Due date performance of POLCA systems: when do workload
balancing capabilities matter? A simulation study
Jaco van Burgsteden S2748045
Master Thesis
MSc. Technology and Operations Management MSc. Supply Chain Management
University of Groningen, Faculty of Economics and Business
June 30, 2017
ii
Abstract
Purpose – This study looks into the usefulness of POLCA’s workload balancing capability when it comes to due date performance. Soepenberg et al. (2012) and Bontjer (2016) found that for SME MTO firms using POLCA not meeting due dates had little or no consequences or that these firms tend to quote due dates with a lot of slack. Hence, the purpose of this study is to look into the due date performance of POLCA. What due date performance is POLCA capable of achieving and under which circumstances is POLCA’s workload balancing capability able to improve a firm’s due date performance.
Method – This study is performed through the use of discrete-event simulation using a three-stage POLCA production system with a divergent topology. Due dates are set with decreasing slack to find the breaking point of POLCA, where it is unable to achieve satisfactory performance. This amount of due date slack is then used to evaluate the effect of workload balancing on the due date performance by measuring order tardiness.
Findings – POLCA’s workload balancing capability made a small difference when it comes to due date performance and is only relevant within a specific frame of due date slack. Workload balancing can result in an improvement of 0,3% less order tardiness, but this only happens under specific circumstances. Namely when there are random inter arrival times, constant processing times and higher levels of utilization. With the presence of variability in processing times, workload balancing gets eradicated from POLCA systems and thus an improvement in due date performance then cannot be made.
iii
List of abbreviations
CONWIP Constant work in progress CV Coefficient of variation MTO Make-to-order
OPT Order pool throughput time PC Production control
POLCA Paired-cell overlapping loop of cards with authorization PPC Production planning and control
SME Small and medium-sized enterprises STT Shop floor throughput time
TTT Total throughput time
iv Table of Contents
Abstract ... ii
List of abbreviations ... iii
List of Tables and figures ... v
1 Introduction ... 1
2 Literature Background ... 3
2.1 Production planning and control ... 3
2.1.1 Order acceptance ... 3 2.1.2 Order release ... 4 2.1.3 Order dispatching ... 5 2.2 Pull systems ... 5 2.2.1 Kanban ... 5 2.2.2 CONWIP ... 6 2.2.3 POLCA ... 6 2.3 Workload balancing ... 8
2.4 Due date setting policies ... 10
3 Methodology ... 11 3.1 Research method ... 11 3.2 Model design ... 12 3.3 Experimental design ... 14 3.4 Model validation ... 15 4 Results ... 16
4.1 Optimal card count and throughput time ... 16
4.2 Due date adherence ... 17
4.3 Order tardiness and card count ... 20
4.4 Effect of processing time variability ... 22
5 Discussion ... 24
5.1 Main findings ... 24
5.1.1 Due date setting ... 24
5.1.2 Total throughput time and order tardiness ... 24
5.1.3 Workload balancing ... 25
5.1.4 Processing time variability ... 26
5.2 Implications ... 26
5.2.1 Theoretical implications ... 26
v
5.3 Limitations ... 27
6 Conclusion ... 27
6.1 Future research ... 28
References ... 30
Appendix 1: Model validation ... 33
Appendix 2 ... 34
Appendix 3: TTT and order tardiness per system configuration ... 35
Appendix 4: TTT, STT and their difference in percentage ... 38
Appendix 5: TTT per coefficient of variation ... 39
List of Tables and figures
Tables Table 1: Experimental factors and settings ... 15Table 2: Optimal card count per configuration ... 16
Table 3: TTT and STT improvement (%) compared to push system ... 17
Table 4: Due date slack required for 95% due date adherence and order tardiness ... 19
Table 5: Difference between TTT and tardiness minimization ... 22
Figures Figure 1: Kanban production control system ... 6
Figure 2: CONWIP production control system ... 6
Figure 3: Throughput time measures... 7
Figure 4: POLCA production control system ... 7
Figure 5: Decision making scheme for POLCA ... 8
Figure 6: Illustrative example of effective workload balancing capability ... 9
Figure 7: Illustration workload balancing in POLCA ... 10
Figure 8: Three-stage divergent POLCA topology ... 12
Figure 9: 95% due date adherence ... 14
Figure 10: Total throughput time and order tardiness per card count ... 21
1
1 Introduction
Firms are constantly searching for methods to quote more accurate and shorter due dates for their customers, because reliable short due dates are regarded as order winners and consequently improve profitability (Aitken, Childerhouse, Christopher, & Towill, 2005; Mason-Jones, Naylor, & Towill, 2000). When it comes to quoting accurate and short due dates, choosing the right production planning and control (PPC) system is of strategic importance for firms (Olhager & Wikner, 2000; Stevenson, Hendry, & Kingsman, 2005). When looking at make-to-order (MTO) firms, it becomes clear that they often face difficulties in choosing the right PPC system (Stevenson et al., 2005). Not every PPC system fits the needs of a MTO firm, as these systems are not universally applicable and need to be coordinated.
Pull systems are often used by MTO firms as production control system (PC). Pull systems allow for better customizability since the customer order decoupling point can be placed further upstream than in push systems system (Olhager, 2003). Examples of pull systems are unit-based pull systems like Kanban, CONWIP and POLCA (Germs & Riezebos, 2010). A problem MTO firms face when using unit-bases pull systems appears to be due date setting (Bontjer, 2016) and meeting delivery promises (Soepenberg, Land, & Gaalman, 2012). These firms tend to quote long fixed due dates, because of its simplicity and the fact that these unit-based pull systems in general “do not support the order acceptance” (Bontjer, 2016, p. 46). Also, Soepenberg et al. (2012) found that not delivering on time has little to no consequence for these firms. This raises the question whether MTO firms are using the right production control system to manage their production. Is POLCA, with benefits like workload balancing capabilities (Germs & Riezebos, 2010), the right PC system for these MTO firms to achieve satisfactory due date performance?
