【论文】胡劲松;孙浩;李增强;胡小根;周岩;张桂涛：存在产能和价格限制的模糊供应链网络均衡算法 管理工程学报 2013.04
Abstract:Due to the trend of economic globalization, competition among companies actually turns into a competition among supply chains. The supply chain network has the characteristics of hierarchies and complexities. It reflects the competition among same level’s members and coordination between different levels. Therefore, academia and business communities are interested in how to get the supply chain network’s equilibrium conditions and the optimal behaviors of various decision makers so as to design and operate the supply chains efficiently in the long run. Moreover, in the real supply chain network, several uncertainties exist such as fuzziness. For the sake of dealing with this situation, we investigate a competitive supply chain network equilibrium model which comprises mutualcompetitive manufactures with production capacity constraints and competitive retailers with fuzzy market demand as well a binding price ceiling of the goods. Based on some assumptions, we present the manufactures competing in a non-cooperative fashion who are involved in the homogeneous products which are then shipped to competitive retailers assumed to compete with one another in a non-cooperative manner, who, in turn, ship the products to consumers distributed in various demand markets. And the model is constructed to analyze the inner links between the various decision makers. The paper is organized as follows：The behaviors of the manufacturers are described by means of finite-dimensional variational inequality theory .They seek to determine their profit-maximizing outputs and shipments of the product to the retailers. The behaviors of retailers who are faced with fuzzy demand are established. They are involved in transactions with the manufacturers since they must decide how much to order for the purpose of coping with the fuzzy demand while seeking to maximize their profits simultaneously. Based on the credibility measure of fuzzy event, the expected value of fuzzy sales, fuzzy inventories and fuzzy shortages at the retail outlets are derived, therefore the retailer's expected profit is constructed. The concavity of the retailer's expected profit function is revealed in order to illustrate the existence and uniqueness of the optimal solution. The market equilibrium conditions are constructed to describe the transactions that take place between the retailers with a binding price ceiling of the goods and the consumers. Then the variational inequality model of the whole supply chain network is identified and equilibrium conditions are obtained. The logarithmic-quadratic proximal prediction-correction algorithm (LQPC-PC) is designed for solving the supply chain network equilibrium model. It aims at finding the global optimal convergent solution as well as the optimal lagranian multipliers. Each iteration of the method consists of a prediction and a correction. A self-adaptive policy is presented to obtain easily thepredictor and the corrector with tiny computational load. Numerical examples are given to illustrate the impacts of different production capacity constraints and different price ceilings on the equilibrium solutions. The results show that a shortage of the good arises when the government imposes a binding price ceiling on the competitive markets, which is more serious in case of considering production capacity constraints.