Analysis of single-product continuous-review production/inventory problems with stochastic production operations and demands

Abstract

In this thesis, three continuous review production/inventory problems are investigated, where a single production facility is employed to supply a Poisson demand process for a single product. The first two problems consider a (r,Q) policy (model) that whenever the inventory level falls below r, production operation continues until after producing the fixed amount of Q. A single-machine single-product production/inventory problem is considered first, where demands for the product occur in a compound Poisson process and backordering is allowed. It is also assumed that the unit production time is general. The second problem is an extension of the first problem incorporating the facility utilization for another job (side job) during the period when the facility is idle due to enough inventories over the reorder level r. Whenever the facility is in operation for a side job, the operation cannot be terminated for the main production even though the inventory level falls below r. In the model, it is assumed that demands for product follow a Poisson process, and that unsatisfied demands are backordered, and that the random production times of each unit are exponentially distributed. Moreover, orders for the side job operation occur in a Poisson process. The third problem considers a (r,R) type production/inventory model with side job operation allowed under the same conditions as provided for the second problem. However, the only different thing is that whenever the operation starts as the inventory level falls below r, it continues until the inventory level reaches R. For each of these problems, under the assumption that during each production period the cumulative amount of production is greater than that of demands in expected term, the associated inventory process is found to be a semi-regenerative process which has an ergodic imbedded Markov chain with infinite states. Thereupon, the steady-state probability distribution of the imbedded Markov chain is derived. ...