Starvation Avoidance in POLCA systems

Starvation Avoidance in POLCA systems

A simulation study on the effects of starvation

avoidance dispatching rules

Master Thesis

Niels Venhuizen S2334186

MSc. Technology & Operations Management

University of Groningen, Faculty of Economics and Business

June 26, 2017

Supervisor: N. Ziengs, MSc.

2 Abstract

Purpose: POLCA is a pull production control system that aims to reduce throughput times

and to create a balanced distribution of orders (workload) among workstations on a shop floor (Riezebos, 2010). To do so, POLCA controls the number of orders on the shop floor. Previous literature (Germs & Riezebos, 2010) shows that POLCA systems do not perfectly detect and signal imbalances in workload. These imbalances, together with applying an upper workload limit, lead to starvation of workstations. This paper aims to reduce starvation in POLCA systems by incorporating starvation avoidance dispatching rules. These rules control the sequence in which orders are allowed to be processed by workstations, based on shop floor conditions (e.g. starving workstations).

Method: A discrete-event simulation is used to model a divergent production network with

route-specific customer orders, as in a Make-to-Order environment. Two starvation avoidance dispatching rules are incorporated in POLCA, which both use different mechanisms to prioritize orders in a queue in front of a workstation, to avoid starvation at direct downstream workstations. The performances of these systems are compared to other production control systems.

Findings: It is shown that incorporating the starvation avoidance dispatching rules in POLCA,

improves workload balancing and thus leads to less starvation. As a result, total throughput times of orders are significantly shortened. Besides, it turns out that optimal POLCA configurations hardly limit work-in-progress and therefore almost behave as push systems. As a result, most advantages of POLCA for practice are lacking in these configurations.

Contribution: This study provides two methods to decrease starvation in POLCA systems.

Furthermore, it adds to literature by showing how the mechanisms of existing release triggers can be used as dispatching rules, in order to make them suitable for flow production structures. Finally, we conclude that the suggestion by Stevenson et al. (2005) that POLCA is suitable for MTO environments, is rather questionable.

Keywords: POLCA; starvation; workload balancing; make-to-order production; simulation

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List of Abbreviations

COBACABANA Control of Balance by Card-Based Navigation CONWIP Constant Work In Progress

CV Coefficient of Variation

FCFS First Come First Serve

LUMS COR Lancaster University Management School Corrected Order Release MRP Material Requirements Planning

MTO Make-To-Order

NINQ Number In Next Queue

OPT Order Pool Time

PC Production Control

POLCA Paired-cell Overlapping Loops of Cards with Authorization

PPC Production Planning and Control

PT+WINQ Processing Times + Workload In Next Queue

STT Shop floor Throughput Time

TTT Total Throughput Time

WCPRD Work Center Planned Release Date

4 Contents Abstract ... 2 List of Abbreviations ... 3 1. Introduction ... 5 2. Theoretical Background ... 7 3. Methodology ... 12 §3.1 Model Design ... 12 §3.2 Experimental Design ... 16 §3.3 Model Validation ... 17

4. Results & Interpretations ... 18

§4.1 POLCA +SA ... 18

§4.2 POLCA +lowerbounds ... 20

§4.3 Comparison in System Performances ... 22

5. Discussion ... 24

6. Conclusion ... 27

References ... 28

Appendix A – Welch Method ... 31

Appendix B – Mechanism of +lowerbounds ... 33

Appendix C – OPT as percentage of TTT ... 34

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1. Introduction

Global competition and changing customer requirements cause major challenges for companies that produce make-to-order (MTO) goods. In order to stay competitive, firms need to simultaneously reduce lead times, while guaranteeing high delivery reliability. One way of achieving this is by improving production planning and control systems (Fernandes et al., 2016).

A special category of production control systems are pull systems (Germs & Riezebos, 2010). These systems control throughput times of orders by limiting the amount of work-in-progress (WIP) on the shop floor (Hopp & Spearman, 2004). In this study, we focus on a pull system called ´Paired Overlapping Loops of Cards´ (POLCA), because POLCA seems to be one of the most suitable production control systems for MTO companies (Stevenson et al., 2005). POLCA (Suri, 1998) is a pull system, like Kanban (Sugimori et al., 1977) and CONWIP (Spearman et al., 1990), since work-in-progress is limited by cards (Hopp & Spearman, 2004). POLCA aims to reduce throughput times and to create a balanced distribution of orders (workload) among workstations on a shop floor (Riezebos, 2010).

The problem is that POLCA only proves to balance workload effectively in systems without processing time variability. When processing time variability is present, the workload balancing capabilities of POLCA erode (Germs & Riezebos, 2010; Ziengs et al., 2012). POLCA is not able to perfectly detect and signal imbalances in workload (Germs & Riezebos, 2010). As a result, in front of certain workstations queues may form, whereas some other workstations may starve and wait for orders to be processed.

In literature, starvation is mentioned as a problem in pull systems (e.g. Fernandes et al., 2016; Land & Gaalman, 1998). For a few specific pull systems, methods to decrease starvation can be found. For example, Thürer et al. (2015) developed a starvation avoidance method for COBACABANA and Fernandes et al. (2016) incorporated starvation avoidance triggers in continuous release systems. Furthermore, there are some dispatching rules that control the sequence in which orders are allowed to be processed by workstations, based on shop floor conditions (e.g. starving workstations) (Holthaus & Rajendran, 1997). However, no specific method for decreasing starvation in POLCA systems is available.

