A comparison between centralized and decentralized scheduling approaches in Make-and-Pack Plants

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A comparison between centralized and decentralized

scheduling approaches in Make-and-Pack Plants

A cost minimization objective

Master Thesis

MSc Technology & Operations Management

University of Groningen

Faculty of Economics & Business

Joris Hoelen

Student number: S2760606

Supervisor: Dr. O.A. Kilic

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Abstract

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The production layout in the process industry, especially in the companies that produce customer goods such as food and beverages, can often be divided into two phases: the process and packaging phase (van Dam, Gaalman and Sierksma, 1993). These production plants are referred to in literature as Make-and-Pack plants (M&PP) and are vital to process industries (Baumann & Trautmann, 2013). M&PPs consist of a make stage in which various types of intermediates are manufactured, and a subsequent pack stage in which the intermediates are packed in different formats. Characteristics of the process industry, and hence the Make-and-Pack plants, are large capital investment and very small profit margins (Rajaram and Tian, 2009). Given these characteristics, there is a need for efficient production performance. One of the critical factors in process operations that is crucial for improving the production performance, is scheduling (Méndez et al., 2006). Besides the general scheduling issues in process industries, such as sequence dependent changeovers, intermediate storage policies, and constraints on equipment and labor (Honkomp et al., 2000; Floudas and Lin, 2004), additional difficulties arise in the make-and-pack plants. Especially the large variety of end products and different processing rates of the make and pack stage increase the scheduling problem size (Bilgen and Dogan, 2015).

When approaching scheduling problems, it is common to use a centralized scheduling approach. This refers to the way of scheduling in which the scheduling decisions throughout the production process are made in coordination with each other. The benefit of this approach is that it results in the best optimization of the objective function (e.g. profit maximization, cost or makespan minimization). However, the drawback is that the mathematical complexity and solution time of the corresponding scheduling problem increases (Shah et al., 2009). A way to deal with this issue is decentralized scheduling, which involves decomposition of the overall scheduling problem into sub-systems which are easier to solve (Shah et al., 2009). The drawback of this approach is that each sub-system is optimized considering an individual stage and hence ignores the other subsystems, resulting in a suboptimal schedule.

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However, according to the authors knowledge, and supported by Shah et al. (2009), there are relatively few papers that compared the performance of centralized and decentralized scheduling approaches. Quantifying and analyzing the behavior of the performance difference could be of high value, because when a large performance gap between the two scheduling approaches is present, potential efficiency gains could be accomplished. On the other side, whenever performance differences are small, managers could focus more on the simpler decentralized approach.

The only article to the authors knowledge that sheds light on the comparison between centralized and decentralized scheduling in M&PPs is Bontes (2016). The aim of this research was to identify differences with respect to minimization of the makespan. According to Günther, Grunow and Neuhaus (2006), minimization of the makespan, i.e. to complete the given production orders within the shortest possible time, is often used as the appropriate objective function in industries such as fresh-food, as this would increase the shelf-life of products. Results from Bontes (2016) show that a significant gap between the centralized and decentralized approach was always present. However, the suggestion was made that a cost minimization perspective could result in a smaller performance gap. An important reason was that, compared to the decentralized approach, additional batches are necessary to enable the timing and sequencing potential of the centralized approach (Bontes, 2016). However, additional batches imply more changeovers, and these are often related to high cost. Although the overall production time might also influence the overall cost, it is likely that the performance difference with a cost perspective are smaller than with a makespan objective (Bontes, 2016).

Despite the pressure to reduce cost in the process industry (Floudas and Lin, 2005), literature has paid little attention to the comparison between the two scheduling approaches from a cost perspective. Furthermore, the possibility of combining centralized and decentralized scheduling approaches has, to the authors knowledge, not been touched upon in literature yet. This research sets out to get better insights in these matters and the corresponding research questions are described as follows:

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scheduling perform when compared to the individual scheduling approaches?

In order to answer the research questions, an existing mathematical model is used to develop scheduling models for the different approaches, that can solve a specific Make-and-Pack scheduling problem. Thereafter, an extensive numerical study is performed to compare and analyze the behavior of the performance gap. Furthermore, a novel model is introduced, tested and discussed.

The structure of this research is as follows. The literature review will follow the introduction. In section 3 the research methodology will be discussed. Section 4 will present the numerical study and the corresponding results. Section 5 will discuss the results of the novel scheduling model. Section 6 will consist of a discussion about the findings together with the limitations and practical implications of the research. Section 7 will end this research with a conclusion.

2. Literature Review

This literature review section will elaborate on past literature on the topic. First, scheduling in the process industry will be discussed in Section 2.1, after which scheduling in the make-and-pack plants is considered in Section 2.2. Thirdly, centralized and decentralized scheduling will be elaborated on in Section 2.3.

2.1 Scheduling in the process industry

‘Scheduling refers to the strategies of allocating equipment and utility or manpower resources over time to execute processing tasks required to manufacture one or several products’ (Pinto and Grossmann, 1998). Traditionally, scheduling was manually done by schedulers using pen and paper, planning cards or spreadsheets (Harjunkoski et al., 2014). However, when time progressed and increasing product volumes, larger product portfolio’s and volatile customer orders led to higher pressure to save on production, manual scheduling became extremely challenging (Harjunkoski et al., 2014). For this reason, optimization support was necessary and many approaches to deal with the scheduling issues were developed.

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could entail. To start, it is important to be aware of the process typology e.g. sequential, single or multi stage processes, as this has an important impact on the complexity of the problem (Harjunkoski et al., 2014). More stages and machines most likely result in more complex scheduling problems. Furthermore, sequence dependent changeovers are an important aspect. A changeover that only requires a different packaging material is obviously faster and less costly than when a cleaning procedure needs to be performed (Doganis and Sarimveis, 2008). Another issue is the storage policy of products. Some industries might face products with a perishable nature, have shared storage tanks or have constraints on storage capacity. It can also be the case that products need a minimum storage time (e.g. cheese). Taking such specifications into account translates into a larger the problem size.

2.2 Scheduling in make-and-pack plants

Production processes that consist of only one single production stage after which a packaging stage packs the products and ships them to distribution centres or individual customers are make-and-pack plants (Bilgen and Günther, 2010). Often, these stages are decoupled by a set of storage tanks of various capacities (Baumann and Trautmann, 2013). In Figure 1, a typical M&PP is displayed. As can be seen, the make stage (production area) produces a moderate number of intermediates which are then stored at a storage point. When ready, the packaging stage uses these intermediates to produce a large variety of end products.

