Stochastically Minimizing Total Penalty Costs in the Two-Machine Flow Shop with Random Processing Times

摘要

A set of n jobs is to be processed on two machines in series. The job processing times are independent random variables. We first develop a sufficient condition on the processing time distributions to reduce stochastically a total penalty cost function. We then establish, for exponential job processing times, a set of sufficient and transitive conditions for stochastically minimizing a total penalty cost function. Two examples are given to illustrate the results.