  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.
