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 more challenging and expensive. This article investigates forecast horizons for a two-product dynamic lot-sizing model under (i) 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 (ii) a changeover cost when production switches from one product to the other. It is assumed that only one of the two products can be produced in a period. 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. The concept of regeneration points is used to justify the use of a practically relevant restricted version of the problem to obtain forecast horizons. A dynamic programming-based polynomial-time algorithm for the restricted version is developed and, subsequently, an efficient procedure for obtaining minimal forecast horizons by establishing the monotonicity of the regeneration points is obtained. Using a comprehensive test bed of instances, useful insights are obtained on the impact of substitution and production changeovers on the length of the minimal forecast horizons. Finally, for infinite-horizon problems, a practical rolling-horizon procedure is developed that uses forecasting costs to balance the benefit of additional information. It is shown that, instead of fixing the duration of the rolling horizon at a predetermined value, changing it dynamically based on the lengths of the minimal forecast horizons can significantly reduce the combined production and forecasting cost.

[Supplemental materials are available for this article. Go to the publisher’s online edition of IIE Transactions to view the supplemental file.]

Keywords:

• Forecast horizon
• production planning
• rolling horizon
• product substitution

Acknowledgements

Amit Bardhan’s research was supported by a BOYSCAST fellowship from the Department of Science and Technology, Government of India. Yinping Mu’s research was supported by the National Natural Science Foundation of China (Grants 70932005 and 71172096).

Notes

†On sabbatical leave from Johnson Graduate School of Management, Cornell University