Title: Workload Balancing Capability of a Unit-based Polca Material Control System Author: N. Ziengs Supervisor (1

(1)

Title: Workload Balancing Capability of a Unit-based Polca Material Control System Author: N. Ziengs

Supervisor (1st): J. Riezebos Supervisor (2nd): R. Germs Date: 31 / august / 2009

Master programme: Technology Management Master programme coordinator: G. C. Ruël

Organisation: Department of Operations of the Faculty of Economics and Business, University of Groningen

Web-address of the organisation: http://www.rug.nl/feb/Faculteit/Vakgroepen/Operations/ Key-words: Polca; Workload Balancing; Optimal Card Configuration; Discrete-event Simulation

(2)

1

Workload Balancing Capability of a Unit-based Polca

Material Control System

N. Ziengs (s1469584) J. Riezebos (1st supervisor)

R. Germs (2nd supervisor)

Department of Operations

Faculty of Economics and Business, University of Groningen PO BOX 800, 9700 AV Groningen, the Netherlands

31 August 2009

Abstract

(3)

2

List of figures

Figure 1: Throughput time performance measures ... 6

Figure 2: Segmented and joint pull structures ... 9

Figure 3: Throughput time performance curve ... 10

Figure 4: Shop floor topology and structure ... 17

List of tables

Table 1: Experimental design ... 19

Table 2: Optimal throughput time performance for restricted configurations ... 21

Table 3: Optimal throughput time performance for unrestricted configurations ... 22

Table 4: Relative influence on the optimal configuration for three stages ... 25

Table 5: Relative influence of initial and closing control loops for three stages ... 25

Table 6: Relative influence on the optimal configuration for four stages ... 26

Table 7: Relative influence of initial, intermediate, and closing control loops for four stages 26

1 Introduction

Manufacturing companies employ different strategies in order to meet their customers’ demands. These strategies can often be classified as either (1) make-to-stock (MTS) or (2) make-to-order (MTO). These approaches differ mainly with respect to the extent to which the customers’ orders are able to penetrate the manufacturing process. Make-to-stock production aims to fill an inventory of end products, based on forecasted demand. Whereas make-to-order production starts production after the make-to-order is received. A make-to-make-to-order strategy is therefore generally better suited for those companies which are faced with a high degree of demand uncertainty.

These make-to-order companies have several prominent characteristics. First, they tend to produce a wide variety of products. Frequently, this includes both standard as well as customized products for a large number of different customers. A wide variety of both standard and custom products results in a large number of different routings and varying processing times. A large number of different customers also results in varying arrival times. Second, usually production is done in small volumes. Small volume production increases the variability of the arrival times, thereby increasing demand uncertainty. Therefore, in comparison to make-to-stock companies, make-to-order companies are faced with a more complex flow of orders on the shop floor. This makes it difficult to achieve short and reliable throughput and delivery times.

One way companies are able to control their throughput time performance is by regulating the flow of orders to and on the shop floor. This is handled by a material control system. On the one hand, these systems need to enable short and reliable throughput times, which requires both short queue lengths and an unobstructed flow of orders. On the other hand, they also need to ensure an adequate use of shop floor resources. Both require decisions related to timing, priority, and quantity of orders to be release or dispatched (Hopp and Spearman, 2008)

(5)

4

applicable by make-to-order companies. In addition, they stated that there were a limited number of empirical and simulation studies to support this conclusion and that further research into the suitability and performance of Polca is warranted. Furthermore, others have also argued that even though there is a need for intuitive card-based material control systems, as there are relatively few of those systems which seem to be able to handle the requirements of make-to-order companies (Land, 2008). Here, we aim to contribute to this perceived need by exploring one of the characteristics which could make a unit-based Polca system suitable for make-to-order companies.

One of the qualities that makes Polca more suitable for make-to-order companies, as opposed to the more traditional material control systems, is the ability to handle a more complex flow of orders (Suri, 1998). This is due to the structure of overlapping loops Polca employs to control the flow of orders on the shop floor. Suri reasons that this ability makes Polca ideally suited to handle a large number of different products as well as production in small volumes. Polca is able to handle these challenges primarily by limiting the workload on the shop floor and re-directing – or balancing – the flow of orders based on the availability of downstream capacity. Workload balancing allows for the even distribution of the workload on the shop floor, which should result in a shorter throughput times due to a reduction in the blocking and starving of workstations on the shop floor. Germs and Riezebos (2009) have shown that Polca does indeed balance the workload effectively under certain circumstances.

Polca controls the workload primarily by setting the number of production authorization cards throughout the system. Setting the number of cards limits the workload in that specific section of the system. Therefore, adjusting the number of cards plays an important part in achieving the desired throughput time performance through restriction of the workload. However, Germs and Riezebos (2009) found that the optimal number of cards – the number of cards for which the total throughput time is shortest – did not restrict the workload in the first section of their chosen system. This results in a build-up of work-in-progress inventory on the shop floor. As a consequence the workload is not distributed evenly amongst all of the workstations on the shop floor and the last section of the production system is solely responsible for balancing the workload. Furthermore, the release of orders to the shop floor is not constrained. Even though, a restricted release to the shop floor is an important part of any pull system (Riezebos, 2009) and is often has a greater impact on throughput time performance than the dispatching decisions (Haskose, Kingsman, and Worthington, 2004).

(6)

5

therefore, to further explore the relation between the shop floor topology and the workload balancing capability of a unit-based Polca system.

The structure of this paper is as follows. In the next section the workload balancing capability of Polca and the literature related to the subject is discussed in further detail. The third section provides an overview of the research framework and the research question. In the fourth section the research approach will be discussed. This will include the discussion of the chosen shop floor models used for this paper. In section five the results will be presented. In the final section the research findings will be discussed and opportunities for additional research will be provided.

2 Background

2.1 Pull systems

The classification of material control systems relies on the distinction between (1) push and (2) pull. Both systems control the flow of orders differently and are often seen as opposites. The main difference relates to the handling of work-in-progress inventory. A pull system sets an explicit limitation on the amount of work-in-progress inventory that is allowed onto the shop floor, whereas a push system does not set such a limitation (Hopp and Spearman, 2004). Therefore, in a push system production is initiated by upstream information. The release and movement of orders is scheduled in accordance with actual or perceived demand. Production at a workstation starts when capacity becomes available and the schedule allows for the production to commence. As a consequence work-in-progress inventory is allowed to build up on the shop floor, thereby increasing queue length on the shop floor. Material requirements planning (Orlicky, 1974) is often considered as the foremost example of such a push system. Alternatively, in a pull system production is initiated by downstream information. Orders are released to the shop floor or dispatched to the next workstation in their routings depending on the state of the system. Production starts if the downstream signal is received and capacity becomes available. Kanban (Ohno, 1988) is the most commonly used example of a pull system. Most material control systems, however, cannot strictly be classified as either purely pull or push. Instead, most systems have both pull as well as push characteristics (Karmakar, 1991).

(7)

6

smaller amount of work-in-progress inventory (Hopp and Spearman, 2008). However, this depends on the pull or push system used and the setting it is used in (Krishnamurthy, 2004). Second, orders that are not allowed to continue to the shop floor due to the workload limitation are pooled before the shop floor. Thereby, adding an additional waiting period for each order.