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According to Bilgen and Gunther (2010) and Gunther et al. (2006), three main characteristics of a M&PP can be described. Firstly, different variants of a product are produced by adjusting process parameters, such as process duration and the mix of raw materials. Additionally, a multitude of packaging formats are available for each product, which further increases the number of variants. As a second characteristic they state that, in general, the total demand of the final products is relatively stable, but the allocation among the individual variants differs significantly from time to time. Furthermore, to-stock, make-to-order or a combination of the two can be found, depending on the shelf life of the products and how well demand can be predicted. As a third characteristic Bilgen and Gunther (2010) state that, to provide a flexible response to variations in customer demand, multi-product equipment is used, and hence cleaning and changeover operations are required. In some instances, sequence-dependent changeover times exist due to differences in product and process specifications (Gunther et al., 2006). According to Baumann and Trautmann (2014), another typical operating condition of M&PPs include batch splitting. Batch splitting is when a single production batch is used to satisfy demand for several end products (Honkomp et al., 2000). For example, when a single batch is split up in smaller amounts to be used in several packaging lines.

Besides aforementioned characteristics, the aspect that makes Make-and-Pack plants especially hard to schedule is that the packaging lines have a larger variety of products that need to be processed compared to the make stage. Additionally, the packaging stage produces products in smaller quantities than the make stage (van Dam, Gaalman and Sierksma, 1993). Furthermore, according to Méndez and Cerda (2002), packing campaigns are generally shorter than the related production runs that supply the required intermediates. Consequently, the packing lines could be idle for a long time or start processing very late. Good synchronization could for instance use more changeovers to better coordinate the two stages and lower the starting and idle time of the packaging lines. As a result, the total production time of the schedule can be compressed. However, incorporating extra changeovers comes at a cost.

2.3 Centralized and decentralized scheduling

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problem into several sub-systems is a ‘natural way to deal with this type of optimization problems’ (Shah et al., 2009). Despite easier use and computational efforts, there is a drawback of this decentralized approach. Because there is no coordination between the different sub-systems, the eventual schedule will lack synchronization and results in less than optimal outcome.

In the context of M&PPs, both scheduling approaches can be found in literature. An example of the centralized approach is the study of Méndez and Cerdá (2002). Their developed model is built on the assumption of unlimited storage for each intermediate product, resulting in feasible schedules for real-time industrial problems. Another study that used a centralized approach was that of Baumann and Trautmann (2012), who developed an efficient model that led to good outcomes within short CPU time for small- and moderate-sized problems.

Next to the centralized approaches, literature also accounts for decentralized scheduling approaches. Belaid et al. (2010, 2011) present a two-stage decomposition approach where the storage point decouples the two stages. In this research, the pack stage is scheduled first, after which the make stage is scheduled. Another study that used a decentralized approach was Shah et al. (2009), which decomposed the system by also using the storage point to decompose the system. In their study, each decentralized subsystem is solved to optimality, where after the solution for the entire system is acquired by integrating these individual schedules.

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Bontes (2016) takes them into account. Referring to section 2.2 of this research, assuming no changeovers times is in in sharp contrast with what is defined as a characteristic of M&PPs. To go even further, Bontes (2016) found changeovers to be of crucial importance to the improved performance of centralized scheduling. By implementing many changeovers good coordination between the make- and pack stage was achieved. This resulted in small idle times and an early start of the packaging lines, which compressed the makespan. The decentralized approach on the other hand, aimed at minimizing the specific stages by implementing large batches and few changeovers. Although beneficial for an individual stage, the result was a poor synchronization that stretched the overall makespan.

Although the difference in makespan was found to be large between the two scheduling approaches, it could be argued that the performance gap is smaller when aiming to minimize cost. The coordination advantage of centralized scheduling is achieved by more changeovers. However, incorporating more changeovers at high cost would be disadvantageous. In that case, it is reasonable to assume that the number of changeovers will be small, just as in the decentralized models, resulting in similar schedules. However, just looking at changeover cost could give a distorted image of reality as a total cost objective could include more cost factors. According to Pinedo (2005), due dates could also be part of the total cost function. As described in his research, due dates represent the promised delivery date to customers, where completion of the order after this date is allowed, but penalized. However, it is usually not beneficial to complete an order early, as this might lead to additional storage and handling costs (Pinedo, 2005). This brings about an interesting point. If due dates are set very tight, the pressure of reducing makespan increases and hence a trade-off becomes visible. Completing later than the due date means incurring tardiness cost, whereas reducing makespan implies higher changeover cost. Including more cost factors such as inventory or processing cost could complicate the interaction further.

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facilities is still likely to affect the difference. The following methodology section will elaborate on the research design of this thesis.

3.Methodology

Section 3.1 provides a description of the scheduling problem that is analysed in this research. In turn, Section 3.2 motivates the choice of the mathematical model that is used to model the scheduling problem. Section 3.3 explains how this model is used for the purpose of this research.

3.1 Problem description

The production system under consideration is a make-and-pack facility that consists of one processing unit in the make stage and 2 parallel, nonidentical, packaging lines in the pack stage. The packaging lines are nonidentical in the sense that their suitability for processing the end products is different. The process starts with raw materials that are transformed into intermediate products in the make stage, after which they can be packed into end products in the pack stage. Raw materials are assumed to always be available. Additionally, it is assumed that unlimited storage space is available for raw materials, intermediates as well as end products and that no further restrictions on storage are applied. Furthermore, the number of different intermediates in the make stage is significantly lower than the variety of products produced in the pack stage. The production recipe (the needed material and the processing times of the tasks at their suitable machine), differs between products. Furthermore, sequence dependent changeovers exist for both the make- and pack stage. Moreover, changeover times between two batches of the same product apply. Scheduling decisions that need to be made are determining (i) the optimal sequence of the tasks that take place in each unit, (ii) the amount of material that is processed at each machine at each time, (iii) the production time of each task in each unit and (iv) the start and finishing times of each task in each unit. The aim is to minimize the total costs, which is composed of changeover cost and tardiness cost. The changeover cost are related to the time necessary to complete a changeover, hence a longer changeover time means higher cost. The tardiness cost are related to the completion time of the entire demand. Consequently, the tardiness cost in this research is not based on multiple intermediate due dates, but on the completion time of the entire demand (makespan). If every product is produced within the set timespan, which is called the

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multiple products finishes later than the set time deadline, tardiness cost will be incurred based on the finishing time of the product that finishes latest. Although no hard constraint is set for finishing the demand, it has to be produced and the deadline is implemented to penalize late finishing times.

