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A LOWER BOUND FOR THE SINGLE‐LEVEL DYNAMIC HORIZON LOT‐SIZING PROBLEM
Author(s) -
Karni Reuven
Publication year - 1985
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1985.tb01680.x
Subject(s) - time horizon , heuristics , sizing , upper and lower bounds , horizon , mathematical optimization , scheduling (production processes) , heuristic , holding cost , schedule , computer science , range (aeronautics) , production (economics) , economics , mathematical economics , mathematics , microeconomics , engineering , art , mathematical analysis , geometry , visual arts , aerospace engineering , operating system
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.