Therefore, when considering pull systems the time an order spends in the production system can be partitioned into (1) the time the order spends on the shop floor and (2) the time an order spends waiting before the shop floor. The average time between the entry of an order and the departure of that order from the production system is referred to as the (average) total throughput time (ttt). The time an order spends on the shop floor is referred to as the (average) shop floor throughput time (stt). The time an order spends on the shop floor is marked by the release of the order to the shop floor and the departure of the order from the production system. The additional (average) waiting time before the shop floor is referred to as the order pool time (opt). The introduction of a workload limit results in a trade-off between a decrease in shop floor throughput time and an increase in order pool time. When using a pull system the increase in order pool time should not offset the decrease in shop floor throughput time. In figure 1 the partitioning of the throughput time is shown for both a pull and a push system (Land, 2004; Germs and Riezebos, 2009).

stt opt ... ttt order entry order release order departure shop floor order pool stt ... ttt

order entry & order release order departure shop floor

opt = order pool time

stt = shop floor throughput time ttt = total throughput time

Figure a : pull system Figure b: push system

Figure 1: Throughput time performance measures

(8)

7

Furthermore, this delay is then used for the incorporation of downstream information into the release and dispatching decisions. For instance, in a traditional Kanban system production authorization cards are issued after the depletion of a downstream inventory point or buffer. The card signals the release of an order to the first workstation on the shop floor. Card-based systems first require an order to wait for a production authorization card to become available and then for capacity to become available. In order to emphasize the difference between both waiting periods we refer to the first queue as the assembly queue and to the second as the internal queue (Riezebos, 2009). Some pull systems, other than the traditional Kanban system mentioned above, are able to use downstream information to evenly distribute the workload amongst all of the workstations on the shop floor.

Although pull systems all incorporate downstream information into the release decision not all pull systems are able to distribute the workload evenly amongst the workstations on the shop floor. Such an even distribution of the workload is also referred to as a balanced workload. Those systems that are able to evenly distribute the workload are said to exhibit workload balancing capability and are able to balance the workload by including routing information into the release or dispatching decisions. Pull systems can either be product-specific or product-anonymous (Riezebos, 2009). Product-specific control relies on signals requesting the refill of a depleted inventory point tied to a specific product type, such as in Kanban systems. Product-anonymous control releases newly arrived orders regardless of product type, such as Conwip (Spearman and Hopp, 1990). Route-specific control is derivative of product-anonymous control as it does not take product type into consideration when releasing orders. Additionally, route-specific control does incorporate information about the availability of downstream capacity for a routing or specific sections of a routing. Hence, those systems using route-specific control should be able to balance the workload.

(9)

8

Workstations can be part of multiple control loops if several different routings share the same shop floor resources.

2.2 Pull structure and configuration

The design and implementation of the control loops is an important aspect in material control system design. Two important design issues need to be addressed, namely (1) pull structure and (2) pull configuration (Gaury, 2000; Gaury, Kleijnen, and Pierreval, 2001). First, the structure refers to the arrangement of control loops used to control the flow of orders. This arrangement consists of (1) the number of control loops, (2) the placement of those control loops, and (3) the length each control loop. The length of each control loop refers to the number of workstations it contains. Different structures can be outlined by varying one of these elements. Second, the configuration of the pull system refers to the number of cards controlling the workload limitation throughout each of the control loops. Whilst the structure controls the direction of the flow of orders and is therefore closely related to the physical layout, the configuration controls the amount of orders which will be released or dispatched.

As multiple control loops can be part of the same structure, the design of a pull system could require dividing the production system into several segments (Gstettner and Kuhn, 1996; Gaury, 2000). A segmented system refers to a system which is divided into several segments, each of which is controlled by a different control loop. Also, each segment is controlled by a single control loop. Furthermore, the control loops of a segment do not overlap. For each segments one or more workstations can be part of the segment and control loop. However, each individual workstation is only part of one segment though it can be controlled by several control loops. For instance, Conwip has a single control loop and therefore cannot be divided into segments. Kanban has multiple, but similar control loops and can therefore not be viewed as a segmented system. Sections containing one or multiple overlapping control loops are referred to as joint systems (Gaury, 2000). Only those segments using a form of pull control have control loops and, thus, limit the workload. Push control does not require a control loop as there is no workload limit. Therefore, the definition by Hopp and Spearman (2004) does not necessarily apply to production systems as a whole, but rather to the segments of those systems. A number of overlapping control loops can be regarded as a single segment. Figure 2 shows a segmented and a joint system.

(10)

9

Control loop Control loop Control loop

Figure a : segmented Figure b: joint Figure 2: Segmented and joint pull structures

A segmented structure will prohibit the transfer of route-specific information to upstream workstations. Segments are separated by a junction point (Gaury, 2000). This junction point prohibits the transference of route-specific information about the availability of capacity. Therefore, in order for route-specific information to become available upstream the structure cannot be segmented. For instance, figure 2a represents a segmented system. The first segment is not controlled by a control loop and acts as a push system. Any order will progress through this workstation regardless of the availability of downstream capacity. Route-specific information can only be passed to an upstream workstation if the structure is joint. These joint structures use overlapping control loops to link separate workstations or a single route-specific control loop. In the example of figure 2b an order can only progress through the first workstation if downstream workload requirements are met. Systems with a segmented structure are at most partially able to balance the workload, depending on whether or not one of those segments exhibits a joint structure.

Although, both the structure and configuration are important design elements, once the structure is set adjusting the configuration becomes increasingly more important. Mostly, once the structure has been implemented it will not be frequently altered and the control will predominantly be exercised through adjusting the configuration. In based systems, card-setting (Huang, Rees, and Taylor, 1983; Gupta and Gupta, 1989) or card-controlling (Framinan, Gonzalez, Ruiz-Usano, 2006; Gonzalez and Framinan, 2009) are instrumental to controlling throughput time performance.

(11)

10

immediately released onto the internal queue of the first workstation in their routings. This configuration resembles a push system. When moving to the left of the curve the configurations become increasingly constraint. The total throughput time and shop floor throughput time performance are now as shown in figure 1b. This results in a decrease of shop floor throughput time and an increase of order pool time. The increase in order pool time has the potential to outweigh the decrease in shop floor throughput time. This would result in an increase in the total throughput time. As stated, the total throughput time is the lowest for the optimal configuration, at the critical point of the curve. This – critical point – represents the maximum total throughput time reduction a pull system can obtain as compared to its non-limited counterpart. Both the total throughput time and the shop floor throughput time are reduced compared to the non-limited system. When moving even further to the left on the curve, after the critical point, the increase in order pool time starts to outweigh the decrease of shop floor throughput time. Finally, the decrease in shop floor throughput time will entirely be offset by the increase of order pool time. Here, the system has become too constrained to offer any throughput time performance improvements over a non-limited system.

ttt stt ttt reduction stt reduction Decrease stt > Decrease ttt Decrease stt < Increase ttt Decrease stt > Increase opt Decrease stt < Increase opt Optimal configuration

: Pull system (with different configurations) : Push system : Optimal configuration

Figure 3: Throughput time performance curve

(12)

11

not. For those systems, the reduction of shop floor throughput time often results in an increase of total throughput time. For instance, Conwip was not able to outperform a push system and achieve a reduction in total throughput time (Germs and Riezebos, 2009). Only those systems which incorporate route-specific information into the release and/or dispatching decisions were able to outperform their non-limited counterparts. Therefore, a pull system is only capable of achieving a reduction in both shop floor throughput time and total throughput time if it can effectively balance the workload. Hence, the workload balancing capability of a pull system is said to be effective when it results in a reduction of the total throughput time as compared to a non-limited system.

2.3 Pull structure and configuration of Polca

Paired-cell overlapping loops of cards with authorization, better known by its acronym Polca, is a card-based material control system which was first introduced by Suri (1998). As stated in the introduction, Polca is referred to as a pull system. Polca aims to control the flow of orders by restricting the workload on the shop floor and therefore fits the definition as presented before. In addition, Polca is one of the few unit-based pull systems mentioned in literature which is able to balance the workload (Germs and Riezebos, 2009). Both the workload limitation and the workload balancing capability of Polca contribute to an improved control of throughput times on the shop floor. Therefore, depending on the circumstances Polca should be better suited for a make-to-order company than traditional pull or push systems in regard to throughput time performance.

(13)

12

variability was not included in the experimental design even though Polca is able to balance the workload (Germs and Riezebos, 2009). However, due to its workload balancing capability Polca was able to outperform a push system and Conwip for other experimental designs.

