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BI-LEVEL PROGRAMMING APPROACH TO OPTIMAL STRATEGY FOR VENDOR-MANAGED INVENTORY PROBLEMS UNDER RANDOM DEMAND

Part of: Design of experiments Artificial intelligence (68Txx)

Published online by Cambridge University Press:  20 November 2017

YINXUE LI ,
ZHONG WAN Open the ORCID record for ZHONG WAN [Opens in a new window]  and
JINGJING LIU
YINXUE LI
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email liyinxuecsu@163.com, wanmath@csu.edu.cn, 1428552550@qq.com
ZHONG WAN*
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email liyinxuecsu@163.com, wanmath@csu.edu.cn, 1428552550@qq.com
JINGJING LIU
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email liyinxuecsu@163.com, wanmath@csu.edu.cn, 1428552550@qq.com
*
✉wanmath@csu.edu.cn
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Abstract

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We present an extension of vendor-managed inventory (VMI) problems by considering advertising and pricing policies. Unlike the results available in the literature, the demand is supposed to depend on the retail price and advertising investment policies of the manufacturer and retailers, and is a random variable. Thus, the constructed optimization model for VMI supply chain management is a stochastic bi-level programming problem, where the manufacturer is the upper level decision-maker and the retailers are the lower-level ones. By the expectation method, we first convert the stochastic model into a deterministic mathematical program with complementarity constraints (MPCC). Then, using the partially smoothing technique, the MPCC is transformed into a series of standard smooth optimization subproblems. An algorithm based on gradient information is developed to solve the original model. A sensitivity analysis has been employed to reveal the managerial implications of the constructed model and algorithm: (1) the market parameters of the model generate significant effects on the decision-making of the manufacturer and the retailers, (2) in the VMI mode, much attention should be paid to the holding and shortage costs in the decision-making.

Keywords

game theorystochastic modelssmoothing algorithmoptimizationvendor-managed inventory problems

MSC classification

Primary: 90C30: Nonlinear programming
Secondary: 62K05: Optimal designs 68T37: Reasoning under uncertainty
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 247 - 270
Copyright
© 2017 Australian Mathematical Society 

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