Buffer size determination for drum-buffer-rope controlled supply chain networks. Zhaleh Parsaei and Nasim Nahavandi*

Transcription

1 Int. J. Agile Systems and Management, Vol. 5, No. 2, Buffer size determination for drum-buffer-rope controlled supply chain networks Zhaleh Parsaei and Nasim Nahavandi* Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, P.O. Box , Tehran, Iran Fax: (+98) *Corresponding author Tarek ElMekkawy Department of Mechanical and Manufacturing Engineering, University of Manitoba, Postal code: MBR3T 5V6, Winnipeg, Canada Fax: Abstract: The theory of constraints drum-buffer-rope (DBR) system is a method for achieving effective supply chain management (SCM) and is now being implemented by a growing number of companies. Buffer size determination is the most difficult step in using DBR in SCM, however, it received less attention and the buffer level is usually determined by trial and error. The focus of this paper is first is to develop an efficient approach to determine the sizes of time buffers of control points of the DBR controlled supply chain. The approach is constructed according to the supplier network reliability analysis in the control points of networks; second, the proposed approach is compared with the most common approach in literature by means of a simulation study using enterprise dynamics (ED). Simulation results show that the developed approach is more effective than the most common approaches in literature. Keywords: theory of constraint; TOC; drum-buffer-rope; DBR; time buffer; reliability; control point; supply chain, supply chain networks. Reference to this paper should be made as follows: Parsaei, Z., Nahavandi, N. and ElMekkawy, T. (2012) Buffer size determination for drum-buffer-rope controlled supply chain networks, Int. J. Agile Systems and Management, Vol. 5, No. 2, pp Biographical notes: Zhaleh Parsaei is a PhD student in Industrial Engineering, Tarbiat Modares University of Iran (TMU). Her researches focus on theory of constraint, supply chain. She is now continuing her research as a Visitor Scholar at University of Manitoba. She has a published paper in International Journal of Business Innovation and Research. Copyright 2012 Inderscience Enterprises Ltd.

2 152 Z. Parsaei et al. Nasim Nahavandi is an Assistant Professor at the Department of Industrial Engineering at Tarbiat Modares University. She received her PhD in Industrial Engineering from Tarbiat Modares University, Tehran, in She received her MS in Industrial Engineering from the Polytechnique University, in 1995 and BS degree from the Sharif University of Technology, in Her major research is in the areas of material flow control management (with specific research on TOC), multiple criteria decision-making, simulation, supply chain management and system dynamics. Her researches have appeared in International Journal of Production Research, African Journal of Business Management, American Journal of Applied Sciences, Scientia Iranica, International Journal of Industrial Engineering and Production Research, and World Applied Sciences Journal. Tarek ElMekkawy is an Associate Professor at the Department of Mechanical and Manufacturing Engineering at University of Manitoba. He received his PhD in Industrial and Manufacturing Systems Engineering from University of Windsor, Ontario, Canada, in His interest is in applications of operational research and industrial engineering techniques to improve healthcare delivery, production planning, scheduling and control, systems modelling and simulation and productivity improvement. His publications are available in International Journal of Production Economics, Journal of Flexible Services and Manufacturing, Robotics and Computer Integrated Manufacturing, European Journal of Industrial Engineering, International Journal of Production Research, Int. J. of Operational Research, Int. J. of Engineering, Journal of Mechanical Design, Int. J. of Flexible Manufacturing Systems, Int. J. of Science and Technology, Canadian Biosystems Engineering Journal, Int. J. of Advanced Manufacturing Technology, Int. J. of Computer Integrated Manufacturing, and Int. J. of Advanced Manufacturing Technology. 1 Introduction Supply chain management (SCM) is a philosophy based on the belief that each firm in the supply chain network directly and indirectly affects the performance of all other members of the network, as well as ultimately, the overall supply chain performance (Lockamy, 2008). Increasingly, firms are adopting SCM to improve competitiveness (Gunasekaran et al., 2008; Li et al., 2006; Singh et al., 2005). There are many obstacles, however, that prohibit the achievement of effective SCM within supply networks (Sohn and Lim, 2008; Akkermans et al., 1999). One of the most important obstacles is the fluctuation in demand and inevitably the challenge of having the right inventory in the right place (node) at the right time. Hence, one of the key factors of achieving low inventory while maintaining high customer delivery performance is using effective inventory method in the supply chain (O Donnell et al., 2006). Theory of constraint (TOC) techniques such as drum-buffer-rope (DBR) and buffer management, V-A-T analysis can assist organisations surmounting the mentioned challenges in SCM. Although TOC has been developing quickly and become a general theory in operations management, SCM is an area in which TOC principles have been explored less (Gupta and Boyd, 2008). Although Goldratt (1994) had already addressed this issue for the first time, Perez (1997), Schragenheim and Dettmer (2001), and Holt (1999) directly addressed the application of the TOC in SCM. The main objective of these papers was to describe the TOC pull methodology, and systematically explore the

