Renzo Akkerman

Dirk Van Der Meer

Dirk Pieter Van Donk

Van Donk

Dirk Pieter

Make to stock and mix to order: Choosing intermediate products in the food-processing industry

Keywords: POSTPONEMENT, OPERATIONS food industry, decoupling point food industry, decoupling point, postponement, intermediate storage, case study

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Introduction

In the food processing industry, a typical production plant produces a multitude of intermediate products in an even wider range of packages. Often, the output variety is based on a relatively small number of (agricultural) raw materials. In general, such a divergent product structure is typical for the process industries [START_REF] Fransoo | A typology of production control situations in process industries[END_REF]. Differences in products can be associated with customer-specific products, either in packaging form, size, or print, labelling, or (more fundamental) product recipe. Recipes normally differ with respect to a bundle of product quality attributes. Often a recipe can be characterised in terms of minimal requirements for each attribute. Different options might exist in relation to where in the process a recipe is made specific: either adding specific ingredients early or late in the process.

A number of factors and trade-offs determine at what stage a product will become customerspecific. Generally, product specifications are assumed to be known for each stage of the production process. In other words, the final product determines the requirements and specification of all intermediates univocally. However, in food-processing companies -specifically those that mix and blend -recipes of final products can sometimes be manufactured in different ways. Two extreme possibilities are either starting with a customer-specific recipe and process the resulting relatively small batches and store final product waiting for orders, or process raw materials in large batches, store these and mix them to recipe as the last step as customer orders arrive. It might be clear that there is an endless number of variants in between in terms of the amount and nature of possible intermediate recipes that can be stored, and deciding how to organize this is an essential factor in determining the operational performance of many mix or blend production systems. Finally, given the nature of recipes, one might decide to deliver products having a too high quality for one or two requirements. In general, each of the alternatives has implications for the processing costs, but, additionally, it might also affect the costs of the raw materials used. This problem has some similarities with binning, where quality grades are determined and subsequently downgrade possibilities are used to satisfy demand with higher quality levels to save setups (see [START_REF] Lyon | Matching assets with demand in supply-chain management at IBM Microelectronics[END_REF]. However, their problem is operational (how to satisfy orders), whereas we focus on a tactical decision (what are the recipes for a certain period of time). Moreover, in discrete manufacturing far less possibilities exist for the product structure (recipe).

So far, the literature has not addressed the problem of jointly determining (i) when to specify a product to customer specifications, (ii) which recipes to use for flexible products -i.e., intermediate products that can still be used to mix various customer orders, and (iii) how many intermediate products to use. This paper develops an approach to decide on the number and composition of intermediate products in two-stage food production systems, supported by quantitative modelling. More specifically, we consider the case of a flour mill, facing the problem of how much and which intermediate recipes to store and to determine the consequences of different options. These consequences range from operational issues such as the costs of ingredients to more tactical and strategic decisions such as the required number of intermediate silos. More generally, the aim of this paper is also to contribute to the understanding of product specification in the food industry if end products can either be made to stock, mixed to order, or made to order.

The paper is structured as follows. In the next section, the theoretical background of the studied problem is discussed. Then, the case study is introduced, also outlining the quality parameters of the products in question. The following section then presents the solution procedure for determining the number and composition of the intermediate products. Subsequently, the results of the application of the model in the case study are discussed. Finally, the last section will present our conclusions and a discussion on the paper's contribution and the future research opportunities.

Theoretical background

Resulting from increasingly powerful retailers [START_REF] Dobson | Buyer power and its impact on competition in the food retail distribution sector of the European Union[END_REF], food manufacturers find themselves in a situation where the downstream supply chain requires more and more flexibility, whereas the characteristics of the production systems involved often do not support this [START_REF] Van Donk | Opportunities and realities of supply chain integration: The case of food manufacturers[END_REF]. To improve their flexibility, while still trying to produce in efficient volumes, food manufacturers often try to postpone the diverging of their product mix as long as possible (e.g., [START_REF] Van Donk | Make to stock or make to order: The decoupling point in the food processing industries[END_REF][START_REF] Soman | Combined make-to-order and make-to-stock in a food production system[END_REF]. This late specification allows for shorter lead times, while keeping production efficiency before the specification on an acceptable level. Early product specification would lead to an early diverging of the number of different products and would result in increased requirement of storage facilities (as each product requires its own tank or silo), and numerous additional changeovers and/or cleaning activities.

This concept of 'postponement' (or delayed differentiation) has been extensively studied in the literature. In manufacturing situations, postponement aims to retain products in a neutral and noncommitted status as long as possible (Yang et al., 2004b). An overview of the research on postponement can be found in [START_REF] Van Hoek | The rediscovery of postponement: a literature review and directions for research[END_REF], which was updated and extended by [START_REF] Boone | Postponement: an evolving supply chain concept[END_REF]. They propose several new challenges for further research. Among others, they conclude that the application of postponement was not as widespread as was expected based on the attention in the literature. Recently, [START_REF] Forza | Form postponement effects on operational performance: a typological theory[END_REF] developed a typology that identifies three types of postponement. They stress that it is important to clarify which type is studied, to be able to carefully assess the resulting operational performance. The first type they identify deals with postponement of product specification from the forecast-driven production stages to the order-driven production stages. In our work, when deciding on when to specify products, and what flexible recipes to use to mix final products, this is the kind of situation we are dealing with. However, the specific role of recipes in the product structure encountered in most process industries is not explicitly considered by [START_REF] Forza | Form postponement effects on operational performance: a typological theory[END_REF].

Next to his 2001 review, Van Hoek also wrote specifically about postponement in the food industry [START_REF] Van Hoek | Postponement and the reconfiguration challenge for food supply chains[END_REF]. Here, he noted that, in comparison with other industries, the application of postponement in the food industry is fairly low. Food-specific characteristics like e.g. perishability and short lead times limit the applicability of postponement. Van Hoek however sees a strong focus on product standardization in the food industry, as this is the only way to increase capacity utilization of capital intensive production technology. The problem here is that standardization is often difficult to achieve, as customers nowadays demand more and more product variety. For this reason, [START_REF] Abukhader | Postponement strategies in food supply chains -an empirical investigation[END_REF] encourage food companies to analyze their product mix and product development process in detail, to see where postponement can be applied.

