Algorithms for Optimal Production Scheduling and Employment Smoothing

This paper seeks here a minimum cost production plan over a finite number of time periods. There is a known demand requirement (stated in production hours) to be met in each period from current and previous hours of production (stored as inventory). A production policy consists of scheduled amounts of hours, some of which are costed at regular-time wage rates, the remainder costed at overtime rates. Expansion or contraction of the work force (stated in production hours) is charged against the period-to-period variations in regular-time employment. The fluctuations in overtime production do not incur such hiring and firing costs. The amount of overtime used, however, is constrained not to exceed a specified fraction of regular-time utilized in any period. We describe algorithms for rinding an optimal policy under the assumption that all costs are described by linear functions and where demands are either monotonic increasing or decreasing in time. In addition to presenting the algorithms, we also examine certain planning horizon results implied by these algorithms. Specifically, we ascertain when optimal first period decisions can be made without knowing the precise values of all future demands and costs.