- Email: [email protected]
A study of an enhanced simulation model for TOC supply chain replenishment system under capacity constraint
Expert Systems with Applications 37 (2010) 6435–6440
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
A study of an enhanced simulation model for TOC supply chain replenishment system under capacity constraint Horng-Huei Wu a, Ching-Piao Chen b, Chih-Hung Tsai c,*, Tai-Ping Tsai a a
Department of Industrial Engineering and System Management, Chung Hua University, No. 707, Sec. 2, WuFu Rd., Hsin-Chu 300, Taiwan, ROC Department of Industrial Engineering and Management, Ta-Hwa Institute of Technology, 1 Ta-Hwa Road, Chung-Lin, Hsin-Chu 30050, Taiwan, ROC c Department of Information Management, Yuanpei University, No. 306, Yuanpei Street, Hsin-Chu, Taiwan, ROC b
a r t i c l e
i n f o
Keywords: Supply chain management Inventory replenishment Theory of constraints (TOC) TOC supply chain replenishment system
a b s t r a c t The Theory of Constraints-supply chain replenishment system (TOC-SCRS) is a replenishment method of the TOC supply chain solution and now being implemented by a growing number of companies. The performance reported by the implemented companies includes reduction of inventory level, lead-time and transportation costs and increasing forecast accuracy and customer service levels. However, when the TOC-SCRS is applied in a plant or a central warehouse, the determination of reliable replenishment time will encounter a conflict with the replenishment quantity, especially under the constraint of limited factory capacity. An enhanced simulation replenishment model for TOC-SCRS under capacity constraint is then developed. A numeric example and a sensitivity analysis are utilized to evaluate the application of the proposed model. Employing this proposed methodology will facilitate a plant or a central warehouse to successfully implement an effective TOC-SCRS. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction A supply chain is a set of nodes which consist of production plants (PP), central warehouse (CW), regional warehouses (RW) and points of sales (POS), as shown as Fig. 1. The chain links supplies and customers, beginning with the production of products by a supplier, and ending with the consumption of a product by the customer (Beamon, 1998). The need for regional warehouse stems from the need to supply the market very quickly. In the business market of flaming competition in recent years, companies are plagued by the fluctuations in demand and inevitably present inventory management challenges of the right inventory in the right place (node) at the right time. An effective inventory replenishment method employed in the supply chain is one of the key factors to achieving low inventory while maintaining high customer delivery performance. An effective replenishment method should resolve the following three basic issues: (1) how often the inventory status should be determined? (2) when a replenishment order should be placed? and (3) how large the replenishment order should be? Replenishment methods proposed in the traditional inventory theory can be classified as either continuous review systems ((s, S) or (s, Q) * Corresponding author. Tel.: +886 3 6102338; fax: +886 3 6102343. E-mail addresses: [email protected] (H.-H. Wu), [email protected], [email protected] (C.-H. Tsai). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.02.074
policy) or periodic review systems ((R, S) or (R, s, S) policy) (Silver, Pyke, & Peterson, 1998). However, researches report that order based on these replenishment methods swing due to downstream supply chain partners’ fluctuation of demand. The swing is amplified as the order moves up to the supply chain. This phenomenon of demand amplification is named as bullwhip effect. Bullwhip effect causes excessive inventory, loss of revenue, and inaccurate production plans throughout supply chain systems (O’Donnell et al., 2006). The improvement of bullwhip effect in a supply chain is a key challenge for a manager. The Theory of Constraints-supply chain replenishment system (TOC-SCRS) is one of the solutions for the improvement of the bullwhip effect in a multi-echelon supply chain (Holt, 1999; Perez, 1997; Simatupang, Wright, & Sridharan, 2004; Smith, 2001; Yuan, Chang, & Li, 2003). The TOC-SCRS is a replenishment method of the TOC supply chain solution (Cole & Jacob, 2002; Goldratt, 1994). The TOC is a global managerial methodology that helps the manager to concentrate on the most critical issues. It has been applied to a wide range of fields including Operation (Production), Finance and Measures, Project, Distribution and Supply Chain, Marketing, Sales, Managing People, and Strategy and Tactics (Blackstone, 2001; Kendall, 2006). The TOC-SCRS is based on the following two strategies to decouple the bullwhip effect (or excess inventory in each node) and maintain the inventory availability to consumers (previous nodes), as shown in Fig. 2: (1) each node holds enough stock to cover demand during the time it takes to reliably replenish. (2) Each node orders only to
6436
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440
POS
RW
PP
RW
CW
RW
POS
Fig. 1. A typical supply chain structure. Note: PP: production plant; CW: central warehouse; RW: regional warehouse; POS: point of sale.
Previous Node
Next Node
Reliable Replenishment Time and
Demand
Buffer Level
Previous Node
Demand
Frequency of Replenishment Demand
Demand
Previous Node Previous Node
Fig. 2. The basic concept of TOC-SCRS.
replenish what was sold (Cole & Jacob, 2002). The TOC-SCRS is now being implemented by a growing number of companies. The performance reported by the implemented companies includes reduction of inventory level, lead-time and transportation costs and increasing forecast accuracy and customer service levels (Belvedere & Grando, 2005; Hoffman & Cardarelli, 2002; Novotny, 1997; Patnode, 1999; Sharma, 1997; Tsai, You, Lin, & Tsai, 2008; Waite, Gupta, & Hill, 1998; Watson & Polito, 2003). In application of the TOC-SCRS in a node, the reliable replenishment time (RRT) composes of the two parameters, which are the replenishment frequency and replenishment lead time, as shown in Fig. 3. Generally, the replenishment frequency of a node depends on the public transportation schedule such as ship schedules etc. or its private conveyor schedule. And the replenishment lead time is the required transportation time from upstream node to this node. For example, the ship schedule is once a week and replenishment lead time from upstream node is also a week, then the RRT is two weeks. Based on the two weeks of RRT, this node orders only to replenish what was sold in the last two weeks, i.e., replenishment quantity. That is the replenishment quantity is a function of RRT
Frequency of Replenishment (FR) Reliable Replenishment Time (RRT)
Consumption
TOC-SCRS
Buffer Level Quantity of Replenishment Fig. 3. The conceptual model structure of TOC-SCRS.
