Simulation-based Procedure for Implementing Theory ...

Simulation-based Procedure for Implementing Theory of Constraints: Extension for Cases with Multiple Bottlenecks Chompoonoot Kasemset†1and Voratas Kachitvichyanukul†2 Industrial Engineering and Management,  School of Engineering and Technology, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand Tel: (66 2) 0-2524-5675; Fax: (66 2) 0-2524-5697 Email: [email protected] [email protected] 2

Abstract. This paper presents a simulation-based procedure to implement TOC policy in a manufacturing environment with multiple bottlenecks. The procedure is an extension of the single bottleneck case originally proposed by Kasemset and Kachitvichyanukul (2005). The procedure uses simulation to identify bottlenecks, set up DBR system and evaluate the performance of the new system. The cases with multiple bottlenecks are much more difficult than the cases with single bottleneck. Starting with bottleneck identification, bottlenecks are identified by conducting simulation experiments to identify all system bottlenecks. After the real bottlenecks are identified, more simulation experiments are carried out to determine buffer size for each bottleneck station. The final step is to establish the DBR (Drum-Buffer-Rope). The performance evaluation is done to verify the effectiveness of the resulting DBR. An example is given to illustrate the procedure. Keywords: Theory of Constraints (TOC), Simulation-based Procedure, Multiple Bottlenecks, DBR (DrumBuffer-Rope).

1. INTRODUCTION “An hour lost at the bottleneck is an hour lost for the entire system. An hour saved at a non-bottleneck is a mirage”. Theory of constraint concentrates on how to manage the system constraint, i.e., the bottleneck resource or CCR, to drive more income and for company to survive in the real world business (Goldratt and Cox 1986). The key TOC concept is “The system output rate is limited by the machine with the slowest rate”. In TOC, there are only two types of machines; a bottleneck machine or CCR (Capacity constraint resource) and a nonbottleneck machine or non-CCR. Bottleneck Resource or CCR is the resource that its capacity is equal or less than the demand. There are fewer resources of this type in the factory. The other type is the non-bottleneck machine or non-CCR. It is the resource that its capacity is greater than the demand. The main point of this procedure is to balance flow of product by making the output rate at the bottleneck equal to or a little bit more than the market demand. In order to implement TOC, there are five steps as listed below.

Step1: Identify the system’s constraint Step2: Exploit the system’s constraint Step3: Subordinate the system’s constraint Step4: Elevate the system’s constraint Step5: Return to first step but prevent inertia from being the next constraint The execution of all steps can result in a shifting of the system constraint. Thus, it is necessary to return to the first step and identify the new system constraint. Preventing inertia means examining the new system configuration to ensure that it remains appropriate. In this study, the system proposed by Kasemset and Kachitvichyanukul (2005) is extended for cases with multiple bottlenecks.

2. PREVIOUS RESEARCH Kasemset and Kachitvichyanukul (2005) proposed a simulation-based system which consists of two generic models (Physical job flow model and Information control flow model). The models are implemented in ARENA. The users can model various production systems simply by

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference defining basic manufacturing data: machines, jobs, processes, demand target, warehouse limitation etc. The procedure to use the model in accordance with the five steps of TOC is described below.

significantly higher mean confident interval of throughput than the base case is identified to be the system bottleneck, (see Kasemset 2005 and Kasemset and Kachitvichyanukul 2007).

Step 0: Preparation

Step 2 to Step 4: Bottleneck Exploitation, System Subordination and Elevation

Users define the manufacturing input data for baseline case. This step is done whenever there are changes in the production system.

Step 1: Bottleneck Identification The simulation is run for existing system to collect statistics of the following key performance indicators; (1) Throughput of existing system and (2) Utilization of each machine and (3) Time between arrival and departure of each process.