3 Buffer size determination for drum-buffer-rope controlled supply chain 153 TOC principles in relation to SCM. Goldratt and Goldratt (2007) used TOC distribution to find a conflict in distribution environments that blocks the maximisation of their performance; Rahman (2002) used TOC thinking process (TP) to develop strategies in SCM; and Kim et al. (2008) described SCM as an area of application of the TPs. Some researchers identified the control points and determined the location of the buffers (Lockamy, 2008; Holt, 1999; Umble, 2002); however much less attention has been given to determining the size of the buffer. Nevertheless, the size of the buffer significantly affects the performance of supply chain networks. For example, Lockamy (2008) suggested V-A-T analysis for material flow in supply chain networks. Lockamy also mentioned that organisations may overcome the challenges of supply chain networks by understanding the nature of network control points via the application of V-A-T analysis in their supply chains. He suggested placing the buffer into these control points but he did not propose any approach to determine these buffer levels. Goldratt (2002) considered the average demand in replenishment time plus 50 present of safety as the buffer size in each control points of supply chain. This method does not work well in many cases and result to lose demand when unreliability is high during supply chain and increasing the inventory in high reliability. Wu et al. (2010) proposed a model for TOC supply chain replenishment system using the maximum expected usage during the time to reliably replenish for buffer size determination. They did not explain that how the reliably replenishment time should be calculated. Pawlewski et al. (2009) defined buffer as the multiplied minimum cumulative processing time for the individual part. It is necessary to use a multiplier for safety but they did not mentioned how these multipliers should be calculated. This paper describes a novel efficient approach, based on reliability analysis, to determine the sizes of the time buffer in control points of the DBR controlled supply chain. In this approach first, the supplier system of each control point in supply chain networks is defined and then according to the relation of the control point and its feeding nodes, the reliability of the supplier system is defined; finally buffer size is determined. This approach is examined for a supply chain network by using simulation. For showing the efficiency of the proposed approach, it is compared with Goldratt (2002) approach which is the most common approach in the literature. In the other word, the simulated model is run with two scenarios of buffer size determination, the Goldratt approach and the proposed one, and the results are then compared to show the effectiveness of proposed model. 2 TOC TOC was developed by Eliyahu M. Goldratt during the 1980s (Reid, 2007). The core idea of TOC is that every organisation has at least one constraint that prevents management from achieving the goal of the organisation to a larger degree. The constraint may be physical, such as a machine with limited capacity, a policy or a behaviour constraint. Policy constraints often arise when the company environment changes while its policies remain unchanged. Most significantly, policy constraints are usually under the control of the organisation s management (Mabin and Balderstone, 2003). TOC comprises three separate but interrelated areas, logistics, performance measurement, and logical thinking