(or the replenishment frequency and replenishment lead time) and what is sold in RRT. Therefore, the determination of RRT is one key factor to successful apply the TOC-SCRS in a node. However, when the TOC-SCRS is applied in a plant or a central warehouse, the determination of RRT will encounter a conflict with the replenishment quantity. That is because the replenishment frequency depends on the set up frequency in the plant and the replenishment lead time depends on the production lead time. As we know, however, the set up frequency and the replenishment lead time in the plant depend on the production quantity (i.e., replenishment quantity). It means that the replenishment frequency and the replenishment lead time must depend on the known replenishment quantity, especially under the constraint of limited plant capacity. However, in TOC-SCRS, the replenishment quantity depends on the known parameters of the replenishment frequency and the replenishment lead time. Therefore, this is a big conflict and an issue to apply the TOCSCRS in a plant or a central warehouse. An enhanced replenishment model for TOC-SCRS under capacity constraint is then required to be provided to solve this conflict. Although TOC-SCRS concept has been implemented by a growing number of companies, its model is not described in the literatures. The model of TOC-SCRS is then modeled in next section first. Feasibility of application in central warehouse is discussed. An enhanced replenishment model for TOC-SCRS under capacity constraint is then developed. A numeric example and its sensitivity analysis are utilized to evaluate the application of the proposed method. Employing this proposed methodology will facilitate manufacturing plants or central warehouses to successfully implement an effective TOC-SCRS. 2. The Model of TOC-SCRS As shown in Fig. 3, the inputs of the model of TOC-SCRS include frequency of replenishment, reliable replenishment time, and consumption. And the outputs or decision variables are buffer level and quantity of replenishment. The detailed descriptions are as follows. 2.1. Notations and descriptions I: Total product types. i: Product index, i = 1, 2, . . . , I. J: Total planning periods. j: Period index, j = 1, 2, . . . , J. di,j: Consumption of product i in period j. fi: Frequency of replenishment for product i, i.e., the time period between delivers, such as 2 days. li: Lead time required to reliably process and transfer product i from next node to our node. ri: Time to reliably replenish product i, ri = fi + li. ti,j: Total consumption of product i during period (j ri + 1) to period ri. Si: Buffer level of product i. Qi,j: Quantity of replenishment for product i during period j. Ri,j: Quantity of receipt for product i during period j. Vi,j: Inventory level of product i in the end of period j.
2.2. Buffer Level Based on the concept of TOC-SCRS (Cole & Jacob, 2002; Goldratt, 1994) as shown in Fig. 2, each node holds enough stock to cover demand during the time it takes to reliably replenish. In other word, the buffer level of a product i in a node is determined by the maximum expected usage or consumption during the time to reliably replenish. That is, given a product i, the consumption of
6437
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440 Table 1 An example to illustrate the determination of buffer level. Period (j) Consumption (di,j) Consumption in 3 periods (ti,j)
1 4 –
2 7 –
3 3 14
4 2 12
5 8 13
6 5 15
7 12 25
8 7 24
9 4 23
10 9 20
Period (j) Consumption (di,j) Consumption in 3 periods (ti,j)
11 1 14
12 4 14
13 7 12
14 11 22
15 8 26
16 9 28
17 1 18
18 11 21
19 7 19
20 5 23
product i in the last some periods (i.e., j periods) must first be collected to determine the buffer level of product i. Then the total consumption (i.e., ti,j) of product i during the time to reliably replenish (i.e., ri) must be evaluated during the last j periods as shown in Eq. (1).
t ij¼
ri X
di;x ;
j ¼ r i ; r i þ 1; . . . ; J;
i ¼ 1; 2; . . . ; I:
Table 2 gives an example to demonstrate the determination of the quantity of replenishment of a product i. The consumptions during the future 20 periods are supposed to show in the second row in Table 2. For example, the consumption in the 5th period is 5 pieces. Suppose that the replenishment frequency of product i is 2 periods and its replenishment lead time is one period. And a is assumed to be 0. Therefore, Using Eq. (3), the quantity of replenishment for each period are shown in third row in Table 2. For example, the quantity of replenishment in 5th period is 0 for mod(5/2) is not equal to 0. And the quantity of replenishment in 6th period is 14 pieces (= 5 + 9) for mod(6/2) is equal to 0. In order to further illustrate the receipt or inventory level variation, we assume that the goods of a replenishment order which is released in period j li will be delivered (or arrived at) in j period (i.e., after li periods). And the quantity of receipt is equal to the quantity of replenishment. Therefore, the quantity of receipt in period j can be represented as Eq. (4).
ð1Þ
x¼jr i þ1
Finally, the buffer level (Si) is determined by the maximum ti,j, or using Eq. (2).
" Si ¼ Max
ri X
# di;x ; j ¼ r i ; ri þ 1; . . . ; J ;
i ¼ 1; 2; . . . ; I:
ð2Þ
x¼jr i þ1
Table 1 gives an example to demonstrate the determination of the buffer level of a product i. The consumptions during the last twenty periods are collected first and are shown in the second row in Table 1. For example, the consumption in the 5th period is 8 pieces. Suppose that the replenishment frequency of product i is 2 periods and its replenishment lead time is one period. Therefore, the time to reliably replenish product i is then 3 periods. Using Eq. (1), the total consumption during 3 periods can be evaluated from 3rd period to 20th period, which are shown in third row in Table 1. For example, for 5th period, the total consumption during 3 period (i.e., from 3rd period to 5th period) is 13 pieces (= 3 + 2 + 8). Because the maximum total consumption in 3 periods is 28 pieces for 16th period, the buffer level is then 28 pieces using Eq. (2).
Ri;j ¼ Q i;jli
ð4Þ
Then, the inventory level in the end of period j is equal to the inventory level of previous period minus the consumption in period j and plus the quantity of receipt in period j, as shown in Eq. (5).
V i;j ¼ V i;j1 di;j þ Ri;j
ð5Þ
Using Eq. (4), the quantity of receipt in each period is shown in 4th row in Table 2. And using Eq. (5), the inventory level in the end of each period is also shown in 5th row in Table 2.
2.3. Quantity of replenishment 3. The problems of TOC-SCRS
The second concept of TOC-SCRS as shown in Fig. 2 is that each node order only to replenish what was consumed. In other word, the quantity of replenishment of a product i in a node is determined by the quantity of consumption between two replenishments. Therefore, the quantity of replenishment of a product i in a period j can be represented as Eq. (3).
Q i;j ¼
8 > <
j P
di;w ; w¼jfi þ1 > : 0; else
if modððj aÞ=fi Þ ¼ 0
Although TOC-SCRS can be utilized in a supply chain and get outstanding improvements, a conflict issue exists when it is utilized in production plants or central warehouses in which the production capacity is limited. Replenishments in plant mean to require setup or changeover processes and these setup processes require production capacity. If a plant has enough capacity, enough idle or backup capacity can be used to set up or changeover. The setup frequency (i.e., replenishment frequency) is as smaller as possible or one period. However, if the plant capacity is limited, its setup frequency must be determined by the quantity of
ð3Þ
where a is selected integer parameter and 0 < a < fi . Table 2 An example to illustrate the determination of quantity of replenishment.
a b
Period (j) Consumption (di,j) Quantity of replenishment (Qi,j) Quantity of receipt (Ri,j) Inventory level (Vi,j)b
1 8
Period (j) Consumption (di,j) Quantity of replenishment (Qi,j) Quantity of receipt (Ri,j) Inventory level (Vi,j)
11 4
7a 27
16 31
2 3 11 24 12 9 13 22
3 11 11 24 13 5 13 30
4 7 18 17 14 3 8 27
5 5 18 30 15 8 8 27
The arriving quantity in the first period is supposed to have been replenished in previous period. The initial inventory level is supposed to be 28 pieces.