3.2 Model motivation

To solve the scheduling problem described above, several mathematical models could have been used. The mathematical model in this research is based on previous work of Ierapetritou and Floudas (1998a, 1998b) and formulates the aforementioned problem as a Mixed Integer Linear Programming (MILP) model. It is chosen because it has several advantages that are beneficial for this research. The first advantage is that a State-Task Network framework is used as representation of the problem. The framework divides the problem in states and tasks. States represent raw materials, intermediates and end products, whereas tasks represent the process operation in which material transformation takes place. One advantage of this framework is that batch splitting can be easily implemented (Baumann and Trautmann, 2013). Batch splitting is very relevant in this research, as a single batch of intermediates produced in the make stage could be used for several end products on different packaging lines.

A second advantage of the model is that it uses a continuous representation of time. This approach reduces the number of events or time intervals in comparison with discrete-time representations (Floudas and Lin, 2005). In turn, the problem size is decreased, which results in less computational time. Furthermore, a new form of event points was introduced in Ierapetritou and Floudas (1998a). The proposed formulation avoids unnecessary time slots and only requires the decision on the number of event points. Where other continuous-time models have the same starting and finishing times of an event point across units, the newly introduced concept of event points can best be explained as:

Each event point can be located at different positions along the time axis for different units, allowing different tasks to start at different time instances in different units for the same event point (Floudas and Lin, 2005:143)

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Besides the advantages of this model, several drawbacks need to be addressed. Although continuous models often yield a faster solution time than discrete-time models, they tend to be more challenging in terms of modelling (Floudas and Lin 2005). However, as the scheduling problem in this research is relatively simple, this is not yet a problem.

Another disadvantage of the model lurks in determining the number of event points that are needed for an optimal outcome. An underestimation of the number of event points leads to suboptimal solutions or in some cases even infeasible problems, whereas an overestimation increases the problem size and solution time considerably (Floudas and Lin 2005). A way to deal with this problem is to start off with a small number of event points and gradually increase them by 1 until no better solution has been achieved (Ierapetritou and Floudas, 1998a). However, according to Castro, Barbosa-Póvoa, and Matos (2001), the solution may improve only when more than 1 event point is included. Although no decisive rule exists for determining the amount of even points, the possibility that adding more than 1 event point leads to better solutions is much smaller in the model introduced by Floudas (1998a) compared with other continuous time models. For this reason, the problem is somewhat mitigated. In this research, the number of event points is based on the procedure of gradually increasing the amount of event points until adding an extra event point does not result in a better solution.

3.3 Scheduling models

The models of Ierapetritou and Floudas (1998a, 1998b) are used to create scheduling models that can solve the earlier presented scheduling problem. Note that the aforementioned articles do not include the cost variables that are incorporated in this research. The paper of Ierapetritou, Hene and Floudas (1999) is used as inspiration for scheduling the changeover cost, but the eventual formulation of both the changeover and tardiness costs is mathematically derived.

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The centralized model includes all decisions in the production system to optimize the problem as a single optimization problem. By doing so, there is good coordination between the make and the pack stage resulting in the possibility to adapt the sequence and timing of batches to minimize the incurred cost.

For the decentralized approach, two models are created. As there are two stages in the production system, there are 2 ways of sequencing the scheduling. In the first decentralized model, Make-Pack, the make stage is optimized first. This model starts with looking at the demand for the intermediates and schedules the production hereof in the most cost-efficient way. Here after, the schedule is passed on to the pack-stage, which needs to optimize the pack stage based on the fixed start and finishing times of the make stage. Obviously, the pack stage cannot start before the make stage has produced a batch of intermediates. In the second decentralized model, Pack-Make, it is the other way around. First, the demand for the end products is scheduled in the most cost-efficient way. The schedule is then passed on to the make stage, which needs to optimize the make stage based on the fixed start and finishing times of the pack stage. Important to note is that when the pack stage is scheduled first there are 2 packaging lines that will start simultaneously. Consequently, the make stage needs to produce at least 2 batches before this time. The sequential way of scheduling, optimizing one stage, fix their start and finishing times and pass it on to the next stage is also adopted in several studies such as Shah et al. (2009) and Bontes (2016). An important note is that in this process, no coordination between the stages is present.

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of the tasks (𝑤𝑣(𝑖, 𝑛)) are used as fixed input for the centralized model. These variables state which task needs to take place at which event point, but do not state the quantity that needs to be produced. By fixing these, the remaining decision variables in the centralized model are heavily reduced. In turn, the solution time is shortened largely. The centralized model is now “bounded” to a certain allocation and sequence of the production. However, despite the fact that the centralized model needs to perform the specified task at the specified event point, it can still choose how much units to produce. Furthermore, it can add extra allocations of tasks as long as they do not violate the fixed allocations and the existing constraints. An important note here is that, when there are minimal batch sizes, at least this amount has to be produced at the fixed event point and hence there is less freedom in choosing the batch size. Furthermore, when no minimal batch sizes apply, the centralized model might choose not to produce at a certain event point despite the fixed allocation. This might seem strange; however, it does treat the event point as occupied by the specific task. Consequently, no other task can be produced at that event point and changeovers still apply as if a production were to take place. To highlight, the hybrid model is not overestimated by this happening. As there are two decentralized models in this thesis, there are also 2 Hybrid models. The first is the Pack-Make Hybrid, which uses the allocation and sequence variables from the Pack-Make model as input for the centralized model. The second Hybrid model is the Make-Pack Hybrid. In this model the Make-Pack model determines the allocation variables, which are then fixed and used for the centralized model.

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4. Numerical study

In Section 4, a numerical study is performed on the problem as described in Section 3.1 of this research. The presented “base case” production system is able to produce 2

intermediate products in the make stage, whereas the pack stage produces 7 end products. For each end product, the suitability, demand, production rate and required intermediate are shown in Table 1. Information on the production rate and the required number of produced intermediates in the make stage can be found in Table 2. Note that the required number of intermediates is the sum of the demand of corresponding end products.

Changeover times between intermediates can be found in table 3, whereas changeover times between end products can be found in Table 4 and 5. Most of the aforementioned data is collected from the study of Bontes (2016), which is referred to for more detailed information. The cost parameters in this research are displayed in Table 6. The deadline for the scheduling problem is set at 24 hours. If the entire production is completed before this deadline, no tardiness cost are incurred. However, if one or multiple products are completed after the deadline, there will be. These costs are based on the finishing time of the product that finishes last (makespan). To illustrate, if production of only one end product finishes 1 hour after the deadline, 1 hour of tardiness cost is incurred. However, if in addition there would be another product that finishes 3 hours after the deadline, then the total tardiness cost is based on the latest finishing time and hence 3 hours of tardiness cost are incurred, not the combined hours of 4.

