考虑一个时变需求环境下集成多级供应链问题，在有限的规划时间内销售商以固定周期订货，而生产商以不同的周期生产，目的是寻找销售商最优的订货周期和生产商最佳的生产策略，从而使供应链系统的总运营成本最少.建立了该问题的混合整数非线性规划模型，求解该模型分为两步：先求对应一个订货周期的最佳生产策略，再求最优的订货周期，第一步用到了图论里求最短路方法.给出了两个步骤的算法和程序，实验证明它们是有效的.通过算例对模型进行了分析，研究了各参数对最优解及最小费用的影响.
An integrated multi-stage supply chain problem with time varying demand, fixed interval orders and different production cycles over a finite planning horizon is considered in this paper. The objective is to find the retailer’s optimal order cycle and devise the manufacturer’s best production strategy to minimize the total operational cost of the supply chain system. The problem is formulated as a mixed integer nonlinear programming model. The model is solved in two steps: to obtain the optimal production strategy for an order cycle and to determine the optimal order cycle. The method of finding the shortest path in graph theory is used in the first step. Algorithms and programs for the two steps are proposed which are proved to be effective by experiments. The influence of each parameter on the optimal solution and the minimum cost is studied by the examples calculated to illustrate the model.
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