On the evaluation of investment proposals having multiple attributes

A framework is developed for analyzing the likelihood of acceptance of an investment project proposal when objectives are uncertain. The foundation is a utility model of top management's choice process, modified if need be through a Bayesian approach which takes into account any apparent inconsistency in the history of past proposal acceptances and rejections.     

Optimal design of a multi-item,multi-location,multi-repair type repair and supply system

The design of a system with many locations, each with many items which may fail while in use, is considered. When items fail, they require repair; the particular type of repair being governed by a probability distribution. As repairs may be lengthy, spares are kept on hand to replace failed items. System ineffectiveness is measured by expected weighted shortages over all items and locations, in steady state. This can be reduced by either having more spares or shorter expected repair times. Design consists of a provisioning of the number of spares for each item, by location; and specifying the expected repair times for each type of repair, by item and location. The optimal design minimizes expected shortages within a budget constraint, which covers both (i) procurement of spares and (ii) procurement of equipment and manning levels for the repair facilities. All costs are assumed to be separable so that a Lagrangian approach is fruitful, yielding an implementable algorithm with outputs useful for sensitivity analysis. A numerical example is presented.     

The single server queue in discrete time-numerical analysis I

This is the first of a sequence of papers dealing with the computational aspects of the transient behavior of queues in discrete time It is shown that for a substantial class of queues of practical interest, a wealth of numerical information may be obtained by relatively unsophisticated methods This approach should prove useful in the analysis of unstable queues which operate over a limited time interval, but is by no means limited to such queues Mathematically the service unit is modeled in terms of a multivariate Markov chain, whose particular structure is used in iterative computation. Many important queue features may then be derived from the n-step transition probabilities of this chain.     

The single server queue in discrete time-numerical analysis II

This paper deals with the numerical problems arising in the computation of higher order moments of the busy period for certain classical queues of the M|G|I type, both in discrete and in continuous time The classical functional equation for the moment generating function of the busy period is used. The higher order derivatives at zero of the moment generating function are computed by repeated use of the classical differentiation formula of Fá di Bruno. Moments of order up to fifty may be computed in this manner A variety of computational aspects of Fá di Bruno's formula, which may be of use in other areas of application, are also discussed in detail.     

The single server queue in discrete time-numerical analysis IV

The nonlinear difference equation for the distribution of the busy period for an unbounded discrete time queue of M|G| 1 type is solved numerically by a monotone iterative procedure. A starting solution is found by computing a first passage time distribution in a truncated version of the queue.     

Optimal inventory policy when stockouts alter demand

An inventory model in which future demand is affected by stockouts has been considered recently by B. L. Schwartz. Some generalizations of Schwartz's model are presented in this paper and properties of the optimal policies are determined. In the case of deterministic demand, a set-up cost is included and a mixture of backlogged and nonbacklogged orders is allowed during stockout. It is proved that the optimal policy entails either no stockout or continual stockout, depending on the values of three parameters. For stochastic demand, the effect of stockouts on demand density is postulated, the resulting optimal inventory policy is discussed, and an example involving an exponential density function is then analyzed in detail.     

Armor configurations via dynamic programming

The problem of selecting materials, their thicknesses and order for armor designed for the defeat of shaped charge threats, has been formulated as a constrained optimization problem. The mathematical model provides an optimal order and thickness of each layer of material such that the resulting armor configuration will be of minimum mass per unit area subject to constraints on total thickness and shaped charge jet tip exit velocity.     

Optimal multicommodity network flows with resource allocation

The problem of determining multicommodity flows over a capacitated network subject to resource constraints may be solved by linear programming; however, the number of potential vectors in most applications is such that the standard arc-chain formulation becomes impractical. This paper describes an approach—an extension of the column generation technique used in the multicommodity network flow problem—that simultaneously considers network chain selection and resource allocation, thus making the problem both manageable and optimal. The flow attained is constrained by resource availability and network capacity. A minimum-cost formulation is described and an extension to permit the substitution of resources is developed. Computational experience with the model is discussed.