End product Packaging line Demand Production rate (kg/h) Required intermediate

P1 Pack-Line 1 4100 772 Int 1 P2 Pack-Line 1 990 212 Int 2 P3 Pack-Line 1 2220 440 Int 1 P4 Pack-Line 2 666 440 Int 1 P5 Pack-Line 2 1590 414 Int 2 P6 Pack-Line 2 2300 414 Int 2 P7 Pack-Line 2 1512 374 Int 2

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Table 2: Product specifications of make stage

Table 3: Changeover times Production unit Table 6: Cost parameter value

Table 4: Changeover times of Pack-Line 1 Table 5: Changeover times of Pack-Line 2

The previously presented base case scheduling problem is solved for the centralized and decentralized models and results are compared. However, in order to understand the behaviour of the performance difference, a sensitivity analysis is conducted. In order to illustrate the effect of different parameter values on the performance difference, multiple parameters are manipulated. To also get a grasp of the interaction effect between some parameters, a factorial design (partial) is applied. As exuberantly discussed earlier in this research, changeovers are a very important aspect and hence changeover times will be manipulated. Shorter changeover times yield lower costs and hence more flexibility, whereas longer changeover times lead to higher costs and possibly reduce the potential of centralized scheduling. The second manipulated factor is demand, as this determines the production output, is variable in a real-life setting and has an influence on the batch sizes and changeovers. Thirdly, capacity will be adjusted because this affects potential

Intermediate Required amount Production rate kg/h

Int 1 6986 850

Int 2 6392 850

Production unit 1 Int 1 Int 2

Int 1 0.5 2

Int 2 1 0.5

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bottlenecks. With capacity is meant the production speed of just the packaging line. In this way, the relative difference between the make and pack stage changes, which is the goal of the capacity change. Furthermore, changeover costs and tardiness costs are manipulated as the relative difference between them has an impact on the decision whether or not an extra changeover is beneficial or not. Lastly, the deadline for completing the demand will be changed. When increasing the deadline, there is more time to produce demand without incurring tardiness cost. For the factorial design analysis, a combination of demand & changeover cost and capacity & tardiness cost is used. Due to time constraint and the long solution time of this analysis, it is only performed for two combinations. Furthermore, top and bottom ranges of the parameters have been decreased based on the expected added value of an extra step.

The analysis in this research are all performed by an Acer Intel Core i5-7200, 2.5Ghz laptop with 4GB of RAM running the Windows 10 operating system. For programming the models, Python 2.7 is used with the solver package of Gurobi 8.1. Samples of the results have been included in Appendix A, whereas the programmed scripts of all models can be found in Appendix C.

The rest of the section will be organised as follows. Section 4.1 will start with the base case results, after which the other subsections will show the results of demand, capacity, changeover times and costs, tardiness costs and the deadline manipulations. The sensitivity is performed with increasing and decreasing steps of 10% until 180% and 20% of original value have been reached. Section 4.7 and 4.8 contain the factorial experiments. Note, some sections include Gantt-charts where others do not. For convenient reporting, the Gantt-charts are only included in the sections if they add a lot of value. In some sections, there is referred to Gantt-charts in the appendix, as they are not critical in the understanding of the results but could serve as visualisation support.

4.1 Results base case

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Besides the total cost, the tardiness costs and changeover cost of both stages are displayed. As can be seen, the different costs are not all minimized in the centralized approach. As the decentralized models first focus on one of the stages, it comes as no surprise that for that stage the costs are minimized. However, as no coordination takes place between the stages, there is a lack of synchronization between them.

This lack of synchronisation becomes clear from Table 8 and from Figure 2. Although the centralized and Pack-Make approach use exactly the same number and time for changeovers, bad synchronisation leads to a far larger tardiness cost in the Pack-Make. Because in the Pack-Make model the pack lines are scheduled simultaneously, they start later compared to the centralized approach. Consequently, the makespan and tardiness cost are

Centralized Pack-Make Make-Pack Changeover cost make 150,0 150,0 100,0 Changeover cost pack 550,0 550,0 650,0

Tardiness Cost 124,7 167,5 122,9

Total cost 824,7 867,5 872,9

Table 7: results base case

Centralized Pack-Make Make-Pack Number of changeovers make 2,0 2,0 1,0 Number of changeovers pack 5,0 5,0 5,0

Total changeovers 7,0 7,0 6,0

Changeovertime make 1,5 1,5 1,0

Changeovertime pack 5,5 5,5 6,5

Total changeover time 7,0 7,0 7,5

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higher. Make-Pack on the other hand uses less changeovers, but the lack of coordination results in nonoptimal sequence in the pack stage as end product P3 and P2 are switched.

Figure 2: Gantt charts from the base case

From the previous study of Bontes (2016), we know that the centralized and Pack-Make model could have smaller makespan than they have now. However, the necessary changeovers are more expensive than the reduction in tardiness cost. Still, the changeover costs are also not minimized. This shows that the trade-off between changeover and tardiness cost is present.

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4.2 Effects of demand

In this section the effects of demand changes are discussed. Demand changes are relevant as these affect the required production time and output. Note that when changing demand for the end products, the demand for the intermediate products is changed accordingly. Figure 3 presents the total cost for each scheduling model when changing demand. When increasing demand, the total cost of all models increases. Interestingly, the centralized approach performs increasingly better compared to the decentralized approaches. The difference between the centralized and Pack-Make increases from 5,2% in the base case to 10,5% in the case of an 180% of original demand. For the Make-Pack this increases from 5,8% to 13%. Furthermore, the Pack-Make is performing increasingly better compared to the Make-Pack.

Figure 3: The total cost with manipulated demand.

When demand decreases, something else happens. In general, the total cost of all models decreases. The performance gap between centralized and decentralized scheduling fluctuates before eventually becoming 0% at 60% and 70% of original demand for the Pack-Make and Pack-Make-Pack respectively. Before reaching 0%, the performance gap fluctuates between of 2,4%-5,7% (Pack-Make) and 5,8%-7,1% (Make-Pack).

600 800 1000 1200 1400 1600 20% 30% 40% 50% 60% 70% 80% 90% _100% _110% _120% _130% _140% _150% _160% _170% _180% To ta l Cos t

% of base case demand Total cost

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Figure 4: Tardiness cost with demand manipulations Figure 5: Changeover time with demand

An interesting pattern can be observed when looking at the changeover time in Figure 5. When increasing the demand, the changeover times of the Pack-Make and centralized model at some point increases (Gantt-charts in Appendix B). In contrast, whenever demand decreases, both the centralized and decentralized approaches reduce their changeover time until they all have 6,5 hours of changeover. Regarding tardiness cost in Figure 4, a similar pattern can be observed except that when increasing demand, the centralized and Pack-Make models at some point decrease their tardiness cost.

