Single-Machine Scheduling of Indivisible Multi-Operation Jobs

Abstract

This paper considers a single-machine scheduling problem of multi-operation jobs where each job consists of several operations processed contiguously, rather than being intermingled with the operations of different jobs. That is, the jobs are indivisible. A sequence-independent setup is required if the machine switches from one operation to another. However, no setup is necessary before the first operation of a job if this first operation is the same as the last operation of the immediately previous job. A job is complete when all of its operations have been processed. We investigate the problem for two cases. Makespan, which is the time needed to complete all jobs, is minimised in the first case; whereas the total completion time, which is the sum of the job completion times, is minimised in the second case. We show that the makespan problem is solvable in polynomial time. For the problem of minimising total completion time, we develop a mixed integer linear programming (MILP) model, which is capable of solving small and medium-sized problem instances optimally, and obtain a very small gap between the solution found and the best possible solution for the unsolved large-sized problem instances.