A LOWER BOUND FOR THE SINGLE-LEVEL DYNAMIC HORIZON LOT-SIZING PROBLEM.

Conventional production planning methods assume the existence of a medium- or longrange demand horizon. However, demand usually is known over a much shorter range; scheduling decisions must be made within this "decision window," which rolls forward in time. This paper presents a new lower bound for lot-sizing heuristics in a rolling-horizon framework and compares it to the well-known Wagner-Whitin bound. The new bound indicates heuristic schedules that have costs close to the optimum. Rolling-horizon schedule costs are compared to corresponding static-horizon schedule costs (assuming the whole horizon is known in advance), using the ratio of decision-window size to the natural order cycle as a parameter. For values below unity, the rolling-horizon policy is significantly more costly. For values above one, the two policies have similar costs and actually converge as the parameter value increases. [ABSTRACT FROM AUTHOR]