When demand decreases, the necessary production time decreases and hence production can be finished earlier. In this way, the tardiness cost become less and less, putting more pressure on changeover cost. As a consequence, all the scheduling models reduce their changeover times (Figure 5). Eventually, all approaches produce in the same sequence and are able to finish before the deadline. The Pack-Make approach takes longest to do so because of the simultaneous start of its pack lines, which causes it to have the longest makespan when minimizing changeovers.

With increasing demand, more production time is needed, and this will stretch the makespan. Consequently, this will lead to higher tardiness cost (Figure 4). In order to decrease the tardiness cost, more changeovers could be implemented. As stated earlier in Section 4.1, the centralized and Pack-Make model were not producing at their shortest makespan in the base case and are able to produce quicker. For these models, at some point it will be more beneficial to reduce the tardiness cost at the expensive of more changeovers. As becomes clear from Figure 4 and 5, the centralized model implements more changeovers right away, whereas the Pack-Make model does this at 180% of demand. Clearly, it is sooner cost-efficient

0 100 200 300 400 500 600 700 800 To ta l co st

% of base case demand Tardiness cost

Centralized Pack-Make Make-Pack

6 6,5 7 7,5 8 8,5 9 9,5 Cha n ge o ve r time (h )

%of base case demand Total changeover time

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for the centralized model to incorporate more changeovers than it is for the Pack-Make. This is due to the ability of better synchronisation. The centralized model is able to better use a changeover to reduce tardiness cost.

In short, the effects of demand changes are twofold. Firstly, a smaller demand increases the pressure to minimize changeover cost. The coordination advantage of the centralized model reduces and eventually the approaches perform equal. Secondly, a larger demand leads to longer production times and hence larger tardiness cost, which increases the pressure to finish early. Finishing early can be best achieved by the centralized approach due to the coordination advantage and hence an increasingly better performance is visible.

4.3 Effects of capacity

This section presents changes in capacity and its effects on the performance gap of the scheduling approaches. With capacity in this study is meant the speed of the machines. Furthermore, only the capacity of the packaging lines is changed. In this way, the make stage becomes relatively faster and slower with decreases and increases of the packaging speed respectively. Figure 6 shows the total cost of the different scheduling approaches when changing capacity. In this figure, a general trend can be observed. Larger capacity is related to

Figure 6: Total cost with manipulations in capacity

lower total cost, whereas the opposite is true when capacity is smaller. This is reasonable, considering that the needed production time will shorten when capacity increases and will stretch when capacity decreases. Keeping everything else equal this would result in lower and higher tardiness cost respectively.

600 1100 1600 2100 2600 20% 30% 40% 50% 60% 70% 80% 90% _100% _110% _120% _130% _140% _150% _160% _170% _180% Tot al Cos t

% of Base case capacity

Total cost

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Besides the general trend, the comparison of the two scheduling approaches shows interesting findings. It seems that when capacity increases, the performance gap first increases, but eventually becomes smaller. The gap increases to 6% at 130% of capacity for the Pack-Make and to 12% at 140% capacity for the Make-Pack. Hereafter, the gap decreases to 0% for the Pack-Make and to 6,1% for the Make-Pack. It becomes clear that with increasing capacity, the Pack-Make outperforms the Make-Pack approach. When decreasing capacity, the performance difference has a more fluctuating pattern. The relative gap between the centralized and the Pack-Make approach is at no point smaller than in the base case. Interestingly, the Make-Pack model starts to perform better than the Pack-Make model and comes as close as 3,1% from the centralized model.

Figure 7: Tardiness cost with capacity Figure 8: Changeover time with capacity

When everything else is equal, an increase in capacity leads to a shorter production time. As explained in Section 4.2, a shorter production time puts more pressure on the changeover cost. The Make-Pack incurs the most changeover costs (Figure 8) and hence performs worse compared to the other two models. However, as the pressure on changeover cost becomes large enough, the Make-Pack model will change the sequence in pack line 1 to minimize the changeover cost (Figure 8). The Pack-Make model uses the same amount of changeover time as the centralized model but has a larger makespan. However, if capacity increases and the completion time will be before the deadline, the longer makespan will not be penalized anymore.

Following the reasoning above, decreasing capacity would place relatively more weight on the tardiness costs. From figure 7, we can clearly see the increase in tardiness cost when

0 500 1000 1500 2000 2500 Tot al cos t

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6 6,5 7 7,5 8 8,5 9 20% 30% 40% 50% 60% 70% 80% 90% _100% _110% _120% _130% _140% _150% _160% _170% _180% Cha n ge o ve r time (h )

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decreasing capacity. Consequently, the centralized model uses its coordination advantage to better synchronize the stages, which reduces the incurred tardiness cost (Gantt-charts in Appendix B). Although the Pack-Make model could also incorporate more changeovers, it does not do so in order to avoid large tardiness cost. Due to this, the makespan of the Pack-Make is longer than the Make-Pack. Hence, the Make-Pack starts to outperform the Pack-Make.

To summarize, when increasing capacity, the changeover cost become more important and the performance gap seems to become smaller. The Pack-Make model performs relatively better than the Make-Pack model, and eventually reaches the same outcome as the centralized model. When decreasing capacity on the other hand, pressure to reduce tardiness cost increases. Similar as with decreases in demand, the centralized model is best at reducing the tardiness cost and hence differences remain. It is clear that there is a trade-off between changeover and tardiness cost. The decentralized models are more limited in this trade-off than the centralized model. Due to coordination between stages, more and better sequence and timing opportunities exist for the centralized model, which result in better synchronisation.

4.4 Effects of changeover cost and changeover time

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With different changeover times, the overall trend is very similar. However, the relative difference between the centralized and decentralized models is somewhat different. With increasing changeover times, the Pack-Make model shows a stable gap around 5%, whereas the Make-Pack now starts to improve (4,4% gap at 180%). Compared to increasing cost, the roles seem to be switched. Furthermore, when decreasing changeover time, the performance gap increases fast, but not as fast as when decreasing cost. The gap with respect to the Pack-Make increases to 13,8% and that for the Make-Pack to 42,2%.

