# American Institute of Mathematical Sciences

April  2011, 7(2): 401-424. doi: 10.3934/jimo.2011.7.401

## An integrated approach for the operations of distribution and lateral transshipment for seasonal products - A case study in household product industry

 1 Department of Transportation Technology and Management, National Chiao Tung University, Hsinchu, Taiwan 2 Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan, Taiwan

Received  November 2009 Revised  January 2011 Published  April 2011

The household product industry often suffers from problems of high operational costs and/or lost sales from selling seasonal products since managers in different divisions/stages of the supply chain make their decisions independently. We are therefore motivated to propose an approach that integrates the operations in the three stages of a supply chain for the management of seasonal products. The goal of this study is to minimize the total costs incurred for the seasonal products in the whole selling period. In the first stage, we employ a newsvendor model to determine the optimal one-time-only order quantities of the seasonal products. Then, we utilize a clustering analysis in the second stage to categorize seasonal products into groups, and establish an optimal replenishment policy for the products in the same group. Finally, the third stage starts when the warehouse runs out of its inventory. We formulate a mathematical model to determine the optimal transshipment quantities among all of the retailers to minimize the expected total costs incurred for the rest of the selling period. Taking a household product company in Taiwan as our case study, we demonstrate the implementation of the proposed (integrated) approach. Based on the real-world data of 17 seasonal products, we show that our integrated approach significantly outperforms the company's current approach. Therefore, our integrated approach may serve as an effective decision support tool for the distribution and lateral transshipment of seasonal products in the household product industry.
Citation: Ming-Jong Yao, James T. Lin, Chen-Hao Yang. An integrated approach for the operations of distribution and lateral transshipment for seasonal products - A case study in household product industry. Journal of Industrial and Management Optimization, 2011, 7 (2) : 401-424. doi: 10.3934/jimo.2011.7.401
##### References:
 [1] L. P. Bertrand and J. H. Bookbinder, Stock redistribution in two-echelon logistics systems, Journal of the Operational Research Society, 49 (1998), 966-975. [2] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. doi: 10.1287/mnsc.1040.0215. [3] J. Chen and L. Xu, Coordination of the supply chain of seasonal products, IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, 31 (2001), 524-532. doi: 10.1109/3468.983410. [4] W-K. Ching, W. O. Yuen and A. W. Loh, An inventory model with returns and lateral transshipments, Journal of the Operational Research Society, 54 (2003), 636-641. doi: 10.1057/palgrave.jors.2601521. [5] M. Fisher, K. Rajaram and A. Raman, Optimizing Inventory Replenishment of Retail Fashion Products, Manufacturing and Service Operations Management, 3 (2001), 230-241. doi: 10.1287/msom.3.3.230.9889. [6] G. Gallego and I. Moon, The distribution free newsboy problem: review and extensions, The Journal of the Operational Research Society, 44 (1993), 825-834. [7] J. Grahovac and A. Chakravarty, Sharing and lateral transshipment of inventory in a supply chain with expensive low-demand items, Management Science, 47 (2001), 579-594. doi: 10.1287/mnsc.47.4.579.9826. [8] Y. Herer and A. Rashit, Lateral stock transshipments in a two-location inventory system with fixed and joint replenishment costs, Naval Research Logistics, 46 (1999), 525-547. doi: 10.1002/(SICI)1520-6750(199908)46:5<525::AID-NAV5>3.0.CO;2-E. [9] D. S. Johnson, C. R. Aragon, L. A. McGeoch and C. Schevon, Optimization by simulated annealing: an experimental evaluation; Part I, graph partitioning, Operations Research, 37 (1989), 865-892. doi: 10.1287/opre.37.6.865. [10] M. Karakul, Joint pricing and procurement of fashion products in the existence of clearance markets, International Journal of Production Economics, 114 (2008), 487-506. doi: 10.1016/j.ijpe.2007.03.026. [11] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by simulated annealing, Science, 200 (1983), 671-680. doi: 10.1126/science.220.4598.671. [12] H. S. Lau and A. H. L. Lau, Some results on implementing a multi-item multi-constraint