However, the divergence in the product mix does not have to happen at the first production stage, but can often be placed later in the production process. Here, the concept of postponement is strongly connected to the decoupling point concept (Hoekstra and Romme, 1992;[START_REF] Olhager | Strategic positioning of the order penetration point[END_REF]. [START_REF] Van Donk | Make to stock or make to order: The decoupling point in the food processing industries[END_REF] elaborates on this concept for the food-processing industry. One of the shortcomings he mentions is its qualitative nature and its focus on individual products as opposed to the entire product portfolio. Another issue is that the decoupling point concept assumes that specifications of products and intermediate products are known and fixed. However, as explained earlier that is often not the case in process industries and food processing.

A number of (process) industries faces the situation where once it is decided to locate the decoupling point at the intermediate product level, the set of intermediate products still has to be determined. That generally applies to the specification and/or the number of intermediates. For instance, in steel mills, an extensive range of slab lengths is demanded by customers. To reduce inventory costs (and often also to increase processing efficiency), a limited number of those slab lengths are held in storage, and are cut to customer specification when final orders arrive. Next to reducing inventory costs, this introduces waste costs due to cutting losses. In the literature we find several approaches dealing with this specific case. Recent examples are the work by [START_REF] Caux | Implementation of delayed differentiation in batch process industries: a standardization problem[END_REF], who develop a mathematical model to evaluate the cost trade-off and the graphical approach presented by [START_REF] Kerkkänen | Determining semi-finished products to be stocked when changing the MTS-MTO policy: Case of a steel mill[END_REF]. A similar example can be found in the cardboard industry, where a limited number of large sheet sizes are subsequently cut into a wide variety of small sheets [START_REF] Wanders | The composition of semi-finished inventories at a solid board plant[END_REF].

In the food industry, determining the set of intermediate products mostly deals with products that are to be used in combinations to comply with the requirements on the final product (e.g. [START_REF] Rajaram | Robust process control at Cerestar's refineries[END_REF]. Once the intermediates are determined, a certain stock level will be maintained from which the intermediates are blended to order to create the final wide range of products. However, in theory, almost any possible set of intermediates could be used, but intermediate storage possibilities are often limited [START_REF] Akkerman | The influence of capacity-and timeconstrained intermediate storage in two-stage food production systems[END_REF], which causes a very complex decision problem. The increasing importance of food safety and food quality (e.g., [START_REF] Griffith | Food safety: Where from and where to?[END_REF] even adds to this complexity, due to additional constraints.

The composition (or recipe) of the intermediate products has to be derived from the required specifications of the final products and the given attributes or qualities of the raw materials. As the composition of raw materials is often variable for food products, the composition of the intermediate products either has to be robust to these changes or should be changed on a regular basis. In related work by [START_REF] Rutten | Balancing stocks, flexible recipe costs and high service level requirements in a batch process industry: A study of a small scale model[END_REF] the concept of recipe flexibility is introduced to deal with (i) variations in raw material quality, (ii) cost minimization by raw material selection, and (iii) substitutions of raw materials in recipes due to unavailability (see also [START_REF] Rutten | The use of recipe flexibility in production planning and inventory control[END_REF]. In [START_REF] Rutten | Balancing stocks, flexible recipe costs and high service level requirements in a batch process industry: A study of a small scale model[END_REF], only a single mixing stage is present, and determining recipes is an operational problem that can be solved for each production order. This also holds for the case of chemical fertilizers studied by [START_REF] Ashayeri | Blending modelling in a process manufacturing: A case study[END_REF]. Similarly, [START_REF] Lyon | Matching assets with demand in supply-chain management at IBM Microelectronics[END_REF] present an operational method in discrete manufacturing that matches different quality grades to orders by using higher qualities than required to prevent set-ups. However, in two-stage production systems, that would imply that both processes can produce order-driven, which is often not the case and certainly not in the case of flour milling we present here.

In this paper, specification (and hence order-driven production) starts at the intermediate storage stage, and the aim is to design several intermediate products that can be used in a mix-to-order strategy to fulfil future demand. This means the determination of recipes takes place not on an operational level, but on a strategic or tactical level, and is only performed once in a while to achieve cost minimization. To support this, we develop a stepwise approach supported by mathematical programming models, which takes a wide variety of typical food-related quality aspects into account. The resulting model can be used to design recipes for intermediate products, which can be used in a cost-efficient mix-to-order strategy. We feel that the approach presented in this paper will support the decision-making on postponement and the decoupling point in practice, taking into account several operational characteristics that are typical for the food industry, and addressing the inherent trade-offs between product flexibility and material costs. Furthermore, it contributes to the theory on postponement and the decoupling point, by providing a structured approach based on quantitative modelling, balancing several cost factors and including the whole product range in the decision making process.

Case description

We study a medium-sized flour manufacturer, supplying flour products to bakeries and industrial manufacturers. Figure 1 shows an outline of the production process. Grains and additional ingredients are pre-processed, blended, and milled to obtain a selection of intermediate products, which can already be blends of various grains. These products are then mixed into a wide range of flour products, transported in bulk to industrial customers and large bakeries, or packaged in bags for smaller traditional bakeries.

[FIGURE 1 ABOUT HERE]