6 9 14 21 16 7 15 20
7 4 14 31 17 11 15 22
8 8 12 23 18 6 17 18
9 6 12 29 19 6 17 29
10 10 16 19 20 8 14 21
6438
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440
production (i.e., quantity of replenishment). This situation is conflict against Eq. (2) in the model of TOC-SCRS in which the replenishment frequency is a known parameter. In other words, the quantity of replenishment which is evaluated by using Eq. (2) may not be produced due to the limited capacity of a plant. For example, a plant produces A and B product. This plant has capacity to output 100 pieces in one hour for either product. And either product requires one hour setup time. If daily consumption of these two products is 2200 pieces, this plant requires 22 h to produce 2200 pieces and has 2 h capacity for setup time. It means that the replenishment frequency is 1 day for either product. However, if daily consumption of these two products is 2300 pieces, then this plant requires 23 h to produce 2300 pieces and has only one hour for setup time. In this case, if the replenishment frequency is still 1 day for either product, this plant has not enough capacity or requires another one hour capacity to produce 2300 pieces of both products and to setup twice. Otherwise, this plant must produce only 2200 pieces and reduces 100 pieces to output. Another solution is to prolong the replenishment frequency, i.e., 2 days. Therefore, when TOC-SCRS is utilized in plants or central warehouses, the replenishment frequency cannot be determined in advance or arbitrarily and must be determined with quantity of replenishment simultaneously. An enhanced replenishment model of TOC-SCRS is then proposed in the next section. 4. An enhanced replenishment model for TOC-SCRS According to TOC, the output of a plant is determined by its bottleneck station. Therefore, the capacity of the bottleneck station is only considered in the following model. Besides, except the notations defined in Section 2, in order to describe the enhanced replenishment model, further notations are required to define as follows. 4.1. Notations and descriptions
e: Working days in a period. h: Working hours in a working day. m: Machines in the bottleneck stations. C: Plant capacity in a period, C = m e h. si: Setup time required for product i in the bottleneck station. pi: Production output per hour for product i in a bottleneck machine. Di: Average consumption of product i in a period. Li: Required capacity for product i in a period, Li = Di/ pi.
l m Li In Eqs. (6), (7), eh is utilized to determine the minimum setup times required for product i in a period. If Li > e h, product i require two or more bottleneck machine to produce simultaneous in a period. Because setup times must be an integer and greater Li , the notation dxe is utilized to represent an than the value of eh integer which is equal to or larger than x. For example, l m Li is the d1:1e; d1:9e or d2e are all the value of 2. Therefore, si eh
setup time required by product i in a period. If the capacity is not enough to produce, the setup frequency of product i must be prolonged, for example from one period to two periods. Therefore, L i si eh is a normalized setup time for product i in a period when the f i
setup frequency of product i is prolonged to be several periods. The object function in Eq. (6) is to minimize the rest capacity which is the total capacity minus the used capacity. The total used capacity composes two parts: one is total production capacity P which is used to produce product (i.e., Ii¼1 Li ) and the other is total L P s i setup time (i.e., Ii¼1 i fieh ). The longer setup frequency the smaller setup time and the larger production quantity are in a period. Therefore, the feasible condition in Eq. (7) requires that the total used capacity must be not greater than the total capacity. In other side, the object function requires an optimal setup frequency or production quantity for all product i. P If C < Ii¼1 Li , it means the plant capacity is not enough to produce all products. We cannot deal with it by prolonging the setup frequency and it is a product-mix decision problem (Luebbe & Finch, 1992; Bhattacharya & Vasant, 2007). In the other way, if P l m PI I Li C , it means the capacity is enough to i¼1 Li þ i¼1 si eh produce all products and to setup once for all products in a period. Therefore, the minimum rest capacity in Eq. (6) is when all fi = 1. P l m PI PI I Li , it means the However, if i¼1 Li < C < i¼1 Li þ i¼1 si eh capacity is enough to produce all products but not enough to setup once for all products in a period. Therefore, we must prolong the setup frequency to reduce the total setup time. The feasible setup frequency of different product i has multiple combination to satisfy Eq. (7). The optimal combination is one to minimize the rest capacity. In the following, an optimal setup frequency is proposed in the condition that all fi are equal. 4.3. An optimal setup frequency in the condition all products have equal setup frequency Let F be the frequency of replenishment for all product i, i..e, fi = F, for all i. Therefore, Eq. (7) can be simplified to be Eq. (8).
C 4.2. An enhanced replenishment model
C
i¼1
Li þ
I si X i¼1
l
Li eh
Li þ
i¼1
si
l
m
Li eh
F
ð8Þ
Using Eq. (8), we can get Eq. (9) after some manipulations.
PI F
l m Li si eh P C Ii¼1 Li
i¼1
ð9Þ
or Eq. (10),
ð6Þ
Subject to: I X
PI
i¼1
The enhanced model is developed on the base of minimum capacity loss (i.e., maximum throughput) and minimum replenishment quantity (i.e., minimum inventory). This model is shown as follows:
l m1 0 Li I I si X X eh A Min C @ Li þ fi i¼1 i¼1
I X
l m3 2PI Li i¼1 si eh 7 F¼6 P 6 7 I 6 C i¼1 Li 7
ð10Þ
m
fi
fi P 1 and fi is an integer.
