Service levels in production-inventory networks: Bottlenecks, trade-offs, and optimization
This thesis studies service-level related issues and relationships among fundamental quantities in a class of assemble-to-order production-inventory systems. An important feature of the systems is that a customer order requires the assembly of a collection of some units of different items which in turn are produced at dedicated facilities under a base-stock policy; the order process and production times are stochastic. We first investigate which facility most constrains the system-wide service level and show, in particular, that it is not necessarily the most highly utilized facility. We identify precise measures of a facility's propensity to constrain service and show both theoretically and numerically that a facility with a minimal measure is a bottleneck for the service level. Next, we characterize the quantitative trade-offs between delivery leadtime and inventory. We show that there is a simple linear trade-off between base-stock levels and delivery leadtime, in a limiting sense, at fixed high service levels. The limiting slope is easy to calculate and can be interpreted as the approximate marginal rate for trading-off inventory against leadtime at a constant level of service. Numerical results demonstrate that the linear trade-off is valid at moderately high service levels. The third topic is efficient rare event simulation, motivated by the estimation of fill rate. We show that very appealing estimators can perform extremely poorly. We give insights about how this can happen and provide alternative estimators with provably good performance. Finally we address the issue of how to set component base-stock levels in assemble-to-order systems to minimize inventory holding costs under service-level constraints. The difficulty of the problem lies in that there is generally no analytical expression for either the objective function or the constraint in terms of the base-stock levels. We propose an approximate formulation, based on the asymptotics of service-levels developed in earlier chapters and obtain closed form solutions. The effectiveness of the approximation is demonstrated through numerical studies.