4 154 Z. Parsaei et al. (Taylor and Poyner, 2008; Nahavandi et al., 2011). Some of the methodologies in TOC logistic area are described here. 2.1 Drum-buffer-rope DBR is one of the methodologies in TOC logistic area which is used for manufacturing planning and control mechanism; it operates as a pull system, translating market demand into the schedule of production at the constraint and then releasing materials into the system based on production at the constraint (Patti and Watson, 2010). In DBR, the drum is considered to be the pacing schedule of the control point, by which an attempt is made to obtain full use of the control point s available capacity. The rope is the schedule for releasing materials as dictated by the control point (Blackstone and Cox, 2008). The time buffer is defined as the summation of processing time, setup time, and an estimate of the aggregated amount of protective time required. It represents the time required to ensure that the released product will get to the control point when needed. Since materials are expected to arrive early, a level of inventory will naturally accumulate. 3 TOC in SCM In spite of quick deployment of TOC in different management issues, fewer explorations have been done in SCM. Rahman (1998) did a literature review and analysis of a comprehensive list of publications on TOC in 1998 but he did not mention the potential contributions of TOC in the scope of SCM. Although Goldratt (1994) had addressed this issue for the first time in Perez (1997) explained how TOC-based operational policies are generated for different links in a supply chain to improve the performance of the whole chain. Rahman (2002) described an application of TP of TOC to identify critical success factors in SCM. Kaihara (2001) established a rapid relation between SCM and TOC, but importance of TOC in the development of his paper did not go much beyond that. Simatupang et al. (2004) applied TOC to overcome difficulties in realising the potential benefits of supply chain collaboration. Pawlewski et al. (2009) presented a conceptual framework for the multi agent approach method that involves the hybrid solutions combining the advantages of MRP simple logic and TOC. Its ability lies in synchronising all production and material flow in supply chain. They have used TOC buffers monitoring procedures to improve the control of synchronised production and material flow in supply chain. Walker (2002) presented a practical application of DBR to synchronise a two stage supply chain. Lockamy (2008) examined the use of V-A-T analysis in the management of supply chain networks and showed how the control points in supply chain networks can be revealed through V-A-T analysis. He also mentioned that control points in the network must be identified and buffered to avoid supply chain disruptions but he has not propped any approach to determine the size of buffer in these points. In the next part, the different approaches for buffer size determination are explained. 3.1 Time buffer size in SCM The time buffer is the amount of time required to reach a control point after the product is released and it protects the utilisation of the control points (Ye and Han, 2008). The

5 Buffer size determination for drum-buffer-rope controlled supply chain 155 suitable size of buffer is very important because high levels of inventory imply high investments and waste of the resources while low level may result to in loosing orders. Although the time buffer concept is justifiable and practicable, unfortunately there is no specific approach in the literature to determine its size. The size of buffer in a stable manufacturing system is three times as long as the average lead time to the constraint from the raw material release point (Guide, 1996). Uncertainty nearly always exists in supply chain. For this reason, the buffer must protect the downstream node or the customer demand, if it is the last node, from fluctuations in both downstream demand and in upstream supply. Goldratt (2002) suggested equation (1) to determine buffer size. Buffer size = Average recent demand in the re-order period + Average recent demand in the re-supply period + A measure of safety An initial suggestion for a good value of safety is +50% (Goldratt, 2002). Wu et al. (2010) used the same concept in their paper; they mentioned that 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 as below: where ri S i = Max d, 1 ix j = r i r i 1,..., J, i 1, 2,..., I. x= j r + = (2) i + () I i J j total product types product index, i = 1, 2,, I total planning periods period index, j = 1, 2,, J d ij consumption of product i in period j f i r i frequency of replenishment for product i, i.e., the time period between delivers time to reliably replenish product i S i buffer level of product i. Pawlewski et al. (2009) defined buffer as the multiplied minimum cumulative processing time for the individual part BS = MULTI. PT (3) i j= 1 ij where BS i is the size of buffer for part i = (1, 2, 3,, n), PT ij is the minimum processing time for operation j on part i and MULTI is a constant multiplier (Pawlewski et al., 2009). As it can be seen, all the researches have emphasised putting a multiplier for safety. However, none of them have mentioned how these multipliers should be calculated. In the next section, a new buffer size approach based on reliability is suggested which helps managers to estimate the suitable measure of safety.