ð7Þ
5. An application example In this section, we present an example to illustrate the model. Consider a plant with two machines in its bottleneck station and
6439
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440 Table 3 An example to illustrate the determination of the setup frequency. Product (i) Average consumption of product i in a period (Di) Setup time required for product i (si) Production output per hour for product i (pi)
A 600 1h 100
B 400 1h 100
C 300 1h 100
D 2,500 1h 100
E 450 1h 100
F 350 1h 100
Table 4 A sensitivity analysis of the example in Table 3. Setup frequency (F)
1 2 3 4 5 6 7
Capacity (C) (1)
48 48 48 48 48 48 48
Total production capacity (2) P I i¼1 Li
Total setup time (3) L i PI si eh
Rest capacity (1)–(2)– (3)
Capacity is feasible or not
46 46 46 46 46 46 46
7 3.5 2.33 1.75 1.4 1.17 1.0
5 1.5 0.33 0.25 0.6 0.83 1.0
N N N Y Y Y Y
i¼1
26
0 1
51
D,(25) 31 32
D,(5)
A,(6)
D,(25) 48 49
B,(4)
96
76
D,(25)
6 7
0 1
F
D,(20)
61 62
C,(3)
80 81
E,(4.5) i
95
F,(3.5)
: Setup time Fig. 4. An illustrative production schedule for the example in Table 3.
produce 6 products. The average consumption of these products and their production data are shown in Table 3. The planning period is 1 day in which are 24 working hours. We want to find the optimal setup frequency in the condition that the setup frequency is equal for all products. Based on the data shown in Table 3, the total used capacity, i.e., l m 600þ400þ300þ500þ450þ350 6 P PI Li þ 1 ð 24 , is ð i¼1 Li þ Ii¼1 Si jH 100 4 3 25 4:5 3:5 þ 24 þ 24 þ 24 þ 24 þ 24 ÞÞ ¼ 46 þ 7 ¼ 53 h and is greater than the capacity of one period (i.e., C = m j H = 2 1 24 = 48 h). It means that all products cannot be setup every period. Therefore, we can use Eq. (10) to find the optimal setup frequency. That is
&
4 3 25 4:5 3:5’ þ 24 þ 24 þ 24 þ 24 þ 24 F¼ 2 1 24 600þ400þ300þ500þ450þ350 100
7 ¼ d3:5e ¼ 4 ¼ 48 46 1
6 24
In other words, this plant must produce or replenish each product once every 4 days and quantity of replenish is the consumption during 4 days. And using Eq. (6), the rest capacity in one period is
l m1 0 Li I I si X X eh A ¼ 48 46 þ 7 ¼ 0:25 h: C@ Li þ fi 4 i¼1 i¼1 A sensitivity analysis is shown in Table 4. When F = 4, the plant capacity is not only feasible, but also the rest capacity is minimum. Besides, Fig. 4 shows an illustrative production schedule for these six products in this plant. 6. Conclusions When the TOC-SCRS is applied in a plant or a central warehouse, the determination of RRT (i.e., replenishment frequency and
replenishment lea time) will encounter a conflict with the replenishment quantity. That is because the replenishment frequency depends on the set up frequency in the plant and the replenishment lead time depends on the production lead time. As we know, however, the set up frequency and the replenishment lead time in the plant depend on the production quantity (i.e., replenishment quantity). It means that the replenishment frequency and the replenishment lead time must depend on the known replenishment quantity, especially under the constraint of limited plant capacity. However, in TOC-SCRS, the replenishment quantity is determined by the known parameters of the replenishment frequency and the replenishment lead time. Therefore, this is a big conflict and an issue to apply the TOC-SCRS in a plant or a central warehouse. An enhanced replenishment model for TOC-SCRS under capacity constraint is required to be provided to solve this conflict. In this paper, the concept and method of TOC-SCRS was first reviewed. The model of TOC-SCRS was then modeled and its feasibility of application in central warehouse was discussed. An enhanced replenishment model for TOC-SCRS under capacity constraint was then developed. A numeric example and a sensitivity analysis were utilized to evaluate the application of the proposed method. Employing this proposed methodology will facilitate manufacturing plants or central warehouses to successfully implement an effective TOC-SCRS. Acknowledgment The authors would like to thank the National Science Council of the Republic of China, for financially supporting this research under Contract No. NSC 96-2628-E-216-001-MY3. References Beamon, B. M. (1998). Supply chain design and analysis: Models and methods. International Journal of Production Economics, 55(3), 281–294.
6440
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440
Belvedere, V., & Grando, A. (2005). Implementing a pull system in batch/mix process industry through theory of constraints: A case-study. Human Systems Management, 24(1), 3–12. Bhattacharya, A., & Vasant, P. (2007). Soft-sensing of level of satisfaction in TOC product-mix decision heuristic using robust fuzzy-LP. European Journal of Operation Research, 177(1), 55–70. Blackstone, J. H. (2001). Theory of constraints – A status report. International Journal of Production Research, 39(6), 1053–1080. Cole, H., & Jacob, D. (2002). Introduction to TOC supply chain. AGI Institute. Goldratt, E. M. (1994). It’s not luck. England: Gower. Hoffman, G., & Cardarelli, H. (2002). Implementing TOC supply chain: A detailed case study- MACtac. AGI Institute. Holt, J. R. (1999). TOC in supply chain management. In 1999 constraints management symposium proceedings, Phoenix, AZ, USA (pp. 85–87). Kendall, G. I. (2006). Viable vision. Heliopolis Culture Group/SAGA Culture Publishing Co. Luebbe, R., & Finch, B. (1992). Theory of constraints and linear programming: A comparison. International Journal of Production Research, 30(6), 1471–1478. Novotny, D. J. (1997). TOC supply chain case study. In 1997 APICS constraints management symposium proceedings, Denver, Colorado, USA (pp. 78–79). O’Donnell, T., Maguire, L., Mcivor, R., & Humphreys, P. (2006). Minimizing the bullwhip effect in a supply chain using genetic algorithms. International Journal of Production Research, 44(8), 1523–1543. Patnode, N. H. (1999). Providing responsive logistics support: Applying lean thinking to logistics. In 1999 constraints management symposium proceedings, Phoenix, AZ, USA (pp. 93–96).