Bottleneck Candidate Identification Procedure (Kasemset and Kachitvichyanukul 2007) To identify the bottleneck candidates, three factors, utilization, throughput rate and utilization factor are required. Considering each factor; (1) Utilization data: The machines or processes that have high utilization are selected to be the bottleneck candidates. (2) Throughput Rate: Following the basic principle of Factory Physics (Hopp and Spearman 2001), the throughput rate of each station comes from the ratio between the number of processed parts and operation time. In each product route, the output rate of every station is calculated. Among them, Bottleneck Rate (Rb) is the minimum value of output rate. Thus, the station with Rb qualifies to be bottleneck candidates. (3) Utilization Factor: Based on queuing theory, a single-server system with finite queue of no more than K units, M/M/1/K (Radovilsky 1998). The utilization factor (ρ) is calculated from ρ = λ / µ, λ and µ are arrival and departure rate for each process/ machine. If processes or machines have high utilization factor, they are identified to be bottleneck candidates. For the cases with single bottleneck, several bottleneck candidates can be identified from the utilization statistics collected from the simulation runs and from the bottleneck rate calculation. Simulation experiments are then carried out to find the real bottleneck from among the candidates. In the experiment, many scenarios are created by adding one of each bottleneck candidate for each scenario and rerun the simulation to collect throughput statistics for each scenario to construct the mean confident interval of throughput for comparison. The scenario with

After the system bottleneck is identified, DrumBuffer-Rope (DBR) can be defined in the information flow model. Drum is a location of bottleneck. Then, Buffer is placed before the bottlenecks. Time buffer is applied as a waiting line of incoming products before the CCR. Buffer size in the experiment can be calculated based on two concepts; (1) The buffer size (K) can be calculated based on the M/M/1/K system. The buffer size of K units is needed to keep the bottleneck from being idle with probability less than P0 (P0(K) < x) (Radovilsky 1998). (2) Critical WIP based on factory physics (Hopp and Spearman 2001). To set the buffer size for each bottleneck, the simulation experiment is also carried out to collect throughput statistics for every scenario and to construct the confident intervals of throughput mean for comparison. There are many values of buffer size for each bottleneck created depended on threshold value P0 or x that the users want to test and one possible value must be the critical WIP (W0). Rope is used to control the movement of physical flow by changing the control information. There are two ropes to be set; (1) Rope for material release and (2) Rope to protect unneeded parts from processing too soon. The first rope controls material entering the system. The second rope protects the system from processing the unneeded product type.

Step 5: If the results from the first four steps can yield a throughput that exceeds the demand, then the process stop. Otherwise, go back to the Step 1. The mean confident intervals of throughput are calculated and compared with throughput target. The Output Analyzer program in ARENA can help the user to construct the mean confident interval comparison from the results from the simulation runs. After the output is confirmed by comparing the mean throughput with the target throughput and it reaches the target demand, the manufacturing configuration for TOC can be concluded. Figure 1 show the overall proposed system from Kasemset and Kachitvichyanukul (2005).

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference

 

 

             

Figure 1: Overall System Proposed by Kasemset and Kachitvichyanukul (2005and 2007)

3. THE EXTENSION BOTTLENECK CASE

FOR

MULTIPLE

As in Figure 1, the blocks with different color are the steps that were modified for the cases with multiple bottlenecks. The first colored block is in bottleneck identification step. For the cases with multiple bottlenecks, more than one simulation experiment is required because the result from the first experiment may not distinctly identify the real system bottlenecks. The second simulation is carried out while each scenario is created by increasing the capacity of a pair of bottleneck candidates. Simulation is rerun to collect the throughput statistics of each scenario. The comparison and judgment are made similar to the case for single bottleneck. The second and third colored blocks in steps 2 to 4 are different from the single bottleneck case because the

numbers of drums and ropes will increase subsequently as the number of bottlenecks increased. The fourth and fifth highlighted blocks in steps 2 to 4 are for the setting of buffer sizes. In the multiple bottleneck case, each scenario comes from combination of each bottleneck’s buffer size. Various buffer size combinations must be tested to find the optimal situation that can meet the target demand by comparing the throughput mean confident interval with the target throughput. In case of multiple bottlenecks under flow shop, there are four DBR systems introduced by Gilland (2002) and Tanaka et al. (2004); PFB1, PFB2, PFBB1 and PFBB2. In job shop cases the DBR is set depended on each product sequence because each product may pass through different bottleneck processes. The other steps that were not mentioned above are the same as those for cases with single bottleneck. An illustrative example will be shown in the next section.

