Smoothing Start-Up and Shut-Down Costs in Sequential Production

Zero or one unit is produced each period in this finite horizon deterministic nonstationary model of a production process in which units are produced one after another. Demand occurs at the end of each period, after which a holding cost applies to inventory. Other costs include a unit production cost if production is one, a start-up cost whenever production is one this period but zero last period, and a shut-down cost if production was one last period but is zero this period. It is shown that there is an optimal policy with a simple structure. Its exploitation reduces the determination of an optimal policy to finding a shortest route in an acyclic network with one more node than the horizon's length in periods.