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incorporating these dispatching rules, the workload balancing capabilities of POLCA can be improved. As a result, starvation is expected to reduce and throughput times are expected to decrease.

To address our aim, we conduct a discrete event simulation study. The simulation evaluates system performance of five different production control systems, based on indicators as shop floor time and total throughput time. The used production control systems are: a push system and a POLCA system that both do not take shop floor conditions in to account, a push system that does take shop floor conditions into account, and two POLCA system with two different mechanisms that prioritize orders based on shop floor conditions. The performances of the five systems are compared, in order to identify the effects of the dispatching rules on workload balancing. These systems are tested in a divergent production topology with three successive stages, in which the number of workstations doubles at each production stage, resulting in seven workstations.

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2. Theoretical Background

Production Planning and Control

According to Stevenson et al. (2005), Production Planning and Control (PPC) systems are important tools for manufacturers. They describe the main goals of PPC systems as reducing WIP, minimizing throughput times, decreasing inventory costs and increasing responsiveness to changes in demand. Land & Gaalman (2009) categorize three main successive activities of PPC systems: order acceptance, order release and dispatching.

In this paper, we focus on order release and dispatching, since POLCA fulfills these two activities. Zäpfel & Missbauer (1993) distinguish systems that only consider order release and order dispatching as Production Control (PC) systems. The function of order release is to decide the sequence and the time when orders in the order pool are allowed to enter the shop floor. Dispatching rules control the sequence in which orders at the shop floor are allowed to be processed by workstations (Land & Gaalman, 1998).

There are numerous types of production control systems available in literature, like MRP (Orlicky, 1975), Kanban (Sugimori et al., 1977), CONWIP (Spearman et al., 1990) and POLCA (Suri, 1998). For extensive literature reviews about PPC and PC systems, we refer the reader to Zäpfel & Missbauer (1993), Hopp & Spearman (2004) and Stevenson et al. (2005). In general, PPC systems can be categorized in two types: push and pull systems.

Push versus Pull

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Although the way in which pull production control systems use cards to limit WIP differs, they have common advantages. The main advantages of pull systems are shorter shop floor throughput times due to lower average WIP (Hopp & Spearman, 2004). In addition, holding costs are reduced (Hopp & Spearman, 2008) and throughput flows become smoother and more predictable (Hopp & Spearman, 2004). Hopp & Spearman (2004) also argue that short queues will lead to higher quality since time between creation and detection of defects are reduced. According to Cheng & Podolsky (1993), pull systems are by far more responsive to problems and changes in downstream processes, than push systems.

POLCA

Riezebos (2010) provides a clear description about the working of POLCA systems. POLCA is a system that regulates the authorization of orders and controls the flow of work on the shop floor. It aims to decrease total throughput time and to reduce unbalances in the system. To do so, it uses overlapping control loops, which control the WIP in pairs of workstations. As shown in figure 2.1, each control loop introduces two queues for each workstation (A, B, C) on the shop floor. The one queue for storing the physical orders, the other queue for POLCA cards, in figure 2.1 indicated as PolcaXX. An order is not allowed to leave the queue in front of a workstation, until the required production card is available.

For example, an order that have to be processed by workstations A and B, waits in Queue AB until a production card AB becomes available. Then the order, attached with the card, is allowed to enter workstation A. After being processed in workstation A, the order moves to Queue BC. Again, when a card BC becomes available, the order is allowed to enter workstation B. After being processed by workstation B, the order moves to the subsequent queue and the card AB moves back to the queue in front of workstation A. As a result, a new order, which has to be processed by workstations A and B, is allowed to enter workstation A.

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The idea behind these overlapping control loops is that an order only will use capacity in an upstream workstation if it is expected that the subsequent downstream workstation will be available for further processing of the order. In divergent topologies, it can be possible that orders have another subsequent workstation in their routing then workstation B. In that case, workstation A does not have to stay idle when no AB cards are available, but it can produce orders with another routing for which cards are available.

Note that these overlapping control loops together form a route-specific control of material flow. Route-specific control is a special type of so-called product anonymous control. In contrast to product-specific control (as used in Kanban), product-anonymous control, controls the WIP on a shop floor irrespective of product types. Route-specific control, however, takes into account the availability of capacity in downstream workstations in the routing of an order (Riezebos, 2010). By doing so, POLCA aims to create a balanced distribution of the orders among the workstations on the shop floor. This control behavior is called workload balancing (Germs & Riezebos, 2010). Effective workload balancing results in both shop floor throughput time and total throughput time reductions compared to push systems (Germs & Riezebos, 2010).

POLCA in MTO environments

The route-specific control of POLCA is the reason that Stevenson et al. (2005) notice that POLCA seems to be applicable for MTO environments. MTO firms generally have a comprehensive range of products, which are produced in low frequencies (Krishnamurthy et al., 2004), in literature this called non-repeat production.