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference 4. ILLUSTRATIVE EXAMPLE Three different types of jobs move through the production shop. Three job-types are designated as type 1, type 2, and type 3. Each job-type requires that operations be performed at specified machines in a specified sequence. All operation times are exponentially distributed. Job arrives at the shop with exponential inter-arrival times. The details of job sequence and operation time are provided in Tables 1A-1B. Job arrives at the shop with exponential inter-arrival times with a mean of 9.6 minutes. 24% is job type 1, 42% is job type 2 and the remaining is job type 3. The type of arriving job is independent of the job type of the preceding arrival. The operation time of the production shop is 5 separate 40-hour weeks. Working Time is 5 days per week, eight hours per days. The warehouse limits of finish goods storage for each product are set at no more than 60, 105, and 85 unit/month for Products 1, 2, and 3 respectively. The goal is to find the machine configuration of the system that can meet the external demand of target throughput of at least 200 parts per week. The utilization statistics collected from simulation are shown and analyzed in Table 2. The bottleneck rate calculation data is shown in Table 3. The utilization factor calculation is shown in Table 4. The output from simulation run is 187.5 parts per week.

When the utilization factor is calculated and compared among all stations, A and E have highest value (See Table 4). Thus, A and E are accepted to be bottleneck candidates. Based on the discussion above, the bottleneck candidate list consists of machine stations A, B, E, and F. The number of machines for these candidate stations will be varied in the verification experiments as described in Table 5. Table 1B: Product and Process Information for the Example Job Shop

Job Type

Total number of machine to be visited

Machine Visitation Sequence

1

4

Casting Unit Planer Lathe Polishing Machine Shaper Drill Press Lathe Casting Unit Shaper Drill Press Planer Polishing Machine

Table 1A: Machine Information for Test Problem

Machine Group 1 2 3 4 5 6

Description Casting Unit Lathes Planers Drill Presses Shapers Polishing Machine

2

3

3

5

Mean Operation Time (minutes) 125 35 20 60 105 90 65 235 250 50 30 25

Table 2: Machine Information for Test Problem

Number of Machines in Group 12 4 3 6 12

Machine Station Name

Average Utilization %

A (Casting Units)

81.50%

B (Lathes)

67.98%

C (Planners)

47.93%

D (Drill Presses)

74.20%

E (Shapers)

85.43%

F (Polishing Machines)

59.25%

3

4.1 Bottleneck Identification

Table 5: Scenarios for Bottleneck Experiment of Test Problem (1st Step)

Based on the utilization statistics from simulation in Table 2, machines A and E have the highest utilization. Thus, machines A and E are identified as bottleneck candidates. By checking the throughput statistics in Table 3, machines B, E and F are also identified as bottleneck candidates.

Scenario Based 1 2 3 4

Detail All machines are the same. Add A one machine. Add B one machine. Add E one machine. Add F one machine.

