Production scheduling in steel rolling mills with demand substitution: Rolling horizon implementation and approximations

Abstract

This paper tackles the challenging task of finding optimal master production schedules in a steel rolling mill operating in a dynamic environment. The problem is formulated as a mixed integer bilinear program that is optimally solvable for small problem instances. Although the production quantities are decided upon in advance taking into account both demand forecasts and confirmed customer orders, the actual demand figures are usually different due to a highly volatile demand. As such, three families of approximate models, which only generate exact schedules for the immediate time periods, are developed. To better capture the dynamic nature of the problem, the models are implemented on a rolling horizon basis in which key complicating aspects of the exact model, such as major setup time and minimum batch size restriction, are relaxed for the unimplemented portion of the production schedule. Upon carrying out numerical experiments for several problem instances having different degrees of capacity tightness and length of forecasting horizon, the approximate models yield reduced problem dimensionality with substantial savings in computational time while still providing practical proxies for the exact model.