Problem description

Although flour mills seem to be relatively simple processes, the above-sketched situation fully applies: a small amount of raw materials (around 10 types of grain) and an increasing amount of partly customer-specific end products (currently around 50). The two extreme options are either to mix first and then mill, or to mill all raw grains separately and mix them to recipe. Both these extremes are not reasonable due to the fact that it would either lead to a few intermediates, which would always have to be mixed, or many intermediates which would already be customer-specific. The first option would lead to a lot of mixing operations, whereas the latter situation would require a huge storage capacity. Taking this into account, the challenge is to find a solution in-between these extremes. Therefore, it is logical to store a limited number of (possibly blended) intermediate products and use these to mix end products. In terms of the decoupling point, we can characterize this as mix to order. It is worth stressing that some intermediates can be used directly as end products without mixing and after mixing in other products. An important reason for the mix-toorder strategy is the required short delivery time. Operating this system incurs all types of operational problems. Here, we address a more tactical oriented design problem: determining the amount and composition of intermediate products. On the one hand a low number of intermediates will increase the efficiency and quality of the milling operation by enabling milling in larger batches, as well as limiting the number of intermediate storage silos. On the other hand, a low number has two downsides. First, to be able to mix final products from a lower number of intermediate products, more expensive, high-quality raw materials have to be used, leading to an increase in material costs. Secondly, to mix from a smaller number the wide variety of end products, more mixing operations would be necessary, increasing operational cost of mixing. Now, the main problem is to determine the number and composition of intermediate products, increasing operational efficiency, product quality, and flexibility on the one hand, while on the other hand keeping material costs and operational costs from exploding. Currently, this design is based upon intuition, craftsmanship, and habit, which are not supported by an evaluation of costs incurred. Currently, management envisages an increase in volume, which will mainly be realized by adding customer specific recipes, but is afraid that more intermediate products will be needed. The current project aims at benchmarking current practice, developing a sound understanding of the trade-off between different performance measures and costs, and to support future decisions with respect to investments in silos and mixing capacity. The aim is to develop a model to support this important design and selection decision.

Quality parameters

For the final products produced by the company, a variety of quality parameters are important. These parameters also need to be considered in the design of intermediate products. Wherever possible, we will not go into details on the specific details of the chemical properties or the units in which they are measured, as this would only distract from the problem discussed in this paper. There are nine quality parameters relevant in determining the intermediate products (and final products). It concerns:

1. Protein percentage.

Water absorption ability.

3. Dough extensibility, parameter 1, length of the extensometer curve. 4. Dough extensibility, parameter 2, height of the extensometer curve.

5. Deoxynivalenon (DON) level, a mycotoxin that can affect health when present at high levels.

6. A product usability index for use in bread, to cover usage parameters that are difficult to measure, assigned by the baker from the test bakery.

7. A second (similar) product usability index, this one for use in biscuits.

8. Falling number, which indicates the sprout damage of the grain used. 9. Bread volume, which is determined in a test bakery.

In creating different intermediate products or different end products, these parameters have to be considered. Most of these parameters lead to simple linear relationships in a blending process (i.e., weighted averages):

Q pk = f ip Q ik i∈I ∑ { } P p k ∈ ∀ ∈ ∀ , 8 , , 1 K , ( 1
)
where f ip is the blending fraction of raw material i for intermediate product p, Q pk quality parameter k for intermediate product p (or raw material i), I the set of raw materials, P the set of intermediate products, and K the set of quality parameters involved. Only the last (ninth) quality parameter, bread volume (Q p,9 ), acts differently, and is calculated as follows:

Q p,9 = 1000 × ln f ip e Q i ,9 1000 i∈I ∑       ∀p ∈ P (2)
When relating quality parameter Q p,9 to minimum and maximum values Q p,9 min and Q p,9 max , we would normally get a nonlinear constraint like:

Q p,9 min ≤ 1000 × ln f ip e Q i ,9 1000 i∈I ∑       ≤ Q p,

Solution approach

The main aim of the models presented in this paper is to support the current organizational decisionmaking processes. The current process basically consists of three steps: (1) consider all possible intermediates; (2) find the most economical way to make them from raw materials; and (3) select a limited number to be actually used, implicitly aiming at balancing material and mixing costs. As said, this selection process is done a few times a year. Here we aim at supporting the second and third step and leave the first one to the experience of the people involved. However, given the numerical support a wider set of intermediates can be considered. Given the restrictions, we develop two mixed-integer linear programming (MILP) models. The first one simply calculates the optimal composition of an intermediate, while the second one chooses the best intermediate if we restrict the number to be used. This stepwise approach is illustrated in Figure 2.

[FIGURE 2 ABOUT HERE]

First, a set of potential intermediate products is defined. Secondly, the optimal composition of these potential intermediate products is determined using a first MILP model. Third and finally, a selection of the potential intermediate products is made to compose the final products using a second MILP model.

Next to the correspondence with the current decision-making process, this stepwise approach also fits well with the decoupling point concept, as all three steps are centred around the decoupling point. After defining potential products to be stored at the decoupling point, one model aims to optimize the upstream process (blending and milling the intermediate products), while the second model aims to optimize the downstream process (selecting and mixing the intermediate products).

In the following paragraphs, the three stages will be further elaborated upon.

Defining potential intermediate products

Finding the right potential intermediate products is a difficult task. Even for relatively small-scale problems, the number of combinations is enormous. Including nine different quality parameters (as presented in Section 3) also means that care should be taken not to design potentially infeasible recipes.

What we learn from this is the need for careful consideration in the process of defining or designing intermediate products. Given the importance and difficulty, this step is executed by the experts from the recipe management and quality management department. The process of designing intermediates was supported by available recipe information (on raw materials, current intermediate products, and final products) from management information systems to validate the obtained information.

Finally, this resulted in the design of a set of over 70 possible intermediate products, covering a wide range for the quality parameters. Next to newly designed 'flexible' recipes, this set also includes recipes for final products (on customer specification), as this allows the solution approach to store this product on the intermediate storage level, thereby reducing further specification (i.e. mixing) costs. In this way, the approach can select a combination of final recipes and flexible recipes. It is worth noting that both can be used in mixing.

Initially, the model was validated with the current set of intermediate products as potential intermediate products. Allowing all of them to be used in the final solution (i.e., not setting a maximum on the number of intermediate products), and calculating the compositions and costs involved, the case company could get familiar with the model, and grew more confident in its potential.

