Computational experience on an algorithm for the transportation problem with nonlinear objective functions

This paper explores computational implications of allowing nonlinear objective functions in the transportation problem. Two types of nonlinearities, including polynomials, are studied. The choice of these functions resulted from our interest in models of integrated water management. Zangwill's convex simplex method and the primal method of transportation problem form the basis of our algorithm. Innovative features of our work are compact storage and efficient computation procedures. We study the effects on computation time of problem size; the density of nonlinear terms; the size of tolerances for stopping rules; and rules for choice of new variables to enter the solution. We find that problems up to 95 × 95 in size are capable of reasonably fast solution. A particularly surprising finding is that one‐dimensional search for improving solutions performs adequately, at least for the kinds of problems posed in this paper. We are encouraged by our results and believe that models involving nonlinear objective functions may be tractable even for relatively large problems, thus making possible more accurate descriptions of real situations.