Order Pool Sequencing for a Balanced CONWIP in a Make-To-Order Environment: A Simulation study at Neways Leeuwarden

Order Pool Sequencing for a Balanced CONWIP in

a Make-To-Order Environment: A Simulation study

at Neways Leeuwarden

MSc. Technology & Operations Management University of Groningen

Abstract

This study aims at applying a newly developed route-specific order pool sequencing rule, most capacity slack (MCS) rule, to a real-life situation. MCS makes constant work-in-process (CONWIP) control capable of distributing jobs evenly in a MTO job shop, which features high-variety product routing. This research is conducted as a simulation study using Python. The model simulates the production shop floor at an industrial thesis partner, Neways Leeuwarden, and applies CONWIP control with MCS rule to it. In order to benchmark the performance of MCS rule, models of CONWIP with first-in-first-out (FIFO), earliest due date (EDD), and shortest processing time (SPT) are also simulated. Further, MCS rule is also applied to divergent layout, convergent layout and pure job shop layout to provide explanation for the results from Neways case.

Table of Content

Table of Content ... 3

1 Introduction ... 4

2 Theoretical background ... 6

2.1 Constant work-in-process (CONWIP) control ... 6

2.2 CONWIP and MTO environment ... 7

2.3 Workload balancing in CONWIP ... 8

2.4 CONWIP and delivery reliability ... 9

2.5 Order pool sequencing (OPS) rules ... 9

2.5.1 The most capacity slack rule (MCS) ... 10

3 Methodology ... 13

3.1 Case of Neways Leeuwarden ... 13

3.2 Simulation model ... 14

3.3 Experiment design ... 17

3.4 Performance measurements ... 22

4 Analysis and Results ... 24

4.1 Scenario 1: Layout in Neways Leeuwarden ... 24

4.2 Scenario 2: Divergent layout ... 27

4.3 Scenario 3: Convergent layout ... 29

4.4 Scenario 4: Job shop layout ... 32

5 Discussion ... 35

5.1 Applicability of the most capacity slack (MCS) rule ... 35

5.2 Performance of FIFO ... 37

5.3 Limitation ... 38

6 Conclusion ... 39

1 Introduction

Imagine that there is a clearance sale of a popular brand, and lots of people want to get into the store. However, if all customers flood in the store at once without any limit, the store would become too crowded. Customers cannot browse the products comfortably and shop at their own paces. What if the staff of the store make some control over this situation? They could set up a queue in front of the entrance, and a customer would only be “pulled” into the store when another customer finishes shopping and leaves the store. This kind of control is the main idea behind constant work-in-process (CONWIP) control.

CONWIP is classified as one of the pull systems because the release of jobs depends on the status of a system (Hopp, & Spearman, 2011). To be more specific, movement of orders and materials to shop floor is triggered by completion of a job in downstream machines. By controlling the total amount of jobs in a system, the released jobs in the system can go through the production processes smoothly.

This research is conducted at Neways Leeuwarden, a printed circuit board (PCB) manufacturer. They operate in make-to-order (MTO) environment with a variety of products. Neways wishes to control amount of inventory on the shop floor to prevent high inventory cost and chaos. CONWIP seems to be a good choice with simplicity of implementation compared to other pull systems. However, the use of CONWIP in MTO environment is not supported in literature because CONWIP shows its inability to balance workload in MTO environment (Thürer, Stevenson, & Protzman, 2016).

In addition to internal and operational considerations, it is also crucial to keep a high delivery reliability from a marketing perspective of a company (Hill, 2000). Land, & Gaalman (1998) and Thürer et al. (2017) confirmed that balancing capability reduces throughput time and improved due date performance in MTO job shop. This research investigates the performance of CONWIP in terms of both throughput time and delivery reliability in MTO environment. The research gap is identified in the literature. First, research of CONWIP in MTO is really rare because most of the time, CONWIP control is applied to an environment with low product variety (Germs, & Riezebos, 2010). Thürer et al. (2017) proves in a pure job shop that CONWIP is also applicable to high-variety context with the MCS rule they used. However, they do not show how it could perform in different typology such as in a divergent layout, or in a convergent layout. Thus, the research question is formulated as follows:

To what degree can a route-and-load-specific sequencing rule of CONWIP be capable of balancing workload, and improving reliable delivery in different typology settings?

2 Theoretical background

2.1 Constant work-in-process (CONWIP) control

There are a few pull systems developed in recent decades, such as, Kanban, CONWIP, paired-cell overlapping loops of cards with authorization (POLCA), etc. (Thürer et al., 2016). They use cards to visualize, monitor, and control units of work or loads of work. Therefore, card-based system and pull system are always synonyms. Pull systems are more suitable for reducing costs, reducing variability and length of throughput time, and improve quality than push systems because push systems like MRP neglect system status such as aggregated work-in-process or aggregated workload upon releasing the jobs (Jodlbauer, & Huber, 2008). Neglecting system status may lead to unwanted waste through waiting, overproduction, defects, inventory, etc. (Thürer et al., 2016).

