98%-Effective Lot-Sizing for Assembly Inventory Systems with Backlogging

Daning Sun and Derek Atkins
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Daning Sun: The University College of the Cariboo, Kamloops, B.C., Canada, and University of British Columbia
Derek Atkins: University of British Columbia, Vancouver, B.C., Canada

Operations Research, 1997, vol. 45, issue 6, 940-951

Abstract: In the previous work, we have shown that for a production/inventory system arranged in series with backlogging at its final product, the total cost of the best power-of-two frequency lot-size heuristic is within 6% of the optimal (or 2% if the base period is allowed to vary). In this paper, we extend our results to an assembly production/inventory system with constant external demand at its final product with backlogging allowed. By using a submodular property, we show that the total cost of any feasible policy is bounded below by finding the minimum of a set of series systems. In this way, we can get a best power-of-two frequency policy that is within 2% of the optimal: However, the number of series systems to be considered can be proportional to, in the worst case, the factorial of n (the number of nodes in the assembly system). As a consequence, this reduction cannot give us a polynomial algorithm and we have to use a different approach. By using a series of transformations, we reduce our problem to a special case of a polymatroidal network flow problem. The lower bound and the optimal power-of-two frequency policy for assembly systems with backlogging can then be found in O ( n 6 ) time.

Keywords: inventory/production; multiechelon lot sizing; backlogging (search for similar items in EconPapers)
Date: 1997
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