In product-specific control systems like Kanban, cards are directly linked to specific products. In case of non-repeat production, this would lead to an impractical high number of cards (Riezebos, 2010). Therefore, product-specific control is not applicable for firms with a high degree of product or routing variety (Krishnamurthy et al., 2004; Spearman et al., 1990). POLCA creates allowance for non-repeat production (e.g. highly customized products), by using a kind of product-anonymous control (route-specific cards), since an increase in the number of products does not result in an explosion of the number of cards. Although Stevenson et al. (2005) notice that POLCA seems to be suitable for MTO environments because of this allowance for non-repeat production, they notice that more research is needed for decisive conclusions about the applicability of POLCA in MTO environments.

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Starvation in POLCA systems

Land & Gaalman (1998) and Fernandes et al. (2016) state that systems applying upper workload limits, like POLCA, suffer from premature idleness. Orders are withheld in the order pool although a workstation is starving, due to workload situations at other workstations. Especially in divergent production lines, pull control mechanisms may result in losing output due to starvation (Farnoush & Wiktorsson, 2013). It is exactly these unbalances which cause starvation that POLCA aims to prevent (Riezebos, 2010), by workload balancing (see figure 2.2). However, Germs & Riezebos (2010) show that POLCA is only able to effectively balance workload if the number of cards is determined appropriately and no processing time variability is present in the system. This workload balancing capability is mainly apparent in these divergent structures. Besides, they conclude that the overlapping loops in POLCA systems do not perfectly detect and signal imbalances in workload. These imbalances result in non-optimal total throughput times and, as shown in figure 2.2, in starvation of workstations (workstation D).

Figure 2.2: Shop floor without (a) and with (b) workload balancing (adopted from Germs & Riezebos, 2010).

Starvation Avoidance

In literature, a number of methods are available that aim to avoid starvation. One of them is the release trigger ‘Lancaster University Management School Corrected Order Release’ (LUMS COR) (Fernandes et al., 2016). This trigger pulls an order from the order pool to the shop floor when one of the workstations is starving. According to Thürer et al. (2012), LUMS COR is the best solution to reduce starvation, because of its performances and ease of implementation. Another example is ‘Work Center Planned Release Date’ (WCPRD). This method releases an order with the earliest planned release date, if the WIP of any workstation falls below a predetermined lower bound (Thürer et al., 2012).

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like a divergent topology, orders can only be released to the first production stage. Also, a release trigger will not affect the capacity signaling functions of the overlapping loops of POLCA. Therefore, a release trigger is expected to have limited effect on the workload balancing capabilities of POLCA.

Although, the mechanisms that these release triggers use to select orders from the order pool, are interesting. The lower bound mechanism of WCPRD could be used as a dispatching rule. For example, when the WIP of a downstream workstation would fall below a predetermined lower bound, the direct upstream workstation could prioritize orders for this downstream workstation to avoid starvation. Such a mechanism may improve workload balancing, since it can assist the limited capacity signaling function of the overlapping control loops in POLCA. Using the mechanism of WCPRD as a dispatching rule, would show similarities with an existing dispatching rule called ‘Number In Next Queue’ (NINQ). The idea of NINQ is to prioritize orders that will move on to the downstream workstation with the shortest queue (Haupt, 1989). While NINQ does not use lower bounds like WCPRD, it also aims to prioritize orders based on availability of downstream capacity. According to Holthaus & Rajendran (1997), rules as NINQ are able to reduce waiting times of orders by making use of the information about downstream available capacity.

In literature, a lot of other dispatching rules can be found, that prioritize orders based on downstream availability of capacity. For example, Most Capacity Slack (Thürer et al., 2017), which prioritizes orders that have the smallest effect on the availability of downstream capacity. Another example is PT+WINQ, which combines the shortest processing time rule with queue lengths at downstream workstations. Thereby its aims at minimization of throughput times of orders (Holthaus & Rajendran, 1997).

Although there are more capacity focused dispatching rules to discuss, we focus on the mechanisms of WCPRD and NINQ because of their simplicity. These dispatching rules are easy to incorporate in POLCA and seem to be able to improve workload balancing, by assisting the capacity signaling function of the overlapping control loops. Since our aim is to reduce starvation, for clarity we call them ‘starvation avoidance dispatching rules’. In the remainder of this paper, we address the following research question:

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3. Methodology

§3.1 Model Design

The aim of the research is to measure the effects of incorporating starvation avoidance dispatching rules in POLCA on workload balancing. To do so, a discrete event simulation study is conducted. A simulation study is chosen, because simulation models are able to deal with complexity, use of stochastic input and large numbers of interconnections (Robinson, 2014). Next, they are able to control the experimental settings.

The research focuses on production in MTO-environments. In these environments, production cannot start before a customer order is arrived. Next, these production environments are characterized by high routing variability, processing time variability, and inter-arrival time variability (Fernandes et al., 2016). In order to address these characteristics in the study, a divergent topology is used, which enables to simulate different product routings on a shop floor.

Divergent Topology

As in previous research on workload balancing (Germs & Riezebos, 2010; Ziengs et al., 2012), we use a divergent model existing of three successive production stages, as shown in figure 3.1. The number of workstations doubles at each stage, which results in seven workstations (A-G). In front of each workstation is a queue for orders waiting to be processed. These queues and workstations together form the shop floor. Another queue is visualized in front of the shop floor, which is the order pool, where customer orders have to wait before entering the shop floor. The release methods of the simulated production control systems determine when an order is allowed to enter the shop floor. It is assumed that all customer orders are accepted, required materials are available and all necessary information regarding routings and processing times, is known. Transfer times between workstations are negligible, there are no setup times and workstations are continuously available for production.