Polca is able to balance the workload by using a structure of overlapping control loops to control the flow of orders. Each control loop pairs two workstations. The first workstation in each pairing is referred to as the originating workstation and the second is referred to as the destination workstation. The former represents the next workstations to in the routing of an order, whereas the latter represents the downstream workstation to which the order will traverse to after being processed by the originating workstation. Using a single control loop the workload limit for two workstations ensures the availability of downstream capacity before an order is processed by the next workstation. In a unit-based system cards are often used to control the workload limit in each control loop, however other visual cues can be used as well (Vandaele, Claerhout, Nieuwenhuyse, 2008).

Due to this card-based design, Polca introduces an additional waiting period before each workstation. As stated, this is referred to as the assembly queue waiting time. First, an order has to wait until a card is attached. This card is part of the control loop between the next two workstations in the routing of the order. Once attached the order is allowed to progress the internal queue of the first workstation where it resides until capacity becomes available. The choice of the number of cards determines the workload limit and, thus, the length of the internal queue. After the order is processed, the card remains attached to the order. The order then has to wait in a second assembly queue, where it waits for another card to be attached. The choice of the number of cards also determines the length of this assembly queue. After the second card is attached the order is controlled by two overlapping control loops. The order now has two cards attached. The first card indicating the first workstation as the originating workstation and the second card indicating the second workstation as the originating workstation. Once attached the order moves into the internal queue of the following workstation. After the order has been processed by the second workstation the first card is detached. The order then moves to a third workstation, where it again enters an assembly queue. The detached card can subsequently be re-attached to a different order waiting in the assembly queue of the first workstation.

(14)

13

the availability of capacity at the downstream workstations. For instance, if downstream capacity is only available in one of two downstream workstations the flow or orders to the workstation which has capacity available is prioritized regardless of the sequence in which the orders arrived at that workstation. Therefore, Polca is able to balance the workload if an originating workstation passes orders onto multiple different destination workstations. Although the control loops are route-specific they do not necessarily belong to a single routing. A larger number of destination workstation should increase the ability to offload orders to another workstation in case some of the workstations are blocked.

Therefore controlling the entire production system through the use of overlapping control loops should improve the throughput time performance of that system provided that the workload is limited throughout the control loops. If the configuration does not limit the workload the orders will not be prioritized based on the availability of downstream capacity. The control loop will lose its function. The control loops are used to pass information upstream only if all the workstations are included in the overlapping structure of control loops. It can, therefore, be expected that the optimal configuration of Polca should limit the workload throughout the entire production system.

However, findings by Germs and Riezebos (2009) partially contradict this presumption. The authors found that for the optimal configuration not all control loops did limit the workload. Instead, for the optimal configuration Polca showed the last control loop of each routing to be responsible for the balancing of the workload. The separation between limited and non-limited control loops resulted in a push/pull boundary. This effectively created a segmented system. The boundary meant that workload balancing could only occur when dispatching orders to the last workstation and not when releasing them to the shop floor. Normally, a delay of the release of order should improve throughput time performance.

The outcome of the previous study is surprising or even contradicting. On the one hand, it showed a unit-based Polca system to be able to balance the workload. On the other hand, it also showed, for an optimal configuration, the workload not to be balanced among all the workstations on the shop floor. Even though workload balancing is believed to improve the throughput time performance of a system, their partially balance system achieved a shorter total throughput time.

3 Research statement

(15)

14

overlapping control loops to control the flow of orders. The use of these overlapping control loops makes it possible to incorporate route-specific information for both order release and dispatching. Limiting the workload in the control loops could divert the flow of orders and thus should balance the workload. Hence, for the optimal configuration it is expected that all of the control loops are limited. When this is the case the workload should, in principle, be balanced among all of the workstations on the shop floor. Germs and Riezebos (2009) have shown that for an optimal configuration the system limits the workload only in specific control loops, which would arguably result in a partial balance of the workload and segmentation of the system. This section present the research questions.

The previous sections give rise to two important research issues relating to the influence of the shop floor topology on the effective workload balancing capability of Polca system. First, the degree to which the number of alternative routings influences the workload balancing capability of Polca. This relates both the number of workstations in the shop floor topology and the arrangement of those workstations as compared to the other workstations on the shop floor. Second, the influence of workstations in different parts of the routing when it comes to balancing the workload.

First, choices related to the design of planning systems should fit with the manufacturing environment (Jonsson and Mattsson, 2003). The physical characteristics of the shop floor limit the number of choices when designing a control system (Slack, Chambers, and Johnston, 2004). As stated, the structure refers to the number, placement, and length of the control loops. Hence, the number of design choices is dependent on the physical layout of the shop floor. Therefore, the arrangement of workstations or shop floor topology determines the structure to a large degree. Additionally, the topology poses a limit to the number of routings, which in turn also influences the design of the structure. As stated, Polca is able to balance the workload by prioritizing orders based on the availability of downstream capacity and uses the alternative routings. Polca prioritizes based on the difference in downstream capacity requirements. This requires multiple downstream workstations. An increase in the number of downstream workstations should improve the throughput time performance by increasing the number of orders with alternative routings. Thereby, improving the effective workload balancing capability. Therefore, Polca should be able to balance the workload at each stage where the workstations have multiple downstream workstations to transport orders to.

(16)

15

previous study consisted of three-stages. Each routing also consisted of three workstation. Therefore, each routing was controlled by two control loops. Extending the topology with an additional stage allows us to determine if their findings also apply for a Polca system with an initial, intermediate, and closing control loop for each routing. The amount of cards used in the intermediate control loop provides details about the extent of the responsibility of the last stage of workstations. The aim of this paper is to investigate the relation between the chosen shop floor topology and the workload balancing capability of a unit-based Polca system.

Furthermore, intermediate factors related to the arrival variability and processing time variability influence throughput time performance as well (Johnson, 2003). Germs and Riezebos (2009) have established the relation between utilization, batch size, and randomness of inter-arrival and processing times. An increase in batch size, utilization, and randomness of inter-arrival times all increase the numbers of orders with alternative routings with could be prioritized. Therefore, these factors related to the order arrival pattern generally had a positive influence on the workload balancing capability. Alternatively, randomness of processing times has a negative effect on the workload balancing capability. The throughput time performance of an extended Polca system should shown similar results, although it can be expected that due to the increase in choice and the number of workstation both the negative effects and the positive effects of the intermediate factors are amplified.

Research questions:

1. Does an extension of the shop floor topology increase the effective workload balancing capability of Polca?

2. Is only the last set of control loops responsible for the workload balancing capability of Polca?

4 Research approach

Discrete-event simulation will be used to answer the research questions stated in the previous section. The simulation models were constructed in Desimp (Stokking, 1996). Desimp is a discrete-event simulation library of routines within Delphi. The model was validated by comparing several runs of the model by Germs and Riezebos (2009) to the models used for this paper.

(17)

16

throughout each of the stages, and the number of different routings (and/ or product types) that are possible. This section is concluded by providing an overview of the experimental design. This includes the factors and levels used to determine the shop floor throughput time and total throughput time performance for various conditions.

4.1 Shop floor model design

In order to determine the workload balancing capability of a unit-based Polca system and the degree of to which this (workload balancing capability) is influenced by workstations in different stages throughout the production system we use two shop floor models. The first model used is similar to the model by Germs and Riezebos (2009). The second model extends the previous model by adding an additional stage of workstations at the end of their shop floor topology. Comparing the two models allows us to determine if the workstations in the last stage of the shop floor topology are indeed responsible for the workload balancing capability and determine the conditions under which this remarkable effect takes place. Furthermore, comparing similar shop floor topologies allows us to determine if an increase in number of workstations who pass order on to multiple workstations influences the workload balancing capability.

