A logistic regression/Markov chain model for NCAA basketball

Each year, more than $3 billion is wagered on the NCAA Division 1 men's basketball tournament. Most of that money is wagered in pools where the object is to correctly predict winners of each game, with emphasis on the last four teams remaining (the Final Four). In this paper, we present a combined logistic regression/Markov chain model for predicting the outcome of NCAA tournament games given only basic input data. Over the past 6 years, our model has been significantly more successful than the other common methods such as tournament seedings, the AP and ESPN/USA Today polls, the RPI, and the Sagarin and Massey ratings. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

Requirements planning for modular products

The focus of this paper is on determining the requirements of different component options of a modular end‐product in an uncertain environment. We explicitly model two distinct sources of uncertainty: stochastic end‐product demand and unknown market proportions for the different product options available. Our cost minimizing model focuses on determining the optimal requirements policies for component options that meet a pre‐set service level. We show that simple common‐sense requirements policies are not generally optimal; there is a non‐linear connection between service level and component requirements that is hard to characterize without a detailed analysis. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The political command and control of nuclear forces

“Even more than in 1914, governments in our own day are likely to be ignorant of the technical detail of war and the tactical measures that can or cannot (or, more important, must or must not) be taken in various specialized situations. In peacetime the study and preparation of these measures will be relegated to military staffs as being narrow and technical. Today, .... it is almost impossible to get people interested in the tactics and strategy of thermonuclear war. It is now believed that only the prewar moves are of interest, and even those are not too important because deterrence is supposed to be so close to 'automatic'.” Herman Kahn (1960).     

Allocation policies and cost approximations for multilocation inventory systems

Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty-cost/holding-cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem. Each approach provides both a near-optimal order policy and an approximation of the optimal cost of the original problem. In addition, simple but effective allocation policies are discussed.     

A note on a model for evasive vehicle movement along a fixed path

A model for a vehicle moving evasively along a fixed path is defined in terms of a two- state semi-Markov process. An important feature of this model is the continuous movement of the vehicle as a function of time. One potential application of this model is the development of a strategy for the deployment of long-range missiles on long underground tracks.     

Prediction with zero-one loss structure

This paper poses a prediction problem in which a linear model is assumed. With a “zero-one” loss structure as the loss from incorrect prediction, it is suggested that least squares may not be appropriate for estimating the parameters of the model. An alternate criterion is proposed and integer programming is used in order to find the estimates, given the proposed criterion.     

Scheduling with earliest start and due date constraints

We consider the scheduling of n tasks on a single resource. Each task becomes available for processing at time a_i, must be completed by time b_i, and requires d_i time units for processing. The aim is to find a schedule that minimizes the elapsed time to complete all jobs. We present solution algorithms for this problem when job splitting is permitted and when job splitting is not permitted. Then we consider several scheduling situations which arise in practice where these models may apply.     

On the distribution of the optimal value for a class of stochastic geometric programs

An approach is presented for obtaining the moments and distribution of the optimal value for a class of prototype stochastic geometric programs with log-normally distributed cost coefficients. It is assumed for each set of values taken on by the cost coefficients that the resulting deterministic primal program is superconsistent and soluble. It is also required that the corresponding dual program has a unique optimal point with all positive components. It is indicated how one can apply the results obtained under the above assumptions to stochastic programs whose corresponding deterministic dual programs need not satisfy the above-mentioned uniqueness and positivity requirements.