Optimal control policies in production systems with uncertainties.

In this dissertation, we analyze three isolated problems found in production systems and investigate their optimal solutions. We consider in the first chapter a serial production system with stochastic lead times. We assume that an order has been placed and a due date has been set. There are costs for holding semi-finished products at each stage, including holding cost for finished products if production is completed before the due date. There is also a shortage cost per unit of time for missing the due date. The objective is to determine optimal starting times for production at each stage. The problem is generalized to include outside supply parts at each stage. A solution to the resulting stochastic assembly system is presented assuming perfectly reliable suppliers, followed by a generalization that accounts for suppliers uncertainty. The second chapter considers the problem of determining optimal order quantities in a multiple product capacitated system with random demands. The demand for each product is assumed random and occurs at the beginning of a short season, which is well ahead in the future. There is no limit on the quantities ordered off-season. Once these orders are delivered, a second order is placed to make up for short products in the light of more accurate information about the demand. At the time the second order is placed, however, capacity is limited since little time is left before the end of the season. The problem becomes to determine the various off-season order quantities in order to benefit from the limited in-season capacity effectively. In the last chapter, we consider the problem of assigning due dates to a set of jobs with random processing time to be processed on a single machine. This is a generalization of the classical single machine static scheduling problem, in which we allow job processing time to be stochastic. It is required to quote due dates for these jobs at a minimum cost before any processing occurs on the machine. There are three types of costs: a tardiness cost for completing a job after its due date, an earliness cost for completing a job before its due date and the cost of quoting a noncompetitive due date.Ph.D.Applied SciencesIndustrial engineeringOperations researchUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129413/2/9513279.pd