POLCA is argued to result in better total throughput time (TTT) performance over Kanban and CONWIP, because of its workload balancing capability (Germs & Riezebos, 2010; Riezebos, 2010). The reduced TTT enables firms to achieve better due date performance, which in turn results in improved profitability. Workload balancing is a result of POLCA’s route specific authorization signals (Riezebos, 2010), which control the amount of work in progress (WIP) for each specific route. POLCA’s TTT reduction, compared to other pull other systems, is only achieved then workload balancing capability are able to manifest itself.
2 regarding due date setting in card controlled systems like POLCA. Slotnick states that firms need to align order acceptance with their other functions, for example order release, in order to maximize profit. Next to that, Ebben et al. (2005) argue that order acceptance and due date setting are being underestimated by practitioners, leading to poor due date adherence. Hence it is interesting to look into the due date performance of the POLCA PC system, because it is unknown what POLCA is actually able to achieve when it comes to due date performance.
To assess when POLCA results in better due date performance, it should become clear exactly when POLCA’s workload balancing capabilities occur and result in a TTT and due date performance improvement. Improved performance of the POLCA system is expected to occur when the manufacturing process is exposed to higher utilization rates and when due date slack is more restrictive, because workload balancing arises more strongly with higher utilization levels (Germs & Riezebos, 2010). This should point out how a firm should manage their POLCA PC system in order to achieve performance improvement and to achieve satisfactory due date performance under restrictive due dates.
The aim of this research is to find out when exactly workload balancing capabilities result in TTT reduction and thus in better due date adherence. This should show how POLCA as a production control system enables MTO firms to improve their due date adherence. This addresses the lack of knowledge regarding the effect of order acceptance on due date performance in POLCA controlled production environments.
This study will be conducted using discrete event simulation. The simulation experiment consists of a three stage POLCA controlled manufacturing process with a divergent topology. The system is posed with random inter arrival and processing times and different due dates are set with varying slack to assess due date adherence. The goal is to minimize order tardiness within a given percentage of due date slack and to find out what the additional performance improvement of workload balancing is.
This study has both theoretical and practical contributions. Its theoretical contribution is that it should become clear what due date performance POLCA is able to achieve and under how much due date pressure POLCA is able to still yield satisfactory due date performance. Secondly, it should become clear under which circumstances POLCA’s workload balancing capability results in improved due date performance. The practical contribution of this research is that it can help practitioners in improving their due date setting and enable them to quote more accurate due dates to their customers.
3 setting policies. In the methodology section the simulation model is explained and discussed, along with the experimental variables. Next the results of the simulation study are shown, divided into optimal card count setting, throughput times and order tardiness, effects of workload balancing on order tardiness and card count and lastly the effects of processing time variability. Then the results are discussed and this report ends with a conclusion returning to the research question and providing options for further research.
2 Literature Background
2.1 Production planning and control
Production planning and control (PPC) systems are used by companies to “reduce Work in Progress (WIP), minimize Shop Floor Throughput Times (STT) and lead times, …, and improve Delivery Date (DD) adherence” (Stevenson et al., 2005, p. 869) and consist of three main decision points, which are order acceptance, order release and order dispatching (Land & Gaalman, 2009). Stevenson et al. (2005) and Olhager & Wikner (2000) state that choosing the right PPC system is of strategic importance for a MTO company to achieve, for example, satisfactory due date performance.
Card-based systems, like POLCA (Gershwin, 2000; González-R, Framinan, & Pierreval, 2012), only take into account order release and order dispatching and are thus classified as production control (PC) systems (González-R & Framinan, 2009). PC systems are focused on the flow of the goods through the system and can be seen as an optimization problem concerning “when and how much to produce in order to achieve a satisfactory customer service level” (Liberopoulos & Dallery, 2000, p. 325). However, to properly manage the flow of goods, the arrival of orders should also be controlled. This is where the main difference between PPC and PC systems is. PPC systems do control the arrival of orders in the order acceptance stage, where PC systems lack an order acceptance stage.
2.1.1 Order acceptance
4 Order acceptance can be supported by endogenous and exogenous due date setting policies (Cheng & Gupta, 1989; Ramasesh, 1990; Zorzini, Corti, & Pozzetti, 2008). Cheng & Gupta (1989) state that in case of exogenous due date setting, the due date of an order is set by an external party and is provided when the order arrives. This due date can be set constant or random. An example of a constant due date setting policy can be a uniform lead time demanded by a buyer. An example of random due date setting can be a customer set due date (Land, 2004). Exogenous due dates allow firms to assess whether a certain order can be accepted or has to be rejected with the specified due date (Zorzini et al., 2008).
Endogenous due date setting, on the other hand, is done internally by the planning department of the company itself, taking the shop floor into consideration, based on “job characteristics, shop status information and an estimate of the job flow time” (Cheng & Gupta, 1989, p. 158). An example of this, is the total work (TWK) rule, which “estimates the throughput time of a job as a multiple of its total processing time” (Land, 2004, p. 14). Endogenous due date setting takes place after an order has been accepted. The due date set by the producing firm is then quoted to the buyer.
2.1.2 Order release
Orders are released to the shop floor either immediately after acceptance, at a specified time, or when capacity is available. When orders are released to the shop floor much earlier than needed, high average WIP accumulates in in the production process (Zäpfel & Missbauer, 1993). In turn the higher WIP results in a longer throughput time (Hopp & Spearman, 2008; Zäpfel & Missbauer, 1993), which only makes the situation worse. This is called the lead-time-syndrome and is a result from the uncontrolled release of orders (Zäpfel & Missbauer, 1993).
Zäpfel & Missbauer (1993) state that PPC systems can help addressing these order release issues with systems that limit the workload on the shop floor. This is called workload control. The objective of workload control is agued to be “to control the lengths of the queues in front of work stations on the shop floor” (Kingsman, 2000, p. 73). However, Kingsman (2000) states that the true objective of workload control is to “process the jobs so as to meet the promised delivery dates with the machine and workforce capacities and capabilities available” (p. 73). POLCA is one of these systems which limits and controls workload.
5 system must also contain an order acceptance stage to control the inflow of orders to the order pool as well as plan for capacity to ensure that WIP queues are controlled.