6 156 Z. Parsaei et al. 4 Proposed time buffer model In reality, unreliability exists in the supply chain networks at various stages. Buffers are used to decrease loses which incurred on performance due to the unreliability. In this section, first supplier system of a control point is described; second, reliability in a control point supplier system is explained; then based on the reliability of each control point supplier system, the new buffer size approach is suggested. 4.1 Control points supplier system In a given supply chain network, every control point has a supplier system which is composed of all nodes that feed the control point directly or indirectly from raw material or from previous control point (if there is another one) to the control point. For example, in Figure 1, there are two control points in the given network. Because there is another control point before CP 1, its supplier system is composed of A, B, C, D and CP 2 and supplier system of CP 2 is composed of E and F. Figure 1 An example network 4.2 Reliability of a control point supplier system The supplier network reliability models are based on well-known engineering reliability models described in Leemis (1995) and Aven (1992). Other authors have noted the relationship between engineering reliability and reliability in a business operation. Garvin (1987) used engineering reliability to help define the key dimensions of quality. In its simplest form, reliability is a probability that a component or a system of components performs in an adequate fashion. For a single supplier, then, performance might be defined in terms of delivery of goods to a customer location, with a specified quantity, and at a specified time. These engineering system reliability concepts may be readily applied at different levels in a supply chain operation as well. The reliability of a single supplier may be analysed for a particular component or to a selected order of material on a particular day. Hence, following Leemis (1995) and Meixell (2006), the reliability of a control point supplier system can be defined. According to Section 3.1, each control point has a supplier system included in its feeding nodes. Therefore, X i is defined as a binary random variable that describes the state of the i th feeding node as following:

7 Buffer size determination for drum-buffer-rope controlled supply chain if feeding node i is currently not operational/delivering on time Xi = 1 if feeding node i is currently operational/delivering on time where Cp the control point p(j) is the reliability of feeding node j, p(j) = P(X j = 1) R(cp) is the reliability of cp supply system. For defining R(cp), two kinds of supplier system can be considered; series system and parallel system. In a structure of n feeding nodes arranged in a series supplier system, all the feeding nodes supply the control point through different parts which are then assembled in the control point. Assuming no safety stock inventory, if any of the feeding nodes in the series fails, the supply system fails as well and the control points starve. The reliability of the supplier system in control points for the series structure can be computed according to the following pseudo code: R( cp) = p ( j) j s cp if j is upstream node or another control point p (j) = p(j) else ( i s j ) if i is upstream node then p ( j) = p( i) p( j) else i s j p( j) = pi ( ) pi ( ) endif endif i s j A structure of n feeding nodes arranged in parallel if all the feeding nodes supply control point by the same parts. In this system, the control point fails only if all feeder nodes fail to deliver. ( ) Rcp ( ) = 1 1 p ( j) j s cp if j is upstream node another control point p (j) = p(j) else ( i s j ) if i is upstream node then p ( j) = 1 ( 1 pi ( )) ( 1 p( j) ) i s j

8 158 Z. Parsaei et al. else ( ) ( ) p ( j) = 1 1 pi ( ) 1 pi ( ) endif endif i s j 4.3 Buffer size in control points Since the time buffer protects the utilisation of the control points, therefore, the size of time buffer varies according to the degree of the stability of the feeder nodes in front of the control nodes. However, this stability is affected by unpredictable events and uncertainty. Accordingly, maximum time buffer for protecting a control point closely correlates with the reliability of its supplier system. Equation (4) is presented below based on reliability of the control point supplier system which is calculated according to Section 4.2. where BS ( 2 Rcp ( ))max cpj (4) cp j RT BS cp buffer size for the control point R(cp) reliability of the control point supplier system RT cpj replenishment time to the point cp from the previous point or raw material in stage j j the number of stage in supply chain network. Now the buffer size in the control point CP 1 for Figure 1 can be calculated. Table 1 Buffer size in CP 1 k h RT kh RT max[ RT ] cp1 j cp1 j BS cp E CP 2 2 J = 1 F CP C A 4 J = (hr) D B 2 J = 3 A CP B CP 1 3 CP 2 CP 1 1 Table 1 illustrates the preliminary data of an example to show how the equation (4) can be used. In this table, RT kh represents replenishment time from node k to node h. RT cp1 j in columns 3 shows the replenishment time to CP 1 in stages 1 to 3. Column 4 shows the j