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These distributions, together with the divergent topology, enable the production control systems to balance the workload to their capabilities. Since these workload-balancing capabilities determine the occurrence of starvation, the model enables us to identify whether the starvation avoidance dispatching rules improve the workload balancing capabilities of POLCA, and therefore reduce starvation.

Figure 3.1: Used model (three stage topology)

Production control systems

The described model will be simulated with five different production control systems. First, a production control system without WIP limit, and therefore, according to the definition of Hopp & Spearman (2004), a push system will be used. Next, POLCA as described by Suri (1998) will be used. By using these two different production control systems, a comparison in performance between POLCA and push systems can be provided.

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POLCA, on the other hand, does use the control loops as visualized. As shown in figure 3.1, there is a queue in front of each workstation. Next to this queue, a second queue could be assumed, namely one for production cards (as shown in figure 2.1). These production cards allow orders to be processed by the workstation. For example, an order which have to be processed by workstations B and D, has to wait in the queue for workstation B until a production card BD becomes available. These production cards form together the control loops, since the number of cards in a loop determines the maximum allowed WIP for the workstations within the loop. Customer orders waiting in the order pool are released to the shop floor when a production card becomes available at the first production stage. The second and third production stages do use the FCFS policy as dispatching rule, when multiple production cards are available.

Incorporating Two Starvation Avoidance Dispatching Rules

To address the aim of the research, two different starvation avoidance dispatching rules are incorporated in POLCA. Both rules use different mechanisms to prioritize orders in a queue in front of a workstation, to avoid starvation at direct downstream workstations. Although both rules are based on existing methods (WCPRD and NINQ), they are not exactly the same. In order to avoid confusion and to make a clear distinction between the two, we name them: +lowerbounds and +SA.

The first dispatching rule, +lowerbounds, is based on the mechanism of WCPRD as described by Thürer et al. (2012). It uses lower bounds for the number of available cards at downstream POLCA control loops, to prioritize orders. In contrast to WCPRD, this rule is used as a prioritization rule for releasing and dispatching instead of only as release method. The rule prioritizes orders in the order pool or in a queue on the shop floor, when the current number of available cards at a direct downstream workstation exceeds the established lower bound. Therefore, a lower bound for the number of cards is set for all workstations.

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shown in figure B.3 in Appendix B. Finally, since the dispatching rule directly uses the number of available POLCA cards, it cannot be incorporated in a push system.

Figure 3.2: No lower bound is exceeded Figure 3.3: Workstation B exceeds the lower bound

The second dispatching rule, +SA, does not use lower bounds. This rule is based on the mechanism of NINQ (Haupt, 1989). In contrast to NINQ, +SA prioritizes orders for the downstream workstation with the most cards available (as shown in figure 3.5), instead of the shortest queue. As a result, the rule is only able to prioritize orders in a queue, when a workstation has two or more direct downstream workstations. Therefore, the rule is not able to prioritize orders in de order pool, and thus cannot be used as release rule.

The sequence of releasing orders from the order pool to the shop floor is determined by the FCFS rule. The workstations at the last production stage use the FCFS rule as well, since +SA cannot prioritize here, because of the lack of downstream workstations. The sequence of orders in the queues at the first and second production stages, are fully controlled by +SA. Although, if the number of available cards at both downstream workstations are equal, no prioritization takes place, as shown in figure 3.4.

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In contrast to +lowerbounds, +SA can be incorporated in a push system. In the simulation study, this done by using POLCA control loops with 10,000 cards. In this way, the system does not limit WIP, while the +SA mechanism is able to prioritize based on the available number of cards.

Incorporating +SA in a push system and in POLCA, and +lowerbounds in POLCA, results in five different production control systems, as presented in table 3.1.

Table 3.1: Characteristics PC systems to be used

PC system Release Method Dispatching Rules

Push FCFS FCFS

POLCA Available prod. card; FCFS Available prod. card; FCFS

Push +SA FCFS FCFS; +SA rule

POLCA +SA Available prod. card; FCFS Available prod. card; FCFS; +SA rule

POLCA +lowerbounds Available prod. card; FCFS; +lowerbounds rule

Available prod. card; FCFS; +lowerbounds rule

§3.2 Experimental Design

The simulation study exists of five main series of experiments; using five different production control systems in the divergent shop floor model. Next, within these series, several experiments will be simulated. All series of experiments and their experimental settings are summarized in table 3.2. The number of production cards in the push systems is, according to the definition of Hopp & Spearman (2004), infinite. In the POLCA experiments, the number of cards per loop varies between 1 and 65. Inter-arrival times are exponential distributed, to enable workload balancing in POLCA (Germs & Riezebos, 2010). The utilization levels of workstations are 0.8 or 0.9, which are determined by changing the processing times. These processing times are either constant, or Erlang distributed with varying coefficients of variation (CV); 0.5, 1 and 1,5. According to Hopp & Spearman (2008), these CV levels represent respectively low, medium and high variability in processing times.

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The second series of experiments incorporates the +SA dispatching rule in the push system. By doing so, we are able to measure whether the push +SA system is able to improve workload balancing in the system, while using a prioritization rule instead of FCFS. It is expected that the push +SA system will result in less long total throughput times, since the workload balance is expected to be better than in a FCFS-controlled push system.

