American Institute of Mathematical Sciences

Advanced
  • Previous Article
    An integrated approach for the operations of distribution and lateral transshipment for seasonal products - A case study in household product industry
  • JIMO Home
  • This Issue
  • Next Article
    Convergence property of an interior penalty approach to pricing American option
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

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.

[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.

[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.

[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.

[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.

[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.

[7]

J. Geunes, R. Levi, H. E. Romeijn and D. Shmoys, Approximation algorithms for supply chain planning problems with market choice,, Mathematical Programming, ().

[8]

S. Nahmias, "Production and Operations Management,", Irwin, (1997).

[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.

[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.

[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.

[12]

Z. J. Max Shen, A multi-commodity supply chain design problem,, IIE Transactions, 37 (2005), 753. doi: 10.1080/07408170590961120.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

show all references

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.

[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.

[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.

[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.

[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.

[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.

[7]

J. Geunes, R. Levi, H. E. Romeijn and D. Shmoys, Approximation algorithms for supply chain planning problems with market choice,, Mathematical Programming, ().

[8]

S. Nahmias, "Production and Operations Management,", Irwin, (1997).

[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.

[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.

[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.

[12]

Z. J. Max Shen, A multi-commodity supply chain design problem,, IIE Transactions, 37 (2005), 753. doi: 10.1080/07408170590961120.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[1]

Rong Hu, Ya-Ping Fang. A parametric simplex algorithm for biobjective piecewise linear programming problems. Journal of Industrial & Management Optimization, 2017, 13 (2) : 573-586. doi: 10.3934/jimo.2016032
[2]

Behrouz Kheirfam, Kamal mirnia. Multi-parametric sensitivity analysis in piecewise linear fractional programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 343-351. doi: 10.3934/jimo.2008.4.343
[3]

Rui Qian, Rong Hu, Ya-Ping Fang. Local smooth representation of solution sets in parametric linear fractional programming problems. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 45-52. doi: 10.3934/naco.2019004
[4]

Behrouz Kheirfam. Multi-parametric sensitivity analysis of the constraint matrix in piecewise linear fractional programming. Journal of Industrial & Management Optimization, 2010, 6 (2) : 347-361. doi: 10.3934/jimo.2010.6.347
[5]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399
[6]

Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming formulations of deterministic infinite horizon optimal control problems in discrete time. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3821-3838. doi: 10.3934/dcdsb.2017192
[7]

Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1743-1767. doi: 10.3934/dcdsb.2018235
[8]

Charles Fefferman. Interpolation by linear programming I. Discrete & Continuous Dynamical Systems - A, 2011, 30 (2) : 477-492. doi: 10.3934/dcds.2011.30.477
[9]

Ye Tian, Shucherng Fang, Zhibin Deng, Qingwei Jin. Cardinality constrained portfolio selection problem: A completely positive programming approach. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1041-1056. doi: 10.3934/jimo.2016.12.1041
[10]

Shaoyong Lai, Qichang Xie. A selection problem for a constrained linear regression model. Journal of Industrial & Management Optimization, 2008, 4 (4) : 757-766. doi: 10.3934/jimo.2008.4.757
[11]

Jean Creignou, Hervé Diet. Linear programming bounds for unitary codes. Advances in Mathematics of Communications, 2010, 4 (3) : 323-344. doi: 10.3934/amc.2010.4.323
[12]

Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan. Ergodic control for a mean reverting inventory model. Journal of Industrial & Management Optimization, 2018, 14 (3) : 857-876. doi: 10.3934/jimo.2017079
[13]

Le Thi Hoai An, Tran Duc Quynh, Pham Dinh Tao. A DC programming approach for a class of bilevel programming problems and its application in Portfolio Selection. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 167-185. doi: 10.3934/naco.2012.2.167
[14]

Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473
[15]

T. Gilbert, J. R. Dorfman. On the parametric dependences of a class of non-linear singular maps. Discrete & Continuous Dynamical Systems - B, 2004, 4 (2) : 391-406. doi: 10.3934/dcdsb.2004.4.391
[16]

Yuji Harata, Yoshihisa Banno, Kouichi Taji. Parametric excitation based bipedal walking: Control method and optimization. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 171-190. doi: 10.3934/naco.2011.1.171
[17]

Nguyen Huy Chieu, Jen-Chih Yao. Subgradients of the optimal value function in a parametric discrete optimal control problem. Journal of Industrial & Management Optimization, 2010, 6 (2) : 401-410. doi: 10.3934/jimo.2010.6.401
[18]

Ram U. Verma. General parametric sufficient optimality conditions for multiple objective fractional subset programming relating to generalized $(\rho,\eta,A)$ -invexity. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 333-339. doi: 10.3934/naco.2011.1.333
[19]

Yi Xu, Wenyu Sun. A filter successive linear programming method for nonlinear semidefinite programming problems. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 193-206. doi: 10.3934/naco.2012.2.193
[20]

Yanqun Liu, Ming-Fang Ding. A ladder method for linear semi-infinite programming. Journal of Industrial & Management Optimization, 2014, 10 (2) : 397-412. doi: 10.3934/jimo.2014.10.397

2017 Impact Factor: 0.994

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences