A Mathematical Model for the Integrated Problem of Production Network Design and Inventory Positioning

In this paper, an integrated approach is addressed to tackle the production network design and inventory positioning problem in a single-sourcing, multi-product, and multi-period context. The objective of our model is to simultaneously determine the optimal network structure, safety stock amounts, and their respective locations, considering normal demand conditions. The main goal is to minimize the overall production network cost. The proposed model merges the traditional network design formulation with that for inventory positioning using the concept of guaranteed service. The developed model is implemented and tested on a case study of office furniture manufacturing, where the bill of materials is considered. The effectiveness of the proposed model is demonstrated by comparing it to a sequential approach where the network structure and safety stock decisions are made sequentially. The results reveal that the integrated approach surpasses the sequential approach, with cost savings ranging from 1.7% to 3.7%. In addition, a higher optimal cycle service level is obtained by the integrated approach compared to that of the sequential approach. To further evaluate the model's performance, a sensitivity analysis is conducted to examine the influence of the model's parameters, i.e., committed service time and coefficient of variation of demand, on its solutions. The analysis shows that when the coefficient of the demand variation remains unchanged, longer committed service times lead to lower safety stock costs and higher optimal service levels. Moreover, it is observed that more safety stocks of components are kept in the upstream layer of the network than that of finished goods