Figure 1 Illustration of CONWIP concept

Little’s Law, average cycle time is proportional to average amount of work-in-process. The pursuit of low cycle time also contributes to low inventory cost because work-in-process level is controlled. Second, the average cycle time is not only reduced but also stabilized because of a constant work-in-process level. Stable cycle time makes a manufacturer more able to quote reliable due dates to the customers because it is more predictable or less variable.

W = T * P [1]

W: average number of work-in-process in a system (unit of product) T: average cycle time of products or service (time unit)

P: average throughput rate of a system (unit per time unit)

In short, we can briefly summarize the nature of CONWIP control: (1) holding work-in-process level of a production line around a certain level, (2) releasing based on status change of downstream machine, and (3) retaining orders in the order pool until release. There are two advantages that result from its nature: reduced production time variability because of controlled job release, and flexibility to design changes because of late release (Hopp, & Spearman, 2011). 2.2 CONWIP and MTO environment

CONWIP was originally designed for a flow shop environment which produces low variety of products with constant routings, processing times, and linear flow (Spearman, et al, 1990; Prakash, & Chin, 2015). However, in MTO environment, every product or product family requires different combinations of machines to manufacture so there is a variety of production routings in a production plant. In order to cope with a variety of products, most of the MTO companies adopt a job shop layout with universal machines to produce different products (Land, & Gaalman, 1998). Customization may cause two or more products having different processing times on the same machine because of different technical specifications (Stevenson, Hendry, & Kingsman, 2005).

Thürer, et al. (2017) shows that, with a new order pool sequencing rule called most capacity slack (MCS) rule, CONWIP control can achieve shorter TTT and less tardiness at the same time in MTO environment. This promising result is attributed incorporating workload balancing capability into an order pool sequencing rule. The MCS rule is described in Section 2.5.1.

2.3 Workload balancing in CONWIP

First, the workload here and hereafter in this research refers to workload in terms of processing times on machines. Corresponding to the previous section, MTO environment features a variety of routings and different processing times, so the cycle time of each product varies. Because CONWIP retains the release of jobs when the work-in-process cap is reached, it is more likely that CONWIP control leads to TTT and delivery reliability deterioration compared to a push system.

Research shows that reduced TTT and increased delivery reliability can be achieved in another approach of the pull logic called workload control (WLC) with which workload on each machine can be balanced (Land, & Gaalman, 1998; Land, 2004; Thürer et al., 2012; Thürer et al., 2015). The balance embraces that the total workload on each machine should be the same or close to one another. The situation that some of the machines are fully loaded and the others are idling should not happen. In these researches, workload norms will be set for each machine, and a job will be retained in pool if workload added by the job makes any of the machines exceeds its norms. In this way, workload can be balanced at a pre-determined level.

2.4 CONWIP and delivery reliability

Delivery reliability refers to the capability of a company to deliver promised quantity of products on the promised date in a context of make-to-order, or capability of matching demands when it occurs, in a context of make-to-stock (Sarmiento, Byrne, Rene Contreras, & Rich, 2007). In literature, researchers have agreed on the statement that high delivery reliability is an order-qualifier which is a minimum requirement for a manufacturer to be qualified for competition (Sarmiento et al., 2007; Kumar, & Sharman, 1992; Hill, 2000).

In the past, pull system was believed to scores poor in due date performance, but it is then proved not true if workload is balanced evenly (Land, & Gaalman, 1998). On the other hand, CONWIP is mainly researched in the context of make-to-stock (MTS) (Framinan, González, & Ruiz-Usano, 2003), so there is only a few articles that examined the relationship among CONWIP, TTT, and delivery reliability (Germs, & Riezebos, 2010; Harrod, & Kanet, 2013; Thürer, et al., 2017).

2.5 Order pool sequencing (OPS) rules

In a CONWIP system, there are places that need a rule to decide which job goes first, in the order pool, or in a queue of a machine on the shop floor. Thus, this research distinguishes it as order pool sequencing (OPS) rules and shop floor dispatching (SFD) rules. Since there are various production routings in a MTO system and different jobs might happen to require the same resource at the same moment so OPS and SFD rules make significant influence on the overall performance of the system (Harrod, & Kanet, 2013). Due to the scope of this research, SFD is set as first-in-first-out (FIFO), and the focus will be put on OPS rules.

There are several traditional rules that are chosen from literature as OPS in this research, FIFO, shortest processing time (SPT), and earliest due date (EDD). FIFO is the most commonly used in practice because it takes whatever first arrived in a system. It is designed for neither reducing TTT nor improving due date performance. It is still a time-related so due date performance of FIFO may not be too bad (Thürer, et al., 2016).

with long processing time might be late for a long period (Thürer, et al., 2016). On the other hand, it neglects urgency of a job and it makes a job finished either too early or too late. Compared to SPT, EDD prioritizes jobs according to ascending due dates instead, so the mean tardiness can be reduced. EDD chooses the job with the earliest due date, but the chosen job might have a rather long total processing time. The long total processing time can lead to minor tardiness for the following jobs. For example, SPT may cause one tardy job with tardiness of 10 days, and EDD may cause 5 tardy jobs with a mean tardiness of 0.5 day.

