A LOWER BOUND FOR THE SINGLE‐LEVEL DYNAMIC HORIZON LOT‐SIZING PROBLEM
针对滚动计划框架下的批量问题，提出一个新的成本下界，并与Wagner-Whitin下界比较，发现当决策窗口与自然订单周期比值大于1时，滚动计划成本接近最优静态计划。
Abstract 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.