Observing the total number of changeovers in Figure 11 and 12, manipulations in changeover cost and changeover time result in very similar trends. Higher changeover

0 200 400 600 800 1000 1200 1400 1600 1800 20% 40% 60% 80% 100% 120% 140% 160% 180% To ta l Cos t

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5,5 6,5 7,5 8,5 9,5 cha n ge ov er tim e (h)

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Figure 11: Total changeovers with changeover time manipulations

Figure 12: Total changeovers with changeover cost manipulations 5 6 7 8 9 10 Cha n ge o ve r time (h )

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time/cost leads to the total number of changeovers of all models to remain stable. In addition, decreases in changeover time/cost result in increased changeovers of the centralized and Pack-Make model. An observed difference is that when decreasing changeover cost, the centralized approach starts to increase the changeovers earlier and the Pack-Make includes more changeovers (Gantt-charts in Appendix B).

Although manipulations of changeover cost/time lead to similar trends in total changeover time, the trend with respect to tardiness seems to be different (Figure 13 & 14). Where increases of changeover cost lead to no increases in tardiness cost (except for the Make-Pack model at 170%) the tardiness cost do increase when changeover times increase. Furthermore, there seems to be a more subtle decrease in tardiness cost when changeover times decrease than when changeover cost decrease. This implies that the effect of the changeover cost a changeover time are not identical.

The similarity between changeover cost and changeover time is that increases in one of the two lead to more pressure to minimize the changeovers, whereas decreases lead to pressure to reduce tardiness. However, manipulations in changeover time show a more complex relationship. It is observed that changeover time also has an effect on the tardiness of production. While an increase in changeover time makes changeovers more expensive, the production time (and hence the tardiness cost) is also increased. The opposite is true when decreasing the changeover time. When comparing a decrease in changeover times and cost,

0 50 100 150 200 250 300 Tar d in es s cos t

Total tardiness costs

Centralized Pack-Make Make-Pack 0 50 100 150 200 250 300 Tar d in es s cos t

% of base case changeover times

Total tardiness cost

Figure 13: Total tardiness cost with manipulations in changeover times

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decreasing changeover times has a “damping factor” on the pressure on changeover cost and as a result, there is a smaller performance difference between centralized and decentralized scheduling. However, an increase in changeover time leads to higher pressure on tardiness cost compared to a similar increase in changeover cost. Comparing the decentralized approaches, the Make-Pack model prefers the increase in changeover time, because it incurs less tardiness cost compared to the Pack-Make model. The Pack-Make model on the other hand, prefers the increase in changeover cost because it is able to cost-efficiently minimize changeovers quicker than the Make-Pack approach.

To conclude, with decreases in changeover time/cost, the coordination advantage of the centralized approach is less costly and as a consequence more changeovers and smaller batches are employed, resulting in a large increase in performance difference compared with the decentralized approach. Increases on the other hand reduce this advantage and differences remain relatively small. The difference between changeover cost and changeover time lies in the fact that changeover time also affects tardiness. Decreases in changeover time are more beneficial for the decentralized models than are decreases in changeover cost.

4.5 Effects of tardiness cost

In this section, manipulations of this cost and the corresponding effects on the total costs are presented. When looking at Figure 15, the total cost shows interesting patterns.

Figure 15: Total cost with manipulations of the tardiness cost.

The trend that is visible for all approaches is that when decreasing the tardiness costs the total costs of all models goes down. What is interesting is that as the tardiness costs

700 750 800 850 900 950 1000 1050 1100 20% 30% 40% 50% 60% 70% 80% 90% 100%110%120%130%140%150%160%170%180% To ta l Cos t

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approaches zero, the difference models converge to the same total cost. For the Pack-Make model this goes quite steadily from 5,2% in the base case to 1,2% at 20% of tardiness cost. The Make-Pack first slightly increases till 6,3% at 60% of tardiness cost but at tardiness cost lower than 60%, the gap decreases to 0% at 20%. As tardiness cost decrease, changeover cost become more important. As can be seen in Figure 16, changeovers are reduced (centralized follows the same line as Pack-Make). The Pack-Make and centralized model already had a smaller changeover time and hence wait longer before decreasing their changeovers as compared to the Make-Pack (Figure 16).

Figure 16: Total changeover time with manipulations in tardiness cost

With increases in tardiness cost, something different occurs. Performance differences increase rapidly to 17,8% for the Pack-Make and 14,3% for the Make-Pack at 180% of tardiness cost. As discussed in previous sections, increased tardiness cost increase the need for quicker production time and hence the advantage of centralized scheduling is more expressed. As can be seen from Figure 16, the centralized approach increases its changeovers at 130%, whereas the decentralized models do not increase it at all. This implemented increase in changeover time by the centralized approach leads to a shorter schedule and completion time before the deadline. For this reason, no tardiness cost are incurred and consequently, the total cost remain steady beyond 130%. The Make-Pack is not able to produce quicker and hence its tardiness cost will increase in a linear fashion. Although no increase in changeover time can be observed in the Pack-Make model, it is able to do so. However, the necessary increase in changeovers cost exceed the reduction in tardiness cost. It is expected that the Pack-Make at

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some point will increase its changeovers and will start to perform gradually better than the Make-Pack. Still, the Pack-Make cannot produce as quick as the centralized approach and consequently, the difference will remain.

To summarize, the focus of the scheduling models shifts to minimizing the changeovers when the tardiness cost decrease. This reduces the advantage of the centralized model and hence performance differences become smaller. When increasing tardiness cost, the centralized advantage is fully exploited, resulting in an increasing performance gap.

4.6 Effects of the deadline

As explained in Section 3.1 and again at the start of Section 4, the deadline is the time that the production schedule has before incurring tardiness cost. After this point, tardiness cost are calculated based on the difference between the finishing time of the schedule and the deadline. In previous sections there has been often pointed at the trade-off between the changeover costs and the tardiness costs. The deadline plays an important part in this trade-off. The original deadline was set at 24 hours and is changed with steps of 10% (2,4 hours). As 80% already is well below the centralized optimal makespan, the choice of not further decreasing the deadline is made, as this would be a very unrealistic scenario with results that can be drawn from the current scenario. Furthermore, increasing the deadline beyond 150% (36) hours is also not performed.

Figure 17: Total cost when manipulating the deadline.

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% of base case deadline

Total cost with deadline change

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Figure 17 shows the total cost when changing the deadline. As can be observed, when decreasing the deadline, total cost for all models go up and the centralized approach is performing best. Decreasing the deadline implies more tardiness cost and hence the centralized model is performing more changeovers to reduce this (Figure 18). The decentralized models do not change their changeover time. Interestingly, the Pack-Make model does not produce at its shortest makespan but does not implement extra changeovers to avoid tardiness cost. This indicates that it is still not cost efficient to do so, which emphasises the large difference in synchronisation between the Pack-Make and centralized model. The relative difference between the Pack-Make and centralized is decreasing from 5,2% at original deadline to 3,3% at 80% of the deadline. The difference with the Make-Pack is also decreasing from 5,8% to 3,7%.

