Maximizing pseudoconvex transportation problem: a special type

The paper discusses a non-concave fractional programming problem aiming at maximization of a pseudoconvex function under standard transportation conditions. The pseudoconvex function considered here is the product of two linear functions contrasted with a positive valued linear function. It has been established that optimal solution of the problem is attainable at an extreme point of the convex feasible region. The problem is shown to be related to indefinite quadratic programming which deals with maximization of a convex function over the given feasible region. It has been further established that the local maximum point of this quadratic programming problem is the global maximum point under certain conditions, and its optimal solution provides an upper bound on the optimal value of the main problem. The extreme point solutions of the indefinite quadratic program are ranked to tighten the bounds on the optimal value of the main problem and a convergent algorithm is developed to obtain the optimal solution.