Optimal composition of the potential intermediate products

In this stage, the composition of the potential intermediate products is determined, based on a fairly simple MILP model (labelled MILP 1) for each of the intermediates p ∈ P. The objective function minimizes the raw material costs:

∑ ∈I i i ip c f Min , ( 5
)
where c i is the unit cost for raw material i. The quality constraints for the intermediate products are determined according to (1)-( 4):

max min pk I i ik ip pk Q Q f Q ≤ ≤ ∑ ∈ { }, 8 , , 1 K ∈ ∀k (6) e Q p ,9 min 1000 ≤ f ip e Q i ,9 1000 i∈I ∑ ≤ e Q p ,9 max 1000 , ( 7
)
f ip = 1 i∈I ∑ . (8)
Constraint ( 8) deals with the material balance for the intermediate product. For modelling purposes, it was chosen to formulate the quality constraints in (6) in a uniform way, always including a maximum and a minimum. For some of the constraints, we do however not have both. For instance, the DON level (parameter 5) only has a maximum, and the falling number (parameter 8) only has a minimum (as higher falling numbers mean less enzyme activity which is related to less sprout damage). In these cases, the minimum or maximum values are set to zero or infinity, respectively. For quality parameter 2, the water absorption ability, there is another constraint in addition to the one in (6). If a certain intermediate product is already in use, the water absorption ability cannot change too much. This leads to a constraint relating Q p,2 to its current value Q p,2 0 :

0 2 , 2 , 0 2 , 100 1 100 1 p I i i ip p Q u Q f Q l       + ≤ ≤       - ∑ ∈ , (9)
where l and u are percentages that the product can decrease or increase in water absorption. To be able to set constraints on the fractions f ip , we introduce a set of indicator variables. These are necessary to distinguish between raw materials that are used and raw materials that are not used (only the first are constrained):

   = otherwise. , 0 , product te intermedia in used is material raw if , 1 p i ip δ (10)
Now, we can define minimum ( f ip min ) and maximum ( f ip max ) fractions in case a raw material is used in the intermediate products:

δ ip f ip min ≤ f ip ≤ δ ip f ip max I i ∈ ∀ . (11)
Finally, certain customers require that their product contains at least a certain percentage θ p of a certain type of raw material (R ⊂ I), which we therefore also require from a subset of the potential intermediate products P S ⊂ P: (12)

Solving model MILP 1, as defined by equations ( 5)-( 12), for each of the potential intermediate products will result in the optimal composition, in terms of minimal material costs.

Selection of intermediate products

In the third stage, the resulting compositions of potential intermediate products are used in a selection process to determine which intermediate products will eventually be used in the creation of the final products. Again, this results in an MILP model (MILP 2). This time the costs to minimize consist of two parts, mixing operation costs and material costs:

∑ ∑ ∈ ∈         + J j P p j p pj j j D c f c D β β Min , ( 13
)
where c β the mixing cost per unit of final product, which is multiplied by the demand for product j, D j . Whether or not mixing is necessary for a certain product is included through:

   =
Q Q f Q ≤ ≤ ∑ ∈ { } J j k ∈ ∀ ∈ ∀ , 8 , , 1 K , ( 15
) 1000 1000 1000 max 9 , 9 , min 9 , j p j Q P p Q pj Q e e f e ≤ ≤ ∑ ∈ J j ∈ ∀ , (16)
∑ ∈ = P p j pj s f J j ∈ ∀ . ( 17
)
As can be seen, the fractions do not sum to 1 in this model, but to a parameter s j which is often still 1, but sometimes has a value smaller than 1 (typically between 0.85 and 1). This is the case, because some final products have additional ingredients that are added in the final stages. This is left out of the model presented in this paper, because it does not affect the final quality of the product.

The additional constraint for the water absorption ability changes is similar to its MILP 1 version:

0 2 , 2 , 0 2 , 100 1 100 1 j P p p pj j Q u Q f Q l       + ≤ ≤       - ∑ ∈ J j ∈ ∀ . ( 18
)
To make sure the customer requirement of at least a certain percentage of a certain type of raw material (R ⊂ I) is continued from the intermediate products, we use:

j P P p pj I I i ip s s f f θ ≥ ∑ ∑ ⊂ ∈ ⊂ ∈ ) ( ) 1 ( J J j s ⊂ ∈ ∀ . ( 19
)
For reasons of operational simplicity, the management of the company would like to use a maximum number of intermediate products per final product, which can be formulated as:

M P p pj ≤ ∑ ∈ γ J j ∈ ∀ , (20)
where

   = otherwise, , 0 , product in used is p product te intermedia if , 1 j pj γ ( 21
)
and M is the maximum number of intermediate products used per final product. To make sure the binary variables γ pj have the right values, we use the following constraint:

pj pj f γ ≤ J j P p ∈ ∀ ∈ ∀ , . (22)
As the mixing stage has a limited capacity, the following constraint assures that we do not use more than the existing mixing capacity L.

L D J j j j ≤ ∑ ∈ β . ( 23
)
Again, an additional constraint is introduced to set the binary variable used:

j P p pj M β γ ⋅ ≤ - ∑ ∈ 1 J j ∈ ∀ . ( 24
)
One of the most essential constraints in this model is the maximum number of intermediate products we allow the model to choose. This is formulated as:

* P P p p ≤ ∑ ∈ λ , ( 25
)
where the binary variable λ p is defined as:

   = otherwise, , 0 , used is p product te intermedia if , 1 p λ (26)
and this gets the correct value using the following constraint:

p J j pj M f λ ⋅ ≤ ∑ ∈ P p ∈ ∀ . ( 27
)
Furthermore, there are additional constraints due to the fact that some of the intermediates are not allowed to be used in some final products, due to certain characteristics. This leads to a distinction between products that are used to produce bread and products that are not. For this, we define a binary parameter as follows:

α pj = 1, if intermediate p can be used in product j, 0, otherwise,    ( 28
)
which leads to the following constraints:

pj pj f α ≤ J j P p ∈ ∀ ∈ ∀ , . (29)
Solving model MILP 2, as defined by equations ( 13)-( 29), will result in the selection of a preset number of intermediate products. This stage can be repeated for different numbers of resulting intermediate products.

Results

Due to confidentiality requirements, the actual costs are not reported in this section. We do however report the cost differences between various scenarios for the number of intermediate products by using indexed results. To give an indication of the performance of the model, we can compare the solution with 15 intermediate products with the current situation at the company, which would lead to a cost decrease of 0.6%. Although this is fairly limited in terms of the relative difference, the absolute difference still makes the use of the model interesting, as food manufacturers often work with fairly low profit margins. More importantly, the model has proven valuable in tactical and strategic discussions, which we will come back to in the managerial implications in Section 5.3.

The model was implemented in ILOG's OPL software and solved with CPLEX. The calculation times for the results presented in this section range from a few seconds to a few minutes.