(18)

17

As stated, the second model extends the first model by adding an additional stage of workstations at the end of the shop floor topology. The model is shown in Figure 4b. The model exhibits the same divergent structure. Only the workstations are grouped in four consecutive stages and an additional eight workstation are placed in the fourth stage. . In order to keep the utilization constant throughout the system the processing time in the first stage is one time unit, the processing time in the second stage is two time units, the processing time in the third stage is four time units, the processing time in the fourth stage is eight time units. The flow of orders is therefore controlled by fourteen control loops. The number of routings is increases to eight. Again, each routing is equally likely to occur. Extending the model allow us to consider the effects of an initial, an intermediate, and a closing control loop for each routing.

E D G F B C A I H K J D E B M L O N F G C A

Figure a : three-stage topology Figure b: four-stage topology Figure 4: Shop floor topology and structure

4.2 Experimental design

(19)

18

can be simulated. When sufficiently releasing the restriction the behaviour will start to resemble that of a push system. Again, only the defining characteristic of a push system is simulated, namely the lack of a workload limitation. The orders will not be prioritized based on the availability of downstream capacity, but rather on a first-in-first-out or first-come-first-served principle.

The configuration determines the extent to which the workload is limited and therefore serves as the primary means of controlling the flow of orders and affecting throughput time performance. For both models the optimal configuration of Polca is compared to their respective non-limited counterpart. The throughput time performance cannot be measured directly as the additional of a stage of workstations also increases the throughput time by eight time units. The percentage of improvement gained in comparison to the non-limited system will serve as a measure of comparison between the two models. Due to the symmetrical shop floor topology the number of cards of the control loops between the same stages can be held constant as each routing is equally likely to occur. For instance, consider Figure 4a. The number of cards in the control loop between workstations A and B is the same as the number of cards in the control loop A and C. Hence, for the three-stage shop floor topology two sets of cards have to be set. One for the two initial control loops (AB, AC) and four for the closing control loops (BD, BE,CF,C). For the four-stage shop floor topology three sets of cards have to be set. One for the two initial control loops, one for the four intermediate control loops, and one for the eight closing control loops.

(20)

19

Table 1: Experimental design

Factor Experimental levels

Order arrival pattern:

- inter-arrival time - constant, random (negative exponential)

- utilization - 80%, 85%, 90%

- batch size - 1, 10

Processing time variability:

- processing time - constant, random (Erlang-2)

A full factorial design was used and batch processing was used to conduct the large number of experiments. For each of the experimental design the results of the simulation are the average of 100 independent runs. The running time of each of those runs were 100.000 time units. The statistics of the first 25.000 time units were discarded to eliminate the initial transient. The difference between experiments was determined by means of a factorial ANOVA at a 95% confidence level.

5 Results

In this section the outcome of the experiments will be addressed. The intent is to evaluate the effective workload balancing capability of the unit-based Polca system for the two shop floor topologies. In table 2 an overview of the optimal throughput time performance for both shop floor topologies is given. The number of cards throughout the control loops is restricted. Each control loop has the same number of cards. This allows us to determine the optimal configuration for a non-segmented system. The percentage of improvement as compared to a non-limited system is given for each of the combinations of experimental factors and levels as were presented in table 1.

The results in table 2 show that when the configuration is restricted Polca is able to balance the workload effectively. This holds true for the three-stage shop floor topology as well as the four-stage shop floor topology for those experimental designs without randomness of processing times. As expected, the reduction in total throughput time is mostly larger for the four-stage topology. However, this difference diminishes when the utilization increases or when variability of processing times is introduced.

(21)

20

other intermediate factors influencing the order arrival pattern. An increase in the utilization generally results in an improvement of throughput time performance. However, if the batch size increases this result only partially holds. For instance, given a constant inter-arrival and processing time and batch size of one, the increase in utilization from 80% to 85% results in a decrease in total throughput time reduction. However, when increasing the utilization from 85% to 90% this results in an increase in total throughput time performance. This latest increase offsets the total throughput time reduction caused by the preceding decrease. This indicates that the overall the utilization has a positive effect on the workload balancing capability. A larger batch size improves the workload balancing capability as well. These results as described above hold for both the three-stage and four-stage shop floor topologies in case of no randomness of processing times. When comparing both topologies, the positive impact of those three variables on the workload balancing capability is larger for the three-stage topology.

(22)

21

Table 2: Optimal throughput time performance for restricted configurations

Batch size Utilization %TTT %STT %TTT %STT %TTT %STT %TTT %STT

1 80% 0,47% 1,14% 0,80% 1,18% 2,24% 8,56% 1,52% 3,99% 85% 0,70% 1,43% 0,86% 1,59% 2,74% 9,13% 1,74% 3,63% 90% 1,09% 2,49% 1,35% 1,79% 3,32% 11,61% 2,28% 4,85% 10 80% 1,15% 9,17% 0,89% 1,99% 5,26% 38,84% 3,44% 24,66% 85% 1,05% 5,10% 0,86% 1,99% 5,53% 40,50% 3,66% 25,01% 90% 1,21% 4,81% 1,28% 1,87% 5,76% 43,27% 3,95% 28,39%

1 80% 0,10% 0,17% 0,19% 0,23% 0,34% 2,79% 0,18% 0,48% 85% 0,00% 0,00% 0,11% 0,19% 0,36% 1,63% 0,40% 1,28% 90% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 10 80% 0,11% 0,82% 0,04% 0,07% 2,06% 22,10% 1,11% 14,06% 85% 0,10% 0,41% 0,19% 0,33% 2,00% 20,82% 0,13% 20,01% 90% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00%

Three-stage Four-stage Three-stage Four-stage

Random processing time

Constant inter-arrival time Random inter-arrival time Constant processing time

Constant inter-arrival time Random inter-arrival time

In table 3 a different overview of the optimal throughput time performance for both topologies is given. Here, the restriction placed on the number of cards is relaxed. Each control loops between two consecutive stages has the same number of cards. This allows us to determine a different optimal configuration. Even if this configuration introduces a non-limited segment. The experimental designs with the randomness of processing times have been omitted, due to their limited ability to show the effective workload balancing capability. Most of the results of the restricted system still hold. Again, both systems display effective workload balancing capability. The introduction of randomness of inter-arrival times still has a positive effect for both of the topologies. An increase in utilization improves the throughput time performance for the three-stage topology. However, the relation between utilization and total throughput time reduction for the four-stage topology is not as straightforward. Table 3 exhibits the same pattern as for the restricted configuration, as presented in table 2. Even though the results of the reduction in total throughput time are largely similar, those of the reduction in shop floor throughput time are not.

(23)

22

However, the increase of the reduction in total throughput time suggests that the downstream control loops are still limited. This holds for both systems. Therefore, although the system as a whole behaves as a push system a segment still restricts limits and balances the workload. For both topologies only the last control loops are limited and therefore contribute to the workload balancing capability. This does not hold for all of the combinations of experimental factors and levels. For instance, given random inter-arrival and constant processing times and a batch size of ten, the reduction in both shop floor and total throughput time for the three-stage topology differ. For a utilization of 85% and 90% the results resemble those shown in table 2. The shop floor throughput time reduction is larger than the total throughput time reduction. For these, experimental factors and levels the system as a whole acts as a pull system. The first control loops are limited resulting in an order pool, for reference see also figure 1a. The intermediate control loops are not limited, therefore the systems is still segmented. These last findings largely contradicts with the findings by Germs and Riezebos (2009). Here, the last control loops are not entirely responsible for the workload balancing capability.

