服务水平约束下基于可调节鲁棒优化的固定比例生产与库存计划模型

在不确定需求环境下,研究由原材料供应商、制造商和客户组成的三级供应链中,具有固定比例生产系统的制造商多周期生产与库存计划问题.采用区间不确定集描述市场需求不确定性,并利用联合机会约束刻画制造商的服务水平要求,在线性决策规则下建立带有联合机会约束的固定比例生产系统生产与库存仿射可调节鲁棒优化模型.进一步,将所建模型等价转换为易于求解的线性规划问题.考虑到不确定扰动系数在模型鲁棒性与解的保守性之间的调节作用,给出能够有效提高具有固定比例生产系统的制造商利润并同时满足预设服务水平的不确定扰动系数优化算法.数值算例表明,基于所提出模型获得的运作方案能够有效应对供需平衡程度的变化,并且能以较高利润满足预设服务水平要求.

Fixed proportions production and inventory planning model under service level constraint based on affinely adjustable robust optimization

A multi-period production and inventory planning problem of a manufacturer with a fixed proportions production system in a three-stage supply chain consisting of a raw material supplier, a manufacturer and customers is studied under the uncertain demand environment. The interval uncertainty set is used to model market demand uncertainties, and the joint chance constraint is adopted to describe the service level requirement of the manufacturer. An affinely adjustable robust production and inventory optimization model with a joint chance constraint is developed based on the linear decision rule for the fixed proportions production system. Furthermore, the developed robust optimization model is equivalently transformed into a tractable linear programming model. Considering the moderating effect of uncertain disturbance coefficient between model robustness and the conservatism of the solution, an uncertain disturbance coefficient optimization algorithm is proposed, which can effectively improve the total profit of the manufacturer with the fixed proportions production system and satisfy the pre-specified service level. Numerical examples show that the operation scheme obtained based on the proposed model can effectively cope with the changes in the balance degree of supply and demand, and can satisfy the pre-specified service level with a higher profit.