A POLYNOMIAL TIME BRANCH AND BOUND ALGORITHM FOR THE SINGLE ITEM ECONOMIC LOT SIZING PROBLEM WITH ALL UNITS DISCOUNT AND RESALE

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MIRMOHAMMADI S.H.; SHADROKH SH.; ESHGHI K.

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Journal Paper

Paper Information

Journal: International Journal of Optimization in Civil Engineering Year:2012 | Volume:2 | Issue:2 Page(s): 183-202

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Title

A POLYNOMIAL TIME BRANCH AND BOUND ALGORITHM FOR THE SINGLE ITEM ECONOMIC LOT SIZING PROBLEM WITH ALL UNITS DISCOUNT AND RESALE

Author(s)

MIRMOHAMMADI S.H. | SHADROKH SH. | ESHGHI K.

Keywords

BRANCH AND BOUND

PURCHASING

ALL-UNITS DISCOUNT

RESALE

COMPLEXITY THEORY

GRAPH THEORY

Abstract

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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APA: Copy

MIRMOHAMMADI, S.H., SHADROKH, SH., & ESHGHI, K.. (2012). 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, 2(2), 183-202. SID. https://sid.ir/paper/329357/en

Vancouver: Copy

MIRMOHAMMADI S.H., SHADROKH SH., 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[Internet]. 2012;2(2):183-202. Available from: https://sid.ir/paper/329357/en

IEEE: Copy

S.H. MIRMOHAMMADI, SH. SHADROKH, and K. ESHGHI, “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, vol. 2, no. 2, pp. 183–202, 2012, [Online]. Available: https://sid.ir/paper/329357/en

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