Lost Sales And Emergency Order Systems Under Stuttering Poisson Demand
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We investigate the (S-1,S) inventory policy under stuttering Poisson demand and exponentially-distributed lead times when demand in excess of on-hand inventory is routed to an emergency order fulfillment system. This system contains a regional stocking location (RSL), which serves two types of facilities: a set of field service locations (FSL) and an emergency stocking location (ESL). The field service locations support technical service representatives who make visits to customer sites to repair equipment. We derive both exact and approximate expressions for the mean and variance of the number of units in emergency resupply. We also estimate the probability of zero units in emergency resupply. Simulation results confirm the quality of these approximations. Later, we use a distribution with an atom at zero and a zero-truncated negative binomial distribution to approximate the shape of this distribution. The quantiles are shown to be well approximated in simulations with various settings. In particular, the approximation is excellent in the upper tail which is the portion of the distribution used to determine the target inventory level for the emergency stocking location. Finally, we develop an optimization algorithm for setting stock levels in such a system with both field service locations and an emergency stocking location. The problem is an integer programming problem with a potential non-convex objective and we explore a heuristic algorithm for solving the optimization problem. For empirical studies, we compare the results of our heuristics with PSWARM, a general purpose algorithm for such problems.
dissertation or thesis