Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables
提出一种递归方法，高效求解带界变量的凸背包问题，适用于运营管理、金融、人力规划等领域中资源在竞争方案间的分配，尤其适合层次规划系统的分解决策。
The allocation of a specific amount of a given resource among competitive alternatives can often be modelled as a knapsack problem. This model formulation is extremely efficient because it allows convex cost representation with bounded variables to be solved without great computational efforts. Practical applications of this problem abound in the fields of operations management, finance, manpower planning, marketing, etc. In particular, knapsack problems emerge in hierarchical planning systems when a first level of decisions need to be further allocated among specific activities which have been previously treated in an aggregate way. In this paper we provide a recursive procedure to solve such problems. The method differs from classical optimization algorithms of convex programming in that it determines at each iteration the optimal value of at least one variable. Applications and computational results are presented.