2.5.1 The most capacity slack rule with direct load in number of jobs (MCS)

The most capacity slack rule was proposed by Thürer, et al. (2017) to sequence the jobs according to both routing and workload information. Including workload consideration in a sequencing rule enables CONWIP to balance workload among machines. Thürer, et al. (2017) design 4 variations of capacity slack rule, and each variation calculates workload differently. The workload of every machine can be viewed as two parts: direct load and indirect load. Indirect load of a machine implies that the workload that is still in upstream operations and is coming to the considered machine for sure (Oosterman, Land, & Gaalman, 2000). Direct load only takes into account the jobs that are really in the queue at a station (Oosterman et al., 2000). The jobs coming in the near future are not included in calculation of direct load. This research chooses to incorporate the best performing capacity slack variation for job shop in Thürer, et al. (2017), the most capacity slack rule with direct load in number of jobs, which will be called MCS hereafter in this report.

This section will first explain the idea behind the MCS rule and then present it in mathematical expressions. The MCS rule incorporated in this research is adapted for the purpose of applying in a CONWIP system by Thürer, et al. (2017). Though this rule considers workload of machines, it views workload in number of jobs rather than hour of work.

The calculation of the MCS rule is mainly about how many percent will a job occupy available

capacity from each machine on its routing on average. To calculate the “to-be-occupied”

percentage of available capacity on a machine by a job, the denominator is the theoretically available capacity which was explained in last paragraph, WIP cap for each machine subtracts the actual number of jobs on a machine. The nominator is the occupied capacity which is “1” for sure because it is mentioned that the capacity here is counted in number of jobs. A job of course occupies only one unit of capacity.

The percentage obtained by the denominator and nominator here is the percentage of an operation, so percentages of occupied capacity from each machine on a job’s routing should be summed up. Last step, the sum is divided by number of operations. This is because the action of dividing number of operations makes two jobs comparable when there are two jobs with different number of operations.

The result means the mean percentage of available capacity a job occupies from each machine

on its routing. The smaller the result is, the smaller mean portion of available capacity on each

machine is occupied by a job. In other words, the smaller the result is, the smaller impact on a balanced system a job has, and the less possible the job is to violate a evenly distributed system. With smaller result, a job gets more priority.

The mathematical expression of the priority calculation of the MCS rule is shown in [2]. 𝑃𝑟𝑖𝑜𝑟𝑖𝑡𝑦 = ) *+,-.+, +∈01 21 [2] 𝑁₄5_{: 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑗𝑜𝑏𝑠 𝑎𝑙𝑙𝑜𝑤𝑒𝑑 𝑜𝑛 𝑚𝑎𝑐ℎ𝑖𝑛𝑒 𝑖.} 𝐴₄5_{: 𝑎𝑐𝑡𝑢𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠𝑙𝑦 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑 𝑗𝑜𝑏 𝑜𝑛 𝑚𝑎𝑐ℎ𝑖𝑛𝑒 𝑖}

Equation [3] is used to translate WIPs cap of the whole system into WIP cap of each machine. 𝑁₄I ₌ J

2 [3]

𝑐: 𝑊𝐼𝑃 𝑐𝑎𝑝 𝑜𝑓 𝐶𝑂𝑁𝑊𝐼𝑃 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑤ℎ𝑜𝑙𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑛: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑐ℎ𝑖𝑛𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

2 minus 2, which is 0, on machine 2, 2 minus 3, which is -1, and on machine 4, 2 minus 3, which is also -1. On the other hand, the nominators for the percentage of each machine are 1. Thürer, et al. (2017) make it a rule that the percentage will be replace with a large number, L, when the denominator is equal to or smaller than 0. This is because when denominator, i.e. available capacity, is equal to or smaller than 0, this job is violating a balanced situation where jobs are evenly distributed. As a result, the sum of percentages of job A is 3L. The calculation for job B remains, on machine 1, available capacity is 2 minus 2, which is 0, on machine 3, 2 minus 2, which is 0, and on machine 5, 2 minus 0, which is also 2. The sum of percentages on each machine is 2L+1/2.

Eventually, the sums obtained from job A and job B are all divided individually by number of operations for jobs A and job B, which are both 3. Job A has a mean percentage of occupied available capacity on each machine of L, and the mean percentage of occupied available capacity on each machine for job B is 2L/3 + 1/6, which is smaller than that of job A. Job B has smaller MCS calculation result, and it means that job B occupies less percentage of available capacity on each machine on average job A does. In other words, letting job B enter the system helps to maintain a balanced system. This decision simply matches the selection of intuitive judgment upon seeing Figure 2. We can see that the routing machine 1-machine 3- machine 5 is emptier than the routing machine 1-machine 2- machine 4.

3 Methodology

3.1 Case of Neways Leeuwarden 3.1.1 Background information

Neways Leeuwarden manufactures printed circuit boards (PCBs) according to specifications required by customers, which we called it as MTO company in the previous section. It was confirmed by the production manager of Neways Leeuwarden that they want to reduce average inventory level resulted from a variety of product family, and increase delivery reliability. Choosing CONWIP as a solution for Neways Leeuwarden can be explained from two perspectives.