Table 3: Optimal throughput time performance for unrestricted configurations

1 80% 3,72% 3,72% 5,34% 5,34% 6,12% 6,12% 6,80% 4,06% 85% 5,57% 5,57% 7,03% 7,03% 7,76% 7,76% 11,07% 6,36% 90% 8,30% 8,30% 9,24% 9,24% 9,69% 9,69% 9,04% 9,04% 10 80% 3,36% 3,36% 4,72% 4,72% 6,31% 6,31% 8,04% 37,45% 85% 4,56% 4,56% 6,29% 6,29% 8,71% 63,23% 7,28% 38,49% 90% 6,77% 6,77% 8,50% 8,50% 9,17% 65,66% 7,13% 38,49%

Constant processing time

Constant inter-arrival time Random inter-arrival time

For most of the experimental designs for both of the topologies the optimal configuration leads to a segmented system. In table 4 a number of configuration for the three-stage topology are shown, starting with a completely restricted system. First, the workload limitation throughout the first control loops is relaxed until the optimal configuration is reached. Next, the workload limitation throughout the last control loops is relaxed until the configuration does not limit the workload throughout the entire production system.

(24)

23

of one, it takes a larger number of cards for the decrease in total throughput time to show for a utilization of 90% than it would for a utilization of 85%. The same holds for an increase in batch size, albeit less pronounced. When considering an increase in the number of cards in the second control loop the same results show. However, the first control loops have a larger impact on the throughput time performance. Therefore, it is more important to set the number of cards in the first control loops The increase in the number of cards had less effects for those experiments with a larger utilization and batch size. The experimental designs that did not have non-limited first control loops displayed a higher reduction in throughput time for a limited number of cards (i.e. consider the configurations with random inter-arrival times, constant processing times, a batch size of ten, and a utilization of 80% and 85%).

The last control loops have a greater impact on workload balancing capability for a three-stage system. Table 5 shows the relative importance of the initial and last control loops. The workload balancing capability of both sets of control loops is reviewed independently. First, the workload limit in the first control loops is imposed and the last control loops are non-limited. Second, the workload limit in the last control loops is imposed and the first control loops are non-limited. The table shows the workload balancing capability when only a single set of control loops are limited. Independently viewed, the last control loops have a greater impact on the effective workload balancing capability. For instance, given a constant processing and inter-arrival time, a batch size of one, and a utilization of 80%, limiting the first stage results in a increase in total throughput time and limiting the second stage results in a decrease in total throughput time.

Table 6 provides a similar overview as table 4, but only for the four-stage topology. Again, starting with a completely restricted system. First, the workload limitation throughout the first control loops is relaxed until the optimal number of cards for the first control loops is reached. Next, the workload limitation throughout the second set of control loops is relaxed until the optimal configuration is reached. Lastly, the workload limitation throughout the last control loops is relaxed until the configuration does not limit the workload throughout the entire production system. This holds for most of the experimental designs. However, those designs for which the optimal configuration did not result in a workload limitation for the first control loops display the opposite behaviour.

(25)

24

because restricting the workload too much has a more severe impact on throughput time performance. Again, the experimental designs that did not have non-limited first control loops display higher reduction in throughput time for a limited number of cards (i.e. consider the configurations with random inter-arrival times, constant processing times, a batch size of ten, and a utilization of 80% and 85%).

(26)

25

Table 4: Relative influence on the optimal configuration for three stages

Batch size Utilization set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT%

1 80 2,2 -5682,79 25,97 ∞,2 3,72 3,72 2,2 -4515,27 44,23 ∞,2 6,12 6,12 5,2 -4,89 7,66 ∞,5 1,45 1,45 5,2 -6,78 23,31 ∞,5 3,35 3,35 10,2 3,36 3,92 ∞,10 0,09 0,09 10,2 5,49 9,90 ∞,10 0,57 0,57 20,2 3,72 3,72 ∞,20 0,00 0,00 20,2 6,12 6,24 ∞,20 0,01 0,01 ∞,2 3,72 3,72 ∞,∞ 0,00 0,00 ∞,2 6,12 6,12 ∞,∞ 0,00 0,00 85 2,2 -2,6E+04 39,35 ∞,2 5,57 5,57 2,2 -19261,14 55,53 ∞,2 7,76 7,76 5,2 -26,09 15,03 ∞,5 3,27 3,27 5,2 -32,73 34,66 ∞,5 5,42 5,42 10,2 3,32 6,67 ∞,10 0,53 0,53 10,2 4,41 17,23 ∞,10 1,67 1,67 20,2 5,55 5,58 ∞,20 0,01 0,01 20,2 7,75 8,57 ∞,20 0,10 0,10 ∞,2 5,57 5,57 ∞,∞ 0,00 0,00 ∞,2 7,76 7,76 ∞,∞ 0,00 0,00 90 2,2 n.s. n.s. ∞,2 8,30 8,30 2,2 -13716,58 68,27 ∞,2 9,69 9,69 5,2 -435,68 30,78 ∞,5 6,61 6,61 5,2 44,20 50,37 ∞,5 8,26 8,26 10,2 -6,74 13,60 ∞,10 2,49 2,49 10,2 -8,51 30,93 ∞,10 4,30 4,30 20,2 7,53 8,64 ∞,20 0,20 0,20 20,2 8,74 14,61 ∞,20 0,79 0,79 ∞,2 8,30 8,30 ∞,∞ 0,00 0,00 ∞,2 9,69 9,69 ∞,∞ 0,00 0,00 10 80 2,2 -4194,70 45,35 ∞,2 3,36 3,36 2,2 -2132,91 79,91 ∞,2 6,31 6,31 5,2 -2,64 19,70 ∞,5 1,26 1,26 5,2 -23,01 68,69 ∞,5 5,02 5,02 10,2 3,23 4,80 ∞,10 0,08 0,08 10,2 3,30 52,57 ∞,10 2,53 2,53 20,2 3,36 3,37 ∞,20 0,00 0,00 20,2 7,56 30,90 ∞,20 0,50 0,50 ∞,2 3,36 3,36 ∞,∞ 0,00 0,00 ∞,2 6,31 6,31 ∞,∞ 0,00 0,00 85 2,2 -2,1E+04 52,70 ∞,2 4,56 4,56 2,2 -6600,54 -54,14 ∞,2 6,84 6,84 5,2 -22,65 28,21 ∞,5 2,62 2,63 5,2 -66,98 75,83 ∞,5 5,96 5,96 10,2 3,08 8,99 ∞,10 0,42 0,42 10,2 -3,57 62,49 ∞,10 3,75 3,75 20,2 4,55 4,63 ∞,20 0,01 0,01 20,2 7,41 42,28 ∞,20 1,23 1,23 ∞,2 4,56 4,56 ∞,∞ 0,00 0,00 ∞,2 6,84 6,84 ∞,∞ 0,00 0,00 90 2,2 n.s. n.s. ∞,2 6,77 6,77 2,2 n.s. n.s. ∞,2 7,34 7,34 5,2 -413,42 41,94 ∞,5 5,47 5,47 5,2 -416,86 83,14 ∞,5 6,91 6,91 10,2 -6,81 19,13 ∞,10 2,06 2,06 10,2 -27,44 73,24 ∞,10 5,30 5,30 20,2 6,19 7,77 ∞,20 0,17 0,17 20,2 3,51 56,57 ∞,20 2,66 2,66 ∞,2 6,77 6,77 ∞,∞ 0,00 0,00 ∞,2 7,34 7,34 ∞,∞ 0,00 0,00

Random inter-arrival time Constant processing time Constant inter-arrival time

Table 5: Relative influence of initial and closing control loops for three stages

Batch size Utilization set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT%