Perez, J. L. (1997). TOC for world class global supply chain management. Computers & Industrial Engineering, 33(1), 289–293. Sharma, K. (1997). TOC supply chain implementation: System strategies. In 1997 APICS constraints management symposium proceedings, Denver, Colorado, USA (pp. 66–74). Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory management and production planning and scheduling (3rd ed.). John Wiley & Sons Inc. Simatupang, T. M., Wright, A. C., & Sridharan, N. (2004). Applying the theory of constraints to supply chain collaboration. Supply Chain Management: An International Journal, 9(1), 57–70. Smith, D. A. (2001). Linking the supply chain using the theory of constraints logistical applications and a new understanding of the role of inventory/buffer management. In 2001 constraints management technical conference proceedings, San Antonio, Texas, USA (pp.64–67). Tsai, K. M., You, S. Y., Lin, Y. H., & Tsai, C. H. (2008). A fuzzy goal programming approach with priority for channel allocation problem in steel industry. Expert Systems with Applications, 35(3), 1870–1876. Waite, J., Gupta, S., & Hill, E. (1998). Meritor HVS story. In 1998 APICS constraints management symposium proceedings, Seattle Washington, AZ, USA (pp. 1–9). Watson, K., & Polito, T. (2003). Comparison of DRP and TOC financial performance within a multi-product, multi-echelon physical distribution environment. International Journal of Production Research, 41(4), 741–765. Yuan, K. J., Chang, S. H., & Li, R. K. (2003). Enhancement of theory of constraints replenishment using a novel generic buffer management procedure. International Journal of Production Research, 41(4), 725–740.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
A study of an enhanced simulation model for TOC supply chain replenishment system under capacity constraint Horng-Huei Wu a, Ching-Piao Chen b, Chih-Hung Tsai c,*, Tai-Ping Tsai a a
Department of Industrial Engineering and System Management, Chung Hua University, No. 707, Sec. 2, WuFu Rd., Hsin-Chu 300, Taiwan, ROC Department of Industrial Engineering and Management, Ta-Hwa Institute of Technology, 1 Ta-Hwa Road, Chung-Lin, Hsin-Chu 30050, Taiwan, ROC c Department of Information Management, Yuanpei University, No. 306, Yuanpei Street, Hsin-Chu, Taiwan, ROC b
a r t i c l e
i n f o
Keywords: Supply chain management Inventory replenishment Theory of constraints (TOC) TOC supply chain replenishment system
a b s t r a c t The Theory of Constraints-supply chain replenishment system (TOC-SCRS) is a replenishment method of the TOC supply chain solution and now being implemented by a growing number of companies. The performance reported by the implemented companies includes reduction of inventory level, lead-time and transportation costs and increasing forecast accuracy and customer service levels. However, when the TOC-SCRS is applied in a plant or a central warehouse, the determination of reliable replenishment time will encounter a conflict with the replenishment quantity, especially under the constraint of limited factory capacity. An enhanced simulation replenishment model for TOC-SCRS under capacity constraint is then developed. A numeric example and a sensitivity analysis are utilized to evaluate the application of the proposed model. Employing this proposed methodology will facilitate a plant or a central warehouse to successfully implement an effective TOC-SCRS. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction A supply chain is a set of nodes which consist of production plants (PP), central warehouse (CW), regional warehouses (RW) and points of sales (POS), as shown as Fig. 1. The chain links supplies and customers, beginning with the production of products by a supplier, and ending with the consumption of a product by the customer (Beamon, 1998). The need for regional warehouse stems from the need to supply the market very quickly. In the business market of flaming competition in recent years, companies are plagued by the fluctuations in demand and inevitably present inventory management challenges of the right inventory in the right place (node) at the right time. An effective inventory replenishment method employed in the supply chain is one of the key factors to achieving low inventory while maintaining high customer delivery performance. An effective replenishment method should resolve the following three basic issues: (1) how often the inventory status should be determined? (2) when a replenishment order should be placed? and (3) how large the replenishment order should be? Replenishment methods proposed in the traditional inventory theory can be classified as either continuous review systems ((s, S) or (s, Q) * Corresponding author. Tel.: +886 3 6102338; fax: +886 3 6102343. E-mail addresses: [email protected] (H.-H. Wu), [email protected], [email protected] (C.-H. Tsai). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.02.074
policy) or periodic review systems ((R, S) or (R, s, S) policy) (Silver, Pyke, & Peterson, 1998). However, researches report that order based on these replenishment methods swing due to downstream supply chain partners’ fluctuation of demand. The swing is amplified as the order moves up to the supply chain. This phenomenon of demand amplification is named as bullwhip effect. Bullwhip effect causes excessive inventory, loss of revenue, and inaccurate production plans throughout supply chain systems (O’Donnell et al., 2006). The improvement of bullwhip effect in a supply chain is a key challenge for a manager. The Theory of Constraints-supply chain replenishment system (TOC-SCRS) is one of the solutions for the improvement of the bullwhip effect in a multi-echelon supply chain (Holt, 1999; Perez, 1997; Simatupang, Wright, & Sridharan, 2004; Smith, 2001; Yuan, Chang, & Li, 2003). The TOC-SCRS is a replenishment method of the TOC supply chain solution (Cole & Jacob, 2002; Goldratt, 1994). The TOC is a global managerial methodology that helps the manager to concentrate on the most critical issues. It has been applied to a wide range of fields including Operation (Production), Finance and Measures, Project, Distribution and Supply Chain, Marketing, Sales, Managing People, and Strategy and Tactics (Blackstone, 2001; Kendall, 2006). The TOC-SCRS is based on the following two strategies to decouple the bullwhip effect (or excess inventory in each node) and maintain the inventory availability to consumers (previous nodes), as shown in Fig. 2: (1) each node holds enough stock to cover demand during the time it takes to reliably replenish. (2) Each node orders only to
6436
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440
POS
RW
PP
RW
CW
RW
POS
Fig. 1. A typical supply chain structure. Note: PP: production plant; CW: central warehouse; RW: regional warehouse; POS: point of sale.
Previous Node
Next Node
Reliable Replenishment Time and
Demand
Buffer Level
Previous Node
Demand
Frequency of Replenishment Demand
Demand
Previous Node Previous Node
Fig. 2. The basic concept of TOC-SCRS.
replenish what was sold (Cole & Jacob, 2002). The TOC-SCRS is now being implemented by a growing number of companies. The performance reported by the implemented companies includes reduction of inventory level, lead-time and transportation costs and increasing forecast accuracy and customer service levels (Belvedere & Grando, 2005; Hoffman & Cardarelli, 2002; Novotny, 1997; Patnode, 1999; Sharma, 1997; Tsai, You, Lin, & Tsai, 2008; Waite, Gupta, & Hill, 1998; Watson & Polito, 2003). In application of the TOC-SCRS in a node, the reliable replenishment time (RRT) composes of the two parameters, which are the replenishment frequency and replenishment lead time, as shown in Fig. 3. Generally, the replenishment frequency of a node depends on the public transportation schedule such as ship schedules etc. or its private conveyor schedule. And the replenishment lead time is the required transportation time from upstream node to this node. For example, the ship schedule is once a week and replenishment lead time from upstream node is also a week, then the RRT is two weeks. Based on the two weeks of RRT, this node orders only to replenish what was sold in the last two weeks, i.e., replenishment quantity. That is the replenishment quantity is a function of RRT
Frequency of Replenishment (FR) Reliable Replenishment Time (RRT)
Consumption
TOC-SCRS
Buffer Level Quantity of Replenishment Fig. 3. The conceptual model structure of TOC-SCRS.
