Part commonality effects on integrated network design and inventory models for low-demand service parts logistics systems

Low demand logistics systems with response time based service levels such as service parts supply chains exhibit strong interaction between network design and part stocking decisions motivating integrated models making such decisions simultaneously. Extending the earlier models of single product, single part systems, we formulate a multi-product service parts supply chain design problem with part commonality. In particular, our model captures (1) multiple multi-part products with part commonality across products, (2) system-wide, product-specific, time-based service requirements, and (3) stochastic demand satisfied by facilities operating with one-for-one replenishment inventory policy. We then linearize this naturally non-linear integer program via approximation of fill rate function and introduction of new variables to handle quadratic terms in the constraints. We finally conduct a numerical study to quantify the effects of part commonality on network design and inventory decisions and costs using this linear integer reformulation. Our results show that dedicated parts (ignoring commonality) can lead to significantly suboptimal decisions, not only on stock levels but also on network design (location and demand allocation) decisions. Furthermore, our tests with relatively larger networks show that considering part commonality, even in a sequential approach of deciding network design first and part stocking decisions next, significantly improves the total costs of network design and inventory.