single-period inventory model, International Journal of Production Economics, 48 (1997), 121-128. doi: 10.1016/S0925-5273(97)82104-4. [13] Y. H. Lee, J. W. Jung and Y. S. Jeon, An effective lateral transshipment policy to improve service level in the supply chain, International Journal of Production Economics, 106 (2007), 115-126. doi: 10.1016/j.ijpe.2006.05.007. [14] B. K. Lee, K. H. Kang and Y. H. Lee, Decomposition heuristic to minimize total cost in a multi-level supply chain network, Computers and Industrial Engineering, 54 (2008), 945-959. doi: 10.1016/j.cie.2007.11.005. [15] F. C. Lee and M. J. Yao, On the joint replenishment problem under power-of-two policy, Computers and Operations Research, 30 (2003), 1319-1333. doi: 10.1016/S0305-0548(02)00073-4. [16] A. J. Martin, "DRP: Distribution Resource Planning," John Wiley & Sons, New York, 1995. [17] I. Moon and G. Gallego, Distribution free procedures for some inventory models, Journal of the Operational Research Society, 45 (1994), 651-658. [18] I. Moon and E. Silver, Multi-item newsvendor problem with a budget constraint and fixed ordering costs, Journal of the Operational Research Society, 51 (2000), 602-608. [19] S. Nahmias, "Production and Operations Analysis," $4^{th}$ ed., McGraw-Hill, Boston, 2001. [20] F. Olsson, Optimal policies for inventory systems with lateral transshipments, International Journal of Production Economics, 118 (2009), 175-184. doi: 10.1016/j.ijpe.2008.08.021. [21] E. L. Porteus, Numerical comparisons of inventory policies for periodic review systems, Operations Research, 33 (1985), 134-152. doi: 10.1287/opre.33.1.134. [22] G. Punj and D. W. Stewart, Cluster Analysis in Marketing Research: Review and Suggestions for Application, Journal of Marketing Research, 20 (1983), 134-148. doi: 10.2307/3151680. [23] R. O. Roundy, 98%-effective integer-ratio lot-sizing for one-warehouse multi-retailer systems, Management Science, 3 (1985), 1416-1430. doi: 10.1287/mnsc.31.11.1416. [24] H. Scarf, A min-max solution of an inventory problem, in "Studies in the Mathematical Theory of Inventory and Production," (eds. K. J. Arrow, S. Karlin, and H. E. Scarf), Stanford University Press, (1958), 201-209. [25] L. B. Schwarz, A simple continuous review deterministic one-warehouse n-retailer inventory problem, Management Science, 19 (1973), 555-566. doi: 10.1287/mnsc.19.5.555. [26] K. Shang and J. S. Song, Newsvendor bounds and heuristic for optimal policies in serial supply chains, Management Science, 49 (2003), 618-638. doi: 10.1287/mnsc.49.5.618.15147. [27] S. Sharma, "Applied Multivariate Techniques," John Wiley, & Sons, Inc, New York, 1995. [28] E. A. Silver, D. F. Pyke and R. Peterson, "Inventory Management and Production Planning and Scheduling," John Wiley & Sons, New York, 1998. [29] D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi, "Designing & Managing the Supply Chain," McGraw-Hill, New York, 2003. [30] W. J. Stevenson, "Operation Management," McGraw-Hill, New York, 2002. [31] C. S. Tang and R. Yin, Responsive pricing under supply uncertainty, European Journal of Operational Research, 182 (2007), 239-255. doi: 10.1016/j.ejor.2006.07.011. [32] S. Viswanathan, A new optimal algorithm for the joint replenishment problem, Journal of the Operational Research Society, 47 (1996), 936-944. [33] S. Viswanathan and K. Mathur, Integrating routing and inventory decisions in one-warehouse multiretailer multiproduct distribution systems, Management Science, 43 (1997), 294-312. doi: 10.1287/mnsc.43.3.294. [34] J. H. Ward, Hierarchical grouping to optimise an objective function, Journal of the American Statistic Association, 58 (1963), 236-244. doi: 10.2307/2282967. [35] Z. Weng, Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model, European Journal of Operational Research, 156 (2004), 148-161. doi: 10.1016/S0377-2217(03)00003-1. [36] R. E. Wildeman, J. B. G. Frenk and R. Dekker, An efficient optimal solution method for the joint replenishment problem, European Journal of Operational Research, 99 (1997), 433-444. doi: 10.1016/S0377-2217(96)00072-0. [37] M. J. Yao and Y. C. Wang, Theoretical analysis and a search procedure for the joint replenishment problem with deteriorating products, Journal of Industrial and Management Optimization, 1 (2005), 359-375. [38] M. J. Yao and Y. C. Wang, A new algorithm for one-warehouse multi-retailer systems under stationary-nested policy, Optimization Methods & Software, 21 (2006), 41-56. doi: 10.1080/10556780512331318029.

