Logistics network design with inventory stocking, time-based service and part commonality

Integration and coordination of supply chain decisions is becoming increasingly important in practice and have attracted significant attention from research community. The potential benefit of such integration is clear as more, wider ranges of inherently interdependent supply chain decisions are made simultaneously (i.e., coordinated) for the ultimate optimization of system-wide supply chain performance. However, modeling increasingly more complex problems and developing scalable solution methodologies become a challenge when traditionally separate problems are integrated as the underlying problems themselves are hard. In this dissertation, we model, analyze and develop solution techniques for an integrated network design problem that simultaneously makes both location/allocation and inventory stocking decisions. The motivation for this problem is post-sales service parts logistics (SPL) in which multiple parts are used to repair multiple products that are in use at geographically dispersed customers. The mathematical model captures important features of real SPL systems: (1) multiple multi-part products with part commonality across products, (2) system-wide, product-level, time-based service requirements, and (3) stochastic demand satisfied by facilities operating with one-for-one replenishment inventory policy. A critical component of the model is the time-based service levels which are functions of both (1) distances between located facilities and customers, and (2) part availabilities (fill rates) of parts, which in turn are functions of stock levels and demand allocations that are being decided as part of the model. In addition to capturing this intricate relationship, our model effectively considers varying fill rates of different parts stocked at various facilities to achieve an overall service level for a product, thus allowing optimal allocation of system-wide product-level service requirements across facilities and parts. Starting with a nonlinear integer programming model of the integrated problem, we first present a fill rate approximation approach (through piece-wise linearization), which leads to a fully linearized model that can be solved by direct optimization, useful only for small and medium size problems. To facilitate a more effective solution technique for larger problems, we introduce a new variable substitution scheme for the special case of lost sales fill rates, and take advantage of the concavity of a new function in the substituted variables and develop an outer-approximation mechanism. We then develop a specialized relaxation that produces tight lower bounds and a heuristic algorithm that solves a parametric version of the relaxation to obtain provably near-optimal integrated solutions. Based on our analysis with the single part, single product setting, we expand our model and computational study to the cases with multiple products, both with and without consideration of part commonality. Our extensive computational experiments on variety of problem instances based on industrial data show not only the efficacy of the proposed modeling and algorithmic development, but also the importance of explicit consideration of inventory pooling captured through part commonality. The experiments further show that the improvements through integration of network design and inventory decisions, and through considering part commonality can be significant, which shows the effort behind the overall development is worthwhile.