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International Journal of Latest Research in Science and Technology

DOI:10.29111/ijlrst   ISRA Impact Factor:3.35,  Peer-reviewed, Open-access Journal

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SOLVING THE (0 -1) KNAPSACK PROBLEM BY AN ADAPTED TRANSPORTATION ALGORITHM

Research Paper Open Access

International Journal of Latest Research in Science and Technology Vol.6 Issue 3, pp 20-24,Year 2017

SOLVING THE (0 -1) KNAPSACK PROBLEM BY AN ADAPTED TRANSPORTATION ALGORITHM

Boudjellaba H., Gningue Y. and Shamakhai H.

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Received : 05 May 2017; Accepted : 14 May 2017 ; Published : 30 June 2017

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Abstract

In this paper we link the zero-one knapsack problem to the linear transportation problem then solve it by using an adaptation of the transportation algorithm. The Vogel Approximation Method is applied to find an initial solution. It consists in assigning to each row and column a penalty which is the difference between the two least costs. The largest penalty indicates the line to be allocated first. Then the variable with the least cost on that line is assigned. For the zero-one knapsack problem, the Vogel method is shown to be equivalent to the Greedy Algorithm. That initial solution is then improved by using the dual variable and resulting reduced cost. We detect conditions which indicate that the optimal solution is reached. We also prove that when no further cost’s reduction is possible, then an optimal solution is obtained. This approach opens a new field of research which treats the zero-one knapsack problem as a transportation problem.

Key Words   
Knapsack problem, Linear Transportation problem, Assignment problem, Vogel Approximation M

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References
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To cite this article

Boudjellaba H., Gningue Y. and Shamakhai H. , " Solving The (0 -1) Knapsack Problem By An Adapted Transportation Algorithm ", International Journal of Latest Research in Science and Technology . Vol. 6, Issue 3, pp 20-24 , 2017

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