This paper presents a new production-inventory control (PIC) model for a supply chain network (SCN) where multiple suppliers, manufacturers, and buyers are vertically integrated to provide multiple items to the market. The objective of the model is to simultaneously determine optimal replenishment quantities, replenishment cycles, and production rates in order to minimize the total network cost allowing no shortages of inventory and shutdown periods. We propose closed-form functions of the average annual inventory levels. A novel mixed-integer linear programming (MILP) formulation is developed based on these functions to solve the PIC model. In addition, an algorithm based on a decomposition approach was developed to solve a special case of the PIC model with a less computational burden. The results obtained by the algorithm are compared to the results of the existing models in literature to see if there is any improvement. A case study for designing an integrated SCN and controlling operational decisions is presented to demonstrate the application of the proposed PIC model.

本文为供应链网络 (SCN) 提出了一种新的生产库存控制 (PIC) 模型，其中多个供应商、制造商和买家垂直整合以向市场提供多种产品。该模型的目标是同时确定最佳补货数量、补货周期和生产速度，以最大限度地降低网络总成本，避免出现库存短缺和停工期。我们提出了年平均库存水平的闭式函数。基于这些函数开发了一种新颖的混合整数线性规划 (MILP) 公式来求解 PIC 模型。此外，还开发了一种基于分解方法的算法，以较少的计算负担来解决 PIC 模型的特殊情况。将算法得到的结果与文献中已有模型的结果进行比较，看是否有改进。介绍了设计集成 SCN 和控制操作决策的案例研究，以演示所提出的 PIC 模型的应用。