(or the replenishment frequency and replenishment lead time) and what is sold in RRT. Therefore, the determination of RRT is one key factor to successful apply the TOC-SCRS in a node. However, when the TOC-SCRS is applied in a plant or a central warehouse, the determination of RRT will encounter a conflict with the replenishment quantity. That is because the replenishment frequency depends on the set up frequency in the plant and the replenishment lead time depends on the production lead time. As we know, however, the set up frequency and the replenishment lead time in the plant depend on the production quantity (i.e., replenishment quantity). It means that the replenishment frequency and the replenishment lead time must depend on the known replenishment quantity, especially under the constraint of limited plant capacity. However, in TOC-SCRS, the replenishment quantity depends on the known parameters of the replenishment frequency and the replenishment lead time. Therefore, this is a big conflict and an issue to apply the TOCSCRS in a plant or a central warehouse. An enhanced replenishment model for TOC-SCRS under capacity constraint is then required to be provided to solve this conflict. Although TOC-SCRS concept has been implemented by a growing number of companies, its model is not described in the literatures. The model of TOC-SCRS is then modeled in next section first. Feasibility of application in central warehouse is discussed. An enhanced replenishment model for TOC-SCRS under capacity constraint is then developed. A numeric example and its sensitivity analysis are utilized to evaluate the application of the proposed method. Employing this proposed methodology will facilitate manufacturing plants or central warehouses to successfully implement an effective TOC-SCRS. 2. The Model of TOC-SCRS As shown in Fig. 3, the inputs of the model of TOC-SCRS include frequency of replenishment, reliable replenishment time, and consumption. And the outputs or decision variables are buffer level and quantity of replenishment. The detailed descriptions are as follows. 2.1. Notations and descriptions I: Total product types. i: Product index, i = 1, 2, . . . , I. J: Total planning periods. j: Period index, j = 1, 2, . . . , J. di,j: Consumption of product i in period j. fi: Frequency of replenishment for product i, i.e., the time period between delivers, such as 2 days. li: Lead time required to reliably process and transfer product i from next node to our node. ri: Time to reliably replenish product i, ri = fi + li. ti,j: Total consumption of product i during period (j ri + 1) to period ri. Si: Buffer level of product i. Qi,j: Quantity of replenishment for product i during period j. Ri,j: Quantity of receipt for product i during period j. Vi,j: Inventory level of product i in the end of period j.
2.2. Buffer Level Based on the concept of TOC-SCRS (Cole & Jacob, 2002; Goldratt, 1994) as shown in Fig. 2, each node holds enough stock to cover demand during the time it takes to reliably replenish. In other word, the buffer level of a product i in a node is determined by the maximum expected usage or consumption during the time to reliably replenish. That is, given a product i, the consumption of
6437
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440 Table 1 An example to illustrate the determination of buffer level. Period (j) Consumption (di,j) Consumption in 3 periods (ti,j)
1 4 –
2 7 –
3 3 14
4 2 12
5 8 13
6 5 15
7 12 25
8 7 24
9 4 23
10 9 20
Period (j) Consumption (di,j) Consumption in 3 periods (ti,j)
11 1 14
12 4 14
13 7 12
14 11 22
15 8 26
16 9 28
17 1 18
18 11 21
19 7 19
20 5 23
product i in the last some periods (i.e., j periods) must first be collected to determine the buffer level of product i. Then the total consumption (i.e., ti,j) of product i during the time to reliably replenish (i.e., ri) must be evaluated during the last j periods as shown in Eq. (1).
t ij¼
ri X
di;x ;
j ¼ r i ; r i þ 1; . . . ; J;
i ¼ 1; 2; . . . ; I:
Table 2 gives an example to demonstrate the determination of the quantity of replenishment of a product i. The consumptions during the future 20 periods are supposed to show in the second row in Table 2. For example, the consumption in the 5th period is 5 pieces. Suppose that the replenishment frequency of product i is 2 periods and its replenishment lead time is one period. And a is assumed to be 0. Therefore, Using Eq. (3), the quantity of replenishment for each period are shown in third row in Table 2. For example, the quantity of replenishment in 5th period is 0 for mod(5/2) is not equal to 0. And the quantity of replenishment in 6th period is 14 pieces (= 5 + 9) for mod(6/2) is equal to 0. In order to further illustrate the receipt or inventory level variation, we assume that the goods of a replenishment order which is released in period j li will be delivered (or arrived at) in j period (i.e., after li periods). And the quantity of receipt is equal to the quantity of replenishment. Therefore, the quantity of receipt in period j can be represented as Eq. (4).
ð1Þ
x¼jr i þ1
Finally, the buffer level (Si) is determined by the maximum ti,j, or using Eq. (2).
" Si ¼ Max
ri X
# di;x ; j ¼ r i ; ri þ 1; . . . ; J ;
i ¼ 1; 2; . . . ; I:
ð2Þ
x¼jr i þ1
Table 1 gives an example to demonstrate the determination of the buffer level of a product i. The consumptions during the last twenty periods are collected first and are shown in the second row in Table 1. For example, the consumption in the 5th period is 8 pieces. Suppose that the replenishment frequency of product i is 2 periods and its replenishment lead time is one period. Therefore, the time to reliably replenish product i is then 3 periods. Using Eq. (1), the total consumption during 3 periods can be evaluated from 3rd period to 20th period, which are shown in third row in Table 1. For example, for 5th period, the total consumption during 3 period (i.e., from 3rd period to 5th period) is 13 pieces (= 3 + 2 + 8). Because the maximum total consumption in 3 periods is 28 pieces for 16th period, the buffer level is then 28 pieces using Eq. (2).
Ri;j ¼ Q i;jli
ð4Þ
Then, the inventory level in the end of period j is equal to the inventory level of previous period minus the consumption in period j and plus the quantity of receipt in period j, as shown in Eq. (5).
V i;j ¼ V i;j1 di;j þ Ri;j
ð5Þ
Using Eq. (4), the quantity of receipt in each period is shown in 4th row in Table 2. And using Eq. (5), the inventory level in the end of each period is also shown in 5th row in Table 2.
2.3. Quantity of replenishment 3. The problems of TOC-SCRS
The second concept of TOC-SCRS as shown in Fig. 2 is that each node order only to replenish what was consumed. In other word, the quantity of replenishment of a product i in a node is determined by the quantity of consumption between two replenishments. Therefore, the quantity of replenishment of a product i in a period j can be represented as Eq. (3).
Q i;j ¼
8 > <
j P
di;w ; w¼jfi þ1 > : 0; else
if modððj aÞ=fi Þ ¼ 0
Although TOC-SCRS can be utilized in a supply chain and get outstanding improvements, a conflict issue exists when it is utilized in production plants or central warehouses in which the production capacity is limited. Replenishments in plant mean to require setup or changeover processes and these setup processes require production capacity. If a plant has enough capacity, enough idle or backup capacity can be used to set up or changeover. The setup frequency (i.e., replenishment frequency) is as smaller as possible or one period. However, if the plant capacity is limited, its setup frequency must be determined by the quantity of
ð3Þ
where a is selected integer parameter and 0 < a < fi . Table 2 An example to illustrate the determination of quantity of replenishment.
a b
Period (j) Consumption (di,j) Quantity of replenishment (Qi,j) Quantity of receipt (Ri,j) Inventory level (Vi,j)b
1 8
Period (j) Consumption (di,j) Quantity of replenishment (Qi,j) Quantity of receipt (Ri,j) Inventory level (Vi,j)
11 4
7a 27
16 31
2 3 11 24 12 9 13 22
3 11 11 24 13 5 13 30
4 7 18 17 14 3 8 27
5 5 18 30 15 8 8 27
The arriving quantity in the first period is supposed to have been replenished in previous period. The initial inventory level is supposed to be 28 pieces.