First, pull system controls the release of jobs into systems. Controlling release of jobs contributes to lower and more stable average work-in-process lever, less variable cycle time, and late release of jobs (Hopp, & Spearman, 2011). Stable work-in-process level means stable inventory cost and less variable cycle time. Less variable cycle time enables the company to quote due dates more accurately. Additionally, late release of jobs preserves the opportunity for customers to make late design change.

Second, simplicity of CONWIP is the reason why it was developed to replace Kanban system (Spearman, et al, 1990). It uses only one control loop which means that there is only one parameter involved, i.e. the number of work-in-process allowed, so it is easier than other pull systems with multiple control loops. However, in an MTO job shop, more complicated pull systems like POLCA and m-CONWIP were believed to be superior to a traditional CONWIP (Germs, & Riezebos, 2010; Thürer, et al., 2017). With adaption of Thürer et al (2017), CONWIP is equipped also with balancing capability and remains the simplicity it has.

3.1.2 Layout of shop floor at Neways Leeuwarden

Figure 3 Routing of products in Neways Leeuwarden

For telecom and industry products, they have to go through an SMD line and followed by heating, namontage, testing, coating, and final inspection. Defense products require a higher level of accuracy throughout manufacturing stages, so there is a set of dedicated machines for defense products. The generalized layout will be used in the analysis to investigate performance of different sequencing rules. On the other hand, three more production layouts are also investigated, divergent layout, convergent layout, and pure job shop layout. These three additional layouts provide a more generic sense of how MCS and the other sequencing rules perform in different typology setting. They will be further described in the section experiment design.

3.2 Simulation model 3.2.1 Model overview

Figure 4 Combinations of sequencing rules and typologies

The inter-arrival times and processing times of each machine follow exponential distribution, which according to Hopp & Spearman (2011) can be considered moderately variable. The utilization rate of each station is designed to remain 90%, so arrival rate and processing rate will be set accordingly to remain busy in 90% of the time. Due date of each job is determined by adding a random number to the arrival time of a job. This random number is generated from an exponential distribution with a mean of 10 times the total processing time of the job. Kingman’s equation, or VUT formula (Hopp & Spearman, 2011), shows that the average waiting time of a jobs in a 90% utilized system with exponential arrival and processing time is about 9 times the processing time of the job. Thus, 9 times processing time for waiting pluses one time processing time is required by a job to be finished. This is the reason why due dates are determined in this way.

Warm-up period is decided with Welch’s method (Robinson, 2014), and number of repetitions is decided by graphical inspection (Robinson, 2014). Run length is decided by viewing time-series plot of average cycle time. It is chosen at the moment when the time-time-series plot is reasonably smooth and it is also at least 10 times longer than the warm-up period. Specific number of the simulation parameters used are given in the experiment design section.

3.2.2 Simulation approach

The simulation is modeled as a discrete event simulation which updates the system when it is the time for an entity, i.e. a job, to flow from one activity to another (Robinson, 2014). Robinson (2014) pointed out that discrete event simulation is suitable especially for a queueing system. The model in this project is composed of three major parts, an order pool, stations on production shop floor, and a set of update timings for the arrivals and every station.

There are four types of mutually exclusive actions for an event, two for arrival events and two for departure events. For arrival events, if the total WIP in the system is below WIP cap, this arrived job can proceed to its first operation. Otherwise, the job should stay in the order pool. For departure events, when a job is departing from its last operation, the job leaves the system and a new job is allowed to be pulled in if there are jobs waiting in the order pool. When a job is departing but it is not at its last operation, then it is moved to next station according to the routing information of the job.

going to be finished and depart from the current station. This upcoming departure time will be logged as the next update timing of the current station.

Besides update timing of each station, there is also update timing for arriving jobs. Likely, when a job arrives, it will proceed to either the first operation or to the order pool, and the model will generate a random inter-arrival time according to exponential distribution with the given mean. Current time of the system will be added to the generated inter-arrival time, and the sum will be the update timing of next arrival.

The whole simulation model runs on a rolling time horizon starting from current time, 0. Current time goes to the earliest update timing among all of the logged update timings from either new arrival or departures on machines. Then the model executes the action according to the type of the event. The logic of the simulation is shown in pseudo code below.

Terminology:

NOW: current time of the system

WIP_count: current aggregated work-in-process in the system CAP: work-in-process cap for CONWIP implementation Output_count: aggregated output

Run_length: pre-determined number of output which acts as run length of the simulation M = [m0, m1, m2, .., mn] a Set of the order generator m0 and all machines m1 to mn

U = list of update timings of the order generator and stations. Update timing for the order generator is initialized as the arrival time of the first order, and the timings for the rest are initialized as a large number L.

C = ID of the station that is being updated now. C = 0 means new arrival of an order

Pseudo Code:

U = [time of the first arrival, L, L, …, L] while Output_count < Run_length :

NOW = min (U)

C = ID of the station with Min (U). if ( C == 0 AND WIP_count < CAP ) :

ü Proceed the new job to its first operation.

