Algorithms for Optimal Allocation Problems Ha Ving Quadratic Objective Function

In this paper, an optimal allocation problem (APQ) with a quadratic objective function, a total resource constraint and an upper and lower bound constraint is considered. The APQ is a very basic and simple model but it can serve as a sub problem in the solution of the generalized allocation problem. Applying the Lagrange relaxation method, an explicit expression of the dual function associated with the APQ and an equation which the optimal dual variable must satisfy are derived first. Then, some properties of the equation are discussed. Finally, three algortihrns for solving the equation are proposed, and some computational results for the APQ are given. These results reveal the effectiveness of the algorithm.