Forecast and Rolling Horizons Under Demand Substitution and Production Changeovers: Analysis and Insights

Abstract

For most multi-period decision-making problems, it is generally well-accepted that the influence of information about later periods on the optimal decision in the current period reduces as we move farther into the future. If and when this influence reduces to zero, the corresponding problem horizon is referred to as a forecast horizon. For real businesses, the problem of obtaining a minimal forecast horizon becomes relevant because the task of estimating reliable data for future periods gets progressively challenging and expensive. We investigate forecast horizons for a two-product dynamic lot-sizing problem under (a) the possibility of substitution in one direction; that is, one product can be used to satisfy the demand of the other product but not vice-versa and (b) a changeover cost when production switches from one product to the other. The notion of substitution, due to the inherent flexibility it offers, has recently been recognized as an effective tool to improve the efficiency of multi-product inventory systems. Using the concept of regeneration points, we first justify the use of a practically-relevant restricted version of the problem for obtaining forecast horizons. Next, we develop a dynamic programming-based polynomial-time algorithm for the restricted version and, subsequently, an efficient procedure for obtaining minimal forecast horizons by establishing the monotonicity of the regeneration points. Using a comprehensive test bed of instances, we obtain useful insights on the impact of substitution and production changeovers on the length of the minimal forecast horizons. Finally, for infinite-horizon problems, we develop a practical rolling-horizon procedure that uses forecasting costs to balance the benefit of additional information. We show that, instead of fixing the duration of rolling horizon at a pre-determined value, changing it dynamically based on the lengths of the minimal forecast horizons can significantly reduce the combined production and forecasting cost.