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference Table 3: Machine Information for Test Problem Job Type

Sequence

Operation Time (Min)

Operation Time per station (Min)

Rate (part/min)

1

A

125

10.42

0.096

(24%)

C

35

11.67

0.086

B

20

5.00

0.200 0.050

F

60

20.00

Total

240

47.08

2

E

105

8.75

0.114

(44%)

D

90

15.00

0.067

B

65

16.25

0.062

Total

260

40.00

3

A

235

19.58

0.051

(34%)

E

250

20.83

0.048

D

50

8.33

0.120

C

30

10.00

0.100

F

25

8.33

0.120

Total

590

67.08

rb

0.050

0.062

0.048

Table 4: Utilization Factor Comparison for Test Problem Machine Name

A

B

C

D

E

F

λ (part/min)

0.0595

0.0599

0.047

0.065

0.0748

0.0466

0.0534

0.0589

0.0566

0.0633

0.065

0.0456

1.114

1.017

1.008

1.027

1.151

1.02

µ

(part/min)

Utilization Factor, ρ

Figure 2: Comparison of Mean Throughputs for Test Problem (1st Step)

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference In this experiment, Mean Interval Comparison Test is set to observe how the throughput increases in different situation. The result is shown in Figure 2 As can be seen in Figure 2, No test scenario is distinctly different from one another at 75% confident interval, so additional tests must be performed. The number of machines for these candidate stations will be varied in pair in the verification experiments as described in Table 6.

Same as previous step, Mean Interval Comparison Test is used again to compare each scenario throughput. The result is shown in Figure 3. As can be seen in Figure 3, among all means of scenario, only the scenario that machine A and E is added is significantly different from others and higher than based scenario. Therefore, A and E are identified to be the bottleneck.

4.2 DBR Setting Table 6: Detail of the Bottleneck Experiment for Test Problem (2nd Step) Scenario Based 1 2 3 4 5 6

Detail All machines are the same. Add A and B one machine per type. Add A and E one machine per type. Add A and F one machine per type. Add B and E one machine per type. Add B and F one machine per type. Add E and F one machine per type.

After machine stations A and E are identified as bottlenecks, Buffer and Rope can be located. For products 1 and 2, their production sequences pass through only one bottleneck machine, A for product 1 and E for product 2, so DBR setting is the same as in case of single bottleneck. (See in Figure 4A and 4B) The production sequence of Product 3 passes through multiple bottlenecks so the DBR setting should be selected from among PFB1, PFB2, PFBB1 and PFBB2 methods. In this example, PFB 1 is selected to apply. (See Figure 4C)

  nd

Figure 3: Comparison of Mean Throughputs for Test Problem (2 Step) Product 1: Buffer Location: Before A Buffer type: Raw material Rope Location: After A connect to raw material release.

  Figure 4A: DBR Setting for Product 1

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference Product 2: Buffer Location: Before E Buffer type: Raw material Rope Location: After E connect to raw material release.

Figure 4B: DBR Setting for Product 2 Product 3: Buffer Location: Before A Buffer type: Raw material Rope Location: After A connect to raw material release. (Following PFB1 Policy)

Figure 4C: DBR Setting for Product 3

4.3 Buffer Size Calculation The parameter values used in the formula are estimated using statistics collected from the simulation run as shown in Table 7. The buffer values are then set for the next set of simulation runs as given in Table 8. The results are given in Table 9 and Figure 5. As the target throughput is 200, several of the buffer sizes combinations can meet the target

throughput. As can be seen in Figure 5, many cases of buffer setting for both bottlenecks give the throughput that exceeds the target. The users will have to make the final selection. In this problem, the cased of buffer at A 10 and at E 19 is selected because of the least of total buffer size and the highest throughput compared with other cases with the same total buffer size.

Table 7: Buffer Calculation Factors for System Bottleneck

Time Between Arriving to CCR (min)

First Bottleneck (A) 16.80

Second Bottleneck (E) 13.362

Time Between Leaving from CCR (min)

18.72

15.382

Arriving Rate (λ) part/min

0.0595

0.0748

Leaving Rate (µ) part/min

0.0534

0.0650

Utilization Factor (ρ = λ / µ.)

