Stability and optimization of a production inventory system under prioritized base-stock control

Email: dongping.song{at}plymouth.ac.uk Received on 19 July 2007. Accepted on 1 May 2008. A make-to-stock system producing two part-types with stochasticprocessing times and random demands is considered. A prioritizedbase-stock policy is used to control the production to meetexogenous Poisson demands, where the unmet high-priority demandsare partially backordered due to their limited patience andthe unmet low-priority demands are fully backordered. Basedon the matrix analytical method, a necessary and sufficientcondition for the stability of the system is provided. The explicitstationary distribution is derived using the spectral expansionapproach. Interesting steady-state performance measures suchas stock-out probabilities and lost-sale fraction are then calculated.By investigating the structural properties of the objectivefunctions, simple procedures are presented to find the optimalbase-stock levels either to minimize the expected cost or tosatisfy the stock-out probability and the lost-sale fractionconstraints. In addition, the optimization problem with respectto the maximum backlog level for part-type one and two base-stocklevels is addressed and a solution procedure is presented. Numericalexamples are given to demonstrate the results.