## Customer dedicated facilities and inventory sharing in integrated network design and inventory optimization

##### Abstract

Shrinking profit margins in the high technology industry has led companies to attempt to increase profits through an increased focus on after-market services. As part of that effort, service parts logistics, which manages the post-sales distribution of spare parts needed to maintain and repair products in use, has gained importance. In an effort to improve Service Parts Logistics (SPL) operations, we integrate facility location and inventory stocking decisions while classifying facilities based on their assignment; dedicated facilities that are assigned solely to individual customers (located on-site of the customer, serving only that customer), and shared facilities that are assigned to a subset of customers. The introduction of dedicated facilities simplifies the overall problem formulation in certain special cases. In one such special case where there is only one facility and none of the customers are within its service time window, the overall problem reduces to a binary knapsack formulation. This can be solved in pseudo-polynomial time through the dynamic programming algorithm for such problems. Nonetheless, even in the general case, we identify conditions under which a dedicated facility will always be opened. Computational results show that this observation is used by solvers as a preprocessing step, thus loosening some hard constraints. As a result, some of these problems are solved in less time than the corresponding problems without the dedicated facilities. However, dedicated facilities become advantageous mainly in sparse networks as opposed to dense networks. Apart from low network density, low holding cost and relatively high demand are two other system parameters that encourage the opening of dedicated facilities. SPL can be further improved by sharing inventory across shared facilities, which is already a common practice in real SPL systems. In this case, Markov chains can be used to estimate fill rates, but the process is iterative. However, under the low demand assumption of parts in SPL, we derive analytical formulae of estimating fill rates and thus incorporate inventory sharing within the network design and inventory optimization model. Special cases of this problem can be solved by an alternative binary knapsack formulation. Computational results show that large instances can be solved instantaneously, and we also identify a greedy heuristic that provides bounds on average within 0.12% of the optimal solution. We observe maximum benefit from inventory sharing when there exists large demand in the area overlapping the time window of both shared facilities and when inventory replenishment rates are high. However, we also identify conditions on the system parameters where inventory sharing could increase cost and/or decrease service in comparison with not-sharing. The combined problem of inventory sharing with customer dedicated facilities is formulated based on a binary knapsack structure. However, the problem size increases exponentially with solution time. Therefore, we construct another greedy heuristic by combining the inventory sharing heuristic and a special case algorithm for a single dedicated facility. A large size problem that takes almost a minute to be solved by conventional branch and bound is solved in less than a second using the greedy heuristic. We also show that for a given demand network, the combined problem achieves 40-60% reduction in total cost within 1% of the time taken by the problem without inventory sharing and without dedicated facilities. Another interesting result is that in some cases, adding new customers to a given inventory sharing system helps to reduce the cost and/or increase service.

##### Description

text