Figure 18: Total changeover time with manipulations in deadline

A longer deadline seems to converge the total cost of the scheduling approaches. Figure 18 shows a reduction in changeover time (centralized follows the same line as the Pack-Make). The Make-Pack adopts the same schedule and cost as the centralized model at 140% deadline. At 130% the Pack-Make is equal to the centralized model, however, after both reducing their changeover time with half an hour, the centralized model outperforms the Pack-Make again. Just as described above, this points out the large difference in synchronisation possibilities. When implementing the lowest changeover cost schedule, the Pack-Make model has a longer makespan compared to the Make-Pack and centralized models.

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This is due to the simultaneous start of the pack lines in the Pack-Make model and causes it to achieve the lowest cost later.

In short, an increase in the deadline gives the centralized and decentralized models more time before tardiness cost are incurred, hence reducing their cost. When the deadline is shifted far enough, each model can finish at the lowest possible changeover costs without incurring tardiness costs. With shorter deadlines, centralized scheduling uses more changeover, but relative cost differences decrease.

4.7 Interaction effect of demand & changeover cost

Demand is very important in every business and its fluctuations can influence the performance difference between the different modes as could have been observed in Section 4.2 of this thesis.

Figure 19: Relative total cost difference between the centralized and decentralized models with demand & changeover cost manipulations

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that high demand and low changeover cost are beneficial for the centralized model when considered separately. Combining these two seems to have an even more enhancing effect on the coordination advantage (Gantt-charts in Appendix B). However, increasing demand seems to work best when slightly increased. If demand is increased further, the gap towards the decentralized models seems to shrink. As no model changes its schedule, absolute differences remain equal, but their relative difference decreases with further increases in

demand.

Figure 20: Total changeover time with manipulations of demand & changeover cost.

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To conclude, higher demand with low changeover cost is extra beneficial for centralized scheduling compared with the individual effects. However, this effect seems to be lower than the sum of the individual factors. Furthermore, where solely increasing demand entails a larger performance difference due to more changeovers in the centralized model, this is largely reduced when simultaneously increasing changeover cost. Lastly, when decreasing demand the performance differences is rather insensitive to changes in changeover cost and rather quickly becomes zero.

4.8 Interaction effect of capacity & tardiness cost

As observed in previous section of this research, the ratio between tardiness and changeover costs is very influencing on the behaviour of the scheduling models. It makes sense to hence include tardiness costs in this factorial analysis. Furthermore, capacity in-or decreases could have an effect on the performance difference under certain tardiness vs changeover cost ratios. In addition, if a company is not able to do anything about the tardiness or changeover costs, it could better understand what capacity changes could mean for the performance of their implemented centralized or decentralized scheduling approach.

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The tables in Figure 21 show that lowering the tardiness cost causes capacity to have less influence on the performance difference. As tardiness becomes lower, the models will focus more on minimizing changeovers and less on completion time (Figure 22).

Interesting to see is that with increasing tardiness cost, the decentralized models start performing different. The Pack-Make model seems to perform worst at high tardiness cost and reduced capacity. Additionally, Make-Pack has more trouble with increasing tardiness cost and increased capacity. From Sections 4.3 and 4.5 in this research we know that decreasing capacity and increasing tardiness cost separately, widens the performance gap with respect to the Pack-Make. It seems that when these two factors are combined, they cause an even larger widening of the performance gap, which is even larger than the sum of their individual impact. For the Make-Pack model, an increase in solely tardiness cost or capacity (at least until 140%) increases the performance gap. Their combined effect is higher than the individual effect, but smaller than the sum of them.

Figure 22: Total changeovers with capacity & tardiness manipulations

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changeovers. Whereas if this pressure decreases due to higher capacity or reduced tardiness cost, it implements less. The decentralized models are far more limited and barely change their changeovers, causing bad timings and longer than necessary makespan. The number of changeovers explains the earlier mentioned difference in performance between the two decentralized models. When tardiness cost are high and capacity is low, more changeovers are beneficial because they reduce the tardiness cost. They are higher in the Make-Pack than in the Pack-Make. At high tardiness and high capacity, a lower number of changeovers is beneficial, which is the case in the Pack-Make model

In short, the influence of capacity changes on the performance difference reduces when tardiness cost reduce. However, with increases in tardiness cost capacity does have an impact. Interestingly, the Pack-Make prefers the higher capacity, whereas the Make-Pack prefers the lower capacity. Nevertheless, at high tardiness cost the difference between the centralized and decentralized always remains.

5. Hybrid scheduling

Although Section 3.3 of this study already discussed the workings of the Hybrid models, it will be shortly summarized before results are presented and discussed. The Hybrid model combines the centralized and decentralized models by first optimizing the decentralized model, fixing its allocation variables (wv[i, n]), and use them as input for the centralized model. As there are two decentralized models in this study, there are 2 Hybrid models: The Pack-make Hybrid and the Make-Pack Hybrid. The results of the base case scheduling problem are presented in Table 9.

Table 9: Results of base case scheduling problem including Hybrid models.

As can be observed from Table 9, the centralized model has the lowest total cost of all other models but requires by far the longest solution time. Furthermore, the Make-Pack model and its Hybrid show both the highest cost. Interestingly, the Pack-Make-Hybrid shows a better outcome than the Pack-Make model. The difference with respect to the centralized

Base case Centralized Pack-Make Make-Pack Pack-Make

Hybrid

Make-Pack Hybrid

Total cost 824,7 867,5 872,9 851,6 872,9

Difference with centralized 5,2% 5,8% 3,1% 5,8%

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model is reduced from 5,2% to 3,1%. The solution time for this Hybrid is very fast, less than a second. In Figure 23, Gantt-charts for the Pack-Make model and the Pack-Make Hybrid are shown. Interestingly, the Hybrid model splits the production of P7 into two different batches. The first batch starts as soon as the first make batch is ready, and the second batch is very small.

Figure 23: Gantt-chart for the centralized, Pack-Make and its Hybrid

Consequently, all lines finish earlier than in the Pack-Make model. The Hybrid model is better able to synchronize the stages, which compresses the overall schedule. The difference with the centralized model is the extra changeover, and hence larger changeover cost are incurred. Furthermore, pack line 2 takes longer than in the centralized schedule, causing a slightly larger tardiness cost. The later finishing time of pack line 2 in the Hybrid model seems odd. From Figure 23 can be observed that there is a large idle time between P5 and P4, implying that P4 should be able to start early. However, due to the predetermined assignment of tasks to event points, the possibilities of the Hybrid model are limited.

