Some Optimum Algorithms for Scheduling Problems with Changeover Costs

We consider a production line that can produce one of n items per day. The demand schedule for all items is known in advance, and all items must be produced on or before their deadlines. We want a production schedule that meets all demand deadlines and minimizes the total changeover cost. The changeover cost has a special structure: it is (i) one dollar if the production line changes from producing item i to item j and i is less than j, and (ii) zero if i is greater than or equal to j. We also consider multiple identical production lines with all demands due at the end of every month, and assume that there is exactly enough demand at the end of every month. We obtain optimum production schedules for both the single-line and multiple-line case.