6 9 14 21 16 7 15 20
7 4 14 31 17 11 15 22
8 8 12 23 18 6 17 18
9 6 12 29 19 6 17 29
10 10 16 19 20 8 14 21
6438
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440
production (i.e., quantity of replenishment). This situation is conflict against Eq. (2) in the model of TOC-SCRS in which the replenishment frequency is a known parameter. In other words, the quantity of replenishment which is evaluated by using Eq. (2) may not be produced due to the limited capacity of a plant. For example, a plant produces A and B product. This plant has capacity to output 100 pieces in one hour for either product. And either product requires one hour setup time. If daily consumption of these two products is 2200 pieces, this plant requires 22 h to produce 2200 pieces and has 2 h capacity for setup time. It means that the replenishment frequency is 1 day for either product. However, if daily consumption of these two products is 2300 pieces, then this plant requires 23 h to produce 2300 pieces and has only one hour for setup time. In this case, if the replenishment frequency is still 1 day for either product, this plant has not enough capacity or requires another one hour capacity to produce 2300 pieces of both products and to setup twice. Otherwise, this plant must produce only 2200 pieces and reduces 100 pieces to output. Another solution is to prolong the replenishment frequency, i.e., 2 days. Therefore, when TOC-SCRS is utilized in plants or central warehouses, the replenishment frequency cannot be determined in advance or arbitrarily and must be determined with quantity of replenishment simultaneously. An enhanced replenishment model of TOC-SCRS is then proposed in the next section. 4. An enhanced replenishment model for TOC-SCRS According to TOC, the output of a plant is determined by its bottleneck station. Therefore, the capacity of the bottleneck station is only considered in the following model. Besides, except the notations defined in Section 2, in order to describe the enhanced replenishment model, further notations are required to define as follows. 4.1. Notations and descriptions
e: Working days in a period. h: Working hours in a working day. m: Machines in the bottleneck stations. C: Plant capacity in a period, C = m e h. si: Setup time required for product i in the bottleneck station. pi: Production output per hour for product i in a bottleneck machine. Di: Average consumption of product i in a period. Li: Required capacity for product i in a period, Li = Di/ pi.
l m Li In Eqs. (6), (7), eh is utilized to determine the minimum setup times required for product i in a period. If Li > e h, product i require two or more bottleneck machine to produce simultaneous in a period. Because setup times must be an integer and greater Li , the notation dxe is utilized to represent an than the value of eh integer which is equal to or larger than x. For example, l m Li is the d1:1e; d1:9e or d2e are all the value of 2. Therefore, si eh
setup time required by product i in a period. If the capacity is not enough to produce, the setup frequency of product i must be prolonged, for example from one period to two periods. Therefore, L i si eh is a normalized setup time for product i in a period when the f i
setup frequency of product i is prolonged to be several periods. The object function in Eq. (6) is to minimize the rest capacity which is the total capacity minus the used capacity. The total used capacity composes two parts: one is total production capacity P which is used to produce product (i.e., Ii¼1 Li ) and the other is total L P s i setup time (i.e., Ii¼1 i fieh ). The longer setup frequency the smaller setup time and the larger production quantity are in a period. Therefore, the feasible condition in Eq. (7) requires that the total used capacity must be not greater than the total capacity. In other side, the object function requires an optimal setup frequency or production quantity for all product i. P If C < Ii¼1 Li , it means the plant capacity is not enough to produce all products. We cannot deal with it by prolonging the setup frequency and it is a product-mix decision problem (Luebbe & Finch, 1992; Bhattacharya & Vasant, 2007). In the other way, if P l m PI I Li C , it means the capacity is enough to i¼1 Li þ i¼1 si eh produce all products and to setup once for all products in a period. Therefore, the minimum rest capacity in Eq. (6) is when all fi = 1. P l m PI PI I Li , it means the However, if i¼1 Li < C < i¼1 Li þ i¼1 si eh capacity is enough to produce all products but not enough to setup once for all products in a period. Therefore, we must prolong the setup frequency to reduce the total setup time. The feasible setup frequency of different product i has multiple combination to satisfy Eq. (7). The optimal combination is one to minimize the rest capacity. In the following, an optimal setup frequency is proposed in the condition that all fi are equal. 4.3. An optimal setup frequency in the condition all products have equal setup frequency Let F be the frequency of replenishment for all product i, i..e, fi = F, for all i. Therefore, Eq. (7) can be simplified to be Eq. (8).
C 4.2. An enhanced replenishment model
C
i¼1
Li þ
I si X i¼1
l
Li eh
Li þ
i¼1
si
l
m
Li eh
F
ð8Þ
Using Eq. (8), we can get Eq. (9) after some manipulations.
PI F
l m Li si eh P C Ii¼1 Li
i¼1
ð9Þ
or Eq. (10),
ð6Þ
Subject to: I X
PI
i¼1
The enhanced model is developed on the base of minimum capacity loss (i.e., maximum throughput) and minimum replenishment quantity (i.e., minimum inventory). This model is shown as follows:
l m1 0 Li I I si X X eh A Min C @ Li þ fi i¼1 i¼1
I X
l m3 2PI Li i¼1 si eh 7 F¼6 P 6 7 I 6 C i¼1 Li 7
ð10Þ
m
fi
fi P 1 and fi is an integer.
ð7Þ
5. An application example In this section, we present an example to illustrate the model. Consider a plant with two machines in its bottleneck station and
6439
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440 Table 3 An example to illustrate the determination of the setup frequency. Product (i) Average consumption of product i in a period (Di) Setup time required for product i (si) Production output per hour for product i (pi)
A 600 1h 100
B 400 1h 100
C 300 1h 100
D 2,500 1h 100
E 450 1h 100
F 350 1h 100
Table 4 A sensitivity analysis of the example in Table 3. Setup frequency (F)
1 2 3 4 5 6 7
Capacity (C) (1)
48 48 48 48 48 48 48
Total production capacity (2) P I i¼1 Li
Total setup time (3) L i PI si eh
Rest capacity (1)–(2)– (3)
Capacity is feasible or not
46 46 46 46 46 46 46
7 3.5 2.33 1.75 1.4 1.17 1.0
5 1.5 0.33 0.25 0.6 0.83 1.0
N N N Y Y Y Y
i¼1
26
0 1
51
D,(25) 31 32
D,(5)
A,(6)
D,(25) 48 49
B,(4)
96
76
D,(25)
6 7
0 1
F
D,(20)
61 62
C,(3)
80 81
E,(4.5) i
95
F,(3.5)
: Setup time Fig. 4. An illustrative production schedule for the example in Table 3.
