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This paper analyzes the problem of balancing resource capacity utilization against the costs of user delay or inventory investment. Instead of formulating algorithms to solve more classical versions of the problem, this paper describes ways that organizations can drop the cost curve prior to applying an optimizing algorithm. This is done by classifying the techniques and giving examples from organizations which have faced serious smoothing problems. Other organizations can improve their coat performance by adopting some of these techniques. [ABSTRACT FROM AUTHOR]

The author responds to the paper "The Loading Problem," by Eilon and Christofides. He focuses on suggesting a solution to the problem. The recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the one proposed by Eilon and Christofides. It is suggested that the simpler algorithm offered by the author reaches mathematical optimization as often as the aforementioned algorithm. It is further proposed that the algorithm presented by Eilon and Christofides cannot be used to solve multi-dimensional programming problems. The author goes on to discuss a numerical analysis that can be used for the allocation of industrial resources. Related mathematical models are discussed in detail. A table comparing the results of the two algorithms is also presented.

Part I of this paper presented a method for primal decomposition of large convex separable programs into a sequence of smaller subproblems. In this part, additional theory and development of a parametric subproblem-solution and step-size-determination technique completes the algorithm. A previously unsolved problem in the operations-research literature, the generalized modular design problem of Evans [Opns. Res. 18, 562--4 (1970)] is solved by the algorithm and numerical results provided. [ABSTRACT FROM AUTHOR]

The problem considered in this paper is that of allocating a budget of resources among the links of a network for the purpose of increasing its flow capacity relative to given sources and sinks. On the assumption that the cost of increasing each link capacity is linear, a labeling algorithm is described that permits rapid calculation of optimal allocations for all budgets. [ABSTRACT FROM AUTHOR]

The article presents the authors' reply to a response to their paper "The Loading Problem," by B. Lev. Lev's response focused on suggesting adjustments to the authors' method of solving a multi-dimensional programming problem, which relates to the economic theory of production. Lev's recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the algorithm proposed by Eilon and Christofides. The authors suggest that the algorithm offered by Lev neglects to take into consideration relevant elements that are related to a problem of industrial capacity and time management. Mathematical models depicting the allocation of industrial resources, such as boxes used for the shipment of goods, are also presented. The authors further discuss the modifications recommended by Lev.

The loading problem is defined as the allocation of given items with known magnitude to boxes with constrained capacity, so as to minimize the number of boxes required. Two methods of solution are considered: The first is by a zero-one programming model, for which the solution procedure is described; the second is by a heuristic algorithm. Fifty problems were solved by the two methods and in all but two the second method yielded the optimal solution with significantly less computing time than that needed by the first method. [ABSTRACT FROM AUTHOR]

An integer programming formulation for the problem of sequencing jobs on a single machine to minimize the number of late jobs is developed. The structure of the formulation is exploited to obtain the easily stated algorithm (previously developed by Moore [5]) for the solution of the problem and then to compare it to other similar allocation problems, among which is the Knapsack problem. [ABSTRACT FROM AUTHOR]