Considering inventory in service parts logistics network design problems with time-based service constraints
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We study the integrated logistics network design and inventory stocking problem as characterized by the interdependency of design and stocking decisions in service parts logistics. These two sets of decisions usually have been considered sequentially in practice, and their associated problems have been tackled separately in the research literature. The overall problem is typically further complicated due to time-based service constraints that provide lower limits for the percentages of demand satisfied within specified time windows. We introduce an optimization model that explicitly captures the interdependency between network design (location of facilities, and allocation of demands to facilities) and inventory stocking decisions (stock levels and their corresponding stochastic fill rates), and present computational results from our extensive experiments that investigate the effects of several factors including demand levels, time-based service levels, and costs. Our findings indicate that the integrated approach can provide significant cost savings over the decoupled approach (solving the network design first and inventory stocking next), shifting the whole efficient frontier curve between cost and service level to superior regions. Furthermore, we show that the decoupled and integrated approaches may generate totally different solutions, even in the number of located facilities and in their locations, magnifying the importance of considering inventory as part of the network design models. Our analysis consists of a special case of integrated logistics network design and inventory stocking problem in service parts logistics, where each customer requires a certain time-based service level. Introduced is a non-linear mixed integer optimization model that is beyond our current solution technologies, yet it explicitly captures the interdependency between network design (locating facilities, and allocating customers to facilities) and inventory stocking decisions (stock levels and their corresponding stochastic fill rates). We provide two different linearized mixed integer formulations for this problem that can solve small and medium size instances. We reveal that this problem can be formulated as a capacitated facility location problem with polynomially solvable sub cases. However, it is still a challenging problem for which we have a Lagrangian-relaxation based approach that provides extremely tight lower and upper bounds. By applying the methodology and insights of the customer-centric problem, we succeed in providing upper and lower bounds to the original system-wide service level problem, even with large instances and with medium demand levels.