The outcomes of the third series of experiments serve as a benchmark for evaluating what the effects are of incorporating a starvation avoidance dispatching rule in POLCA. It is expected that the third series result in shorter total throughput times, compared to the push systems. The fourth and fifth series enfold the aim of this paper; showing the actual effects of incorporating a starvation dispatching rule in POLCA. Both described rules are separately incorporated in POLCA. The outcomes show whether the rules result in better system performance in terms of workload balancing.

Table 3.2: Experimental factors

Series Experimental

factors Push Push +SA POLCA POLCA +SA

POLCA +lowerbounds

Number of cards ∞ ∞ 1-65 1-65 1-65

Inter-arrival times Exponential Exponential Exponential Exponential Exponential Processing times Constant;

Variable Constant; Variable Constant; Variable Constant; Variable Constant; Variable CV of proc. times 0.5; 1; 1.5 0.5; 1; 1.5 0.5; 1; 1.5 0.5; 1; 1.5 0.5; 1; 1.5 Utilization 0.8; 0.9 0.8; 0.9 0.8; 0.9 0.8; 0.9 0.8; 0.9 §3.3 Model Validation

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4. Results & Interpretations

In this section, the outcomes of the simulation studies are presented. These outcomes are provided in three subsections. First, the behavior and optimal configurations of POLCA +SA and POLCA +lowerbounds are presented in separate sections. Finally, the performances in workload balancing (measured in STT and TTT reductions) of these systems are compared with push and (FCFS-controlled) POLCA systems.

§4.1 POLCA +SA

In order to research the system performance of POLCA +SA, first the optimal configuration for minimizing TTT, is determined. This is done by adjusting the number of cards in the system. As initially done in the study of Germs & Riezebos (2010), we use the same number of cards for all loops. To do so, configurations with 1 up to 65 cards per loop are simulated. The outcomes of these simulations are plotted in figures 4.1 and 4.2. In these graphs, the performance of a push system is considered as index. Each marker illustrates the performance, in terms of STT and TTT, of POLCA +SA with a certain number of cards per control loop as configuration.

From the graphs, it can be noticed that adding more cards to the system improves its performance. Although, this holds to a certain point. Near to the minimum of all lines, clusters of markers are located. This means that at that certain point, adding more cards to the control loops does not result in better or worse system performance. Table C.1 in Appendix C shows that optimal POLCA +SA configurations result in minimal order pool times (OPT), which means that WIP is hardly limited.

Furthermore, it is interesting that the increase in system performance diminishes for systems with no and low processing time variability. Especially in figure 4.1, the differences in patterns between no process variability and high process variability are noticeable. This means that the increase in system performance by adding one card, is the largest for systems with high processing time variability.

19 Figure 4.1: System performances of POLCA +SA at 80% utilization

Figure 4.2: System performances of POLCA +SA at 80% utilization

Table 4.1 lists the optimal configurations of POLCA +SA with the same number of cards per loop. In addition, we have tested whether POLCA +SA would perform better when the loops in the first production stage are ‘relaxed’, as POLCA does (Ziengs et al., 2012). These results can be found in Appendix D, however it appears that POLCA +SA performs worse, when the loops in the first production stage do not limit WIP.

Table 4.1: Optimal configurations POLCA +SA

80 % Utilization 90 % Utilization

Constant processing times [9,9] [13,13]

Low processing time variability [14,14] [24,24]

Medium processing time variability [12,12] [45,45]

High processing time variability [16,16] [30,30]

75% 80% 85% 90% 95% 100% 105% 75% 80% 85% 90% 95% 100% 105% TTT STT

80% Utilization

Constant Proc. Times Low Proc. Times Variability Medium Proc. Times Variability High Proc. Times Variability

65% 70% 75% 80% 85% 90% 95% 100% 105% 65% 70% 75% 80% 85% 90% 95% 100% 105% TTT STT

90% Utilization

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§4.2 POLCA +lowerbounds

In order to optimize system performances of POLCA +lowerbounds, several lower bound levels are simulated. All these simulations used the card configuration as was found optimal for POLCA. As done by POLCA +SA, we used the same number of cards in each loop. For example, if an optimal POLCA configuration counts 26 cards per loop, lower bound levels from 10 up to 25 are simulated. The results of these simulations are plotted in figures 4.3 and 4.4. Performance is measured in TTT as percentage of TTT results by push systems.

From figures 4.3 and 4.4 can be concluded that establishing a too high lower bound level significantly affects system performance. This can be observed by the steep increases in the graphs. Next, establishing a too low lower bound results in small performance losses, compared to the optimal lower bound level.

Figure 4.3: System performance at different lower bound levels (80 % utilization)

Figure 4.4: System performance at different lower bound levels (90 % utilization)

75% 80% 85% 90% 95% 100% 0 5 10 15 20 25 30 35 40 TTT

Lower bound level

80% Utilization

Constant Proc. Times

Low Proc. Times Variability Medium Proc. Times Variability High Proc.Times Variability 75% 80% 85% 90% 95% 100% 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 TTT

Lower bound level

90% Utilization

Constant Proc. Times

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Furthermore, the graphs show for both utilization levels the same patterns in system performance. POLCA +lowerbounds is able to obtain larger TTT reductions in systems with 90 percent utilization, compared to systems with 80 percent utilization.

