Optimal inventory policies for serial-type and assembly-type supply chains with equal sized batch

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July 2015, 11(3): 1021-1040. doi: 10.3934/jimo.2015.11.1021

Optimal inventory policies for serial-type and assembly-type supply chains with equal sized batch

Jason Chao-Hsien Pan ^1, , Ku-Kuang Chang ^2, and Yu-Cheng Hsiao ^2,

1.	Department of Business Administration, Takming University of Science and Technology, 56 Huan-Shan Rd, Section 1, Taipei 114, Taiwan
2.	Department of Logistics, Takming University of Science and Technology, 56 Huan-Shan Rd, Section 1, Taipei 114, Taiwan, Taiwan

Received May 2013 Revised May 2014 Published October 2014

Abstract
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This study focuses on the inventory problems for serial-type and assembly-type supply chains. Since the mainline and each branch line of the assembly-type supply chain can be treated as a serial-type supply chain, a model of a serial-type supply chain is first constructed and then an integrated model is developed for the whole assembly-type supply chain. Both problems are solved optimally by the proposed polynomial-time algorithm, which determines the economic lot size, the optimal batch sizes, and the number of batches for each stage. Numerical examples are included to illustrate the algorithmic procedures.

Keywords: lot size., supply chain, Inventory.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: Jason Chao-Hsien Pan, Ku-Kuang Chang, Yu-Cheng Hsiao. Optimal inventory policies for serial-type and assembly-type supply chains with equal sized batch. Journal of Industrial & Management Optimization, 2015, 11 (3) : 1021-1040. doi: 10.3934/jimo.2015.11.1021

References:

[1]	G. P. Cachon and P. H. Zipkin, Competitive and cooperative inventory policies in a two-stage supply chain,, Management Science, 45 (1999), 936. doi: 10.1287/mnsc.45.7.936. Google Scholar
[2]	H. Glock, Batch sizing with controllable production rates,, Int. J. Prod. Res., 48 (2010), 5925. doi: 10.1080/00207540903170906. Google Scholar
[3]	S. K. Goyal, Determination of optimum production quantity for a two-stage production system,, Oper. Res. Q., 28 (1977), 865. doi: 10.1057/jors.1977.174. Google Scholar
[4]	S. K. Goyal, Economic batch quantity in a multi-stage production system,, Int. J. Prod. Res., 16 (1978), 267. doi: 10.1080/00207547808930019. Google Scholar
[5]	S. K. Goyal, Note on: Manufacturing cycle time determination for a multi-stage economic production quantity model,, Management Science, 23 (1976), 332. doi: 10.1287/mnsc.23.3.332. Google Scholar
[6]	S. K. Goyal and A. Z. Szendrovits, A constant lot size model with equal and unequal sized batch shipments between production stages,, Eng. Costs Prod. Econ., 10 (1986), 203. doi: 10.1016/S0167-188X(86)80002-7. Google Scholar
[7]	W. T. Ho, J. C. H. Pan and Y. C. Hsiao, Optimizing multi-stage production for an assembly-type supply chain with unequal sized batch shipments,, J Optim Theory Appl., 153 (2012), 513. doi: 10.1007/s10957-011-9951-y. Google Scholar
[8]	J. K. Jha and K. Shanker, Two-echelon supply chain inventory model with controllable lead time and service level constraint,, Comput. Ind. Eng., 57 (2009), 1096. doi: 10.1016/j.cie.2009.04.018. Google Scholar
[9]	H. T. Lee and J. C. Wu, A study on inventory replenishment policies in a two-echelon supply chain system,, Comput. Ind. Eng., 51 (2006), 257. doi: 10.1016/j.cie.2006.01.005. Google Scholar
[10]	R. R. Lummus, R. J. Vokurka and K. L. Alber, Strategic supply chain planning,, Journal of Production Inventory Management, 39 (1998), 49. Google Scholar
[11]	N. Y. Shenas, A. E. Jahromi and S. T. A. Niaki, General bounds for the optimal value of retailers' reorder point in a two-level inventory control system with and without information sharing,, Int. J. Adv. Manuf. Technol., 48 (2010), 383. doi: 10.1007/s00170-009-2280-8. Google Scholar
[12]	Z. Szendrovits, Manufacturing cycle time determination for a multi-stage economic production quantity model,, Management Science, 22 (1975), 298. doi: 10.1287/mnsc.22.3.298. Google Scholar
[13]	Z. Szendrovits and Z. Drezner, Optimizing multi-stage production with constant lot size and varying numbers of batches,, Omega-International Journal of Management Science, 8 (1980), 623. doi: 10.1016/0305-0483(80)90003-1. Google Scholar
[14]	C. Vercellis, Multi-plant production planning in capacitated self-configuring two-stage serial systems,, Eur. J. Oper. Res., 119 (1999), 451. doi: 10.1016/S0377-2217(99)00146-0. Google Scholar
[15]	S. Wang and B. R. Sarker, An assembly-type supply chain system controlled by kanbans under a just-in-time delivery policy,, Eur. J. Oper. Res., 162 (2005), 153. doi: 10.1016/j.ejor.2003.10.038. Google Scholar