ü If the new job that just arrives is directly processed, update timing of the current station in U is updated.

else if ( C == 0 AND WIP_count >= CAP ): ü Hold the job in the order pool. else if ( C is the last operation of a job ):

ü The current job at the station leaves the system

ü If there is at least 1 job waiting in the order pool for entering, release 1 job to the shop floor.

ü If the released job is processed directly, update timing of the current station in U is updated

else:

ü The current job proceeds to next operation. If the job is directly processed at next station, update timing of next station in U is updated.

ü If there is at least 1 job waiting in the queue of the current station. The job starts to be processed and update timing of the current station in U is updated.

3.3 Experiment design

The layout in Neways Leeuwarden cannot be classified as either a pure job shop or a pure flow shop. Production environment at Neways Leeuwarden is of high-variety for sure because they can comply with different specifications from customers with the same set of machines. The layout itself is more or less a job shop. Departments are grouped by functions. However, the material flows in the same direction from SMD to final inspection in sequence. It is not a pure flow shop which produces low-variety products. Still, it looks like a flow shop in a general sense because materials flow from a station to an adjacent station (Tompkins, White, Bozer, & Tanchoco, 2010).

On the other hand, there are two main parts of the plant, the area for telecom and industry products, and the area for defense products. From this point of view, it takes on a product family, or focused factory, layout (Tompkins et. al, 2010). As a result, the layout at Neways Leeuwarden is considered as a hybrid situation.

flow in any direction to any stations. Every station is only be allowed to be visited at most once. Settings of each layout are illustrated below.

(a) Divergent layout (b) Convergent layout

(c) Job shop layout

Figure 5 Typologies for three generic routings

3.3.1 Scenario 1: Layout in Neways Leeuwarden

The configuration of the simulation model with Neways’ setting is shown in Figure 6. The mean processing time of the dedicated line for defense products is set at 10 because it is assumed to be close to and slightly higher than the sum of heating, namontage, and testing machines for the other two product families. The arrival rate is set to meet 90 % utilization.

Figure 6 Mean of inter-arrival time and processing times in layout of Neways Leeuwarden

the fluctuation of moving averages generated by Welch’s method with a window length of 5 periods. By graphical inspection, the warm-up period is chosen with generosity as 600 periods. Additionally, run length is chosen as 10.000 periods which is sufficiently longer than ten times of warm-up period. In order to avoid encountering cool down effect that the jobs before termination face an emptier system, the last 100 periods are not included in result calculation. Number of repetitions is chosen by observing the fluctuation of accumulated average of TTT when number of repetition increases. It is shown in Figure 8. As a result, the number of repetition is chosen to be 40.

The run length of 10.000 periods, warm-up length of 600 periods, cool down length of 100 periods, and 40 repetitions are also used in the experiments of the other three layout scenarios.

Figure 7 Warm-up period determination

Figure 8 Repetition determination

Utilization rate Number of Stations

WIP limit Pattern of

inter-arrival time

Pattern of Processing Time

90% 7 40~110 Exponential Exponential

Table 1 Summary of model characteristics

3.3.2 Scenario 2: Divergent layout

The configuration of the simulation model with a divergent layout is shown in Figure 9. The mean processing time is two times greater than the mean processing time in the previous production stage in order to meet 90 % utilization.

Figure 9 Mean of inter-arrival time and processing times in layout of divergent layout

The characteristics of the simulation model are summarized in Table 2. With some preliminary runs, the WIP cap used for CONWIP control ranges from 40 to 90. The distribution of inter-arrival times and processing times are both exponential distribution.

Utilization rate Number of

Stations

WIP limit Pattern of

inter-arrival time

Pattern of Processing Time

90% 15 40~90 Exponential Exponential

Table 2 Summary of model characteristics

3.3.3 Scenario 3: Convergent layout

Figure 10 Mean of inter-arrival time and processing times in layout of convergent layout

The characteristics of the simulation model are summarized in Table 3. With some preliminary runs, the WIP cap used for CONWIP control ranges from 20 to 90. The distribution of inter-arrival times and processing times are both exponential distribution.

Utilization rate Number of

Stations

WIP limit Pattern of

inter-arrival time

Pattern of Processing Time

90% 15 20~70 Exponential Exponential

Table 3 Summary of model characteristics

3.3.4 Scenario 4: Job shop layout

The configuration of the simulation model with a divergent layout is shown in Figure 11. The mean processing time of every machine is set to 2.88 time unit. The arrival rate is set to meet 90 % utilization. The characteristics of the simulation model are summarized in Table 4.

Utilization rate Number of Stations

WIP limit Pattern of

inter-arrival time

Pattern of Processing Time

90% 8 3~25 Exponential Exponential

Table 4 Summary of model characteristics

3.3.5 Verification and validation

Verification

The purpose of verification is to check if the model works correctly as expected and whether the logic structure of the computer model corresponds to the original conceptual model (Robinson, 2014). Logic error was easily identified and corrected during the process of coding because the model can only be compiled when apparent logic errors are rooted out. After that, a trial run with only 10 jobs released was simulated to check if the jobs move among stations in an expected manner. System information such as, timing of an event, aggregated work-in-process in the system, queue of every station, etc. are printed out for visual and manual verification.

