OPTIMAL-CONTROL OF JOBS FOR PRODUCTION SYSTEMS

This paper investigates the problem of accepting or rejecting arriving jobs to a job shop in which the flow times of jobs are stochastic. A fixed amount of reward will be earned if a job, or a batch of jobs, is accepted, whereas a penalty cost for late delivery and a carrying cost for early finish will be incurred at the same time. The problem is to decide whether or not the arriving job should be accepted to the shop. An optimal release time must be determined, which is shown to be a unique optimum of the convex cost functions, before making the optimal control decision. The model is quite general since no specific distribution of job's flow time is assumed. Numerical examples are provided to illustrate the decision procedure. The model considered in this paper provides the decision maker with not only a means for accepting or rejecting arriving jobs, but also a helpful managerial tool in negotiating the due date, earliest delivery date, and penalty cost with the customer so as to maximize the expected net profit.