2.1.3 Order dispatching
The last function of PPC and PC systems is order dispatching. Order dispatching revolves around the choice “which job should be processed next at a workstation after the operation of another job has been completed” (Land, 2004, p. 18). Order dispatching can be assisted by the use of order priority rules. A great variety of order priority rules exist. Based on the goal of the order priority rule, they can be broadly be grouped into three categories, namely flow conserving priority rules, throughput improving priority rules and lateness dispersion reducing priority rules (Land, 2004). Land gives a few examples of order priority rules, a flow conserving priority rule is first-come-first-served, a throughput improving priority rule is shortest processing time and an example of a lateness dispersion reducing priority rule is the earlies due date rule.
2.2 Pull systems
Production control systems can either be classified as push or pull systems. In a push system an order is released as soon as it is accepted, because the workload is not limited (Spearman & Zazanis, 1992, p. 521). On the other hand, in a pull system an order is pulled through the system by “downstream work centers pulling stock from previous operations” (p. 521). This is the result of pull system’s workload control. Pull systems have advantages over push systems, as they limit the amount of WIP, shorten cycle times, allow for smoother production flow, enable quality improvement and reduce costs (Hopp & Spearman, 2004). Card-based systems, like Kanban, CONWIP and POLCA, are often used in pull manufacturing systems and can aid in controlling WIP (Gershwin, 2000).
2.2.1 Kanban
6 Queue
Workstation Flow of jobs Pull signal
Figure 1: Kanban production control system
2.2.2 CONWIP
The constant work in progress (CONWIP) production control system (Spearman, Woodruff, & Hopp, 1990) manages WIP in a different way than Kanban, namely by placing one control loop over the whole production system. Within this control loop, a set amount of orders may be on the job floor which is controlled by the number of cards available (Framinan, González, & Ruiz-Usano, 2003). Hence a new order can only enter the production system when another order leaves the system. A card, representing a pull signal, is then freed up at the last workstation and send to the first workstation, indicating capacity is available in the production process. This limits the total number of orders in the system to the number of cards available to the system.
The basic system is shown in figure 2. Orders enter the system, being pulled from the order pool or backlog list, and progress through the system based on a fist come first serve queueing discipline (Spearman et al., 1990). The performance of the CONWIP system is strongly dependent on the number of cards available in the system (Framinan et al., 2003).
Queue Workstation Flow of jobs Pull signal
Figure 2: CONWIP production control system
2.2.3 POLCA
7
Figure 3: Throughput time measures (adopted from (Germs & Riezebos, 2010))
The main difference between POLCA and Kanban is that Kanban uses inventory signals, indicating that materials are used and need to be replenished. POLCA on the other hand uses capacity signals, indicating production capacity availability when a product has left the workstation (Suri, 2010). These control loops overlap each other, as can be seen in figure 3, indicating that one workstation is dependent on both the upstream and the downstream adjacent workstations. This enables control of the flow between two work cells, “increasing the speed of job transfer between cells” (Riezebos, 2010, p. 1456) and reducing unbalance located within the production system (Riezebos, 2010). The cards used in POLCA are fixed between two workstations, either accompanying an order going to one cell to another or going back to the first cell to indicate available capacity (Stevenson et al., 2005).
POLCA differs from CONWIP mainly it its workload balancing capabilities and its route specific card setting. The route specificity of POLCA enables workload balancing, as it controls the flow of materials between workstations. The card allocation in POLCA, which happens between each two adjacent workstations, is graphically displayed in figure 4. Figure 4 shows a decision-making scheme which depicts which decisions are made when allocating cards to orders.
Queue Workstation Flow of jobs Pull signal
8
Assign due date
Assign due date
Wait in orderpool or buffer Wait in orderpool or buffer POLCA card available? POLCA card available? Release order Release order Workstation idle? Workstation idle?
Sort buffer and release on priority
Sort buffer and release on priority
Wait in buffer for workstation
Wait in buffer for workstation
Process order
Process order
Due date met?
Due date met? Yes No No No Yes Order fully processed? Order fully processed? No Yes Order arrives Order arrives
Due date adhered
Due date adhered Tardy orderTardy order Figure 5: Decision making scheme for POLCA
2.3 Workload balancing
9 Germs and Riezebos (2010) have shown that workload balancing capabilities exist in POLCA. This results in a reduction of both STT and TTT. The effect of this is illustrated in figure 5. The diagonal line shows where TTT and STT are equal; this is where the push system is located on as there is no order pool time in a push system. The line of the pull system here illustrates the TTT and STT reduction.
Germs and Riezebos showed in the same study that increased inter-arrival time variability and higher levels of utilization improved workload balancing capabilities in pull systems. On the other hand, they found that processing time variability has a strong negative influence on workload balancing capabilities. Next to that, Fernandes & Carmo-Silva (2011) found that workload balancing decreases the time orders spend in the system and the percentage of tardy orders.
Riezebos (2010) states divergent structures are well suited for workload balancing capabilities. It is important to note here that workload balancing only works effectively when the appropriate number of cards is used within a control loop (Germs & Riezebos, 2010). This is confirmed by Ziengs, Riezebos, & Germs (2012) who state that placing WIP limits affects the workload balancing capabilities in a POLCA production system, which in turn affects the TTT of an order. When workload balancing capabilities are strengthened, both TTT and STT
10 are reduced compared to a push system. However, when too little or too much WIP is present in the system does TTT increase.
S1
S1
S2
S2
S3
S3
1 1 1 2 1 1 1 2 Order poolFigure 7: Illustration workload balancing in POLCA
Figure 6 shows an example illustrating workload balancing in POLCA: in the queue for S1 are zero orders and there are four orders in the order pool. Three of these orders follow route 1 and one order follows route 2. In the queue in front of S2 are three orders, which all follow route 1. Alternatively, all orders following route 2 need to be processed by S3. S3 has a queue of just one order. The maximum number of cards is determined to be three, and all workstations are empty and idle.
Since the maximum amount of orders which follow route 1 is set to be three, and the current amount of orders which follow route 1 is three, orders which follow route 1 will not be released out of the order pool, as there is no card available. Instead the last arrived order, which follows route 2, will be released from the order pool. This results in a more even distribution of orders among the routings, which is called workload balancing.
