American Institute of Mathematical Sciences

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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

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), 936-953. doi: 10.1287/mnsc.45.7.936.  Google Scholar

[2]

H. Glock, Batch sizing with controllable production rates, Int. J. Prod. Res., 48 (2010), 5925-5942. 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), 865-870. 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), 267-273. 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), 332-333. 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), 203-210. 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), 513-531. 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), 1096-1104. 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), 257-263. 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), 49-58. 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), 383-393. 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), 298-308. 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), 623-629. 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), 451-460. 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), 153-172. doi: 10.1016/j.ejor.2003.10.038.  Google Scholar

show all references

References:
[1]

G. P. Cachon and P. H. Zipkin, Competitive and cooperative inventory policies in a two-stage supply chain, Management Science, 45 (1999), 936-953. doi: 10.1287/mnsc.45.7.936.  Google Scholar

[2]

H. Glock, Batch sizing with controllable production rates, Int. J. Prod. Res., 48 (2010), 5925-5942. 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), 865-870. 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), 267-273. 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), 332-333. 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), 203-210. 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), 513-531. 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), 1096-1104. 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), 257-263. 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), 49-58. 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), 383-393. 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), 298-308. 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), 623-629. 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), 451-460. 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), 153-172. doi: 10.1016/j.ejor.2003.10.038.  Google Scholar

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