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

37 Pages Posted: 14 Jun 2010 Last revised: 27 Mar 2011

See all articles by Amit K. Bardhan

Amit K. Bardhan

University of Delhi

Milind Dawande

University of Texas at Dallas - Department of Information Systems & Operations Management

Srinagesh Gavirneni

Cornell University - Samuel Curtis Johnson Graduate School of Management

Yinping Mu

University of Science and Technology of China (USTC)

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: June 11, 2010

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.

Keywords: Multiperiod Problems, Forecast Horizons, Rolling Horizons, Decision Horizons, Planning Horizons, Solution Horizons, Forecasting, Dynamic Lot Size Models, Operations Management, Production changeover, demand substitution, downward substitution, product substitution, polynomial algorithm

JEL Classification: M11, C61, C63, C53, M30

Suggested Citation

Bardhan, Amit Kumar and Dawande, Milind and Gavirneni, Srinagesh and Mu, Yinping and Sethi, Suresh, Forecast and Rolling Horizons Under Demand Substitution and Production Changeovers: Analysis and Insights (June 11, 2010). Johnson School Research Paper Series No. 23-2011. Available at SSRN: https://ssrn.com/abstract=1624008 or http://dx.doi.org/10.2139/ssrn.1624008

Amit Kumar Bardhan

University of Delhi ( email )

Faculty of Management Studies
University Road
Delhi, New Delhi 110 007
India

Milind Dawande

University of Texas at Dallas - Department of Information Systems & Operations Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Srinagesh Gavirneni

Cornell University - Samuel Curtis Johnson Graduate School of Management ( email )

Ithaca, NY 14853
United States

Yinping Mu

University of Science and Technology of China (USTC) ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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