Making Short-Run Changes in Production when the Employment Level is Fixed

In a factory with a given employment level, there are often opportunities to make adjustments to that level via overtime, the use of subcontractors, a curtailed work week, etc. These temporary adjustments are unlike those in production smoothing models where any change in the employment level during one period is carried over to the beginning of the next one. For a single product having stochastic demand, we characterize optimal production policies when the temporary adjustments have proportional costs. Other production costs in the model are proportional to the quantity produced and expected inventory holding and penalty costs are convex. The cases treated include nonstationary finite horizon stationary infinite horizon, discounted cost, average cost, and excess demand being either backlogged or lost. The infinite-horizon problems have optimal policies that depend on two parameters that can be computed with relatively small linear programming problems. The computations exploit the structure of the streamlined separable version of our Markovian decision problem.