Volume 2, Issue 2 (6-2012)
2012, 2(2): 183-202 |
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Mirmohammadi S, Shadrokh S, Eshghi K. A POLYNOMIAL TIME BRANCH AND BOUND ALGORITHM FOR THE SINGLE ITEM ECONOMIC LOT SIZING PROBLEM WITH ALL UNITS DISCOUNT AND RESALE . International Journal of Optimization in Civil Engineering 2012; 2 (2) :183-202
URL: http://ijoce.iust.ac.ir/article-1-86-en.html
URL: http://ijoce.iust.ac.ir/article-1-86-en.html
Abstract: (17345 Views)
The purpose of this paper is to present a polynomial time algorithm which determines the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand with zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system and resale of the excess units is possible at the ordering time. The properties of an optimal order policy are argued and on the basis of them, a branch and bound algorithm is presented to construct an optimal sequence of order policies. In the proposed B&B algorithm, some useful fathoming rules have been proven to make the algorithm very efficient. By defining a rooted tree graph, it has been shown that the worst-case time complexity function of the presented algorithm is polynomial. Finally, some test problems which are randomly generated in various environments are solved to show the efficiency of the algorithm.
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