Finally, it is interesting that in case of constant processing times, TTT is reduced irrespective of the lower bound level. All used lower bound levels, from 2 up to 6 cards, result in TTT reductions compared to a push system. While in systems with processing time variability, a too high lower bound level results in the same TTT as obtained by a push system.

Table 4.2 shows the optimal lower bound levels for POLCA +lowerbounds. Notice that there is no fixed proportion between the number of cards per loop and the optimal lower bound level. The lower bound levels fluctuate between 55 and 71 percent of the number of cards per loop. Note that these fluctuations may seem to be large, while the actual difference in number of cards can be small. For example, increasing the lower bound for 90 percent utilization and low process variability with 1, would result in a proportion of 67 percent.

Table 4.2: Optimal lower bound levels

Configuration lower bound % of number of cards

80 % utilization

Constant Process Variability [7,7] 4 57%

Low Process Variability [16,16] 11 69%

Medium Process Variability [26,26] 18 69%

High Process Variability [35,35] 25 71%

90% utilization

Constant Process Variability [11,11] 6 55%

Low Process Variability [21,21] 13 62%

Medium Process Variability [41,41] 23 56%

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§4.3 Comparison in System Performances

This section provides a comparison in performances of the five different PC systems that are used in the simulation studies; push, POLCA (both controlled by FCFS), push +SA, POLCA +SA and POLCA +lowerbounds. In order to enable a comparison between the system performances, the optimal configurations for all systems are used.

Table 4.3 lists system performance differences, in terms of TTT and STT, compared to the performance of a push system controlled by FCFS. Note that reductions in both STT and TTT imply effective workload balancing (Germs & Riezebos, 2010), which reduces starvation. None of the systems results in longer STT and TTT than those of a push system.

It can be observed that in case of processing time variability, POLCA leads to modest to no reductions in STT and TTT. These outcomes are as expected from previous research (Germs & Riezebos, 2010; Ziengs, et al., 2012). Like POLCA +lowerbounds, POLCA results in larger STT reductions than POLCA +SA, when no processing time variability is present. Although, the TTT reductions of POLCA are significantly smaller than those of POLCA +SA. This emphasizes the limited workload balancing capabilities of POLCA.

It appears that POLCA +SA results in the largest TTT reductions for all levels of process time variability and utilization (up to 26.8%). In almost all cases, POLCA +SA results also in the largest STT reductions. However, when processing times are constant, POLCA +lowerbounds results in the largest STT reduction (12,1% at 90% utilization). This reduction compared to POLCA +SA, is caused by the lower number of cards that POLCA +lowerbounds uses. Notice that STT and TTT reductions for push +SA are always equal, since push does not limit WIP. Therefore, orders do not have to wait in an order pool, resulting in a STT equal to TTT. In cases of medium and high processing time variability, POLCA +lowerbounds does not limit WIP either, since its obtained STT and TTT reductions are equal. The same counts for POLCA +SA in case of medium processing time variability and 90 percent utilization.

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Table 4.3: Throughput Time Reductions compared to push (POLCA configurations optimized for minimalizing TTT)

80% utilization 90% utilization Conf. TTT reduction STT reduction Conf. TTT reduction STT reduction

Constant Processing Times

POLCA [7,7] -1.0 % -5.1 % [11,11] -2.5 % -11.7 %

Push +SA [∞,∞] -3.1 % -3.1 % [∞,∞] -5.1 % -5.1 %

POLCA +SA [9,9] -3.3 % -4.9 % [13,13] -6.1 % -12.1 %

POLCA +lowerbounds [7,7] -2.2 % -6.2 % [11,11] -4.2 % -13.2 %

Low Process Variability

POLCA [16,16] 0.0 % -0.1 % [21,21] -0.2 % -1.0 %

Push +SA [∞,∞] -9.2 % -9.2 % [∞,∞] -15.7 % -15.7 %

POLCA +SA [14,14] -9.3 % -9.4 % [24,24] - 15.7 % - 15.8 % POLCA +lowerbounds [16,16] -6.1 % -6.1 % [21,21] -9.7 % -9.8 %

Medium Process Variability

POLCA [26,26] 0.0 % 0.0 % [41,41] 0.0 % -0.1 %

Push +SA [∞,∞] -13.2 % -13.2 % [∞,∞] -21.9 % -21.9 %

POLCA +SA [12,12] -13.4 % -14.0 % [45,45] -21.9 % -21.9 % POLCA +lowerbounds [26,26] -10.8 % -10.8 % [41,41] -17.0 % -17.0 %

High Process Variability

POLCA [35,35] 0.0 % 0.0 % [63,63] 0.0 % 0.0 %

Push +SA [∞,∞] -17.4 % -17.4 % [∞,∞] -26.6 % -26.6 %

POLCA +SA [16,16] -17.8 % -18.0 % [30,30] -26.8 % -27.0 % POLCA +lowerbounds [35,35] -15.9 % -15.9 % [63,63] -23.5 % -23.5 %

24 5. Discussion

Previous research (Germs & Riezebos, 2010; Ziengs et al., 2012) show that POLCA is only able to balance workload effectively if the number of cards is determined appropriately and no processing time variability is present in the system. The outcomes of this research are in line with these studies and show that FCFS-controlled POLCA systems result in modest STT and TTT reductions compared to push systems. Thus, POLCA shows rather limited workload balancing capabilities, when processing time variability is present. As a result of these limited capabilities, starvation is likely to occur.

