A market selection and inventory ordering problem under demand uncertainty

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April 2011, 7(2): 425-434. doi: 10.3934/jimo.2011.7.425

A market selection and inventory ordering problem under demand uncertainty

Jia Shu ^1, , Zhengyi Li ^1, and Weijun Zhong ^1,

1.	Department of Management Science and Engineering, School of Economics and Management, Southeast University, Nanjing 211189, China, China, China

Received October 2010 Revised January 2011 Published April 2011

Abstract
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We study an integrated market selection and inventory control problem that was initially proposed by Geunes et al. [Naval Research Logistics, 51(1):117-136, 2004]. This problem generalizes the classical EOQ problem by incorporating the market choice decisions. In this note, we further consider the problem with stochastic demand in which we assume the demand mean and variance are known for each market. We show that the problem can be formulated as an unconstrained nonlinear binary IP model. Its special structure leads to efficient solution algorithms and we summarize some interesting observations via numerical experiments.

Keywords: Market selection, parametric linear programming., inventory control.

Mathematics Subject Classification: Primary: 90B80, 90C1.

Citation: Jia Shu, Zhengyi Li, Weijun Zhong. A market selection and inventory ordering problem under demand uncertainty. Journal of Industrial & Management Optimization, 2011, 7 (2) : 425-434. doi: 10.3934/jimo.2011.7.425

References:

[1]	I. S. Bakal, J. Geunes and H. E. Romeijn, Market selection decisions for inventory models with price-sensitive demand,, Journal of Global Optimization, 4 (2008), 633. doi: 10.1007/s10898-007-9269-3. Google Scholar
[2]	K. Chahar and K. Taaffe, Risk averse demand selection with all-or-nothing orders,, OMEGA-International Journal of Management Science, 37 (2009), 996. doi: 10.1016/j.omega.2008.11.004. Google Scholar
[3]	A. K. Chakravarty, J. B. Orlin and U. G. Rothblum, Consecutive optimizers for a partitioning problem with applications to optimal inventory groupings for joint replenishment,, Operations Research, 33 (1985), 820. doi: 10.1287/opre.33.4.820. Google Scholar
[4]	M. S. Daskin, C.R. Coullard and Z. J. Max Shen, An inventory-location model: formulation, solution algorithm and computational results,, Recent developments in the theory and applications of location models, 110 (2002), 83. doi: 10.1023/A:1020763400324. Google Scholar
[5]	J. Geunes, Z. J. Max Shen and H. E. Romeijn, Economic ordering decisions with market selection flexibility,, Naval Research Logistics, 51 (2004), 117. doi: 10.1002/nav.10109. Google Scholar
[6]	J. Geunes, H. E. Romeijn and K. Taaffe, Requirements planning with dynamic pricing and order selection flexibility,, Operations Research, 54 (2006), 394. doi: 10.1287/opre.1050.0255. Google Scholar
[7]	J. Geunes, R. Levi, H. E. Romeijn and D. Shmoys, Approximation algorithms for supply chain planning problems with market choice,, Mathematical Programming, (). Google Scholar
[8]	S. Nahmias, "Production and Operations Management,", Irwin, (1997). Google Scholar
[9]	M. Önal and H. E. Romeijn, Two-echelon requirements planning with pricing decisions,, Journal of Industrial and Management Optimization, 5 (2009), 767. doi: 10.3934/jimo.2009.5.767. Google Scholar
[10]	L. Ozsen, C. R. Coullard and M. S. Daskin, Capacitated warehouse location model with risk pooling,, Naval Research Logistics, 55 (2008), 295. doi: 10.1002/nav.20282. Google Scholar
[11]	L. Ozsen, M. S. Daskin and C. R. Coullard, Facility location modeling and inventory management with multisourcing,, Transportation Science, 43 (2009), 455. doi: 10.1287/trsc.1090.0268. Google Scholar
[12]	Z. J. Max Shen, A multi-commodity supply chain design problem,, IIE Transactions, 37 (2005), 753. doi: 10.1080/07408170590961120. Google Scholar
[13]	Z. J. Max Shen, C. R. Coullard and M. S. Daskin, A joint location-inventory model,, Transportation Science, 37 (2003), 40. doi: 10.1287/trsc.37.1.40.12823. Google Scholar
[14]	J. Shu, C. P. Teo and Z. J. Max Shen, Stochastic transportation-inventory network design problem,, Operations Research, 53 (2005), 48. doi: 10.1287/opre.1040.0140. Google Scholar
[15]	L. V. Snyder, M. S. Daskin and C. P. Teo, The stochastic location model with risk pooling,, European Journal of Operational Research, 179 (2007), 1221. doi: 10.1016/j.ejor.2005.03.076. Google Scholar
[16]	K. Taaffe, J. Geunes and H. E. Romeijn, Target market selection and marketing effort under uncertainty: the selective newsvendor,, European Journal of Operational Research, 189 (2008), 987. doi: 10.1016/j.ejor.2006.11.049. Google Scholar
[17]	K. Taaffe, H. E. Romeijn and D. Tirumalasetty, A selective newsvendor approach to order management,, Naval Research Logistics, 55 (2008), 769. doi: 10.1002/nav.20320. Google Scholar
[18]	V. N. Vapnik and A. Y. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities,, Theory of Probability and Its Applications, 16 (1971), 264. doi: 10.1137/1116025. Google Scholar
[19]	L. Zhang and S.-Y. Wu, Robust solutions to euclidean facility location problems with uncertain data,, Journal of Industrial and Management Optimization, 6 (2010), 751. doi: 10.3934/jimo.2010.6.751. Google Scholar

