Production lot sizing for deterministic rolling schedules

Abstract

Abstract In this article, we study production planning for a rolling horizon in which demands are known with certainty for a given number of periods in the future (the forecast window M). The rolling horizon approach implements only the earliest production decision before the model is rerun. The next production plan will again be based on M periods of future demand information, and its first lot‐sizing decision will be implemented. Six separate lot‐sizing methods were evaluated for use in a rolling schedule. These include the Wagner‐Whitin algorithm, the Silver‐Meal heuristic, Maximum Part‐Period Gain of Karni, Heuristics 1 and 2 of Bookbinder and Tan, and Modification 1 to the Silver‐Meal heuristic by Silver and Miltenburg. The performance of each lot‐sizing rule was studied for demands simulated from the following distributions: normal, uniform (each with four different standard deviations); bimodal uniform (two types); and trend seasonal (both increasing and decreasing trends). We considered four values of the setup cost (leading to natural ordering cycles in an EOQ model of three, four, five, and six periods) and forecast windows in the range 2 ⩽ M ⩽ 20. Eight 300‐period replications were performed for each combination of demand pattern, setup cost, and lot‐sizing method. The analysis thus required consideration of 2304 300‐period replications (6 lot‐sizing methods × 12 demand patterns × 4 values of setup cost × 8 realizations), each of which was solved for nineteen different values of the forecast window M. The performance of the lot‐sizing methods was evaluated on the basis of their average cost increase over the optimal solution to each 300‐period problem, as though all these demands were known initially. For smaller forecast windows, say 4 ⩽ M ⩽ 8, the most effective lot‐sizing rules were Heuristic 2 of Bookbinder and Tan and the modified Silver‐Meal heuristic. Rolling schedules from each were generally 1% to 5% in total cost above that of the optimal 300‐period solution. For larger forecast windows, M ⩾ 10 or so, the most effective lot‐sizing method was the Wagner‐Whitin algorithm. In agreement with other research on this problem, we found that the value of M at which the Wagner‐Whitin algorithm first becomes the most effective lot‐sizing rule is a decreasing function of the standard deviation of the demand distribution.

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