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arXiv · 2002.03289

Application of KKT to Transportation Problem with Volume Discount on Shipping Cost

Issaka Haruna·Mubarack Ahmed·Shaibu Osman
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Abstract

Nonlinear programming problems are useful in designing and assigning work schedule and also in transporting goods and services from known sources to specified destinations. The objective function could be linear or nonlinear depending on the mode or rout of transportation. In supplying goods and services during emergency cases, the objective cost function is always assumed to be nonlinear. The purpose of this research is to study the nature of the cost function of the transportation problem and provide solution algorithms to solve such nonlinear cost functions. The cost per unit commodity transported may not be fixed since volume discounts are sometimes available for large shipments of goods and services. This will make the cost function either piecewise linear, separable concave or convex. The approach to solving such problems as they arise is to apply existing general nonlinear programming algorithms and when necessary make modifications to fit the special structure of the problem. We describe theoretically , algorithms for the nonlinear cost function and state conditions under which stability is achieved with both sufficient and necessary cases.

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Issaka Haruna, Mubarack Ahmed, Shaibu Osman. 2020-02-09. Application of KKT to Transportation Problem with Volume Discount on Shipping Cost. https://arxiv.org/abs/2002.03289

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