1 80 2,∞ -1,22 6,45 ∞,2 3,72 3,72 2,∞ 3,63 22,70 ∞,2 6,12 6,12 5,∞ -0,08 0,23 ∞,5 1,45 1,45 5,∞ 1,99 7,72 ∞,5 3,35 3,35 10,∞ 0,00 0,00 ∞,10 0,09 0,09 10,∞ 0,37 1,11 ∞,10 0,57 0,57 20,∞ 0,00 0,00 ∞,20 0,00 0,00 20,∞ 0,01 0,02 ∞,20 0,01 0,01 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 85 2,∞ -1,5E+00 9,74 ∞,2 5,57 5,57 2,∞ 4,53 27,15 ∞,2 7,76 7,76 5,∞ -0,32 0,90 ∞,5 3,27 3,27 5,∞ 3,16 12,48 ∞,5 5,42 5,42 10,∞ -0,01 0,02 ∞,10 0,53 0,53 10,∞ 1,02 3,15 ∞,10 1,67 1,67 20,∞ 0,00 0,00 ∞,20 0,01 0,01 20,∞ 0,06 0,16 ∞,20 0,10 0,10 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 90 2,∞ -1,13 14,30 ∞,2 8,30 8,30 2,∞ 5,59 32,24 ∞,2 9,69 9,69 5,∞ -0,60 3,32 ∞,5 6,61 6,61 5,∞ 4,69 19,44 ∞,5 8,26 8,26 10,∞ -0,08 0,32 ∞,10 2,49 2,49 10,∞ 2,49 8,19 ∞,10 4,30 4,30 20,∞ 0,00 0,00 ∞,20 0,20 0,20 20,∞ 0,47 1,28 ∞,20 0,79 0,79 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 10 80 2,∞ 2,66 29,05 ∞,2 3,36 3,36 2,∞ 8,17 60,61 ∞,2 6,31 6,31 5,∞ 1,09 6,50 ∞,5 1,26 1,26 5,∞ 7,03 49,52 ∞,5 5,02 5,02 10,∞ 0,02 0,08 ∞,10 0,08 0,08 10,∞ 5,10 35,34 ∞,10 2,53 2,53 20,∞ 0,00 0,00 ∞,20 0,00 0,00 20,∞ 2,58 17,67 ∞,20 0,50 0,50 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 85 2,∞ 2,2E+00 28,50 ∞,2 4,56 4,56 2,∞ 8,71 63,23 ∞,2 6,84 6,84 5,∞ 1,59 8,47 ∞,5 2,62 2,63 5,∞ 7,88 54,48 ∞,5 5,96 5,96 10,∞ 0,09 0,35 ∞,10 0,42 0,42 10,∞ 6,25 42,57 ∞,10 3,75 3,75 20,∞ 0,00 0,00 ∞,20 0,01 0,01 20,∞ 3,83 25,71 ∞,20 1,23 1,23 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 90 2,∞ 1,73 28,32 ∞,2 6,77 6,77 2,∞ 9,17 65,66 ∞,2 7,34 7,34 5,∞ 2,18 11,67 ∞,5 5,47 5,47 5,∞ 8,65 59,41 ∞,5 6,91 6,91 10,∞ 0,44 1,62 ∞,10 2,06 2,06 10,∞ 7,42 50,40 ∞,10 5,30 5,30 20,∞ 0,01 0,02 ∞,20 0,17 0,17 20,∞ 5,35 36,07 ∞,20 2,66 2,66 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00 ∞,∞ 0,00 0,00

(27)

26

Table 6: Relative influence on the optimal configuration for four stages

Batch size Utilization set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT% 1 805,5,5 -2,64 2,34 ∞,5,5 0,92 0,92 ∞,∞,5 2,59 2,595,5,5 -3,98 -0,06 ∞,5,5 1,28 1,28 ∞,∞,5 3,13 3,13 10,5,5 0,14 1,24 ∞,10,5 2,49 2,49 ∞,∞,10 0,31 0,31 10,5,5 1,15 8,60 ∞,10,5 3,10 3,10 ∞,∞,10 0,52 0,52 20,5,5 0,86 0,95 ∞,20,5 2,59 2,59 ∞,∞,20 0,00 0,00 20,5,5 1,15 1,47 ∞,20,5 3,13 3,13 ∞,∞,20 0,01 0,01 50,5,5 0,92 0,92 ∞,50,5 2,59 2,59 ∞,∞,50 0,00 0,00 50,5,5 1,28 1,28 ∞,50,5 3,13 3,13 ∞,∞,50 0,00 0,00 ∞,5,5 0,92 0,92 ∞,∞,5 2,59 2,59 ∞,∞,∞ 0,00 0,00 ∞,5,5 1,28 1,28 ∞,∞,5 3,13 3,13 ∞,∞,∞ 0,00 0,00 855,5,5 -31,19 4,72 ∞,5,5 -2,67 -2,67 ∞,∞,5 4,61 4,615,5,5 -39,52 15,48 ∞,5,5 -2,96 -2,96 ∞,∞,5 5,06 5,06 10,5,5 -10,80 0,12 ∞,10,5 3,70 3,70 ∞,∞,10 1,13 1,13 10,5,5 -14,43 6,35 ∞,10,5 4,12 4,12 ∞,∞,10 1,53 1,53 20,5,5 -4,02 -2,11 ∞,20,5 4,58 4,58 ∞,∞,20 0,04 0,04 20,5,5 -5,14 -0,44 ∞,20,5 5,08 5,08 ∞,∞,20 0,09 0,09 50,5,5 -2,69 -2,66 ∞,50,5 4,61 4,61 ∞,∞,50 0,00 0,00 50,5,5 -2,98 -2,93 ∞,50,5 5,06 5,06 ∞,∞,50 0,00 0,00 ∞,5,5 -2,67 -2,67 ∞,∞,5 4,61 4,61 ∞,∞,∞ 0,00 0,00 ∞,5,5 -2,96 -2,96 ∞,∞,5 5,06 5,06 ∞,∞,∞ 0,00 0,00 905,5,5 -1846,10 18,77 ∞,5,5 -29,33 -29,33 ∞,∞,5 7,68 7,685,5,5 -1588,91 31,90 ∞,5,5 -31,13 -31,13 ∞,∞,5 7,73 7,73 10,5,5 -402,86 -0,95 ∞,10,5 1,17 1,17 ∞,∞,10 3,56 3,56 10,5,5 -409,00 14,71 ∞,10,5 0,59 0,59 ∞,∞,10 4,02 4,02 20,5,5 -82,41 -17,25 ∞,20,5 7,32 7,32 ∞,∞,20 0,46 0,46 20,5,5 -94,88 -4,47 ∞,20,5 7,38 7,38 ∞,∞,20 0,72 0,72 50,5,5 -32,33 -28,08 ∞,50,5 7,68 7,68 ∞,∞,50 0,00 0,00 50,5,5 -35,18 -25,46 ∞,50,5 7,73 7,73 ∞,∞,50 0,00 0,00 ∞,5,5 -29,33 -29,33 ∞,∞,5 7,68 7,68 ∞,∞,∞ 0,00 0,00 ∞,5,5 -31,13 -31,13 ∞,∞,5 7,73 7,73 ∞,∞,∞ 0,00 0,00 10 805,5,5 -1,80 6,69 ∞,5,5 0,93 0,93 ∞,∞,5 2,28 2,285,5,5 -21,60 46,26 ∞,5,5 -1,66 -1,66 ∞,∞,5 4,22 4,22 10,5,5 0,24 1,78 ∞,10,5 2,21 2,21 ∞,∞,10 0,27 0,27 10,5,5 -9,57 34,87 ∞,10,5 3,53 3,53 ∞,∞,10 1,66 1,66 20,5,5 0,88 0,98 ∞,20,5 2,28 2,28 ∞,∞,20 0,00 0,00 20,5,5 -3,38 19,54 ∞,20,5 4,36 4,36 ∞,∞,20 0,20 0,20 50,5,5 0,93 0,93 ∞,50,5 2,28 2,28 ∞,∞,50 0,00 0,00 50,5,5 -1,59 2,31 ∞,50,5 4,22 4,22 ∞,∞,50 0,00 0,00 ∞,5,5 0,93 0,93 ∞,∞,5 2,28 2,28 ∞,∞,∞ 0,00 0,00 ∞,5,5 -1,66 -1,66 ∞,∞,5 4,22 4,22 ∞,∞,∞ 0,00 0,00 855,5,5 -28,92 11,13 ∞,5,5 -2,35 -2,35 ∞,∞,5 4,12 4,125,5,5 -93,45 55,56 ∞,5,5 -10,93 -10,93 ∞,∞,5 5,37 5,37 10,5,5 -10,03 2,66 ∞,10,5 3,32 3,32 ∞,∞,10 1,01 1,01 10,5,5 -45,70 45,27 ∞,10,5 1,87 1,87 ∞,∞,10 2,87 2,87 20,5,5 -3,59 -1,41 ∞,20,5 4,09 4,09 ∞,∞,20 0,04 0,04 20,5,5 -22,43 29,49 ∞,20,5 5,34 5,34 ∞,∞,20 0,64 0,64 50,5,5 -2,37 -2,37 ∞,50,5 4,12 4,12 ∞,∞,50 0,00 0,00 50,5,5 -11,84 2,21 ∞,50,5 5,40 5,40 ∞,∞,50 0,00 0,00 ∞,5,5 -2,35 -2,35 ∞,∞,5 4,12 4,12 ∞,∞,∞ 0,00 0,00 ∞,5,5 -10,93 -10,93 ∞,∞,5 5,37 5,37 ∞,∞,∞ 0,00 0,00 905,5,5 -1708,38 24,95 ∞,5,5 -27,13 -27,13 ∞,∞,5 7,07 7,075,5,5 -892,66 67,37 ∞,5,5 -48,33 -48,31 ∞,∞,5 6,70 6,70 10,5,5 -385,60 6,12 ∞,10,5 1,05 1,05 ∞,∞,10 3,29 3,29 10,5,5 -376,93 58,51 ∞,10,5 -7,09 -7,09 ∞,∞,10 4,69 4,69 20,5,5 -79,03 -11,98 ∞,20,5 6,73 6,73 ∞,∞,20 0,43 0,43 20,5,5 -151,26 76,24 ∞,20,5 4,67 4,67 ∞,∞,20 1,86 1,86 50,5,5 -29,96 -25,47 ∞,50,5 7,07 7,07 ∞,∞,50 0,00 0,00 50,5,5 -66,26 11,51 ∞,50,5 6,79 6,79 ∞,∞,50 0,09 0,09 ∞,5,5 -27,13 -27,13 ∞,∞,5 7,07 7,07 ∞,∞,∞ 0,00 0,00 ∞,5,5 -48,33 -48,31 ∞,∞,5 6,70 6,70 ∞,∞,∞ 0,00 0,00

