TY - JOUR
TI - Make-to-stock production-inventory systems with compound Poisson demands, constant continuous replenishment and lost sales
DO - https://doi.org/doi:10.7282/T39W0F8T
PY - 2010
AB - Supply contracts are designed to minimize inventory costs or to hedge against undesirable events (e.g., shortages) in the face of demand or supply uncertainty. In particular, replenishment terms stipulated by supply contracts need to be optimized with respect to overall costs, profits, service levels, etc. This thesis considers a continuous-review, single-product Make-to-Stock production-inventory system with infinite base-stock level, compound Poisson demands and constant continuous replenishment under the lost-sales policy, in which the inventory is subject to a cost function consisting of holding costs and lost-sale penalties. The main objective is to minimize pertinent inventory cost functions (the expected discounted cost and the time average cost) with respect to the replenishment rate. For the expected discounted cost case, we first derive an integro-differential equation system for the expected discounted cost incurred up until the first loss occurrence, conditioned on an initial inventory level, from which we obtain the Laplace transform for the conditional expectation of the discounted cost over an infinite time horizon. For a system starting from an arbitrary initial inventory level, we obtain a closed form formula for the expected discounted cost via the inversion of its Laplace transform. For the special cases of constant or proportional penalty function and exponentially distributed demand sizes, we exhibit an explicit expression for the conditional expectation of the discounted cost. Finally, we minimize the cost function with respect to the replenishment rate and provide an algorithm to compute the attendant optimal replenishment rate. We further obtain a closed form formula for the time-average cost under a suitable stability condition. For exponentially distributed demand sizes, we exhibit explicit solutions for the optimal replenishment rate for both the expected discounted cost function conditioned on initial empty inventory, as well as the time-average cost function. For each case, numerical studies are conducted to illustrate our results and investigate further properties of the system.
KW - Management
KW - Production management
KW - Inventory control
KW - Costs, Industrial
LA - eng
ER -