A solid transportation problem for an item with fixed charge, vechicle cost and price discounted varying charge using genetic algorithm

Authors:
A. Ojha;B. Das;S. Mondal;M. Maiti
Affiliations:
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India;Department of Mathematics, Jhargram Raj College, Midnapore 721507, India;Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India;Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
Venue:
Applied Soft Computing
Year:
2010

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Abstract

In this paper, discount in transportation cost on the basis of transportated amount is extended to a solid transportation problem. In a transportation model, the available discount is normally offered on items/criteria, etc., in the form AUD (all unit discount) or IQD (incremental quantity discount) or combination of these two. Here transportation model is considered with fixed charges and vechicle costs where AUD, IQD or combination of AUD and IQD on the price depending upon the amount is offered and varies on the choice of origin, destination and conveyance. To solve the problem, genetic algorithm (GA) based on Roulette wheel selection, arithmetic crossover and uniform mutation has been suitably developed and applied. To illustrate the models, numerical examples have been presented. Here, different types of constraints are introduced and the corresponding results are obtained. To have better customer service, the entropy function is considered and it is displayed by a numerical example. To exhibit the efficiency of GA, another method-weighted average method for multi-objective is presented, executed on a multi-objective problem and the results of these two methods are compared.