Number of intermediate products

The main aspect the company was interested in was an overview of how changing the number of intermediate products (P * ) would affect costs, and how large the cost increases were that they expected to see with a decrease in the number of intermediate products (assuming this would require more flexible, higher quality, and more expensive raw materials). This decrease was expected to simplify the operations and the efficiency of the milling process. We set the cost (including raw material cost and mixing cost) found for the solution with 15 intermediate products as 100, as this is the current number of intermediate products. This presentation format facilitates the understanding of what happens to the costs when changing the number of intermediate products.

[FIGURE 3 ABOUT HERE]

Figure 3 shows that decreasing the number of intermediate products below the current number of 15 does increase costs, in what seems to be an exponential curve. Based on these results, it seems that the number of intermediate products can be decreased down to 10 while only marginally increasing costs. Reducing the number of intermediate products further has a larger impact on the costs. It seems that more expensive intermediate products are necessary to provide the flexibility to mix the required end products. This is reflected in e.g. the set of intermediates used in case of 8 intermediates that is not totally part of the larger sets of intermediates. It should be noted that for numbers of intermediates below 7, it is not possible anymore to design a set of intermediates that can be mixed to create all required final products, and therefore no results can be generated for these scenarios.

Choosing the decoupling point: deliver-from-stock or mix-to-order

As both final products and flexible (still to be mixed) products are considered for intermediate products, deciding on which ones to use also decides on the decoupling point for all final products. Essentially, the choice is between deliver-from-stock (when final products are selected as intermediates) and mix-to-order (when flexible recipes are stored and subsequently mixed when customer orders arrive). It should be noted that in case a final product is selected as an intermediate, it can then also be used as an ingredient in mix-to-order products.

In the scenario with 15 intermediate products, we can see that 9 existing final products are selected as intermediates, in addition to 6 flexible products. Furthermore, due to overlapping intervals in quality specifications, some of the selected final products have such specifications that they can also be substituted for other final products, thereby actually increasing the number of deliver-from-stock products from 9 to 14, and further reducing mixing operations.

[FIGURE 4 ABOUT HERE] Figure 4 illustrates how the split between flexible and final products changes for fewer or more intermediate products. For final products, a distinction is made between final products that are also used as ingredients for other final products (multi-use), and final products that are not (single-use). We can see that, for fewer intermediate products, all of them are used in mixing other final products. When the number of intermediate products increases, there is an increasing share of single-use final products. Furthermore, these results illustrate that the final products that are chosen to be stored as intermediates often have quality specifications that make them useful as ingredients in other products. Only if we allow a significant increase in the number of intermediate products, we will see a decrease in the use of intermediates as ingredients for other products.

Comparing the final products that still have to be mixed with the ones that can now be delivered directly from storage, we see that the products that can be delivered without mixing have -on average-a larger demand volume; out of the top-10 products in terms of demand volume, only 4 products still need to be mixed. Based on a typical month of demand data, Table 1 illustrates the difference in demand volumes. Like in the previous section, the data is again indexed, here by setting the average demand per product in this specific month to 100.

[TABLE 1 ABOUT HERE]

These results correspond to what one might expect based on decoupling point theory: for products with large demand volumes earlier specification seems sensible. Although it was not considered in our model, the predictability of demand for these products might also be higher, which would also argue for an upstream effect on the decoupling point [START_REF] Van Donk | Make to stock or make to order: The decoupling point in the food processing industries[END_REF].

To be able to use the 6 flexible intermediate products (from the scenario with 15 products) to mix the remaining final products, it would be sensible to choose a set of products that cover a wide quality spectrum. To see how the model results relate to this, we analyzed the quality specifications of the 6 selected products, in relation to the 30 potential intermediate products designed by the quality management department of the case company.

As it is not practical to illustrate all 9 dimensions of the quality spectrum, we illustrate the results using the parameters protein content and bread volume (quality parameter 1 and 9 as described in Section 3.2). Figure 5 shows the values for these parameters for all 30 flexible intermediate products, and highlights the 6 selected products. Again, results were indexed; here by setting the average value for the specific parameter to 100. We can see that the model indeed selected a set of products that cover the quality spectrum to a large extent. It is worth noting that the six products shown have fairly similar values for the other quality parameters, with the exception of the 3 products clusters around a protein index of 105-110. These products differ significantly in terms of the fifth quality parameter: DON level, which also explains why these three products are quite close to each other in this illustration. Further outcomes for other quality parameters are not presented in this paper, but show similar results.

[FIGURE 5 ABOUT HERE]

Managerial implications

Based on the results presented in Sections 5.1 and 5.2, the research team and management along with people directly involved, have discussed the approach and outcomes of the model. All agreed that well-informed decisions can be made regarding the number of intermediate products, their compositions, and whether they are made to stock or mixed to order. The company acknowledges the value of the outcomes and their validity. The outcomes of the model confirmed the viability of the company's policy of having as little as possible intermediates, while keeping all costs low as well. This also confirmed the market approach of the company to provide a broad range of customer-specific products and to further increase that range in the future. The model illustrated that this would not have to be matched by an increase in intermediate products. Further, the model's outcomes facilitate discussion on the overall production strategy, investments in processing equipment, intermediate storage silos and mixing capacity, based on facts and figures. Although the results are consistent with the current way of working and are accepted by the company, the detailed outcomes of the model are not used yet, for reasons of product integrity. Moreover, running the mill involves daily small changes in the recipes to accommodate for small differences in lots of ingredients. Below we discuss some of the above issues in some more depth.

When making the final decision on the number of intermediate products, the amount of intermediate storage tanks and the possible cost of investment in additional intermediate storage tanks could play a deciding role. For example, additional cost savings on raw materials and operating costs might not be high enough to warrant the investment in additional storage tanks.

Also, factors like required customer lead times could influence the final decision, as it is very well possible that certain final products have to be available on the intermediate storage level (delivered from stock) to ensure immediate delivery or packaging without further processing operations. If such preferred customer treatment should exist, this could easily be formulated in the model to see if and how that would change the selection of the remaining intermediate products.

