Suchergebnisse

AbstractIn application of operations research models in the area of logistics, important constraints are typically encountered in the form of limitations on the funds appropriated. A supply system must be operated within whatever budgeted funds are appropriated by Congress. In the present article, various possible types of budget constraints are discussed as well as their impact on certain types of operations research models. The possible misallocations that can result from the setting of specific budgets designated for particular purposes are discussed. The confusion existing in the literature concerning the type of constraints that are actually encountered versus those that are imposed upon the mathematical models is pointed out as well as the typical inconsistency of budget constraints and steady‐state models. The difference between a steady‐state budget and a transition‐phase budget is clarified.

AbstractMany problems arising in logistics and in the application of mathematics to industrial planning are in the form of constrained maximizations with nonlinear maximands or constraint functions or both. Thus a depot facing random demands for several items may wish to place orders for each in such a way as to maximize the expected number of demands which are fulfilled; the total of orders placed is limited by a budget constraint. In this case, the maximand is certainly nonlinear. The constraint would also be nonlinear if, for example, the marginal cost of storage of the goods were increasing. Practical methods for solving such problems in nonlinear programming almost invariably depends on some use of Lagrange multipliers, either by direct solution of the resulting system of equations or by a gradient method of successive approximations (see [5], Part II). This article discusses a part of the sufficient conditions for the validity of the multiplier method.

AbstractAfter a definition of resource flow models, the study of production constraints is broken into three parts: knowing the effect of a finished equipment upon the economy, recognizing the constraint of the economy, and determining the reactions to be made because of the constraints. Then various methods of analysis are considered: one method being current mobilization planning and another being a model based on the Census of Manufactures. Because of problems encountered in these methods, an abstract analysis is presented that is identified with steps in the desigr of an equipment.