Optimal cycle times in multistage serial systems with set-up and inventory costs

Scheduling of multistage serial production systems under constant demand and infinite horizon is considered. The production stages operate with periodic shut-downs and startups. An integer nonlinear programming formulation is presented for determining a stationary, cyclic schedule with no stock-outs in any inventory and minimum sum of set-up and inventory costs. It allows a lot-sizing policy involving arbitrary, noninteger splitting/merging of lots. Three, almost optimal, heuristic algorithms and an exact branch and bound algorithm are developed using analytical results. Their evaluation using simulated problems shows the branch and bound algorithm to be the best, as it is fast even for systems with as many as 11 stages.