Abstract

Vendor managed inventory (VMI) is an improved sustainable inventory management system, but it is difficult to establish and solve an integrated Stackelberg game model under the complicated practical environment. In this paper, a bilevel programming model is proposed to formulate the VMI system by taking into account the uncertainty of demand, the competition among retailers, the cooperative advertising, the shortage and holding costs, and the practical constraints. For the established stochastic model being associated with continuously random demands, a deterministic mathematical program with complementarity constraints (MPCC) is first derived by expectation method and the first-order optimality conditions of the lower-level problem. Then, with a partially smoothing technique, the MPCC is solved by transforming it into a series of standard smooth optimization subproblems. Finally, owing to complexity caused by evaluating the integrals with unknown decision variables in the objective function, an efficient algorithm is developed to solve the problem based on the gradient information of model. Sensitivity analysis has been employed to reveal a number of managerial implications from the constructed model and algorithm. (1) The participation rate depends on advertising expenditures from both the manufacturer and the retailer. There exists an optimal threshold of participation rate for the manufacturer, which can be provided by the intersection point of the manufacturer and retailer’s cost-profit curves. (2) The manufacturer’s advertising policy is less sensitive to uncertainty of demand than the change of the retailer’s advertising policy. (3) The manufacturer in the VMI system should concern about the differences caused by symmetric or asymmetric retailers.

Highlights

  • BackgroundVendor managed inventory (VMI) is an improved sustainable inventory management system with cooperative strategy between vendors (manufacturers) and buyers (retailers) [1]

  • Vendor managed inventory (VMI) is an improved sustainable inventory management system with cooperative strategy between vendors and buyers [1]

  • We have constructed a stochastic bilevel programming model to formulate the VMI problems. e holding cost, shortage cost, competition of retailers, and randomness of demand have been taken into consideration such that optimal policies of distributed quantities, coop advertising expenditures, and pricing are obtained for the VMI problems

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Summary

Background

Vendor managed inventory (VMI) is an improved sustainable inventory management system with cooperative strategy between vendors (manufacturers) and buyers (retailers) [1]. When the information flows from the retails to the manufacturers, the VMI system can reduce fluctuation amplification of the customers’ demand. Erefore, instead of centralized decision-making in an ordinary supply chain, how to make an optimal operational strategy for the VMI system is basically in a framework of the Stackelberg game, in which the vendor is the leader and the buyers are the followers [4, 5]. Mathematical Problems in Engineering (ii) In the case that the established model of VMI system is complicated as it is more in line with the practical operational process of this system, the question is how to develop an algorithm to efficiently find its solution?. From the viewpoint of more applicability of models, we concern what are the deficiencies of these results

Literature Review
Solution methods
Bilevel Programming Model for VMI Problems
Reformulation of Bilevel Programming Model
Development of Gradient-Based Algorithm
Sensitivity Analysis
Conclusions and Directions of Future Research
Full Text
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