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##### References:
 [1] L. P. Bertrand and J. H. Bookbinder, Stock redistribution in two-echelon logistics systems, Journal of the Operational Research Society, 49 (1998), 966-975. [2] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. doi: 10.1287/mnsc.1040.0215. [3] J. Chen and L. Xu, Coordination of the supply chain of seasonal products, IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, 31 (2001), 524-532. doi: 10.1109/3468.983410. [4] W-K. Ching, W. O. Yuen and A. W. Loh, An inventory model with returns and lateral transshipments, Journal of the Operational Research Society, 54 (2003), 636-641. doi: 10.1057/palgrave.jors.2601521. [5] M. Fisher, K. Rajaram and A. Raman, Optimizing Inventory Replenishment of Retail Fashion Products, Manufacturing and Service Operations Management, 3 (2001), 230-241. doi: 10.1287/msom.3.3.230.9889. [6] G. Gallego and I. Moon, The distribution free newsboy problem: review and extensions, The Journal of the Operational Research Society, 44 (1993), 825-834. [7] J. Grahovac and A. Chakravarty, Sharing and lateral transshipment of inventory in a supply chain with expensive low-demand items, Management Science, 47 (2001), 579-594. doi: 10.1287/mnsc.47.4.579.9826. [8] Y. Herer and A. Rashit, Lateral stock transshipments in a two-location inventory system with fixed and joint replenishment costs, Naval Research Logistics, 46 (1999), 525-547. doi: 10.1002/(SICI)1520-6750(199908)46:5<525::AID-NAV5>3.0.CO;2-E. [9] D. S. Johnson, C. R. Aragon, L. A. McGeoch and C. Schevon, Optimization by simulated annealing: an experimental evaluation; Part I, graph partitioning, Operations Research, 37 (1989), 865-892. doi: 10.1287/opre.37.6.865. [10] M. Karakul, Joint pricing and procurement of fashion products in the existence of clearance markets, International Journal of Production Economics, 114 (2008), 487-506. doi: 10.1016/j.ijpe.2007.03.026. [11] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by simulated annealing, Science, 200 (1983), 671-680. doi: 10.1126/science.220.4598.671. [12] H. S. Lau and A. H. L. Lau, Some results on implementing a multi-item multi-constraint single-period inventory model, International Journal of Production Economics, 48 (1997), 121-128. doi: 10.1016/S0925-5273(97)82104-4. [13] Y. H. Lee, J. W. Jung and Y. S. Jeon, An effective lateral transshipment policy to improve service level in the supply chain, International Journal of Production Economics, 106 (2007), 115-126. doi: 10.1016/j.ijpe.2006.05.007. [14] B. K. Lee, K. H. Kang and Y. H. Lee, Decomposition heuristic to minimize total cost in a multi-level supply chain network, Computers and Industrial Engineering, 54 (2008), 945-959. doi: 10.1016/j.cie.2007.11.005. [15] F. C. Lee and M. J. Yao, On the joint replenishment problem under power-of-two policy, Computers and Operations Research, 30 (2003), 1319-1333. doi: 10.1016/S0305-0548(02)00073-4. [16] A. J. Martin, "DRP: Distribution Resource Planning," John Wiley & Sons, New York, 1995. [17] I. Moon and G. Gallego, Distribution free procedures for some inventory models, Journal of the Operational Research Society, 45 (1994), 651-658. [18] I. Moon and E. Silver, Multi-item newsvendor problem with a budget constraint and fixed ordering costs, Journal of the Operational Research Society, 51 (2000), 