For verifying the sequencing rules, the focus is thus on the order pool. The verification was carried out in the same way mentioned before. The jobs in the order pool were printed out first and then checked manually to see if the right job was selected by the coded sequencing rules.

Validation

Validation has to check difference between a model and the reality. In this research, queueing theory is used to validate the model. The models are validated with the help of Kingman’s equation, or sometimes called VUT formula (Hopp & Spearman, 2011), as demonstrated in equation [4]. The average performance output from the simulation is compared to theoretical results calculate with [4].

𝐶𝑦𝑐𝑙𝑒 𝑇𝑖𝑚𝑒 = PQRS PTR U ∗ W XYW∗ 𝑡Z [4] 𝐶_[: 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟 − 𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 𝐶Z: 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 𝑢: 𝑈𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 3.4 Performance measurements

Throughput time indicators

Throughput time indicators include STT and TTT. From Little’s law, we can know that low work-in-process level brings short STT. However, improper control over work-in-process leads to long waiting time in the order pool and thus the TTT of jobs can be longer than a push system. The effectiveness of a OPS rule in balancing workload can be seen from TTT (Germs, & Riezebos, 2010). It is called effective if TTT is successfully reduced to less than that of a push system.

Delivery reliability indicators

4 Analysis and Results

The results of every layout setting are presented in the following paragraphs. The performance is presented in terms of the indicators mentioned in the previous section, shop floor throughput time, total throughput time, mean tardiness, and percentage of tardy jobs. The squared coefficient of variance (SCV) is used to indicate the stability of total throughput time under different sequencing rules. SCV is used rather than simply using variance is because of comparability. SCV is the squared ratio of variance over mean. It considers the relative magnitude of the variance. For example, a variance of 5 hours is acceptable for a system with a mean cycle time of 100 hours but it is not the case if the system has a mean cycle time of only 1 hour. SCV is 0.0005 for the situation with a mean of 100 hours and SCV is 5 for the situation with a mean of 1 hour. The bigger the SCV is, the performance is more volatile and more fluctuating.

4.1 Scenario 1: Layout in Neways Leeuwarden

The result of throughput time is presented in Figure 12, a graph with STT one the X-axis and TTT on the Y-axis. The arrangement of the graph is for the purpose of examining how each rule influences two types of throughput time at the same time. Every curve in the graph represents the performance of a sequencing rule; and every point on the curve represents the result of that specific sequencing rule under a certain level of WIP cap.

As mentioned before, the difference between STT and TTT is the time a job spends waiting in the order pool. When the WIP cap is small, or strict, there are only a few jobs allowed to enter the shop floor, so jobs have to wait in the order pool for a long period. Therefore, the average TTT, i.e. STT pluses order pool waiting time, is high under a small WIP cap. In every curve of Figure 12, from top to down, TTT decreases with the increase of WIP cap.

CONWIP control. With a WIP cap that is too bug to reach, jobs do not stay in the order pool, and STT is thus equal to TTT.

In Figure 12, the ranking of performance of the four sequencing rules is as follow: FIFO works the best, and then EDD, Most Capacity Slack rule, and SPT is the worst in this scenario. Under a same level of WIP cap, the difference among STT of the four rules is somewhat close, but it shows big difference when looking at TTT. Before WIP cap goes beyond 70 jobs, SPT causes the most, MCS the second, EDD the third, and FIFO the least TTT under same level of WIP cap. It can be easily recognized in Figure 12.

Figure 12 Throughput time performance of layout in Neways

While looking at squared coefficient of variance (SCV) of total throughput time in Figure 13, SCVs of SPT are very big when WIP caps are smaller than 70 jobs. The best performing FIFO rule in terms of throughput time is also the best when looking from the angle of SCV before the WIP cap is bigger than 90 jobs. After 90 jobs, SCVs of each rule are similar. The MCS rule is the second best before the WIP cap is bigger than 90 jobs. Moreover, when the WIP cap is set at 40 or 50, MCS is as good as FIFO.

Figure 13 SCV of total throughput time of layout in Neways

As in Figure 14, the performance of the four rules in terms of mean tardiness ranks in the same way as the performance in terms of throughput time. FIFO is the best, and then EDD, MCS and SPT is the worst.

Figure 14 Mean tardiness performance of layout in Neways

As for the performance of the percentage of tardy jobs, before the work-in-process of 50 jobs, SPT works better than FIFO. When WIP cap is greater than 50 jobs, FIFO outperforms SPT rule. MCS and EDD remain third and fourth along with the increase in WIP cap.

Figure 15 Mean percentage of tardy jobs of layout in Neways

4.2 Scenario 2: Divergent layout

In Figure 16, in terms of throughput time, ranking of performance of the four sequencing rules is not very clear. Under a same work-in-process level, STTs of the four rules are similar and the difference lies in TTTs. MCS performs worse than any other rules and the ranking of other three rules is changing when WIP cap changes, and it is shown in Table 5.