By using a limited number of flexible intermediate products (6 in the scenario discussed in Section 5.2), postponement of specification for a large range of final products (here 31) can be achieved. This downstream effect in terms of the decoupling point can be used to control demand uncertainty, both in terms of which products will be ordered and when they will be ordered (Yang et al., 2004a).

Finally, it is worth noting that, following [START_REF] Graman | Implementation issues influencing the decision to adopt postponement[END_REF], successful implementations of postponement not only build on selecting the right products, but also on how the results are translated into other organizational functions such as operations scheduling, where different types of products might have to be dealt with in different ways. Graman and Magazine also stress that care should be taken related to possible changes in product integrity. As our case study concerns an application in the food industry, this relates to food quality and safety, which is indeed something that should be considered very carefully.

All in all, based on the experiences gathered in our case study, we are sure that the model can provide a valuable tool to support decision making at several levels. As with all models it will not replace decision making.

Conclusion and discussion

In this paper, we develop a method to design intermediate products in a two-stage food production process, taking into account a wide variety of quality-related attributes. The method consists of a two-stage mathematical programming model that aims to find a balance between material cost and operating cost. The model is developed and applied in a case study concerning a medium-sized flour manufacturer.

The results show that the number of intermediate products can be reduced, simplifying operations and increasing efficiency of the milling process, while only leading to a marginal cost increase. Several scenarios have been studied for operational costs and raw material availability to validate the results, also illustrating the usefulness of the model as a decision support tool for the make or mix to order decision. It also shows that the costs increase if the number of intermediate products decreases, although cost changes are marginal above a certain number of intermediates. The model is designed to be used for what-if analysis and should be solved on a regular basis, to make sure the current market environment (including developments in the raw material supply and the customer demand) is reflected in the composition of the intermediate products. Even more important is that the results and scenarios of the model can be used to discuss and develop the production strategy, explore consequences in terms of investments needed, etc., based on objective figures and comparisons, in addition to experience, traditions and tacit knowledge.

Although the paper largely describes one single case study, the model developed can easily be adapted for other food production systems, as many of these can be seen as two-stage production systems with intermediate storage and a divergent product flow. Furthermore, a lot of the quality attributes modelled in the case study are typical for the food industry, which suggests numerous possible applications of the approach and the model.

Scientifically, this paper contributes in several ways. We incorporate the design of intermediate products to Decoupling Point theory, whereas such intermediates are normally given. We help in developing quantitative, but also integral decision tools to that body of knowledge. It is clear that the model can help managers to make better-informed decisions regarding what products to store as intermediates.

Future research could follow a number of directions. One possible way is to incorporate more elements into our quantitative model: constraints relating to raw material usage or availability, or capacity limitations such as storage or batch sizes. Related to these additional constraints, it might be beneficial to create an integrated model instead of the decomposed approach presented in this paper. This would allow for better ways to include e.g. constraints on raw material usage. Also, in an integrated model, we would not need to limit the list of potential flexible intermediate products, as we could let the model design these, based on the available raw materials and the required final products. An integrated model would be more complex from a computational viewpoint, but methods that could be used to solve such a problem in an efficient way are available in the literature (e.g. [START_REF] Benders | Partitioning procedures for solving mixed-variables programming problems[END_REF]. However, for the approach presented in this paper, we aimed at supporting the current organizational decision-making process and did not pursue an integrated modelling approach. Also the results of the current model are therefore accepted more easily. Finally, more research is also needed to further explore how a tool like the one developed here, should and can be used in the organisational context. Here, we need to decide how often the models have to be solved with updated information, and identify which decisions (be they strategic, tactical or operational) the tool could also support, next to the issues discussed in this paper.

Protein index Bread volume index

Figure 1 -

 1 Figure 1 -Outline of the production process of the flour mill.

Figure 2 -

 2 Figure 2 -Schematic representation of the solution approach.

Figure 3 -FlexibleFigure 4 -

 34 Figure 3 -Cost results (indexed) for several scenarios for the number of intermediate products.

Figure 5 -

 5 Figure 5 -Illustration of the quality parameter range covered by the six selected flexible intermediate products. Page 19 of 20

  For use in the MILP models in the remainder of the paper, the nonlinearity of this restriction on f ip is undesirable. However, such a constraint can be linearized in f ip by 'moving' the nonlinearity into the quality parameters, as follows:

	e	Q p ,9 min 1000 ≤	∑	f ip e	Q i ,9 1000	≤ e	max Q p ,9 1000	∀p ∈ P	(4)
			i∈I
				F o r
							P
							e
							e r
							R
							e
							v i e
								w
								O n l
								y
							9 max	∀p ∈ P	(3)

  the quality parameter values of the intermediate products Q pk , and the blending fractions f pj .

	, 1	if	mixing	is	necessary	for	product	j	,
	, 0				otherwise.
	min			max
	jk	pj	pk	jk
	p	P

j β (14)

Material cost is based on f pj , the fractions of intermediate products p in final product j, and c p is the material cost for intermediate product p, which are both outcomes of MILP 1.

Similar to MILP 1, we again include quality constraints for all final products, based on

Table 1 -

 1 Comparison of final product demand volumes (indexed) for different products.

				Page 20 of 20
	Product type	Number of	Average demand	Share of
		products	volume (+ st. dev.)	demand
	Deliver-from-stock	14	191.7 (194.1)	60%
	Mix-to-order	31	58.6 (96.1)	40%
	Total/average	45	100 (146.0)	100%

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

uk International Journal of Production Research

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Acknowledgements

The authors would like to thank the company involved for their willingness to participate in this research and for their suggestions and remarks during discussion sessions. Also, the first author would like to acknowledge support from a H.C. Ørsted postdoctoral fellowship from the Technical University of Denmark.


S Reynaud

Corvec

ME Juvin Pascale Bemer
email: pascale.bemer@chu-nantes.fr

Alain Reynaud

G Le Gargasson

H Drugeon

S Corvec

Correlation between VITEK2 system and cefoxitin disk diffusion for the daily detection of oxacillin resistance 8 in a large number of clinical Staphylococcus aureus isolates

Keywords: detection, mecA, oxacillin, cefoxitin, resistance, VITEK2 system detection, mecA, oxacillin, cefoxitin, resistance, VITEK2 system 18

Correlation between the VITEK2 system and cefoxitin disk diffusion for the daily detection of oxacillin resistance in a large number of clinical isolates

-the sensitivity-specificity-NPV-PPV were removed from the revised manuscript as the results were similar to the other studies.

