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Nonlinear programming problems are useful in designing and assigning workschedule and also in transporting goods and services from known sources tospecified destinations. The objective function could be linear or nonlineardepending on the mode or rout of transportation. In supplying goods andservices during emergency cases, the objective cost function is always assumedto be nonlinear. The purpose of this research is to study the nature of thecost function of the transportation problem and provide solution algorithms tosolve such nonlinear cost functions. The cost per unit commodity transportedmay not be fixed since volume discounts are sometimes available for largeshipments of goods and services. This will make the cost function eitherpiecewise linear, separable concave or convex. The approach to solving suchproblems as they arise is to apply existing general nonlinear programmingalgorithms and when necessary make modifications to fit the special structureof the problem. We describe theoretically , algorithms for the nonlinear costfunction and state conditions under which stability is achieved with bothsufficient and necessary cases.

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