Gittins-index heuristics for research planning

The classical work of Gittins, which resulted in the celebrated index result, had applications to research planning as an important part of its motivation. However, research planning problems often have features that are not accommodated within Gittins's original framework. These include precedence constraints on the task set, influence between tasks, stopping or investment options and routes to success in which some tasks do not feature. We consider three classes of Markovian decision models for research planning, each of which has all of these features. Gittins-index heuristics are proposed and are assessed both analytically and computationally. They perform impressively. © 1995 John Wiley & Sons, Inc.     

Tabular aids for fitting weibull moment estimates

Moment estimators for the parameters of the Weibull distribution are considered in the context of analysis of field data. The data available are aggregated, with individual failure times not recorded. In this case, the complexity of the likelihood function argues against the use of maximum-likelihood estimation, particularly for relatively large sets of data, and moment estimators are a reasonable alternative. In this article, we derive the asymptotic covariance matrix of the moment estimators, and provide listings for BASIC computer programs which generate tables useful for calculation of the estimates as well as for estimating the asymptotic covariance matrix using aggregated data.     

Hybrid heuristics for minimum cardinality set covering problems

Minimum cardinality set covering problems (MCSCP) tend to be more difficult to solve than weighted set covering problems because the cost or weight associated with each variable is the same. Since MCSCP is NP-complete, large problem instances are commonly solved using some form of a greedy heuristic. In this paper hybrid algorithms are developed and tested against two common forms of the greedy heuristic. Although all the algorithms tested have the same worst case bounds provided by Ho [7], empirical results for 60 large randomly generated problems indicate that one algorithm performed better than the others.     

On estimating population characteristics from record-breaking observations. i. parametric results

Consider an experiment in which only record-breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. We treat the problem of estimating the mean of an underlying exponential distribution, and we consider both fixed sample size problems and inverse sampling schemes. Under inverse sampling, we demonstrate certain global optimality properties of an estimator based on the “total time on test” statistic. Under random sampling, it is shown than an analogous estimator is consistent, but can be improved for any fixed sample size.     

Modified fictitious play

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and apply it to both symmetric and general games. If the original game is not symmetric, the basic idea is to transform the given matrix game into an equivalent symmetric game (a game with a skew-symmetric matrix) and use the solution properties of symmetric games (the game value is zero and both players have the same optimal strategies). The fictitious play method is then applied to the enlarged skew-symmetric matrix with a modification that calls for the periodic restarting of the process. At restart, both players' strategies are made equal based on the following considerations: Select the maximizing or minimizing player's strategy that has a game value closest to zero. We show for both symmetric and general games, and for problems of varying sizes, that the modified fictitious play (MFP) procedure approximates the value of the game and optimal strategies in a greatly reduced number of iterations and in less computational time when compared to Brown's regular fictitious play (RFP) method. For example, for a randomly generated 50% dense skew-symmetric 100 × 100 matrix (symmetric game), with coefficients |a_ij| ≤ 100, it took RFP 2,652,227 iterations to reach a gap of 0.03118 between the lower and upper bounds for the game value in 70.71 s, whereas it took MFP 50,000 iterations to reach a gap of 0.03116 in 1.70 s. Improved results were also obtained for general games in which the MFP solves a much larger equivalent symmetric game. © 1996 John Wiley & Sons, Inc.     

A class of Bayes-optimal two-stage screens

Items are characterized by a set of attributes (T) and a collection of covariates (X) associated with those attributes. We wish to screen for acceptable items (T ∈ C_T), but T is expensive to measure. We envisage a two-stage screen in which observation of X_ is used as a filter at the first stage to sentence most items. The second stage involves the observation of T for those items for which the first stage is indecisive. We adopt a Bayes decision-theoretic approach to the development of optimal two-stage screens within a general framework for costs and stochastic structure. We also consider the important question of how much screens need to be modified in the light of resource limitations that bound the proportion of items that can be passed to the second stage. © 1996 John Wiley & Sons, Inc.     

Relaxation method for the solution of the minimax location-allocation problem in euclidean space

A method previously devised for the solution of the p-center problem on a network has now been extended to solve the analogous minimax location-allocation problem in continuous space. The essence of the method is that we choose a subset of the n points to be served and consider the circles based on one, two, or three points. Using a set-covering algorithm we find a set of p such circles which cover the points in the relaxed problem (the one with m < n points). If this is possible, we check whether the n original points are covered by the solution; if so, we have a feasible solution to the problem. We now delete the largest circle with radius r_p (which is currently an upper limit to the optimal solution) and try to find a better feasible solution. If we have a feasible solution to the relaxed problem which is not feasible to the original, we augment the relaxed problem by adding a point, preferably the one which is farthest from its nearest center. If we have a feasible solution to the original problem and we delete the largest circle and find that the relaxed problem cannot be covered by p circles, we conclude that the latest feasible solution to the original problem is optimal. An example of the solution of a problem with ten demand points and two and three service points is given in some detail. Computational data for problems of 30 demand points and 1–30 service points, and 100, 200, and 300 demand points and 1–3 service points are reported.     

Testing for positive quadrant dependence in ordinal contingency table

Two new randomization tests are introduced for ordinal contingency tables for testing independence against strictly positive quadrant dependence, i.e., P(X > x,Y > y) ≥ P(X > x)P(Y > y) for all x,y with strict inequality for some x and y. For a number of cases, simulation is used to compare the estimated power of these tests versus those standard tests based on Kendall's T, Spearman's p, Pearson's X², the usual likelihood ratio test, and a test based upon the log-odds ratio. In these cases, subsets of the alternative region are identified where each of the testing statistics is superior. The new tests are found to be more powerful than the standard tests over a broad range of the alternative regions for these cases.     

An approach to postoptimality and sensitivity analysis of zero-one goal programs

In this article we present a methodology for postoptimality and sensitivity analysis of zero-one goal programs based on the set of k-best solutions. A method for generating the set of k-best solutions using a branch and bound algorithm and an implicit enumeration scheme for multiple objective problem are discussed. Rules for determining the range of parameter changes that still allows a member of the k-best set to be optimal are developed. An investigation of a sufficient condition for postoptimality analysis is also presented.