Figure 16 Throughput time performance of divergent layout

WIP cap FIFO EDD SPT 40 Rank 2nd _{Rank 1}st _{Rank 3}rd

50 Rank 2nd Rank 1st Rank 3rd 60 Rank 1st _{Rank 3}rd _{Rank 2}nd

70 Rank 3rd _{Rank 2}nd _{Rank 1}st

80 Rank 2nd Rank 1st Rank 3rd 90 Rank 1st Rank 3rd Rank 2nd No cap Rank 1st _{Rank 2}nd _{Rank 3}rd

Table 5 Ranking of FIFO, EDD, SPT when WIP limit changes (TTT performance)

When looking at SCV of total throughput time in Figure 17, SCVs of EDD and MCS are higher than SCVs of FIFO and SPT. However, before the WIP cap of 60 jobs, the SCVs are all between 0.3 and 0.35. After the limit of 60 jobs, SCVs of EDD and MCS go bigger when limit of work-in-process increases, and MCS performs the worst.

Figure 17 SCV of total throughput time of divergent layout

As in Figure 18, the performance of MCS in terms of mean tardiness ranks much worse than any other sequencing rules. Like the performance of throughput time, the ranking of other three rules is changing when WIP cap changes. In Figure 19, the situation holds also for the performance in terms of percentage of tardy jobs, only that EDD rule replace MCS as the worst performing when looking at percentage of tardy jobs.

Figure 18 Mean tardiness performance of divergent layout

Figure 19 Mean percentage of tardy jobs of divergent layout

4.3 Scenario 3: Convergent layout

Figure 20 Throughput time performance of convergent layout

WIP cap FIFO EDD SPT

20 Rank 1st Rank 2nd Rank 3rd 25 Rank 1st _{Rank 2}nd _{Rank 3}rd

30 Rank 1st _{Rank 3}rd _{Rank 2}nd

35 Rank 3rd _{Rank 2}nd _{Rank 1}st

40 Rank 1st _{Rank 2}nd _{Rank 3}rd

45 Rank 3rd Rank 2nd Rank 1st 50 Rank 2nd _{Rank 3}rd _{Rank 1}st

55 Rank 1st _{Rank 2}nd _{Rank 3}rd

60 Rank 3rd Rank 1st Rank 2nd 65 Rank 1st Rank 3rd Rank 2nd 70 Rank 2nd _{Rank 1}st _{Rank 3}rd

No cap Rank 2nd Rank 1st Rank 3rd

Table 6

When looking at SCV of total throughput time in Figure 21, SCVs of EDD increases more than others when work-in-process level increases. EDD is the most variable rule regarding total throughput time. Overall, MCS results in the most stable TTT of all rules before WIP cap goes beyond 55 jobs. However, one thing noteworthy is that most of the SCVs of the four rules fluctuate between 0.27 and 0.39, which means that the difference is observable but small.

Figure 21 SCV of total throughput time of convergent layout

As in Figure 22, the performance of MCS in terms of mean tardiness ranks much better than any other sequencing rules. Corresponding to the performance of throughput time, the ranking of other three rules is changing when WIP cap changes. In Figure 23, the situation holds also for the performance in terms of percentage of tardy jobs, only that EDD rule become apparently a worst performing sequencing rule when looking at percentage of tardy jobs.

Figure 22 Mean tardiness performance of convergent layout

Figure 23 Mean percentage of tardy jobs of convergent layout

4.4 Scenario 4: Job shop layout

For a job shop layout, MCS can decrease TTT to a low level with a smaller WIP cap. As shown in Figure 24, it is an overview how TTT decreases with different sequencing rules. MCS ranks the first and SPT ranks the second. The difference between FIFO and EDD is not obvious.

Figure 24 Throughput time performance of job shop layout

Figure 25 shows the SVC of four sequencing rules. Regarding SCV, FIFO and EDD can provide stable TTT wth smaller SCV than SPT and MCS. SCV of MCS keeps decreasing with the increase of WIP level, and SCV is around 0.4 when WIP level is 70 jobs. After surpassing

this WIP level, the difference among FIFO, EDD, MCS in terms of SCV is already smaller than 0.1.

Figure 25 SCV of total throughput time of job shop layout

In Figure 26, the performance of mean tardiness is in accordance with the performance of throughput times. MCS remains its advantage. In Figure 27, SPT outperforms MCS slightly in percentage of tardy jobs but the difference is not pretty big. When looking at percentage of tardy jobs, FIFO and EDD perform similarly and on the other hand, SPT and MCS perform similarly.

Figure 26 Mean tardiness performance of job shop layout

5 Discussion

5.1 Applicability of the most capacity slack (MCS) rule Layout in Neways Leeuwarden

For the scenario of Neways, there is a lack of evidence to back up the use of MCS rule. It demonstrates neither a better capability of reducing total throughput time (TTT) nor a superior capability of improving delivery performance. When the WIP cap is low, it is outperformed by FIFO and EDD in TTT and mean tardiness. When the WIP cap goes bigger, the MCS rule shows no difference among all the four rules. Regarding percentage of tardy jobs, MCS only performs slightly better than EDD rule. FIFO and SPT have less percentage of tardy jobs than MCS. In other words, the performance of MCS in Neways’ setting is not worthy of all the efforts to calculate the priority for jobs in MCS rule.