2.4 Due date setting policies
To assess due date performance in a POLCA PC system, an order acceptance stage has to be incorporated. This is assisted through the use of a due date setting policy. Due date setting can take place endogenous and exogenous of the firm. When endogenous due date setting takes place, the due date of an order is set by the firm itself based on for example total work time. On the other hand, the customer may pose a due date for the order, in which case the due date is set externally of the firm and thus exogenous.
11 relatively good average performance”. However, the TWK rule will perform worse when exposed to “equivalently short jobs together with a small number of very long jobs” (p. 130). In these circumstances, an equal slack for all orders due date setting policy may yield better performance.
To summarize, Soepenberg et al. (2012) and Bontjer (2016) found that there is no urgency perceived by small and medium enterprise (SME) MTO companies using POLCA to improve their order acceptance policy as customers do not take any significant measures when due dates were not adhered. Since POLCA addresses production control and not production planning and control, order acceptance is not taken into account by the POLCA system. In order to take order acceptance into consideration, a firm has to add an order acceptance system to POLCA. This can be done with support of a due date setting policy like TWK. POLCA differs from other card-based production control systems, like Kanban and CONWIP, because of its workload balancing capabilities and its route specific workload control. Workload balancing capabilities lead to reduction in TTT and STT, which should enable better due date performance for a firm. The aim of this study is to find out how much due date performance can be improved by POLCA’s workload balancing capabilities and when this workload balancing is able to make the difference between meeting and not meeting due dates.
3 Methodology
3.1 Research method
This research is conducted by means of simulation experiments. Simulation is chosen, because of its ability to incorporate variability, interconnectedness and complexity into a model (Robinson, 2014). A production environment is always faced with variability, for example the order inter-arrival times (demand variability) and order processing times (Slack, Brandon-Jones, & Johnston, 2014). The PC system used, POLCA, has a lot of interconnected production cells, which results in a lot of routing options and thus in high complexity. These characteristics make it very difficult to predict the performance of the POLCA production system when faced with a due date setting policy. Therefore, simulation is a good tool to predict system performance under different environmental settings and to compare system alternatives (Robinson, 2014).
12 is conducted using Tecnomatix Plant Simulation 12 from Siemens (“Tecnomatix Plant Simulation”, 2014). This specialist software is chosen above coding a model, as it is more time efficient. It also allows for easy export of data generated while running the simulation model. 3.2 Model design
The model used in the simulation represents a MTO POLCA production system with a three-stage divergent topology, because it suits POLCA and its workload balancing capabilities well (Germs & Riezebos, 2010). The three-stage divergent model is shown in figure 7. It consists of seven workstations, which each have its own queue, spread over three production stages. There are four different routings possible, namely A-B-D, A-B-E, A-C-F and A-C-G. Every routing has the same probability of 0,25 to be followed by one of the orders and the routing is known when an order enters the system.
Each pair of consecutive work stations has an overlapping POLCA loop, which regulates the amount of WIP at the workstations using the POLCA cards as limitation. The different routing options and the use of cards in the system allows for workload balancing, as the cards signals capacity availability between workstations. The model used in this simulation study is a unit-based POLCA production system.
A B C D E F G Queue Control loop Workcell
Figure 8: Three-stage divergent POLCA topology
13 the order starts being processed at station B or C. Since the production system is MTO based, no semi-finished goods are held in the production process. As a product goes through the stages, the processing time at the consecutive processing stage is randomly generated using an Erlang-2 distribution. However, the mean processing time is always set so it multiples at each workstation. So the mean at station A is 1 hour, at stations B and C 2 hours and at stations D,E,F and G 4 hours. This allows for flow in the system, as there is less starvation and blocking than with complete random processing times.
The system is controlled by the POLCA production system. The aim is to analyze the performance of POLCA systems regarding due date slack needed for 95% due date performance and to determine when workload balancing becomes relevant for upholding satisfactory performance. The order dispatch is initially organized by the first-come-first-served (FCFS) rule. Next to that the shortest processing time (SPT) rule and earliest due date (EDD) rule are used for further analysis of the POLCA system.
In POLCA, there are cards allocated to a pool between two workstations. These cards limit the amount of WIP between these two workstations and hence in the whole production system. Next to that, the cards also indicate capacity availability. The configuration of the system is determined by the number of cards available in the system and per loop. The optimal number of cards is determined through exhaustive search. The number of cards greatly affects the STT and TTT, as more cards result in a higher WIP and a higher WIP results in a higher throughput time according to Little’s law (Hopp & Spearman, 2004). Also, a too high number of cards eliminates the workload balancing capabilities of POLCA. Too many cards effectively results in a push system, as workstation A keeps on pushing the orders into the system as there is capacity available according to the cards. The number of cards per loop used in the simulation first differs between 1 and 30, in order to determine when workload balancing makes a difference in the simulation model. More cards may be used to find optimal values.
14 3.3 Experimental design
In the experiments, several variables are used in different system configurations. Each system configuration consists of a different number of cards, initially ranging from one card per POLCA loop to 30 cards per POLCA loop. Within a configuration, due dates are set based on the TWK due date setting policy. Each order gets a markup, creating the due date slack of an order, starting with 100% of the total work time of the order. This set due date is gradually increased until the point is reached where due date adherence meets a 95% threshold and order tardiness thus is 5%. This is showed in figure 9. Here 5% due date slack threshold is met at 600% due date slack. Additional information about this threshold can be found in appendix 2.
Figure 9: 95% due date adherence
The variability and mean of the order inter arrival time differs to confront the model with differing workloads. This is done in order to expose workload balancing benefits, as variability in inter arrival times and higher utilization levels improve the workload balancing capabilities of POLCA (Germs & Riezebos, 2010). On the other hand, Germs & Riezebos found that high processing time variability negatively influences the workload balancing effects of POLCA, which adds an interesting factor into the simulation possibly counteracting on the positive effect resulting from inter-arrival time variability and utilization. Assuming lower TTT allows for better due date performance, it is interesting how these three experimental factors may influence the actual due date performance. A complete overview of the experimental factors is given in table 1.
