Bi-Level Programming Model of Cloud Manufacturing Services Based on Extension Theory

Zhao, Jinhui; Zhou, Yu

doi:10.1155/2018/9702910

Cited by 4 publications

(1 citation statement)

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“…(i) For the complicated bilevel programming model, how can we develop an efficient algorithm to find its equilibrium solution? Particularly, without assumption of simplification as in [11,[38][39][40], we need to first derive a deterministic equivalent formulation by expectation method for the stochastic nonlinear bilevel programming model [41,42]. en, similar to the approach in [5], it is necessary to convert the bilevel programming problem into the mathematical program with complementarity constraints (MPCC) such that a series of standard smooth optimization subproblems can be solved [43,44].…”

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confidence: 99%

Partially Smoothing and Gradient-Based Algorithm for Optimizing the VMI System with Competitive Retailers under Random Demands

Deng

Wan

2020

Mathematical Problems in Engineering

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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. en, 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) e participation rate depends on advertising expenditures from both the manufacturer and the retailer. ere exists an optimal threshold of participation rate for the manufacturer, which can be provided by the intersection point of the manufacturer and retailer's costprofit curves. (2) e manufacturer's advertising policy is less sensitive to uncertainty of demand than the change of the retailer's advertising policy. (3) e manufacturer in the VMI system should concern about the differences caused by symmetric or asymmetric retailers.

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