In order to avoid starvation, we incorporated two starvation avoidance dispatching rules in POLCA, namely +lowerbounds and +SA. Both starvation avoidance dispatching rules use very different mechanisms. The first rule, +lowerbounds, prioritizes orders in queues at upstream workstations when the number of available cards in a direct downstream control loop exceeds the established lower bound. This mechanism is based on WCPRD, which Thürer et al. (2012) use as release trigger.

Incorporating +lowerbounds in POLCA results in significant reductions in STT and TTT compared to push systems, which imply effective workload balancing according to Germs & Riezebos (2010). POLCA +lowerbounds even shows effective workload balancing capabilities in systems with processing time variability. Besides, it appears that determining the optimal value for the lower bounds is important for system performance in terms of STT and TTT. More in particular, establishing a too high lower bound level results in an explosive increase of TTT. Moreover, it appears that the optimal level of the lower bounds is not a fixed proportion of the total number of cards in the configuration (see table 4.2). As a practical implication, this dispatching rule is difficult to implement in practice, since determining the optimal level for the lower bounds requires a lot of tests.

Finally, in the way the rule is implemented, +lowerbounds does not differentiate between two downstream workstations that both exceed the lower bound (as shown in figure B.3 in Appendix B). As a result, it can happen that an order is processed first while the workstation it is destined for, is not expected to starve first. This limits the workload balancing capabilities potential of POLCA +lowerbounds.

25

inapplicability for flow production structures (like divergent topologies). Thürer et al. (2012) could use WCPRD solely as a release trigger in ‘pure’ job shop structures, without fixed production stages. Thereby we provide a valuable contribution, since especially in divergent production lines, pull mechanisms like POLCA may result in starvation (Farnoush & Wiktorsson, 2013).

The second starvation avoidance dispatching rule, +SA, does not use lower bounds. This rule prioritizes orders based on the downstream workstation with the most cards available. It appears that this simple prioritization rule is able to improve the workload balancing capabilities of POLCA, and thus to reduce STT and TTT. Besides, it turns out that optimal configurations of POLCA +SA use a different number of cards than optimal (FCFS-controlled) POLCA configurations. However, there is no pattern found to determine the number of cards, since it is not consequently higher or lower than the number of cards in an optimal POLCA configuration. In comparison with +lowerbounds, +SA results in better performances and is easier to implement in practice, because no lower bounds have to be determined. POLCA +SA, however, cannot be used as a release rule in a divergent topology with one workstation at the first production stage, since no prioritization can takes place. The mechanism of +SA is based on the dispatching rule NINQ. While NINQ prioritizes orders for the downstream queue with the least number of orders in it (Haupt, 1989), +SA prioritizes based on the number of cards available in downstream queues. By implementing the mechanism in this way, we developed a rule that makes use of the overlapping control loops of POLCA, in order to assist their capacity signaling function.

The STT and TTT reductions of both starvation avoidance dispatching rules may suggest that incorporating these in POLCA, improves the suitability of POLCA for MTO environments as is suggested by Stevenson et al. (2005). However, the results of the optimal configurations show that orders spend only a fraction of their TTT in the order pool (see table C.1 in Appendix C). This implies that the configurations almost behave as push systems. As a result, a number of advantages of POLCA for practice are lacking in these configurations.

26

therefore provide a production environment to improve product quality. Since the optimal POLCA configurations allow for longer queues, the interval between creation and detection of defects becomes larger. So, in this way POLCA does not contribute to product quality improvement. Altogether, the suitability of POLCA for MTO environments, as is suggested by Stevenson et al. (2005), is rather questionable.

This research provides some valuable insights for practitioners who are managing a POLCA system or are considering to implement POLCA. First, if a firm aims to reduce their STT and TTT, it is beneficial to use POLCA in combination with a starvation avoidance dispatching rule. Especially +SA is interesting to incorporate in POLCA, because of its performances and ease of implementation. In order to optimize system performance, the optimal number of cards in the system should be redefined. However, practitioners should be aware that optimal POLCA systems almost behave as push systems, and therefore do not involve the advantages of pull systems as discussed in literature (e.g. Hopp & Spearman, 2004).

27 6. Conclusion

POLCA is a pull system that controls WIP by assigning cards to pairs of workstations. These route-specific cards create allowance for non-repeat production. Based on that, Stevenson et al. (2005) notice that POLCA seems to be suitable for MTO environments, which are characterized by high variability in products. POLCA, however, like other pull systems, suffers from starvation caused by its WIP limits (Land & Gaalman, 1998; Fernandes et al., 2016). Next, POLCA systems do not perfectly detect and signal imbalances in workload which results in starvation of workstations (Germs & Riezebos, 2010).

In this research, two different starvation avoidance dispatching rules (+lowerbounds; +SA) are incorporated in POLCA, in order to reduce starvation in a divergent topology. These rules prioritize orders that are destined for the downstream workstation which is expected to starve first, based on two different mechanisms. This research shows that these rules improve workload balancing and therefore are able to reduce STT and TTT significantly, which answers the research question. Even when processing time variability was present, the dispatching rules are able to do so. This adds to previous research of Germs & Riezebos (2010) and Ziengs et al. (2012), in which POLCA was not able to reduce STT and TTT in systems with processing time variability. The rule +SA, showed the best workload balancing capabilities by obtaining the largest TTT reductions and is the easiest to implement.