Inter-arrival times are generated using a negative exponential distribution and processing times are generated using an Erlang-2 distribution. The Erlang-2 distribution has a coefficient of variation (CV) of 0,71. This is classified as low variability, since a CV of less than 0.75 is regarded as low variability (Hopp & Spearman, 2008).
0% 20% 40% 60% 80% 100% 0 100 200 300 400 500 600 700 800 900 1000 O rder t ardi ness
Due date slack
95% due date adherence threshold
15
Table 1: Experimental factors and settings
Factor Experimental settings
System configuration
Due date policy TWK + multiplier k (%)
Number of cards per loop 1 – 30, ∞
Order arrival pattern
Inter-arrival time variability Constant, negative exponential
Batch size 1
Processing characteristics
Processing time variability Constant, Erlang-2
Utilization 80%, 85%, 90%
To measure the results of the simulation, performance dimensions are used. For this study, we use order tardiness, total throughput time and shop floor throughput time as performance indicator. It is interesting to look how these performance dimensions might affect one another and at which card count these performance dimensions yield the optimal result, because then it can be identified when workload balancing results in decreased order tardiness. 3.4 Model validation
To ensure model and simulation validity, warm-up period, run time and number of replications are determined. These are based on a push model with 90% utilization and both random inter arrival times and processing times. The warm-up period is determined using the Welch method (Welch, 1967). This ensures that the data yielded by the simulation is not biased by inaccurate data from an unloaded system. The warm-up period is determined to be 400 units, which translates to 19 days runtime. To be sure, the simulations are executed using 30 days as warm-up period. The graph of the Welch’s method can be found in appendix 1.
Regarding the choice of run length and/or number of replications, both are determined using the same system configuration as for the Welch method, but with warm-up time in place. The run length is determined using a cumulative means method from three replications (Robinson, 2014, p.190-193), the graph of which can be found in appendix 1. This method determined the run length to be at least 9000 units, which translates to 417 simulation days. When adding the warm-up period, the total run length is set at 450 days. Lastly the number of replications is determined. This is determined to be 25, using a cumulative means method.
16
4 Results
4.1 Optimal card count and throughput time
Per experimental configuration the optimal card count is determined based on minimizing the TTT. Minimizing TTT is chosen, as it is used in multiple studies before for example Germs & Riezebos, 2010 and Ziengs et al., 2012 and as it shows the total time an order spends in the system, from order pool to completion. The optimal card count per system configuration is determined using exhaustive search, the results of which are presented in table 2.
Table 2: Optimal card count per configuration
Processing time Constant Random
Inter arrival Constant Random Constant Random Utilization
level
Dispatch
rule Optimal card count Optimal card count
80% FCFS 7 7 23 26 SPT 7 7 18 16 EDD 7 7 18 21 85% FCFS 9 8 29 32 SPT 9 8 19 22 EDD 9 8 27 26 90% FCFS 12 11 58 64 SPT 12 11 28 26 EDD 12 11 50 56
The optimal card count is the same within each system configuration where no processing time variability is present, namely 7. This is conform expectation, as the prioritization of orders based on SPT or EDD cannot take place, since no difference in processing time is present. The card count however does increase as utilization levels increase. This is also in line with expectations, as the production system gets loaded with more orders and needs a higher amount of WIP to uphold its performance. Also, a higher number of cards is needed to facilitate workload balancing.
17 rises from 7 to 23. Same effects can also be seen in appendix 3, which shows the TTT and STT for each system. The throughput time of orders rises vastly when either inter arrival time variability or processing time variability is present.
Table 3 shows the performance improvement of the optimal card count, which are shown in table 2, compared to the push system. From the results in table 3, it becomes clear that best performance improvement compared to the push system is achieved in an environment with variable inter arrival times, constant processing times and higher levels or utilization. This is also where POLCA’s workload balancing capabilities perform best. At 90% utilization, a TTT reduction of 2,50% is achieved and a STT reduction of 11,74%.
Table 3: TTT and STT improvement (%) compared to push system
Processing
time Constant Random
Inter arrival
Constant Random Constant Random
Utilization level Dispatch rule TTT (%) STT (%) TTT (%) STT (%) TTT (%) STT (%) TTT (%) STT (%) 80% FCFS 0,14% 0,35% 0,97% 5,11% 0,00% 0,00% 0,00% 0,02% SPT 0,14% 0,35% 0,97% 5,11% 0,00% 0,00% 0,00% 0,00% EDD 0,14% 0,35% 0,97% 5,11% 0,01% 0,01% 0,00% 0,05% 85% FCFS 0,27% 0,58% 1,42% 8,72% 0,00% 0,00% 0,01% 0,06% SPT 0,27% 0,58% 1,42% 8,72% 0,00% 0,00% 0,00% 0,00% EDD 0,27% 0,58% 1,42% 8,72% 0,00% 0,00% 0,05% 0,22% 90% FCFS 0,73% 1,26% 2,50% 11,74% 0,00% 0,00% 0,00% 0,00% SPT 0,73% 1,26% 2,50% 11,74% 0,00% 0,00% 0,00% 0,00% EDD 0,73% 1,26% 2,50% 11,74% 0,01% 0,01% 0,01% 0,01%
The results in table 3 also show that for production environments with random processing times, POLCA is not able to yield performance improvement compared to the push system. Here the TTT and STT performance of a push system with order priority rules is compared to the configuration with optimal card counts and order priority rules. This is done in order to be able to isolate the performance of POLCA within a given order priority rule. The performance differences in table 3 are thus purely a result of the POLCA production control system. The results show clearly that POLCA is only able to yield performance improvement in an environment with constant processing times, because that is where POLCA’s workload balancing capabilities are strengthened and perform best.
4.2 Due date adherence
18 and standard deviation of order tardiness are displayed in table 4. This provides a complete overview of each system configuration’s performance.
Table 4A shows the results for constant inter arrival times and processing times. Table 4B shows the results for variable inter arrival times and constant processing time. Table 4C shows the results of the system with constant inter arrival times and variable processing times and lastly Table 4D shows the results for both variable inter arrival times and variable processing times. The due date factor displayed is the factor which has to be added to the total work time.
