Optimal spares for stochastically failing equipment

A mathematical model is formulated for determining the number of spare components to purchase when components stochastically fail according to a known life distribution function and there is a cost incurred when a component is replaced. Bounds are determined for the optimal inventory which indicate that the inclusion of the replacement cost lowers the optimal inventory. Since these bounds are no easier to calculate than the optimal spares level, the theory is specialized to components with exponentially distributed time to failure. Procedures are given for calculating the optimal spares level, and numerical examples are provided.     

An extension of the (szwarc) truck assignment problem

In this journal in 1967. Szware presented an algorithm for the optimal routing of a common vehicle fleet between m sources and n sinks with p different types of commodities. The main premise of the formulation is that a truck may carry only one commodity at a time and must deliver the entire load to one demand area. This eliminates the problem of routing vehicles between sources or between sinks and limits the problem to the routing of loaded trucks between sources and sinks and empty trucks making the return trip. Szwarc considered only the transportation aspect of the problem (i. e., no intermediate points) and presented a very efficient algorithm for solution of the case he described. If the total supply is greater than the total demand, Szwarc shows that the problem is equivalent to a (mp + n) by (np + m) Hitchcock transportation problem. Digital computer codes for this algorithm require rapid access storage for a matrix of size (mp + n) by (np + m); therefore, computer storage required grows proportionally to p². This paper offers an extension of his work to a more general form: a transshipment network with capacity constraints on all arcs and facilities. The problem is shown to be solvable directly by Fulkerson's out-of-kilter algorithm. Digital computer codes for this formulation require rapid access storage proportional to p instead of p². Computational results indicate that, in addition to handling the extensions, the out-of-kilter algorithm is more efficient in the solution of the original problem when there is a mad, rate number of commodities and a computer of limited storage capacity.     

Causative matrix technique for deriving interim period transition probabilities in nonstationary markov process

The Markov assumption that transition probabilities are assumed to be constant over entire periods has been applied in economic and social structures, for example, in the analysis of income and wage distributions. In many cases, however, nonstationary transition probabilities exist over different periods. Based on causative matrix technique, this study shows a binomial approximation for obtaining nonstationary interim transition probabilities under undisturbance when the first and the last transition matrices are known.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

On the aggregation of preferences

The article attempts to show how network theory may be applied to gain new and better insights into basic economic problems. Starting with a precise definition of what is meant by acting and, in particular, by economic acting, we direct the line of argumentation toward solving the problem of how to aggregate economic decisions. Results indicate that network theory might well prove itself to be a powerful instrument in developing a theory of human behavior much more comprehensive than currently used models.     

A targeting model that minimizes collateral damage

This paper considers the problem of allocating weapons to achieve targeting objectives while simultaneously minimizing aggregate damage to surrounding nonmilitary facilities, each of which has an upper limit to the damage it is permitted to incur. A model is formulated which assumes only that damage to individual targets or associated facilities does not decrease as the number of allocated weapons increases. An implicit enumeration algorithm, based on that of Lawler and Bell is described that yields optimal integer solutions. An example is presented.     

A characterization of the value of zero-sum two-person games

For the family D, consisting of those zero-sum two-person games which have a value, the value-function on D is characterized by four properties called objectivity, monotony, symmetry and sufficiency.