Random inter-arrival time Constant processing time Constant inter-arrival time

Table 7: Relative influence of initial, intermediate, and closing control loops for four stages

Batch size Utilization set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT% set TTT% STT% 1 805,∞,∞ -0,04 0,09 ∞,5,∞ 0,62 0,62 ∞,∞,5 2,59 2,595,∞,∞ 0,92 3,65 ∞,5,∞ 1,47 1,47 ∞,∞,5 3,13 3,13 10,∞,∞ 0,00 0,00 ∞,10,∞ -22,23 -22,23 ∞,∞,10 0,31 0,3110,∞,∞ 0,17 0,51 ∞,10,∞ 0,26 0,26 ∞,∞,10 0,52 0,52 20,∞,∞ 0,00 0,00 ∞,20,∞ -67,03 -67,03 ∞,∞,20 0,00 0,0020,∞,∞ 0,00 0,01 ∞,20,∞ 0,00 0,00 ∞,∞,20 0,01 0,01 50,∞,∞ 0,00 0,00 ∞,50,∞ 0,00 0,00 ∞,∞,50 0,00 0,00 50,∞,∞ 0,00 0,00 ∞,50,∞ 0,00 0,00 ∞,∞,50 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 855,∞,∞ -0,15 0,35 ∞,5,∞ 1,32 1,32 ∞,∞,5 4,61 4,615,∞,∞ 1,48 5,89 ∞,5,∞ 2,38 2,38 ∞,∞,5 5,06 5,06 10,∞,∞ -0,01 0,01 ∞,10,∞ 0,24 0,24 ∞,∞,10 1,13 1,13 10,∞,∞ 0,49 1,49 ∞,10,∞ 0,75 0,75 ∞,∞,10 1,53 1,53 20,∞,∞ 0,00 0,00 ∞,20,∞ 0,01 0,01 ∞,∞,20 0,04 0,04 20,∞,∞ 0,03 0,08 ∞,20,∞ 0,05 0,05 ∞,∞,20 0,09 0,09 50,∞,∞ 0,00 0,00 ∞,50,∞ 0,00 0,00 ∞,∞,50 0,00 0,00 50,∞,∞ 0,00 0,00 ∞,50,∞ 0,00 0,00 ∞,∞,50 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 905,∞,∞ -0,26 1,34 ∞,5,∞ -34,85 -34,85 ∞,∞,5 7,68 7,685,∞,∞ 2,19 9,20 ∞,5,∞ 3,60 3,60 ∞,∞,5 7,73 7,73 10,∞,∞ -0,04 0,13 ∞,10,∞ -37,04 -37,04 ∞,∞,10 3,56 3,56 10,∞,∞ 1,17 3,88 ∞,10,∞ 1,89 1,89 ∞,∞,10 4,02 4,02 20,∞,∞ 0,00 0,00 ∞,20,∞ -38,33 -38,33 ∞,∞,20 0,46 0,46 20,∞,∞ 0,22 0,58 ∞,20,∞ 0,35 0,35 ∞,∞,20 0,72 0,72 50,∞,∞ 0,00 0,00 ∞,50,∞ -38,45 -38,45 ∞,∞,50 0,00 0,00 50,∞,∞ 0,00 0,00 ∞,50,∞ 0,00 0,00 ∞,∞,50 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ -38,45 -38,45 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 10 805,∞,∞ 0,58 3,24 ∞,5,∞ 7,97 7,97 ∞,∞,5 2,28 2,285,∞,∞ 4,13 32,32 ∞,5,∞ 2,76 2,76 ∞,∞,5 4,22 4,22 10,∞,∞ 0,01 0,04 ∞,10,∞ 7,41 7,41 ∞,∞,10 0,27 0,27 10,∞,∞ 2,93 22,99 ∞,10,∞ 1,34 1,34 ∞,∞,10 1,66 1,66 20,∞,∞ 0,00 0,00 ∞,20,∞ 7,37 7,37 ∞,∞,20 0,00 0,00 20,∞,∞ 1,43 11,41 ∞,20,∞ 0,27 0,27 ∞,∞,20 0,20 0,20 50,∞,∞ 0,00 0,00 ∞,50,∞ 7,37 7,37 ∞,∞,50 0,00 0,00 50,∞,∞ 0,16 1,27 ∞,50,∞ 0,00 0,00 ∞,∞,50 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 7,37 7,37 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 855,∞,∞ 0,79 4,03 ∞,5,∞ -10,22 -10,22 ∞,∞,5 4,12 4,125,∞,∞ 4,75 35,94 ∞,5,∞ 3,37 3,37 ∞,∞,5 5,37 5,37 10,∞,∞ 0,05 0,18 ∞,10,∞ -11,34 -11,34 ∞,∞,10 1,01 1,01 10,∞,∞ 3,72 28,02 ∞,10,∞ 2,08 2,08 ∞,∞,10 2,87 2,87 20,∞,∞ 0,00 0,00 ∞,20,∞ -11,58 -11,58 ∞,∞,20 0,04 0,04 20,∞,∞ 2,22 16,85 ∞,20,∞ 0,66 0,66 ∞,∞,20 0,64 0,64 50,∞,∞ 0,00 0,00 ∞,50,∞ -11,59 -11,59 ∞,∞,50 0,00 0,00 50,∞,∞ 0,48 3,40 ∞,50,∞ 0,01 0,01 ∞,∞,50 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ -11,59 -11,59 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 905,∞,∞ 1,01 5,29 ∞,5,∞ -46,25 -46,25 ∞,∞,5 7,07 7,075,∞,∞ 5,40 39,76 ∞,5,∞ 3,94 3,94 ∞,∞,5 6,70 6,70 10,∞,∞ 0,22 0,76 ∞,10,∞ -48,42 -48,42 ∞,∞,10 3,29 3,29 10,∞,∞ 4,61 33,70 ∞,10,∞ 2,92 2,92 ∞,∞,10 4,69 4,69 20,∞,∞ 0,00 0,01 ∞,20,∞ -49,71 -49,71 ∞,∞,20 0,43 0,43 20,∞,∞ 3,29 24,10 ∞,20,∞ 1,40 1,40 ∞,∞,20 1,86 1,86 50,∞,∞ 0,00 0,00 ∞,50,∞ -49,83 -49,83 ∞,∞,50 0,00 0,00 50,∞,∞ 1,19 8,48 ∞,50,∞ 0,11 0,11 ∞,∞,50 0,09 0,09 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ -49,83 -49,83 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00 ∞,∞,∞ 0,00 0,00