Then looking at table 4, one can see that due required due date slack increases as inter arrival time variability and processing time variability are present. The due date slack factor shown in table 4 ensures 95% due date adherence. This means for constant inter arrival and constant processing times with 80% utilization, that with less than 300% due date slack the POLCA PC system is not able to uphold its performance. The consequence of this is that due dates are impossible to adhere. On the other hand, when using 400% due date slack, the due date performance is always higher than 95% as the due date is set with such a high amount of slack that it will always be adhered. This is precisely sought after, as one of the observations of Bontjer (2016) was that in practice due dates are often set with such high amount of slack that they are always adhered.
19
Table 4: Due date slack required for 95% due date adherence and order tardiness
(A) (B)
Constant inter arrival & constant processing times Variable inter arrival & constant processing times
Utilization level Dispatch rule Due date slack Mean tardiness (h) St. dev tardiness (h) Utilization level Dispatch rule Due date slack Mean tardiness (h) St. dev tardiness (h) 80% FCFS 300% 6,38 5,70 80% FCFS 450% 9,08 8,09 SPT 300% 6,38 5,70 SPT 450% 9,08 8,09 EDD 300% 6,38 5,70 EDD 450% 9,08 8,09 85% FCFS 400% 8,54 7,55 85% FCFS 650% 11,72 10,11 SPT 400% 8,54 7,55 SPT 650% 11,72 10,11 EDD 400% 8,54 7,55 EDD 650% 11,72 10,11 90% FCFS 650% 10,80 8,96 90% FCFS 950% 15,55 12,03 SPT 650% 10,80 8,96 SPT 950% 15,55 12,03 EDD 650% 10,80 8,96 EDD 950% 15,55 12,03 (C) (D)
Constant inter arrival & variable processing times Variable inter arrival & variable processing times
Utilization level Dispatch rule Due date slack Mean tardiness (h) St. dev tardiness (h) Utilization level Dispatch rule Due date slack Mean tardiness (h) St. dev tardiness (h) 80% FCFS 850% 11,77 10,85 80% FCFS 1100% 14,63 13,13 SPT 350% 20,58 39,40 SPT 450% 30,41 51,62 EDD 450% 9,65 9,15 EDD 600% 12,60 10,73 85% FCFS 1150% 15,46 13,95 85% FCFS 1500% 19,56 17,30 SPT 450% 40,51 72,16 SPT 550% 52,84 89,59 EDD 650% 12,88 10,80 EDD 850% 16,14 12,64 90% FCFS 1750% 21,76 19,19 90% FCFS 2350% 27,32 23,95 SPT 550% 76,83 138,42 SPT 700% 101,35 175,37 EDD 1000% 17,03 14,05 EDD 1350% 21,40 15,45
It becomes clear that higher utilization and variability result in more need for due date slack and also in higher mean tardiness and a higher standard deviation of tardiness. As long as there is no processing time variability present, as shown in table 4A and 4B, the system behaves quite predictably and is not posed to differences as there is nothing to be sorting using the dispatch rules. However, when processing time variability is introduced into the system, shown in 4C and 4D, results start to differ hugely.
20 To summarize, the SPT rule results in least due date slack needed for all experiments with random processing times, but at the cost of higher due date dispersion. The EDD rule is able to reduce mean tardiness and standard deviation of tardiness, but does this at the cost of due date slack required to achieve 95% due date adherence.
4.3 Order tardiness and card count
As shown in the previous paragraphs, the workload balancing capabilities of POLCA only make a distinct difference in performance in an environment with inter arrival time variability and constant processing times. Hence, we look more into the performance of workload balancing within these experimental settings to determine the difference workload balancing can make regarding due date performance and minimizing order tardiness.
The graphs showing order tardiness are based on tardiness as result of the due date slack allowance factors shown in table 4. Hence the results are around 95% due date adherence, and consequently order tardiness is around 5%. The graphs show for which card count both TTT (on the left) and order tardiness (on the right) are minimized within the set due date slack allowance showed in table 4. The graphs below show the TTT and order tardiness for variable inter arrival times and constant processing times for utilization levels of 80%, 85% and 90% respectively.
It can be observed in figure 10 that TTT and order tardiness are minimized at different card counts. Here for u=80% the TTT is minimized at a card count of 7, but order tardiness is minimized at a card count of 9. The same goes for utilization levels of 85% and 90%. At 85% utilization TTT is minimized at 8 cards and tardiness is minimized at 11 cards. For a utilization level of 90% TTT is minimized at 11 cards and order tardiness at a card count of 16.
21
Figure 10: Total throughput time and order tardiness per card count
A possible explanation for the observation that order tardiness minimizes at a higher card count than TTT, is that having more WIP in the system allows for starvation reduction and thus yield more reliable performance. Starvation can happen within each of the four routes, leading to decreased due date performance. Although more WIP has to be in the production system, leading to an increased TTT, it seems to act as a buffer which enables for better due date performance. 96,0% 97,0% 98,0% 99,0% 100,0% 101,0% 102,0% 103,0% 104,0% 4 5 6 7 8 9 10 11 12 13 14 15 To tal Th ro u n gh p u t Ti m e Card count
variable interarrival times and constant processing times
Total Throughput time (h) (u=80%) TTT 3,8% 4,0% 4,2% 4,4% 4,6% 4,8% 5,0% 4 5 6 7 8 9 10 11 12 13 14 15 Or d e r tar d in e ss (% ) Card count
variable interarrival times and constant processing times
Order tardiness (u=80%)
Tardiness 96,0% 97,0% 98,0% 99,0% 100,0% 101,0% 102,0% 103,0% 104,0% 4 6 8 10 12 14 16 18 20 To tal th ro u gh p u t tim e Card count
variable interarrival times and constant processing times
Total Throughput Time (u=85%) TTT 3,8% 4,0% 4,2% 4,4% 4,6% 4,8% 5,0% 4 6 8 10 12 14 16 18 20 Or d e r tar d in e ss (% ) Card count
variable interarrival times and constant processing times
Order tardiness (u=85%)
Tardiness 96,0% 97,0% 98,0% 99,0% 100,0% 101,0% 102,0% 103,0% 104,0% 4 6 8 10 12 14 16 18 20 22 24 To tal Th ro u gh p u t Ti m e Card count
variable interarrival times and constant processing times
Total Throughput Time (U=90%) TTT 4,0% 4,2% 4,4% 4,6% 4,8% 5,0% 4 6 8 10 12 14 16 18 20 22 24 Or d e r tar d in e ss (% ) Card count
variable interarrival times and constant processing times
Order tardiness (u=90%)
22 The exact differences a higher card count is able to make reducing order tardiness performance is shown in table 5. The highest tardiness reduction can be seen in the system configuration with variable inter arrival times and constant processing times with 90% utilization. It clearly shows that workload balancing helps in reducing order tardiness in this system. The absolute difference however is only 0,29%. The relative difference on the other hand is 5,9%, which means that the amount of tardy orders can be decreased by almost 6% through the effects of workload balancing.