produce 6 products. The average consumption of these products and their production data are shown in Table 3. The planning period is 1 day in which are 24 working hours. We want to find the optimal setup frequency in the condition that the setup frequency is equal for all products. Based on the data shown in Table 3, the total used capacity, i.e., l m 600þ400þ300þ500þ450þ350 6 P PI Li þ 1 ð 24 , is ð i¼1 Li þ Ii¼1 Si jH 100 4 3 25 4:5 3:5 þ 24 þ 24 þ 24 þ 24 þ 24 ÞÞ ¼ 46 þ 7 ¼ 53 h and is greater than the capacity of one period (i.e., C = m j H = 2 1 24 = 48 h). It means that all products cannot be setup every period. Therefore, we can use Eq. (10) to find the optimal setup frequency. That is
&
4 3 25 4:5 3:5’ þ 24 þ 24 þ 24 þ 24 þ 24 F¼ 2 1 24 600þ400þ300þ500þ450þ350 100
7 ¼ d3:5e ¼ 4 ¼ 48 46 1
6 24
In other words, this plant must produce or replenish each product once every 4 days and quantity of replenish is the consumption during 4 days. And using Eq. (6), the rest capacity in one period is
l m1 0 Li I I si X X eh A ¼ 48 46 þ 7 ¼ 0:25 h: C@ Li þ fi 4 i¼1 i¼1 A sensitivity analysis is shown in Table 4. When F = 4, the plant capacity is not only feasible, but also the rest capacity is minimum. Besides, Fig. 4 shows an illustrative production schedule for these six products in this plant. 6. Conclusions When the TOC-SCRS is applied in a plant or a central warehouse, the determination of RRT (i.e., replenishment frequency and
replenishment lea time) will encounter a conflict with the replenishment quantity. That is because the replenishment frequency depends on the set up frequency in the plant and the replenishment lead time depends on the production lead time. As we know, however, the set up frequency and the replenishment lead time in the plant depend on the production quantity (i.e., replenishment quantity). It means that the replenishment frequency and the replenishment lead time must depend on the known replenishment quantity, especially under the constraint of limited plant capacity. However, in TOC-SCRS, the replenishment quantity is determined by the known parameters of the replenishment frequency and the replenishment lead time. Therefore, this is a big conflict and an issue to apply the TOC-SCRS in a plant or a central warehouse. An enhanced replenishment model for TOC-SCRS under capacity constraint is required to be provided to solve this conflict. In this paper, the concept and method of TOC-SCRS was first reviewed. The model of TOC-SCRS was then modeled and its feasibility of application in central warehouse was discussed. An enhanced replenishment model for TOC-SCRS under capacity constraint was then developed. A numeric example and a sensitivity analysis were utilized to evaluate the application of the proposed method. Employing this proposed methodology will facilitate manufacturing plants or central warehouses to successfully implement an effective TOC-SCRS. Acknowledgment The authors would like to thank the National Science Council of the Republic of China, for financially supporting this research under Contract No. NSC 96-2628-E-216-001-MY3. References Beamon, B. M. (1998). Supply chain design and analysis: Models and methods. International Journal of Production Economics, 55(3), 281–294.
6440
H.-H. Wu et al. / Expert Systems with Applications 37 (2010) 6435–6440
Belvedere, V., & Grando, A. (2005). Implementing a pull system in batch/mix process industry through theory of constraints: A case-study. Human Systems Management, 24(1), 3–12. Bhattacharya, A., & Vasant, P. (2007). Soft-sensing of level of satisfaction in TOC product-mix decision heuristic using robust fuzzy-LP. European Journal of Operation Research, 177(1), 55–70. Blackstone, J. H. (2001). Theory of constraints – A status report. International Journal of Production Research, 39(6), 1053–1080. Cole, H., & Jacob, D. (2002). Introduction to TOC supply chain. AGI Institute. Goldratt, E. M. (1994). It’s not luck. England: Gower. Hoffman, G., & Cardarelli, H. (2002). Implementing TOC supply chain: A detailed case study- MACtac. AGI Institute. Holt, J. R. (1999). TOC in supply chain management. In 1999 constraints management symposium proceedings, Phoenix, AZ, USA (pp. 85–87). Kendall, G. I. (2006). Viable vision. Heliopolis Culture Group/SAGA Culture Publishing Co. Luebbe, R., & Finch, B. (1992). Theory of constraints and linear programming: A comparison. International Journal of Production Research, 30(6), 1471–1478. Novotny, D. J. (1997). TOC supply chain case study. In 1997 APICS constraints management symposium proceedings, Denver, Colorado, USA (pp. 78–79). O’Donnell, T., Maguire, L., Mcivor, R., & Humphreys, P. (2006). Minimizing the bullwhip effect in a supply chain using genetic algorithms. International Journal of Production Research, 44(8), 1523–1543. Patnode, N. H. (1999). Providing responsive logistics support: Applying lean thinking to logistics. In 1999 constraints management symposium proceedings, Phoenix, AZ, USA (pp. 93–96).
Perez, J. L. (1997). TOC for world class global supply chain management. Computers & Industrial Engineering, 33(1), 289–293. Sharma, K. (1997). TOC supply chain implementation: System strategies. In 1997 APICS constraints management symposium proceedings, Denver, Colorado, USA (pp. 66–74). Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory management and production planning and scheduling (3rd ed.). John Wiley & Sons Inc. Simatupang, T. M., Wright, A. C., & Sridharan, N. (2004). Applying the theory of constraints to supply chain collaboration. Supply Chain Management: An International Journal, 9(1), 57–70. Smith, D. A. (2001). Linking the supply chain using the theory of constraints logistical applications and a new understanding of the role of inventory/buffer management. In 2001 constraints management technical conference proceedings, San Antonio, Texas, USA (pp.64–67). Tsai, K. M., You, S. Y., Lin, Y. H., & Tsai, C. H. (2008). A fuzzy goal programming approach with priority for channel allocation problem in steel industry. Expert Systems with Applications, 35(3), 1870–1876. Waite, J., Gupta, S., & Hill, E. (1998). Meritor HVS story. In 1998 APICS constraints management symposium proceedings, Seattle Washington, AZ, USA (pp. 1–9). Watson, K., & Polito, T. (2003). Comparison of DRP and TOC financial performance within a multi-product, multi-echelon physical distribution environment. International Journal of Production Research, 41(4), 741–765. Yuan, K. J., Chang, S. H., & Li, R. K. (2003). Enhancement of theory of constraints replenishment using a novel generic buffer management procedure. International Journal of Production Research, 41(4), 725–740.