多阶段制造系统调度模型与资源价格研究

Scheduling Model and Resource Pricing in Multi Stage Manufacturing Systems

为时变需求下的多阶段、多工件种类且生产能力可追加的制造系统调度问题构建了一个令总成本最小的数学模型．通过分析最优性条件，得到了工作站生产能力的价格，并解释了它的经济含义．将调度模型转换为一个时空扩展网络上的静态的费用极小流问题，然后用改进的ＦｒａｎｋＷｏｌｆｅ算法求解．

This paper presents a scheduling model of multi stage manufacturing systems with multiple job classes and variable production capacity constraints at workstations. The model aims to minimize the total cost which is the sum of all costs incurred in holding, processing and schedule delay over the whole study horizon. On the basis of analyzing optimality conditions, the prices of production capacities or resources are derived and explained in economic meaning. It is shown that the model can be transferred into an equivalent static minimum cost network flow problem over a space time network which is a temporal expansion of the base workstation network. An adapted network approach based on the Frank Wolfe algorithm is proposed to solve the equivalent problem and tested on a numerical example.