-the Tables 1 and2 were kept with three typewritten pages in length, as recommended.

-Our simple core message was underlined at the end of discussion.

3/Response to Reviewer 2' comments:

-We tried to make a clear comparison between both systems.

-The end of discussion underlined the importance of aminoglycosides and /or fluoroquinolones associated resistances.

the new VITEK2 AST-P551 card with the cefoxitin disk diffusion method for the daily detection of methicillin resistance with a high number of Staphylococcus aureus 28 clinical isolates. Detection of the PBP2a protein or mecA gene was performed for each discordant case. Seventy (3.3%) isolates out of 2107 clinical strains showed 30 discordant results, 2 very major errors, 4 major errors, and 64 minor errors. Fifty-nine (84%) discordant results were resolved with a final overall agreement of 99.5%. 32

Eleven strains (0.5%) remained discordant (mE). Four of 370 MRSA strains were misclassified as susceptible in daily practice by the cefoxitin disk diffusion method. All 34 these strains were resistant to aminoglycosides and/or fluoroquinolones. VITEK2 system is highly reliable for methicillin resistance detection at the routine level. 36 The detection of methicillin-resistant Staphylococcus aureus (MRSA) is still a challenge as some heteroresistant isolates may be classified as oxacillin susceptible 48 based on phenotypic methods. In recent years, the cefoxitin disk diffusion method was recommended by many National Committees and the Clinical and Laboratory 50

Standards Institute (CLSI) [START_REF]Performance 128 Standards for Antimicrobial Susceptibility Testing[END_REF]. The automated VITEK2 system (bioMérieux, Marcy l'Etoile, France) provides S. aureus susceptibility testing categorisation within about 8 52 hours. In the previous published studies comparing several tests for MRSA detection, only a limited number of strains (less than 500) were included. The purpose of this 54 study was to compare the performance of the new VITEK2 system AST-P551 card with the cefoxitin disk diffusion method for the daily detection of SARM with a high 56 number of S. aureus clinical isolates.

A total of 2,107 non-duplicate clinical S. aureus isolates were routinely 58 collected at Nantes University Hospital. All of the isolates were identified to the species level by standard biochemical methods or with the VITEK2 system. VITEK2 60 AST-P551 cards were inoculated according to the manufacturer's instructions. The cefoxitin disk diffusion method was performed with an inoculum of approximately 10 6 62 CFU/mL on Mueller-Hinton agar plates, according to the Antibiogram Committee of the French Microbiology Society (CA-SFM) recommendations [START_REF]Communiqué de l'Antibiogramme de la Société Française de Microbiologie. 150[END_REF]. Zone diameters 64 were interpreted according to CA-SFM [START_REF]Communiqué de l'Antibiogramme de la Société Française de Microbiologie. 150[END_REF]. In the VITEK2 system, MIC interpretative standards for oxacillin followed the recommendations of CLSI and CA-SFM [START_REF]Performance 128 Standards for Antimicrobial Susceptibility Testing[END_REF][START_REF]Communiqué de l'Antibiogramme de la Société Française de Microbiologie. 150[END_REF]. 66 Susceptible or resistant results by both methods were considered as concordant.

Interpretative category errors were assessed: (i) very major error (VME, susceptible 68 with the VITEK2 system, but resistant by diffusion); (ii) major error (ME, resistant with the VITEK2 system, but susceptible by diffusion); (iii) minor error (mE, susceptible or 70 resistant by one system and intermediate results by the other system). For each discordant strain, the VITEK2 AST-P551 card and the cefoxitin disk diffusion test were repeated and detection of mecA gene by PCR [START_REF] Okuma | Dissemination of New Methicillin-Resistant 154 Staphylococcus aureus Clones in the Community[END_REF] and/or penicillin-binding protein 2a (PBP2a) (Mast Diagnostics, Merseyside, U.K.) was performed, with mecA 74 PCR as the gold standard. Overall agreement based on previous category agreement was 96.7%. (Table 1). Seventy (3.3 %) S. aureus isolates yielded 76 discordant results: 2 VME (0.1%), 4 ME (0.2%), and 64 mE (3.0%). Forty-four isolates susceptible by VITEK2 and 20 isolates resistant by VITEK2 showed cefoxitin 78 inhibition zone diameters of 25 and 26 mm (intermediate breakpoints). Of the preliminary 70 discordances, 59 (84%) were resolved, giving final overall agreement 80 of 99.5% (Table 2). Eleven MRSA strains (0.5%) remained discordant (mE). All these 11 MRSA harboured associated resistance to fluoroquinolones and/or 82 aminoglycosides and/or macrolide-lincosamide-streptogramin. The cefoxitin inhibition zone diameter was 2 mm larger or smaller than the CA-SFM recommended criteria 84 for 467 concordant strains (401 MSSA and 66 MRSA).

