Optimal two‐ and three‐stage production schedules with setup times included

TLDR

Production scheduling on two sequential machines with known setup and processing times is a classic combinatorial optimization problem. The paper derives a simple decision rule that minimizes total elapsed time for the two‑machine production schedule. The authors extend the analysis to a three‑machine case, solving a restricted variant of the problem.

Abstract

Abstract Each of a collection of items are to be produced on two machines (or stages). Each machine can handle only one item at a time and each item must be processed through machine one and then through machine two. The setup time plus work time for each item for each machine is known. A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum. A three‐machine problem is also discussed and solved for a restricted case.