602-608. [19] S. Nahmias, "Production and Operations Analysis," $4^{th}$ ed., McGraw-Hill, Boston, 2001. [20] F. Olsson, Optimal policies for inventory systems with lateral transshipments, International Journal of Production Economics, 118 (2009), 175-184. doi: 10.1016/j.ijpe.2008.08.021. [21] E. L. Porteus, Numerical comparisons of inventory policies for periodic review systems, Operations Research, 33 (1985), 134-152. doi: 10.1287/opre.33.1.134. [22] G. Punj and D. W. Stewart, Cluster Analysis in Marketing Research: Review and Suggestions for Application, Journal of Marketing Research, 20 (1983), 134-148. doi: 10.2307/3151680. [23] R. O. Roundy, 98%-effective integer-ratio lot-sizing for one-warehouse multi-retailer systems, Management Science, 3 (1985), 1416-1430. doi: 10.1287/mnsc.31.11.1416. [24] H. Scarf, A min-max solution of an inventory problem, in "Studies in the Mathematical Theory of Inventory and Production," (eds. K. J. Arrow, S. Karlin, and H. E. Scarf), Stanford University Press, (1958), 201-209. [25] L. B. Schwarz, A simple continuous review deterministic one-warehouse n-retailer inventory problem, Management Science, 19 (1973), 555-566. doi: 10.1287/mnsc.19.5.555. [26] K. Shang and J. S. Song, Newsvendor bounds and heuristic for optimal policies in serial supply chains, Management Science, 49 (2003), 618-638. doi: 10.1287/mnsc.49.5.618.15147. [27] S. Sharma, "Applied Multivariate Techniques," John Wiley, & Sons, Inc, New York, 1995. [28] E. A. Silver, D. F. Pyke and R. Peterson, "Inventory Management and Production Planning and Scheduling," John Wiley & Sons, New York, 1998. [29] D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi, "Designing & Managing the Supply Chain," McGraw-Hill, New York, 2003. [30] W. J. Stevenson, "Operation Management," McGraw-Hill, New York, 2002. [31] C. S. Tang and R. Yin, Responsive pricing under supply uncertainty, European Journal of Operational Research, 182 (2007), 239-255. doi: 10.1016/j.ejor.2006.07.011. [32] S. Viswanathan, A new optimal algorithm for the joint replenishment problem, Journal of the Operational Research Society, 47 (1996), 936-944. [33] S. Viswanathan and K. Mathur, Integrating routing and inventory decisions in one-warehouse multiretailer multiproduct distribution systems, Management Science, 43 (1997), 294-312. doi: 10.1287/mnsc.43.3.294. [34] J. H. Ward, Hierarchical grouping to optimise an objective function, Journal of the American Statistic Association, 58 (1963), 236-244. doi: 10.2307/2282967. [35] Z. Weng, Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model, European Journal of Operational Research, 156 (2004), 148-161. doi: 10.1016/S0377-2217(03)00003-1. [36] R. E. Wildeman, J. B. G. Frenk and R. Dekker, An efficient optimal solution method for the joint replenishment problem, European Journal of Operational Research, 99 (1997), 433-444. doi: 10.1016/S0377-2217(96)00072-0. [37] M. J. Yao and Y. C. Wang, Theoretical analysis and a search procedure for the joint replenishment problem with deteriorating products, Journal of Industrial and Management Optimization, 1 (2005), 359-375. [38] M. J. Yao and Y. C. Wang, A new algorithm for one-warehouse multi-retailer systems under stationary-nested policy, Optimization Methods & Software, 21 (2006), 41-56. doi: 10.1080/10556780512331318029.

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