Since 2001, the detection of oxacillin resistance by the cefoxitin disk diffusion 86 method was evaluated using both CLSI [START_REF]Performance 128 Standards for Antimicrobial Susceptibility Testing[END_REF][START_REF] Swenson | Detection of mecA-mediated resistance using reference 144 and commercial testing methods in a collection of Staphylococcus aureus expressing borderline oxacillin MICs[END_REF][START_REF] Pottumarthy | Evaluation of alternative disk diffusion methods for detecting mecA-mediated oxacillin resistance in an 158 international collection of Staphylococci: validation report from the SENTRY Antimicrobial Surveillance Program[END_REF] and non-CLSI recommendations [START_REF] Felten | Evaluation of Three Techniques for Detection of Low-Level Methicillin-Resistant Staphylococcus 136 aureus (MRSA): a Disk Diffusion Method with Cefoxitin and Moxalactam, the VITEK2 system, and the MRSA-Screen Latex Agglutination Test[END_REF][START_REF] Skov | Evaluation of a 30 µg disc on Iso-Sensitest 162 agar for detection of methicillin-resistant Staphylococcus aureus[END_REF]. The standard conditions differed by the use of media (MH agar, Iso-Sensitest 88 agar), a different inoculum size (semi-confluent with 10 6 CFU/mL or confluent with 10 8 CFU/mL), and several incubation temperatures. Felten et al. reported the 90 excellent performance of cefoxitin 30 µg disk on MHA with semi-confluent and confluent inocula [START_REF] Felten | Evaluation of Three Techniques for Detection of Low-Level Methicillin-Resistant Staphylococcus 136 aureus (MRSA): a Disk Diffusion Method with Cefoxitin and Moxalactam, the VITEK2 system, and the MRSA-Screen Latex Agglutination Test[END_REF]. Among 152 S. aureus strains, one MRSA isolate and one 92 MSSA isolate gave a 26-mm cefoxitin inhibition zone diameter [START_REF] Felten | Evaluation of Three Techniques for Detection of Low-Level Methicillin-Resistant Staphylococcus 136 aureus (MRSA): a Disk Diffusion Method with Cefoxitin and Moxalactam, the VITEK2 system, and the MRSA-Screen Latex Agglutination Test[END_REF]. Thus, the cefoxitin disk diffusion method using a semi-confluent inoculum on MHA was recommended 94 by CA-SFM [START_REF]Communiqué de l'Antibiogramme de la Société Française de Microbiologie. 150[END_REF]. Each strain with a cefoxitin zone diameter of 25 or 26 mm should be examined by a mecA-specific test [START_REF]Communiqué de l'Antibiogramme de la Société Française de Microbiologie. 150[END_REF]. In our daily practice, the gap between the 96 measured inhibition zone diameters and the breakpoints was very narrow for 467 (22%) concordant strains. The 3% of intermediate cefoxitin diffusion results mostly resolved in concordant MSSA or MRSA strains after repeated tests underlined the difficulty to perform a well-standardized inoculum. Moreover, the existence of an 100 intermediate zone underscore the need for complementary mecA specific tests [START_REF]Communiqué de l'Antibiogramme de la Société Française de Microbiologie. 150[END_REF].

When the detection of methicillin resistance was only based on oxacillin MIC 102 determination, VITEK2 was shown to be superior to ATB Staph and Rapid ATB Staph with 4.7%, 11% and 23% false-susceptible results respectively [START_REF] Barbier-Frebourg | Comparison of ATB Staph, Rapid ATB Staph, Vitek, and E-Test Methods 132 for Detection of Oxacillin Heteroresistance in Staphylococci Possessing mecA[END_REF]. From the 104 years 2000s, an oxacillin screen test comparable to the oxacillin agar screen test was introduced in the VITEK2 system [START_REF] Felten | Evaluation of Three Techniques for Detection of Low-Level Methicillin-Resistant Staphylococcus 136 aureus (MRSA): a Disk Diffusion Method with Cefoxitin and Moxalactam, the VITEK2 system, and the MRSA-Screen Latex Agglutination Test[END_REF][START_REF] Swenson | Detection of mecA-mediated resistance using reference 144 and commercial testing methods in a collection of Staphylococcus aureus expressing borderline oxacillin MICs[END_REF]. Swenson et al. reported a good sensitivity 106 (91.1%) but a lack of specificity (75%) [START_REF] Swenson | Detection of mecA-mediated resistance using reference 144 and commercial testing methods in a collection of Staphylococcus aureus expressing borderline oxacillin MICs[END_REF]. New VITEK2 antimicrobial susceptibility testing cards were successively developed with the replacement of oxacillin by 108 cefoxitin in the screen test. The VITEK2 cefoxitin screen test allowed to detect more MRSA strains, as shown by the very high sensitivities obtained in two studies with a 110 higher number of tested MRSA strains as before (97.5% and 98.8% respectively [START_REF] Roisin | Evaluation of new 140 Vitek 2 card and disk diffusion method for determining susceptibility of Staphylococcus aureus to oxacillin[END_REF][START_REF] Torres | Evaluation of the Vitek 2 AST-P559 Card for Detection of Oxacillin Resistance in Staphylococcus aureus. 148[END_REF]. 112

Our study is one of the most large-scale ones including S. aureus clinical strains. The results showed the excellent concordance between VITEK2 and cefoxitin 114 disk diffusion methods, as seen with the very low percentage of discordant results in the daily practice. It will be a real advantage for the VITEK2 system users to detect S. 116 aureus oxacillin resistance by the automated system alone in the daily practice.

Nevertheless, according to our results, this choice may be dangerous as some 118 MRSA strains were misclassified as susceptible by the VITEK2 system or by the disk diffusion method. These MRSA strains were resistant to aminoglycosides and/or 120 fluoroquinolones. In any case, the microbiologists should be aware of MRSA strains misclassified as oxacillin susceptible with associated resistances and should perform 122 mecA-specific tests at the slightest doubt.

  Ref.: Ms. No. EJCMID-D-09-00494 Correlation between VITEK2 system and cefoxitin disk diffusion for the daily detection of oxacillin resistance in a large number of clinical Staphylococcus aureus isolates. European Journal of Clinical Microbiology & Infectious Diseases 1/Response to Editor-in-Chief I revised my manuscript as a brief report, as required. 2/Response to Reviewers 1' comments:

Table 1 .

 1 Comparison of cefoxitin disk diffusion method and VITEK2 system 168 for detection of methicillin resistance in 2107 isolates of S. aureus Broken lines indicated intermediate breakpoints: for those inhibition zone diameters, mecA specific tests should be used, according to CA-SFM recommendations[START_REF]Communiqué de l'Antibiogramme de la Société Française de Microbiologie. 150[END_REF].

		FOX inhibition zone diameter (mm)
	 22	23	24	25-26	27	28	 29
	Initial results
	Concordant results 301	29	23		168	233	1283
	Discordant results		2	64	3	1
	After control
	Concordant results 304	36	30		168	233	1325
	Discordant results			11
	170
	172
	174
	176
	178
	180
	182
	184

VME, very major error, S with the VITEK2 system and R with the disk diffusion 190 method, ME, major error, R with the VITEK2 system and S with the disk diffusion method; mE, minor error, S or R with one system and intermediately-resistant with 192 the other system.