Table 5: Difference between TTT and tardiness minimization
Constant inter arrival time & constant processing time
TTT minimization Tardiness minimization Difference
Utilization Cards TTT (h) Tardiness Cards TTT (h) Tardiness TTT (h) Tardiness
80% 7 13,39 4,08% 9 13,40 4,06% 0,01 -0,02%
85% 9 16,30 4,72% 12 16,32 4,69% 0,02 -0,03%
90% 12 21,94 4,02% 12 21,94 4,02% 0,00 0,00%
Variable inter arrival time & constant processing time
80% 7 17,83 4,54% 9 17,89 4,50% 0,06 -0,04%
85% 8 22,33 4,12% 11 22,40 3,89% 0,07 -0,22%
90% 11 31,20 4,94% 16 31,50 4,64% 0,30 -0,29%
The highest difference which workload balancing can make regarding due date performance is quite small, only a 0,3% reduction in order tardiness. It only occurs in very specific circumstances, namely only in systems with variable inter arrival times and constant processing times.
4.4 Effect of processing time variability
From the results so far, it has become clear that variability in processing times has a negative influence on TTT performance and due date adherence. In order to illustrate the effects of processing time variability, the results of simulations using different coefficients of variation are shown in figure 9. Inter arrival times are kept constant to purely illustrate the effect of processing time variability in the POLCA production control system. The graphs show a clear image of the effects of processing time variability. The SPT dispatching rule seems to handle lower amounts of variability in processing time particularly well, especially at a CV of around 0,2 for 80% utilization, a CV of 0,25 for 85% utilization and a CV of 0,3 for 90% utilization. After that, all dispatching rules show the same behavior regarding the TTT. The TTT seems to rise exponentially as the CV increases.
23 is at 90%. The SPT rule appears to perform well when faced with relative small differences in processing times, as the CV is still low at 0,2-0,3. However, as the CV gets higher and more variability is introduced, all dispatching rules behave the same and show a vast increase in TTT. The exact TTT in time units can be found in appendix 4.
Figure 11: TTT per different coefficient of variation
80% 100% 120% 140% 160% 180% 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 To tal Th ro u gh p u t Ti m e Coefficient of variation
Constant interarrival times and variable processing times Total Throughput Time (u=90)
FCFS SPT EDD 80% 100% 120% 140% 160% 180% 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 To tal th ro u gh p u t tim e Coefficient of variation
Constant interarrival times and variable processing times Total Throughput Time (u=85)
FCFS SPT EDD 80% 100% 120% 140% 160% 180% 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 To tal th ro u gh p u t tim e Coefficient of variation
Constant interarrival times and variable processing times Total Throughput Time (u=80)
24
5 Discussion
In general, the results of this simulation study regarding TTT and STT reduction of POLCA presented in table 3 are in line with previous studies. The results did show that both inter arrival time variability and higher levels of utilizations allow workload balancing to manifest itself, in turn leading to a TTT and STT reduction. The occurrence of workload balancing led to a reduction in order tardiness within a set amount of due date slack. However, the card count had to be higher than the optimal card count for tardiness reduction to occur. This is possibly caused by a starvation reduction which is realized by the higher amount of WIP located in the production process.
On the other hand, processing time variability seems so be fatal for workload balancing capabilities, as workload balancing did not occur in the simulations with processing time variability. Therefore, TTT and STT reductions are not found in the results of experiments with random processing times, consequently order tardiness could not be further reduced within the set due date frame.
5.1 Main findings
5.1.1 Due date setting
The use of the TWK rule yielded clear results regarding due date slack needed when using POLCA production control system. The results were clear regarding the effect of presence of variability and the effects of higher utilization levels. The due date slack needed for 95% due date adherence increased drastically when the system was exposed to higher utilization levels, regardless of which order priority rule was used. Regarding the presence of processing time variability in the system, the SPT rule seemed to be well able to address this. It yielded constant low due date slack needed, but at the cost of a high mean tardiness and standard deviation of tardiness.
The EDD due date on the other hand needed more due date slack than the SPT rule, but far less than the FCFS rule. The EDD rule is also able to achieve the lowest mean tardiness and standard deviation of tardiness at 95% due date performance. However, it has to be noted that the due date slack factor needed to achieve 95% adherence is always higher than for the SPT rule. When both priority rules are exposed to the same due date slack factor (TWK markup), the results show a better result for the SPT rule.
5.1.2 Total throughput time and order tardiness
25 in the study of (Weng, Wu, Qi, & Zheng, 2008), were weighted order earliness and tardiness was minimized at a lead time which was higher than the minimum lead time when using a TWK based due date setting rule. Although differences in TTT and order tardiness are minimal, the relative difference in card count differs quite a lot as can be seen in table 5.
The minimization of order tardiness takes place at a higher card count than the minimization of TTT. This can be caused since there are more orders in the system and hence there is more of a buffer in place which benefits the minimization of order tardiness. It can also be observed that the difference in performance between the configurations gets higher as utilization increases. This makes it more likely that the higher WIP, caused by the higher card count, acts as a buffer which enables better due date adherence. Order prioritization rules do not affect the results here, as the processing times are constant and consequently no prioritization can take place.
5.1.3 Workload balancing
Workload balancing only seems to occur under specific circumstances, which is in a system with constant processing times. Inter arrival time variability and higher utilization levels have a strengthening effect for workload balancing.