9 Buffer size determination for drum-buffer-rope controlled supply chain 159 maximum of the RT cp. 1 j Finally, the time buffer size of CP 1 is determined according the reliability of its supplier system and is shown in column 6. 5 Simulation model A simulation model is developed to verify the proposed methodology of determining the time buffer size. Enterprise dynamics (EDs) is used to simulate the performance of supply chain network. The simulated supply chain network, shown in Figure 2, is hypothetical and consists of four echelons and seven nodes. It is supposed that the control point of this network is CP 1, and the supplier system of CP 1 consist of nodes E, C, D, F and G and acts like series supplier system. Figure 2 Four-echelon supply chain network simulation layout The average demand rate follow an exponential distribution with an average rate of 7 units. A transporter moves the products between nodes. Replenishment time between two nodes is given in Table 2 and it is composed of two terms, replenishment lead time and frequency. Replenishment frequency is defined by the transporter schedule time in the model. Each node, except the control points, can fail according to the Poisson distribution with an average rate that is given in Table 2. Hence, the reliability of control point supplier system can be estimated at any given point of time. Table 2 Node The value of input variables of the simulation model Mean time between failure (MTBF) k h Mean replenishment time from k to h A 10 G C 5 B 10 F E 8 C 20 E CP 1 2 D 20 C CP 1 6 E 10 D CP 1 2 F 10 CP 1 A 8 G 10 CP 1 B 10 The reliability of CP 1 supplier system is considered as an independent variable in the simulation model. Two measures of performance are estimated from simulation output: mean work in process (WIP) mean time to respond to an order (MTTRO).

10 160 Z. Parsaei et al. It is worth mentioning that the supply chain performance improves when WIP and mean time to responds an order decrease. The hypothetical network was simulated and run with two different scenarios of CP1 buffer size determination. The buffer size was estimated using equation (1), which is proposed by Goldratt (2002), as first scenario and using equation (4), which is proposed in this paper, as the second scenario. To avoid the bias due to the empty supply chain during the warm-up period, the model was set in advance to run until steady state condition is reached. In other words, output data were captured after a 250 hour of warm-up period. The simulation model was run for 30 replications. The simulation run length is 5,750 hours. Therefore, data is captured for 5,500 hours. Table 3 shows the results of the simulation runs. The results show that the in Scenario 1, control point is idle for 22% of the simulating time and the MTTRO is more than MTTRO of Scenario 2. Moreover, the average WIP of Scenario 1 is significantly more than the WIP of Scenario 2. Table 3 Comparison of Scenario 1 with Scenario 2 Control point utilisation MTTRO WIP Scenario 1 78% Scenario 2 100% For further analysis, two simulation groups, A and B, are performed where in each group different values of reliability are considered; all other variables remained fixed. Again, two scenarios of buffer size determination are considered; Scenario 1 for group A, and Scenario 2 for group B. Figure 3 reveals that the MTTRO in group A, increases sharply when reliability decreased. At a reliability of 0.5 or more, both groups have the same values of MTTRO. The difference between groups A and B becomes larger when the values of reliability decrease. Therefore, the method of buffer size determination according to the value of reliability is more important when reliability is less. Figure 3 Relationship between reliability and MTTRO