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References:

[1]	G. P. Cachon and P. H. Zipkin, Competitive and cooperative inventory policies in a two-stage supply chain,, Management Science, 45 (1999), 936. doi: 10.1287/mnsc.45.7.936. Google Scholar
[2]	H. Glock, Batch sizing with controllable production rates,, Int. J. Prod. Res., 48 (2010), 5925. doi: 10.1080/00207540903170906. Google Scholar
[3]	S. K. Goyal, Determination of optimum production quantity for a two-stage production system,, Oper. Res. Q., 28 (1977), 865. doi: 10.1057/jors.1977.174. Google Scholar
[4]	S. K. Goyal, Economic batch quantity in a multi-stage production system,, Int. J. Prod. Res., 16 (1978), 267. doi: 10.1080/00207547808930019. Google Scholar
[5]	S. K. Goyal, Note on: Manufacturing cycle time determination for a multi-stage economic production quantity model,, Management Science, 23 (1976), 332. doi: 10.1287/mnsc.23.3.332. Google Scholar
[6]	S. K. Goyal and A. Z. Szendrovits, A constant lot size model with equal and unequal sized batch shipments between production stages,, Eng. Costs Prod. Econ., 10 (1986), 203. doi: 10.1016/S0167-188X(86)80002-7. Google Scholar
[7]	W. T. Ho, J. C. H. Pan and Y. C. Hsiao, Optimizing multi-stage production for an assembly-type supply chain with unequal sized batch shipments,, J Optim Theory Appl., 153 (2012), 513. doi: 10.1007/s10957-011-9951-y. Google Scholar
[8]	J. K. Jha and K. Shanker, Two-echelon supply chain inventory model with controllable lead time and service level constraint,, Comput. Ind. Eng., 57 (2009), 1096. doi: 10.1016/j.cie.2009.04.018. Google Scholar
[9]	H. T. Lee and J. C. Wu, A study on inventory replenishment policies in a two-echelon supply chain system,, Comput. Ind. Eng., 51 (2006), 257. doi: 10.1016/j.cie.2006.01.005. Google Scholar
[10]	R. R. Lummus, R. J. Vokurka and K. L. Alber, Strategic supply chain planning,, Journal of Production Inventory Management, 39 (1998), 49. Google Scholar
[11]	N. Y. Shenas, A. E. Jahromi and S. T. A. Niaki, General bounds for the optimal value of retailers' reorder point in a two-level inventory control system with and without information sharing,, Int. J. Adv. Manuf. Technol., 48 (2010), 383. doi: 10.1007/s00170-009-2280-8. Google Scholar
[12]	Z. Szendrovits, Manufacturing cycle time determination for a multi-stage economic production quantity model,, Management Science, 22 (1975), 298. doi: 10.1287/mnsc.22.3.298. Google Scholar
[13]	Z. Szendrovits and Z. Drezner, Optimizing multi-stage production with constant lot size and varying numbers of batches,, Omega-International Journal of Management Science, 8 (1980), 623. doi: 10.1016/0305-0483(80)90003-1. Google Scholar
[14]	C. Vercellis, Multi-plant production planning in capacitated self-configuring two-stage serial systems,, Eur. J. Oper. Res., 119 (1999), 451. doi: 10.1016/S0377-2217(99)00146-0. Google Scholar
[15]	S. Wang and B. R. Sarker, An assembly-type supply chain system controlled by kanbans under a just-in-time delivery policy,, Eur. J. Oper. Res., 162 (2005), 153. doi: 10.1016/j.ejor.2003.10.038. Google Scholar

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