Minimizing the Makespan and Flowtime in Two-Machine Stochastic Open Shops

Abstract

In this paper, we present some new results on the makespan and flowtime in a two-parallel machine open shop. A set of n jobs is to be processed on two machines, the order of processing being immaterial. For the case where the machines are identical, and the jobs are nonoverlapping ordered, we show that the sequences that stochastically minimize the makespan are longest processing time first-shortest processing time first (LPT-SPT). Within this class of sequences, we show that the SPT sequence stochastically minimizes the flowtime.