• Previous Article
    Convergence property of an interior penalty approach to pricing American option
  • JIMO Home
  • This Issue
  • Next Article
    An integrated approach for the operations of distribution and lateral transshipment for seasonal products - A case study in household product industry
April  2011, 7(2): 425-434. doi: 10.3934/jimo.2011.7.425

A market selection and inventory ordering problem under demand uncertainty

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.
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

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.  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

[1]

Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020444

[2]

Yahia Zare Mehrjerdi. A new methodology for solving bi-criterion fractional stochastic programming. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020054

[3]

Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019

[4]

Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHum approach. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020055

[5]

Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020167

[6]

Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020166

[7]

Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017

[8]

Yongge Tian, Pengyang Xie. Simultaneous optimal predictions under two seemingly unrelated linear random-effects models. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020168

[9]

Chao Wang, Qihuai Liu, Zhiguo Wang. Periodic bouncing solutions for Hill's type sub-linear oscillators with obstacles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 281-300. doi: 10.3934/cpaa.2020266

[10]

Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020

[11]

Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020046

[12]

Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347

[13]

M. S. Lee, H. G. Harno, B. S. Goh, K. H. Lim. On the bang-bang control approach via a component-wise line search strategy for unconstrained optimization. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 45-61. doi: 10.3934/naco.2020014

[14]

Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011

[15]

Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. Deep quench approximation and optimal control of general Cahn–Hilliard systems with fractional operators and double obstacle potentials. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 243-271. doi: 10.3934/dcdss.2020213

[16]

Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020032

[17]

Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $ L^2- $norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]