Identifying and ranking a most preferred subset of alternatives in the presence of multiple criteria

In this article an interactive method is developed to identify and rank a most preferred subset, T, of alternatives assuming that the decision maker has an implicit quasiconcave nondecreasing utility function. The method requires the decision maker to compare pairs of selected alternatives. Based on the responses of the decision maker, convex cones are constructed to eliminate alternatives that are proved to be inferior to alternatives in set T. The method aims at keeping the number of pairwise comparisons small. Computational experience with the method indicates that the required number of pairwise comparisons to form set T is usually small. However, the number of pairwise comparisons needed to confirm that this set is best may be large.     

Estimation and prediction in a semi-markov model for evasive vehicle movement along a fixed path

In Turner and Holmes [8] a model for evasive vehicle movement along a fixed track is developed within the mathematical framework of a two-state semi-Markov process. They derive a number of analytical properties of the model. In this article we address problems concerning the estimation of parameters in the model and the construction of data-based prediction equations.     

A model for use in the rationing of inventory during lead time

While the traditional solution to the problem of meeting stochastically variable demands for inventory during procurement lead time is through the use of some level of safety stock, several authors have suggested that a decision be made to employ some form of rationing so as to protect certain classes of demands against stockout by restricting issues to other classes. Nahmias and Demmy [10] derived an approximate continuous review model of systems with two demand classes which would permit an inventory manager to calculate the expected fill rates per order cycle for high-priority, low-priority, and total system demands for a variety of parameters. The manager would then choose the rationing policy that most closely approximated his fill-rate objectives. This article describes a periodic review model that permits the manager to establish a discrete time rationing policy during lead time by prescribing a desired service level for high-priority demands. The reserve levels necessary to meet this level of service can then be calculated based upon the assumed probability distributions of high- and low-priority demands over lead time. The derived reserve levels vary with the amount of lead time remaining. Simulation tests of the model indicate they are more effective than the single reserve level policy studied by Nahmias and Demmy.     

On the number of games played in a best of (2n – 1) series

Let p(⩾0.5) denote the probability that team A beats B in a single game. The series continues until either A or B wins n games. Assuming that these games are independent replications, we study some features of the distribution of X_n, the number of games played in the series. It is shown that X_n is unimodal, has an IFRA distribution, and is stochastically decreasing in p. Close approximations to its mode, mean, and variance are given. Finally, it is shown that the maximum-likelihood estimator of p based on X_n is unique.     

Discount pricing policies for inventories subject to declining demand

Until only recently, the mechanism behind determining item price has been ignored and the discount price taken as a given in quantity-discount inventory decision problems. Inventory subject to declining demand further complicates both pricing and replenishment decisions. This article provides the vendor with the means for optimally determining both the discount price and replenishment order frequency for all buyers in the system in an environment of declining demand. In the multiple-buyer case, we provide an efficient algorithm for classifying buyers into homogeneous subgroups to further enhance joint cost savings among all system participants.     

Should we be using cost of capital in calculating holding costs of consumable inventory?

The DOD directs the usage of 10% of item cost as the cost of capital in the calculation of inventory holding costs. This 10% cost is not totally justified and a complete review must be accomplished to bring this factor to a meaningful and more useful value. The current logic supporting a 10% cost of capital results in a continuing perturbation which forces the Air Force to operate in a less than efficient mode when using the economic order quantity for consumable purchases.     

Algorithms for the design of finite-capacity service units

Finite-capacity queues arise naturally in many practical situations, notably in communications and manufacturing engineering. In this article, the matrix formalism of probability distributions of phase type is used to develop fast algorithms to compute various steady-state distributions for the finite-capacity PH/PH/1 queue. This algorithm is an important ingredient in solving nontraditional but significant design problems. Some of these are described as illustrative examples.     

A survey of preventive maintenance models for stochastically deteriorating single-unit systems

A survey of the research done on preventive maintenance is presented. The scope of the present survey is on the research published after the 1976 paper by Pierskalla and Voelker [98]. This article includes optimization models for repair, replacement, and inspection of systems subject to stochastic deterioration. A classification scheme is used that categorizes recent research into inspection models, minimal repair models, shock models, or miscellaneous replacement models.     

Multiechelon inventory systems with lateral supply

We develop approximations to estimate the expected backorders in a multiechelon system in which lateral supply actions between bases are allowed when a backorder occurs. These approximations are easy to compute, and the average absolute error over a wide range of parameter values is less than 4% when items are depot repairable, even when bases are dissimilar. With lateral supply, backorder reductions of 30-50% are not uncommon, and a 72% reduction was observed in two cases. Lateral supply becomes more important with low demand rates. A similar approach was unsuccessful for base-repairable items. However, lateral supply has a beneficial effect only when the lateral supply time is very short, 1/4 or less of the average base repair time. Even in such cases lateral supply is unlikely to be important in an actual application, because base management can expedite repair of critical items.