11 Buffer size determination for drum-buffer-rope controlled supply chain 161 The relationship of reliability with WIP using both scenarios is plotted in Figure 4. As it can be seen, the gradient of black curve increases sharply when reliability increases, and hence, the cost of the supply chain increase. The WIP of group B decreases when reliability increases while it increases smoothly when reliability decreases. Figure 4 Relationship between reliability and WIP 6 Conclusions There are several difficulties of managing supply chain networks effectively. TOC techniques such as DBR and V-A-T can improve supply chain performance. These techniques can overcome supply chain networks difficulties by understanding the control points in supply chain networks and buffering them with suitable buffers. Since the buffer size determination is the most difficult step in using DBR for SCM and less attention has been given to it, a new approach based on reliability analysis was described in this paper to determine time buffer in control points of DBR controlled supply chain. The supplier system of each control point and the reliability of the supplier system were defined and then the proposed approach was constructed according to reliability of control point supplier system. The effectiveness of the proposed approach was shown using the simulation. A hypothetical supply chain network was modelled in the ED and the simulation model was run with two different scenarios of buffer size determination; Scenario 1 was based on the most common approach for buffer size determination in literature and the Scenario 2 was based on the proposed approach. Results showed that the proposed approach was more effective. For example, MTTRO and WIP of Scenario 2 were less compared to the results of Scenario 1. More analysis was done by changing the reliability of control point supplier system. Results showed that MTTRO of both scenarios were the same when reliability was greater than 0.5. However, MTTRO of Scenario 1 increased sharply when reliability was less than 0.5. WIP as another key performance measure increased with sharp gradient when reliability of supplier system was high.

12 162 Z. Parsaei et al. Determining the size of a buffer in a high uncertainty environment of supply chain is very crucial but in many companies, in practice, the buffer level is still determined by the trial and error approach. The proposed method could be efficiently applied in practice to estimate the lengths of the required time buffer in supply chain control points. By using the proper approach for buffer size determination, the level of WIP through the supply chain remained in a suitable level in which the minimum inventory cost and maximum response to customer demand happen. Since reliability is just one of the different variables that affect the supply chain performance, this paper can be as an important platform for further research regarding the use of other variables that can affect the size of buffers in DBR-controlled supply chain. The proposed method in this paper was used to a hypothetical supply chain network, for further research could focus on using this proposed method in a real supply chain network. References Akkermans, H., Bogerd, P. and Vos, B. (1999) Virtuous and vicious cycles on the road towards international supply chain management, International Journal of Operations & Production Management, Vol. 19, Nos. 5/6, pp Aven, T. (1992) Reliability and Risk Analysis, Elsevier Science Publishers, Essex. Blackstone, J.H. and Cox, J.F. (2008) APICS Dictionary, 12th ed., Vol. 12, APICS, Athens, GA. Garvin, D.A. (1987) Competing on the eight dimensions of quality, Harvard Business Review, Vol. 65, No. 6, pp Goldratt, E.M. (1994) It s Not Luck, North River Press, Great Barrington, MA. Goldratt, E.M. (2002) Theory of constraints self learning program of distribution and supply chain, CD-ROM, Goldratt s Marketing Group. Goldratt, E.M. and Goldratt, R. (2007) TOC insights into distribution, available at (accessed on 20 March 2007). Guide, V.D.R., Jr. (1996) Scheduling using DBR in a remanufacturing environment, International Journal of Production Research, Vol. 34, No. 4, pp Gunasekaran, A., Lai, K. and Cheng, T. (2008) Responsive supply chain: a competitive strategy in a networked economy, Omega, Vol. 36, No. 4, pp Gupta, M.C. and Boyd, L.H. (2008) Theory of constraints: a theory for operations management, International Journal of Operations & Production Management, Vol. 28, No. 10, pp Holt, J.R. (1999) TOC in supply chain management, Constraints Management Symposium Proceedings, Phoenix, AZ, March, pp.85 87, APICS, Falls Church, VA. Kaihara, T. (2001) Supply chain management with market economics, International Journal of Production Economics, Vol. 73, No. 1, pp Kim, S., Mabin, V.J. and Davies, J. (2008) The theory of constraints thinking processes: retrospect and prospect, International Journal of Operations & Production Management, Vol. 28, No. 2, pp Leemis, L.M. (1995) Reliability: Probabilistic Models and Statistical Methods, Prentice-Hall, Englewood Cliffs, NJ. Li, S., Ragu-Nathan, B., Ragu-Nathan, T. and Rao, S. (2006) The impact of supply chain management practices on competitive advantage and organizational performance, Omega, Vol. 34, No. 2, pp Lockamy, A., III (2008) Examining supply chain networks using V-A-T material flow analysis, An International Journal of Supply Chain Management, Vol. 13, No. 5, pp

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