Abstract
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. The APQ is a very basic and simple model but it can serve as a subproblem in the solution of the generalized allocation or transportation problems which have quadratic objective functions. From the standpoint of the mathematical programming theory. the APQ is a strictly convex separable programming problem and is a special class of quadratic programming problem: Therefore. its global optimality is guaranteed.
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