It appears that the obtained STT and TTT reductions are mainly the result of the starvation avoidance dispatching rules and not caused by POLCA. It turns out that the optimal configurations hardly limit WIP and therefore almost behave as push systems. As a result, most advantages of POLCA for practice, are lacking in these configurations. Based on these outcomes, we conclude that the suitability of POLCA for MTO environments, as is suggested by Stevenson et al. (2005), is rather questionable.

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Appendix A – Welch Method

In order to determine a warm-up period that is sufficient for all experiments, we determined it for the experiment with the highest system variability. This is a push system, with exponential inter-arrival times, 90 percent utilization and Erlang distributed processing times. Based on figure A.1, the warm-up period is determined to be 650 units. This number of units is chosen, since the graph is stabilized on that point.

Figure A.1: Warm-up period determined with the Welch method

To determine the run length, three replications with a run length of more than 10,000 units were simulated. Figure A.2 shows the cumulative mean results of these simulations. Based on this graph, we can conclude that producing 9750 units would be a sufficient run length. This is in line with the rule of thumb by Robinson (2014), who stated that the run time should be at least 10 times the warm-up period.

Figure A.2: Determining the run length

0 50000 100000 150000 200000 250000 1 201 401 601 801 1001 1201 1401 1601 1801 2001 Movi ng average Units

Welch Method

Run length

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The number of replications is determined to be 25. Figure A.3 shows that the cumulative mean of the total throughput times is stabilized at 22 replications. Therefore, we conclude that 25 replications are sufficient.

Figure A.3: Determining the number of replications

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Appendix B – Mechanism of +lowerbounds

The dispatching rule +lowerbounds, is based on the mechanism of WCPRD, as described by Thürer et al. (2012). The rule prioritizes orders in a queue on the shop floor, when the number of available cards at a direct downstream workstation exceeds an established lower bound. Figure B.1 shows a scenario in which no workstation exceeds the lower bound. In this case, the sequence of processing orders by workstation A is determined by FCFS. In the scenario as shown in Figure B.2, workstation B exceeds the lower bound, therefore +lowerbounds prioritizes an order that is destined for this workstation in the queue for workstation A.

Figure B.1: No lower bound exceeded Figure B.2: Workstation B exceeds the lower bound

Figure B.3 shows a scenario in which both downstream workstations exceed the lower bound. Since +lowerbounds does not consider the extent in which a workstation exceeds the lower bound, no prioritization takes place. So, although workstation B has more cards available, still the order that is destined for workstation C will be processed first (as determined by FCFS). Note, the prioritization rule of +lowerbounds is only activated when the number of available cards exceeds the established lower bound. In case of the scenario as shown in figure B.4, workstation B equals the lower bound, but does not exceed it. Therefore, the order that is destined for workstation B is prioritized, since this workstation does exceed the lower bound.

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Appendix C – OPT as percentage of TTT

Table C.1: OPT as percentage of TTT

80% utilization 90% utilization

Conf. OPT as % of TTT Conf. OPT as % of TTT

Constant Processing Times

POLCA [7,7] 4.1833 % [11,11] 9.4846 %

POLCA +SA [9,9] 1.6497 % [13,13] 6.4618 %

POLCA +lowerbounds [7,7] 4.1426 % [11,11] 9.4281 %

Low Process Variability

POLCA [16,16] 0.1070 % [21,21] 0.8000 %

POLCA +SA [14,14] 0.0766 % [24,24] 0.0568 %

POLCA +lowerbounds [16,16] 0.0371 % [21,21] 0.1558 %

Medium Process Variability

POLCA [26,26] 0.0233 % [41,41] 0.1648 %

POLCA +SA [12,12] 0.7516 % [45,45] 0.0000 %

POLCA +lowerbounds [26,26] 0.0000 % [41,41] 0.0000 %

High Process Variability

POLCA [35,35] 0.0125 % [63,63] 0.0023 %

POLCA +SA [16,16] 0.2345 % [30,30] 0.1883 %

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Appendix D – Additional results of +SA (loops in first stage ‘relaxed’)

In previous research of Ziengs et al. (2012), it appeared that (FCFS-controlled) POLCA systems perform better (in terms of STT and TTT) when WIP in the first production stage is not limited. By ‘relaxing’ the control loops in the first stage, orders are directly released to the shop floor at the moment of arrival. Figures D.1 and D.2 show the outcomes of POLCA +SA for different cards counts in the second production stage, while the loops in the first stage are relaxed. These outcomes are comparable with the performances of the optimal POLCA +SA configurations (that obey the restriction that all control loops use the same number of cards). This can be explained by the fact that the optimal configurations hardly limit WIP, as shown in figure C.1 in Appendix C.

Figure D.1: Performances of POLCA +SA (loops in first stage are ‘relaxed’) at 80% utilization

Figure D.2: Performances of POLCA +SA (loops in first stage are ‘relaxed’) at 90% utilization

75% 80% 85% 90% 95% 100% 0 5 10 15 20 25 30 35 40 45 TTT

Number of cards in loops at the second production stage

80 % Utilization

Number of cards in loops at the second production stage