(28)

27

6 Discussion

As make-to-order companies often produce products in small quantities and for a relatively large number of different customers orders and their routings are not known in advance and production cannot commence until after the order has arrived. These difficulties are reflected in the complexity of the physical layout of the shop floor and the number of routings used. As stated, this make achieving short and reliable throughput and delivery times more difficult. Yet, those objectives are becoming increasingly more important, especially for make-to-order companies. Therefore, these companies should use a material control system which takes these difficulties into account.

The number of different products and the low production volumes makes the use of dedicated shop floor resources more difficult and costly. Therefore, shop floor resources are often generic and shared between different product types. Product-anonymous and more specifically route-specific material control systems are able to utilize these shared workstations to balance the workload, as long as there are multiple downstream workstations. As Polca uses route-specific information to control the flow of orders by prioritizing those orders that have different routing requirements from those already present downstream on the shop floor. Polca is able to take advantage of some of the characteristics of the shop floor topology in order to effectively balance the workload.

(29)

28

(average) total throughput time. The outcome confirms that the chosen shop floor topology indeed does affect the effective workload balancing capability of Polca. However, the relation between the effective workload balancing capability and the shop floor topology is not as straightforward as was initially expected.

We have reviewed both topologies with a restricted optimal configuration and an unrestricted optimal configuration. Furthermore, we have looked at the deviation in (average) total and (average) shop floor throughput time resulting from independent changes to the number of cards in each of the control loops for both the topologies.

(30)

29

performance increase can be attributed to the increased choice resulting from the increase in the number of downstream workstations. However, due to the increase in the number of workstations the processing time variability has a larger impact on the throughput time performance of the four-stage topology in comparison to the three-stage topology.

Second, the results for the unrestricted configuration showed the four-stage topology to outperform the three-stage topology as well. Again, the influence of the inter-arrival variability results in a better performance of the three-stage shop floor topology, However, unlike with the restricted configuration the tree-stage topology is only able to outperform the four-stage topology in case of a batch size of ten. Furthermore, an increase in batch size results in a decrease in the reduction of (average) total throughput time. This holds for both topologies and for most of the experimental designs. Although, the increase in batch size decreases the performance for both topologies, the decrease in performance for the four-stage topology is larger. This different response for both topologies could also be seen for the restricted configurations. Again, the internal queue of the first workstation or order pool acts not only as a buffer against the variability of inter-arrival times, but also against the simultaneous arrival of a large number of orders.

Third, when considering each of the sets of control loops independently the last set of control loops has the greatest influence on the effective workload balancing capability. For both the three-stage and the four-stage topologies the optimal configuration results in a segmentation of the production systems. These findings are similar to those by Germs and Riezebos (2009). For most experimental designs of the three-stage topology the number of cards in the first control loops approaches infinite. The same holds for the first two sets of control loops for the four-stage topology. Therefore, for both shop floor topologies the last control loops are responsible for the workload balancing effect. The introduction of an intermediate set of control loops does prove the last set of control loops to be responsible for the workload balancing capability for most of the experimental designs.

(31)

30

the last control loops. The first control loops in the beginning of the topology do have a large impact on throughput time performance, but only when the number of cards is set too low.

Future research could look into the increasing the choice in the upstream part of the topology. For instance by adding multiple downstream workstations for the first workstation in the upstream part of the topology. Furthermore, the models can be tested with an increase in demand variability, since demand if often highly uncertain for make-to-order companies. This might increase the importance of balancing the workload in the upstream parts of the production system.

Acknowledgements

I have really enjoyed working on this project and I would like to thank those who were involved. First, I would like to thank Gwenny Ruël for helping me find the right project. I would also like to thank Jan Riezebos and Remco Germs for their advice and insights. Your advice allowed me to gain a new found appreciation for academic research and all the intricacies involved. Furthermore, I would like to thank Frank Schothorst for providing me with additional resources to run the numerous simulations. Finally, I would like to thank Ineke Haakma for supporting me every step of the way.

References

[1] Amaro, G., Hendry, L. & Kingsman, B., 1999. Competitive advantage, customization and a new taxonomy for non make-to-stock companies. International Journal of

Operations & Production Management, 19(4), pp.349-371.

[2] Fernandes, N. & do Carmo-Silva, S. 2006., Generic POLCA - A production and materials flow control mechanism for quick response manufacturing. International

Journal of Production Economics, 104(1), pp.74-84.

[3] Framinan, J. M., Gonzalez-R, P. L., & Ruiz-Usano, R. R., 2006. Dynamic card controlling in a Conwip system. International Journal of Production Economics, 99(1), pp.102-116.

[4] Gaury, E. 2000., Designing pull production control systems: customization and robustness, CentER Dissertation Series, Tilburg University.

[5] Gaury, E.; Pierreval, H. & Kleijnen, J. 2000., An evolutionary approach to select a pull system among Kanban, Conwip and Hybrid. Journal of Intelligent

(32)

31

[6] Gaury, E. G. A.; Kleijnen, J. & Pierreval, H., 2001. A methodology to customize pull control systems. Journal of the Operational Research Society, 52(1), pp.789-799. [7] Germs, R. & Riezebos, J., 2009. Workload balancing capability of pull systems in

MTO production. International Journal of Production Research, pp.1-16.

[8] Gonzalez-R, P. L. & Framinan, J. M., 2009. The pull evolution: from Kanban to customized token-based systems. Production Planning & Control: The Management of Operations, 20(3), pp.276-287.

[9] Gstettner, S. & Kuhn , H., 1996. Analysis of production control systems Kanban and CONWIP. International journal of production research, 34(11), pp.3253-3273. [10] Gupta, P. Y., and Gupta, C. M., 1989. A system dynamic model for a multi-stage

multi-line dual-card JIT-Kanban system. International Journal of Production

Research, 27(2), pp.309-352.

[11] Haskose, A.; Kingsman, B. & Worthington, D., 2004. Performance analysis of make-to-order manufacturing systems under different workload control regimes.

International journal of production economics , 90(2), pp.169-186.

[12] Hendry, L. & Kingsman, B., 1989. Production planning systems and their applicability to make-to-order companies. European Journal of Operational

Research, 40(1), pp.1-15.

[13] Hopp, W. & Spearman, M., 2008. Factory physics. Boston: Irwin/McGraw-Hill. [14] Hopp, W. J. & Spearman, M. L., 2004. To Pull or Not to Pull: What Is the Question?

Manufacturing & Service Operations Management, 6(2), pp.133 – 148.

[15] Huang, P. Y., Rees, P. R., & Taylor, B. W., 1983. A Simulation Analysis of the Japanese Just-In-Time Technique (with Kanbans) for a Multiline, Multistage Production System. Decision Sciences, 14(3), pp.326 – 344.

[16] Johnson, D. J. 2003. A Framework for Reducing Manufacturing Throughput Time.

Journal of Manufacturing Systems, 22(4), pp.283-298.

[17] Jonsson, P. & Mattsson, S., 2003. The implications of fit between planning environments and manufacturing planning and control methods. International