1,…N)		-
	Simulation duration					N days			days
	Lead time of the i-th echelon						L i				days
	Final customer's demand parameters
	Mean							µ				pallets/day
	Standard deviation							σ				pallets/day
	Daily final customer's demand value at time t						d t				pallets/day
	Demand forecasting for echelon i
	(i=1,…N-1)
	Moving average interval						m				days
	Estimated demand mean at day t						µ t,i				pallets/day
	Estimated demand standard deviation at day t						σ t,i				pallets/day
	Demand faced at time t						d i,t				pallets/day
	Inventory management parameters for
	echelon i (i=1,…N-1)
	Order-up-to level at time t under EOI policy					OUL t,i			pallets
	Order interval under EOI policy						∆t				days
	Order point at time t under EOQ policy					OP t,i			pallets
	Quantity ordered at time t	O t	i ,	=	   OUL t Q i , t	-i ,	I	t	-1	i ,	EOI EOQ	policy policy	pallets
	Inventory position at time t						I t,i				pallets
	Service level delivered							k				-
	Amount of out-of-stock at time t				Q stock-out,t,i			pallets
	Overall amount of out-of-stock				Q stock-out			pallets
	Economical values
	Markup applied by echelon i						c i
	Hourly cost of manpower						c m				€/hour
	Unitary order cost						c o				€/order
	Total cost of orders					C orders			€/year
	Unitary transport cost						c t				€/transport
	Total transport cost				C transport			€/year
	Unitary cost of holding stock							h				€/year/pallet
	Total cost of holding stocks					C stocks			€/year
	Total stock-out cost				C stocks-out			€/year
	Unitary handling time						t pallet			hour/pallet
	Total shipping/receiving cost				C shipping/receiving		€/year

TABLE 2 : bullwhip effect results for the scenario examined.

 2

	Bullwhip effect
	σ orders /σ	variance ratio

pag.42 of 44

TABLE 3 : average total costs [€/year] for the scenarios examined. ID SCENARIO TOTAL COSTS Cost of holding stocks Stock-out cost Order cost Transport cost Shipping and receiving cost

 3

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TABLE 4 : statistical analysis of experiments.

 4

	Single effects

  Mse 3.42E+12 F

	Stock-out	costs	3.682	21.367	4.043	9.585	36.047	1.364	0.492	0.214	4.989	4.089	1.277	2.502	0.261	1.063	0.024	0.266	0.004	0.020	0.927	0.049
			sig 0.066	0.000	0.055	0.005	0.000	0.254	0.489	0.648	0.034	0.054	0.269	0.126	0.614	0.312	0.877	0.611	0.947	0.889	0.345	0.827
			A	B	C	D	AB	AC	ABC	AD	ADE	BC	BD	CD	ABD	BCD	ACD	ABCD ACDE ABDE BCDE ABCDE

TABLE 5 : percentage values of total costs and bullwhip effect (used for FIGURE 7÷FIGURE 10). Bullwhip effect (percentage values) Total cost (percentage values)

 5

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Appendix: case study details

The data related to the supply chain considered is this paper were derived from a previous research by [START_REF] Bottani | Economical assessment of the impact of RFID technology and EPC system on the Fast Moving Consumer Goods supply chain[END_REF], in the field of FMCG. In this section, we detail the research methodology followed by the authors and the resulting supply chain data.

The data collection phase involved a panel of 11 enterprises, operating as manufacturers (6 companies) and distributors (5 companies) of FMCG. For each participant, the analysis was focused on a distribution centre (DC), suggested by the company to be enough representative of logistics processes. In addition, for each distributor, a retail store (RS) was identified and investigated. The aim of the analysis was to detail the relevant logistics processes of each participant. To this extent, an appropriate survey phase was carried out, where two different questionnaires have been deployed to collect comprehensive data both for DCs and RSs. In both questionnaires, a first part was aimed at collecting general information about the participant, as well as common data for all processes examined (e.g., products type, average value of pallet/case, number of employees and related costs, DC/RS area). Moreover, specific sections were added to collect data related to the processes performed by DCs and RSs (i.e., "receiving", "putaway", "picking and sorting" and "shipping" for DCs, and "receiving", "backroom management" and "expositive area management" for RSs). For each process, quantitative parameters were examined, such as amount of goods flow, stock levels, amount of safety stock, or stock-outs. A list of quantitative data collected, relevant for the present study, is proposed in the following: The data collection phase, together with site visits, approximately took from November 2004 to April 2005; for each visit, about 2-3 hours were spent for visiting the structure and answering the questionnaire.

Starting from the data collected, as many case studies were edited, detailing the processes currently performed by the DC/RS and the corresponding performance. The case studies were used to outline a "representative" FMGC supply chain, on the basis of the similarities between processes analysed. The "representative" supply chain is composed of three echelons, namely a