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Lot sizes under continuous demand: The backorder case
Author(s) -
Yao David,
Klein Morton
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198910)36:5<615::aid-nav3220360506>3.0.co;2-t
Subject(s) - order (exchange) , monotonic function , mathematical optimization , computer science , function (biology) , piecewise , time horizon , mathematical economics , mathematics , economics , mathematical analysis , finance , evolutionary biology , biology
We study a deterministic lot‐size problem, in which the demand rate is a (piecewise) continuous function of time and shortages are backordered. The problem is to find the order points and order quantities to minimize the total costs over a finite planning horizon. We show that the optimal order points have an interleaving property, and when the orders are optimally placed, the objective function is convex in the number of orders. By exploiting these properties, an algorithm is developed which solves the problem efficiently. For problems with increasing (decreasing) demand rates and decreasing (increasing) cost rates, monotonicity properties of the optimal order quantities and order intervals are derived.