Bicriteria optimization in the newsvendor problem with uniformly distributed demand

This paper analytically addresses the Bicriteria decision newsvendor problem of a retailer with the conflicting goals of maximizing the expected profit and the probability of exceeding it and obtains a closed form solution for a uniformly distributed demand. This is done by using the existence of a closed form solution for the second criterion to arrive at the solution for the Bicriteria problem. The decision variable remains the traditional order quantity intended to satisfy an uncertain demand, but there is no solution that maximizes each goal simultaneously. The search for optimality reduces to simple comparisons between parameters and the estimation of a critical weight. A numerical example is used throughout the paper to highlight the nature of the solutions and to illustrate the key properties of the various elements of the Bicriteria problem.