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Table 10: Results of 50% changeover cost, including the hybrid model

From Tables 10-12, it becomes clear that the Hybrid models always outperform their corresponding decentralized model when the performance difference is large. For the Pack-Make Hybrid, the decreases in performance are there, ranging from 1,1% to 4,6%. With the Make-Pack Hybrid, very large decreases in performance differences can be observed. It shows that the Make-Pack model often has a better sequence of production, which causes it to be easily improved by the centralized part of the Hybrid model. The Pack-Make on the other hand, seems to struggle with this. The problem hereof may lie in the simultaneous start of the pack lines, which also need the same intermediate. This causes the need for a large batch before the pack lines can start, which leaves less room for the centralized model to improve the schedule. Furthermore, the Make-Pack model schedules 2 different products to start at the pack lines, requiring different intermediates. This is optimal for reducing makespan, which enables a better synchronization.

The results shown so far, are based on fixing all allocation variables that the decentralized model produces. However, there is the possibility to only partially fix the allocation constraints. There are several consequences hereof. Fixing less variables leaves

50% of Changeover cost Centralized Pack-Make Make-Pack Pack-Make Hybrid

Make-Pack Hybrid

Total cost 425 511,246 497,85 506.49 440.29

Difference with centralized 20,3% 17.1% 19,2% 3.6%

150% of demand Centralized Pack-Make Make-Pack Pack-Make Hybrid

Make-Pack Hybrid

Total cost 1137,24 1243 1264,28 1227.11 1137.24

Difference with centralized 9,4% 11,2% 7,9% 0%

150% of tardiness cost Centralized Pack-Make Make-Pack Pack-Make Hybrid

Make-Pack Hybrid

Total cost 850 951,29 934,28 912,11 875

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more flexibility for the centralized part to improve the schedule. The drawback hereof is that it increases the solution time. Furthermore, not fixing all implies decisions that need to be made on which allocation variables to fix. This will result in a less easy to handle model. Whereas fixing all output allocation variables is easy and already performs better than the decentralized models. For these reasons, a specific rule of thumb is introduced that, at least for the analysis in this thesis, holds and can be argued to hold in other situations. It is most suitable for the Pack-Make Hybrid. The rule of thumb is to fix the allocation variables of the bottleneck pack line. It is argued that, to have the lowest makespan or costs, it is best to schedule the bottleneck to a maximum such that it will least affect the total outcome. Consequently, a decentralized model that focuses on optimizing the pack stage first, the bottleneck is always optimized. Given this reasoning, the fixed allocation will most likely not hinder the centralized model in solving the problem closer to optimality. Results in Table 13 show that this rule holds in the cases investigated in this study. Solution times lie around 5 seconds, which is still much faster than the centralized approach.

Table 13: Results of different scenarios

To conclude, the Hybrid models look very promising as they often lead to better solutions. The Make-Pack Hybrid seems to perform best, as in most investigated settings the relative cost difference is largely reduced. The Pack-Make Hybrid performs not as good, but when fixing only the bottleneck pack line, the results become much better. The allocation sequence of the decentralized models is found to be a crucial determinant for the better performance of the Hybrid.

Base case 50% changeover cost 150% tardiness cost 150% demand Centralized 824,74 425 850 1137,24

Pack-Make Hybrid, all fixed 851,6 506.49 912,11 1227.11

Pack make Hybrid

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6.Discussion

From this analysis in this research, it has become clear that the centralized model is not always performing better than the decentralized models. This is in sharp contrast with the findings of Bontes (2016), which showed an always significantly better centralized approach. A factor that plays a crucial role in explaining the behaviour of the performance difference is the ratio between tardiness and changeover cost.

When tardiness cost are relatively large compared to the cost incurred for performing changeovers, there is an incentive to complete production as soon as possible. In this case, the cost difference behaves in a way that is similar the makespan difference studied by Bontes (2016). Decentralized models perform increasingly worse than the centralized model. Due to better synchronisation, the centralized model is able to include more changeovers and have a better timing of these. As a result, the makespan is far shorter than those of the decentralized models and hence far less tardiness cost is incurred. A low tardiness cost to changeover ratio results in the opposite. When changeovers are relatively expensive, the different models aim at reducing the changeovers. As changeovers are key to the better alignment between stages in the centralized approach, the performance gap decreases. When observing the decentralized models, it is less clear which one is better to use in a cost minimization problem. Where the Pack-Make model performs better when minimizing makespan (Bontes, 2016), there is a more delicate interplay between the two models in this research. Some situations result in better Make-Pak performance, whereas in other the Pack-Pack performs better. The simultaneous start of pack lines in the Pack-Make model cause the need for many changeovers to decrease its makespan, which is often not cost-efficient. The Make-Pack model is bound to large batches in the make stage, which cause more changeover cost in the pack stage and less sequencing options.

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6.1 Limitations

For the analysis in this research, a rather simple facility set-up is used. Although capacity is changed for the machines in this setting, no other settings have been analysed. Adding machines in the make and/or pack stage yield a different dynamic and could cause different outcomes. The models that are used in this research are able to be extended to include these extra machines. However, constraints on time and the scope of this research have caused it not to be included.

Furthermore, in the decentralized models no coordination between the different stages is assumed. Although in a large facility the communication and coordination between different stages might be limited, the assumption to exclude it completely might be too strict. An obvious example hereof, is that in the decentralized Pack-Make model the starting times of the pack lines start simultaneously and are fixed. As can be seen from the schedule (section 4.1), pack line 2 could start as soon as the batch of Intermediate 2 is finished. However, due to the fixing of the starting times this does not occur. In a real-life setting this could be noticed and acted upon, which would probably benefit the outcome.

Additionally, the models are based on a make stage which produces in batches, which causes the pack lines to start after a batch in the make stage is finished. Although intermediates are often produced in batches in the process industry, a situation where the make stage would produce in a continuous fashion could result different outcomes. This could be accounted for by incorporating a fixed, small batch size with no changeover time between the same product. In this way, the production time would be the same, but it increases the release times of the make stage. The Make-Pack model is especially harmed by the current approach. The pack lines can only start after a long make stage batch, whereas if they could start earlier it might increase the performance.

A comparison between centralized and decentralized scheduling approaches in Make-and-Pack Plants