Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems a...Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm.展开更多
基金Project supported by the National Natural Science Foundation oChina (Grant os.79970107 and 10271073)
文摘Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm.