1.114

1.151

Item

Table 8: Buffer Values for Test Problem x Bottleneck A Bottleneck E

With 1% idle 22 19

With 5% idle 10 9

W0 20 20

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference Table 9: Buffer Evaluation for Test Problem Item (Buffer A, Buffer E) (22, 20) (22, 19) (22, 9) (20, 20) (20, 19) (20, 9) (10, 20) (10, 19) (10, 9)

Average Throughput (part) 211.03 211.83 202.20 213.16 212.33 205.26 208.40 209.36 199.10

Figure 5: Buffer Evaluation Result for Test Problem Table 10 Manufacturing Configuration for a Production Shop Problem Item Target Throughput Tested Throughput Bottleneck Station (Drum) Buffer Location Buffer Size Machine Sequencing Rule Rope

Detail 200 parts/week 187.5 parts/week (current system) 209 part/week (under TOC) Station A (Casting Units) and E (Shapers) In front of station A and E A = 10, B = 19 FIFO 1st Rope is located between ending of process A and the release of material. 2nd Rope is located between ending of process E and the release of material. 3rd Rope is located between system output and the release of material and each machine station.

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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference 4.4 Manufacturing Configuration Conclusion After finishing TOC implementation, the manufacturing configuration can be concluded in Table 10.

5. SUMMARY This paper extends the approach from Kasemset and Kachitvichyanukul (2005) that uses simulation as a decision support tool to manage manufacturing systems with multiple bottlenecks operated under the TOC policy. With the presents of multiple bottlenecks, the procedure to implement TOC is more complicated than that for the single bottleneck case. An illustrative example shows how this procedure works in the case with multiple bottlenecks. Simulation is used to identify the bottleneck and set up DBR, as well as to evaluate system performance of new configuration. In this study, only FIFO machine sequencing rule is used. Other policies can also be applied and compared to find the best policy for improving the system under TOC policy.

REFERENCES Gilland, W.G. (2002) A simulation study comparing performance of CONWIP and bottleneck-based release rule, Production Planning & Control, 13 (2), 211-219. Goldratt, E.M. and Cox, J. (1986) The Goal: A Process of Ongoing Improvement (Revised Edition), North River Press.

production system with multiple bottlenecks: A simulation analysis. Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004. AUTHOR BIOGRAPHIES Chompoonoot Kasemset is a doctoral student in Industrial Engineering and Management, School of Engineering and Technology, Asian Institute of Technology, Thailand. Her research interests include operation management and simulation and applied operation research. Her email address is Voratas Kachitvichyanukul is an Associate Professor in Industrial Engineering & Management, School of Engineering and Technology, Asian Institute of Technology, Thailand. He received a Ph. D. from the School of Industrial Engineering at Purdue University in 1982. He has extensive experiences in modeling of manufacturing systems. He had worked for FORTUNE 500 Companies such as Compaq Computer Corporation and Motorola Incorporated. He had also worked for SEMATECH as technical coordinator of the future factory program. His teaching and research interests include evolutionary algorithms for combinatorial optimization, planning and scheduling, supply chain and logistics, high performance computing and applied operations research with special emphasis on industrial systems. His email address is  

Hopp, W.J. and Spearman, M.L (2001) Factory Physics (Second Edition), McGraw-Hill Inc. Kasemset, C. (2005) Simulation-based Tool for Theory of Constraints (TOC) Implementation, Master’s Thesis, Asian Institute of Technology, Bangkok, Thailand. Kasemset, C. and Kachitvichyanukul, V. (2005), Simulation-based tool for implementing theory of constraints. Proceeding of the 6th APIEMS Conference, Manila, Philippines. Kasemset, C. and Kachitvichyanukul, V. (2007) Simulation-based procedure for bottleneck identification. Proceeding of AsiaSim 2007, Asia Simulation Conference 2007, Seoul, Korea. Radovilsky, Z.D. (1998) A quantitative approach to estimate the size of the time buffer in the theory of constraints, International Journal Production Economics, 55, 113-119. Tanaka, K., Myreshka, Morikawa, K. and Takahashi, K. (2004) Effective order release system for a multistage

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