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References:

[1]	I. S. Bakal, J. Geunes and H. E. Romeijn, Market selection decisions for inventory models with price-sensitive demand,, Journal of Global Optimization, 4 (2008), 633. doi: 10.1007/s10898-007-9269-3. Google Scholar
[2]	K. Chahar and K. Taaffe, Risk averse demand selection with all-or-nothing orders,, OMEGA-International Journal of Management Science, 37 (2009), 996. doi: 10.1016/j.omega.2008.11.004. Google Scholar
[3]	A. K. Chakravarty, J. B. Orlin and U. G. Rothblum, Consecutive optimizers for a partitioning problem with applications to optimal inventory groupings for joint replenishment,, Operations Research, 33 (1985), 820. doi: 10.1287/opre.33.4.820. Google Scholar
[4]	M. S. Daskin, C.R. Coullard and Z. J. Max Shen, An inventory-location model: formulation, solution algorithm and computational results,, Recent developments in the theory and applications of location models, 110 (2002), 83. doi: 10.1023/A:1020763400324. Google Scholar
[5]	J. Geunes, Z. J. Max Shen and H. E. Romeijn, Economic ordering decisions with market selection flexibility,, Naval Research Logistics, 51 (2004), 117. doi: 10.1002/nav.10109. Google Scholar
[6]	J. Geunes, H. E. Romeijn and K. Taaffe, Requirements planning with dynamic pricing and order selection flexibility,, Operations Research, 54 (2006), 394. doi: 10.1287/opre.1050.0255. Google Scholar
[7]	J. Geunes, R. Levi, H. E. Romeijn and D. Shmoys, Approximation algorithms for supply chain planning problems with market choice,, Mathematical Programming, (). Google Scholar
[8]	S. Nahmias, "Production and Operations Management,", Irwin, (1997). Google Scholar
[9]	M. Önal and H. E. Romeijn, Two-echelon requirements planning with pricing decisions,, Journal of Industrial and Management Optimization, 5 (2009), 767. doi: 10.3934/jimo.2009.5.767. Google Scholar
[10]	L. Ozsen, C. R. Coullard and M. S. Daskin, Capacitated warehouse location model with risk pooling,, Naval Research Logistics, 55 (2008), 295. doi: 10.1002/nav.20282. Google Scholar
[11]	L. Ozsen, M. S. Daskin and C. R. Coullard, Facility location modeling and inventory management with multisourcing,, Transportation Science, 43 (2009), 455. doi: 10.1287/trsc.1090.0268. Google Scholar
[12]	Z. J. Max Shen, A multi-commodity supply chain design problem,, IIE Transactions, 37 (2005), 753. doi: 10.1080/07408170590961120. Google Scholar
[13]	Z. J. Max Shen, C. R. Coullard and M. S. Daskin, A joint location-inventory model,, Transportation Science, 37 (2003), 40. doi: 10.1287/trsc.37.1.40.12823. Google Scholar
[14]	J. Shu, C. P. Teo and Z. J. Max Shen, Stochastic transportation-inventory network design problem,, Operations Research, 53 (2005), 48. doi: 10.1287/opre.1040.0140. Google Scholar
[15]	L. V. Snyder, M. S. Daskin and C. P. Teo, The stochastic location model with risk pooling,, European Journal of Operational Research, 179 (2007), 1221. doi: 10.1016/j.ejor.2005.03.076. Google Scholar
[16]	K. Taaffe, J. Geunes and H. E. Romeijn, Target market selection and marketing effort under uncertainty: the selective newsvendor,, European Journal of Operational Research, 189 (2008), 987. doi: 10.1016/j.ejor.2006.11.049. Google Scholar
[17]	K. Taaffe, H. E. Romeijn and D. Tirumalasetty, A selective newsvendor approach to order management,, Naval Research Logistics, 55 (2008), 769. doi: 10.1002/nav.20320. Google Scholar
[18]	V. N. Vapnik and A. Y. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities,, Theory of Probability and Its Applications, 16 (1971), 264. doi: 10.1137/1116025. Google Scholar
[19]	L. Zhang and S.-Y. Wu, Robust solutions to euclidean facility location problems with uncertain data,, Journal of Industrial and Management Optimization, 6 (2010), 751. doi: 10.3934/jimo.2010.6.751. Google Scholar

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