Production-Inventory control model for a supply chain network with economic production rates under no shortages allowed

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 mixedinteger 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.