Oosterman et al. (2000)’s conclusion on shop characteristics may explain why MCS, which use direct load for calculation, is out performed by FIFO and EDD in the scenario of Neways while performing the best in a pure job shop in scenario 4. MCS uses the information of direct load at each station. Oosterman et al. (2000) conclude that calculation with direct load is more suitable for pure job shop like scenario 4, which has more undirected flow, and indirect load should be included in flow shop or in the production system where there exists dominant direction of material flow like scenario of Neways.

Divergent & convergent layout

For divergent and convergent scenarios, the results are quite opposite to each other, so they are discussed together in this section. MCS performs the worst in a divergent layout while it is the best rule among the four under a convergent layout. This result can be explained by the nature of these two layouts.

In a divergent layout, a job starts at stage 1 which consists of only one station, and every routing diverges into 2 after every stage. It can be said that different routings go through more shared machines during upstream stages than downstream stages. It is totally opposite for a convergent layout. A convergent layout has in the design of this research has 8 stations in the beginning, and every 2 routings converge into 1 after every stage. Thus, it can be said that different routings go through less shared machines during upstream stages than downstream stages. Divergent layout and convergent layout both feature dominant direction of material flow, so MCS rule should not work well by only looking at direct load according to Oosterman et al. (2000). Yet, routings in a divergent layout have more shared machines at upstream, so the focus of workload balancing by MCS is mainly balancing the jobs at downstream. Conversely, routings in a convergent layout have more shared machines at downstream, so the focus of workload balancing by MCS is mainly balancing the jobs at upstream. For the reason that direct load is more accurate at upstream than at downstream in a system with dominant flow direction, MCS’s balancing capability is better in the convergent layout.

On the other hand, according to Spearman, & Hopp (2011), manipulation in a manufacturing system is more effective when it is carried out at upstream rather than at downstream of a production line. MCS balances system with convergent layout at upstream and system with divergent layout at downstream. Thus, the effect of MCS should be greater in a convergent layout according to Spearman, & Hopp (2011)’s observation.

Job shop layout

In Thürer et al. (2017), MCS rule is applied to a job shop with CONWIP control and compared with several other order pool sequencing rules. From the result of applying MCS in job shop shown in previous section, MCS is suitable for a job shop setting with CONWIP control. This is in accordance with the conclusion from Thürer et al. (2017).

In short, the applicability of MCS with CONWIP is confirmed in convergent layout and pure job shop layout. When applying this rule, whether to include indirect load of machines or not should be considered according to different shop characteristics (dominant direction of flow or undirected flow) of the system.

Additionally, the idea of MCS is originated from literature of workload control (WLC) so MCS may work perfectly without a CONWIP loop while remaining low level of inventory. However, WLC method still has to set workload norms in hour for each machine so the simplicity of a unit-based and one-parameter CONWIP system will be lost. The accuracy and performance of MCS could be improved by directly counting workload in hour rather than in number of jobs. As a result, constant load (CONLOAD) is one of the possibilities to implement MCS for further investigation.

5.2 Performance of FIFO

Nevertheless, FIFO is a “do-nothing” rule which releases jobs into system according to the natural arrivals of jobs. Therefore, by being a time-related sequencing rule and making no disturbance on the balance nature of a system, it can contribute to an acceptable performance compared to others.

5.3 Limitations

6 Conclusion

CONWIP’s disadvantage that it may not have short throughput time and good due date performance in MTO production like Neways is overcome by Thürer et al. (2017) with MCS rule, which is capable of distributing jobs evenly and in turn results in shorter throughput times (Germs, & Riezebos, 2010) and better due date performance (Land, & Gaalman, 1998). Neways Leeuwarden produces a variety of products, so it is very easy to understand that they want the inventory level under control while not degrading their due date performance. CONWIP with MCS rule is then ideal for Neways to cope with their goals.

This simulation research applied MCS rule by Thürer et al. (2017) and traditional FIFO, EDD, SPT to CONWIP controlled system. The performances of the four rules are first compared in a generalized environment of Neways, but MCS rule does not perform better than the others. As a result, MCS is not suitable for the case of Neways with all the calculation work giving no valuable improvement. However, according to the discussion section, it may be an opportunity to apply the idea of MCS in Neways if the way of workload calculation includes indirect load. Three more scenarios are investigated to describe the applicability of MCS in generic layout settings. The results again confirm the conclusion of Thürer et al. (2017) that with MCS rule, CONWIP is applicable in a high-variety job shop. Further, the results of this report also show that MCS is advantageous in a convergent layout but not recommendable for divergent layout. It adds some insight to the theory and provides more idea for the further research of MCS rule in CONWIP control.

Future research

(WINQ), machine with least utilization (Joseph, & Sridharan, 2011; Thürer et al., 2017), and they may also be helpful for a CONWIP in MTO job shop.

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