Workload balancing does improve TTT and specifically STT quite a bit, as shown in table 3. The STT reduction is very beneficial for MTO companies, as it reduces the risk of orders becoming obsolete due to changing customer specifications. Also, as STT is reduced risk of product damages is decreased, as it less exposed during waiting time. The TTT reduction does still allow for shorter due date quotation, despite due date adherence and order tardiness are not necessarily minimized at the shortest TTT.
26
5.1.4 Processing time variability
Processing time variability is destructive for the performance of the POLCA system, as it is for any other production system (Hopp & Spearman, 2008). It is then interesting to note that the performance of the SPT rule is very positive in systems with processing time variability. It is able to decrease the TTT when the level of variability remains low and is able to perform well under high levels of utilization. The SPT rule also yielded best results regarding due date slack needed to achieve 95% due date adherence.
When firms are posed with processing time variability, it thus seems wise to use a SPT based priority rule. However, the mean tardiness and standard deviation of tardiness should be decreased in order for the priority rule to become interesting. Hence more complex priority rules, combining the due date dispersion reduction of EDD and the TTT and due date performance of SPT, may yield more desired results.
5.2 Implications
5.2.1 Theoretical implications
It has become clear that POLCA is able to reduce both TTT and STT, but under very specific circumstances which are unlikely to be found in practice. TTT and STT reduction are the result of the effects of workload balancing and workload balancing capabilities in POLCA only manifest themselves when there are constant processing times. The effects of workload balancing are more significant when inter arrival time variability is present and at higher utilization levels.
The observation that TTT and order tardiness are minimized at a different card count in the POLCA production control system is an interesting one. A similar observation is done by Weng et al. (2008), who also observed that order tardiness may be minimized under different circumstances than TTT. Hence when due dates get more restrictive, a higher amount of WIP may allow for better due date performance than the shortest TTT. Next to that, it has become clear that the effects of workload balancing occur in such specific situations, that it is unlikely to make a difference in reality as production environments with no processing time variability are highly unlikely.
5.2.2 Practical implications
27 The second practical implication is that when a firm is faced with high due date pressure, better due date performance can be achieved by increasing the amount of POLCA cards, thus allowing more WIP in the system. This performance improvement in terms of decreased order tardiness occurs more strongly in systems with higher utilization levels and constant processing times. Next to that firms should use the SPT priority rule when their main goal is to quote short due dates and the implications of not meeting due dates are not severe, as the SPT rule places large orders in the back of the queue which increases mean order tardiness. When quoting accurate due dates and meeting these due dates becomes more important, the EDD priority rule is better fit to be used as it results in less dispersion of order tardiness.
5.3 Limitations
The software used resulted in a sub-optimal solution used for sorting orders. Orders waiting for card allocation were not properly sorted, hence the dispatch rule for buffers where orders were waiting for cards always behaved like FCFS queues. The queues for workstations on the other hand, did behave properly. Hence the effect of this modelling limitation was limited, because order prioritization only was executed in the queue after card allocation. However, this does not affect the validity of the results, as the effect of the priority rules is still the same but observed in less magnitude. When implemented properly, the effects of EDD and SPT priority rules are likely yield the same results, but more powerful.
The due date slack required for 5% or less order tardiness is sought after using an interval of 50%. This means that the performance of each order priority rule cannot be compared, but the results can merely be used to identify POLCA’s workload balancing capabilities. As was the purpose of this study. When for all possible system configurations an order tardiness level of 5% is determined, the individual priority rules could be compared to one another.
6 Conclusion
28 in real production environment. For MTO firms absence of processing time variability is very unlikely since all orders are customer specific (Stevenson et al., 2005).
To answer the research question, due date restriction does not affect the performance of the POLCA system in terms of STT and TTT. When due dates get more restrictive, order tardiness increases which is to be expected. However, when a POLCA controlled production system is faced with more restrictive due dates, order tardiness can be decreased by increasing the number of cards available per POLCA loop. This can yield a decrease of up to 0,3% in order tardiness, improving due date adherence. It has become clear that TTT optimization does not necessary leads to order tardiness minimization in a POLCA system where workload balancing is able to occur.
Lastly it has to be noted that the possible due date adherence performance improvement which can be gained from workload balancing is quite minimal. Hence the likelihood that workload balancing is relevant to uphold a firm’s delivery reliability is not very likely. As long as a firm quotes realistic due dates, shown in table 4, which the POLCA system is able to uphold, an additional 0,3% improvement should not make the difference when average order tardiness is around 5%. Workload balancing can only make a difference when the production environment is posed with high utilization levels and constant processing times. These circumstances are, as said before, very unlikely in reality and more of theoretical relevance. 6.1 Future research
Future research may be conducted into what the real added value of POLCA is for SME MTO companies. From a company visit, it became clear that POLCA in its original state is only used nowadays for shop floor control. The number of cards may be set more arbitrarily, not necessarily based TTT minimization, but instead based on preservation of flow and minimization of starvation of workstations. This study also showed that the presence of processing time variability is destructive for the performance of a POLCA controlled production system and that workload balancing is unable to occur when processing time variability is present. Hence the question raises why SME MTO firms actually use POLCA for, since TTT and STT reduction as result of workload balancing are unlikely to occur in practice (Stevenson et al., 2005).
29 Another topic for feature research may be to combine the performance improvements of both the SPT and EDD rule, combining the ability to quote short due dates from the use of the SPT rule and the reduction in mean tardiness dispersion gained from the EDD rule into more complex combinational priority rules. Barman (1997) found that deploying a simplistic combination of the SPT and EDD rule on the shop floor at different stations was already effective in reducing both percentage of tardy orders and mean tardiness.
30
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Appendix 1: Model validation
0,0 50000,0 100000,0 150000,0 200000,0 250000,0 300000,0 1 1001 2001 3001 4001 5001 6001 7001 8001 9001 10001 Cum u lative m ean of r esu lt ( s) Period Run length
Series1 Series2 Series3
0 50000 100000 150000 200000 250000 300000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 M ovin g ave rage (s) Units Welch's Method 0 50000 100000 150000 200000 250000 300000 350000 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Cum u lative m ean ave rage Number of replications Number of replications
