Michael J. Brusco

Note: A local-search heuristic for large set-covering problems

In this note we describe a local-search heuristic (LSH) for large non-unicost set-covering problems (SCPs). The new heuristic is based on the simulated annealing algorithm and uses an improvement routine designed to provide low-cost solutions within a reasonable amount of CPU time. The solution costs associated with the LSH compared very favorably to the best previously published solution costs for 20 large SCPs taken from the literature. In particular, the LSH yielded new benchmark solutions for 17 of the 20 test problems. We also report that, for SCPs where column cost is correlated with column coverage, the new heuristic provides solution costs competitive with previously published results for comparable problems.

A variable-selection heuristic for K-means clustering

One of the most vexing problems in cluster analysis is the selection and/or weighting of variables in order to include those that truly define cluster structure, while eliminating those that might mask such structure. This paper presents a variable-selection heuristic for nonhierarchical (K-means) cluster analysis based on the adjusted Rand index for measuring cluster recovery. The heuristic was subjected to Monte Carlo testing across more than 2200 datasets with known cluster structure. The results indicate the heuristic is extremely effective at eliminating masking variables. A cluster analysis of real-world financial services data revealed that using the variable-selection heuristic prior to the K-means algorithm resulted in greater cluster stability.

Service Sweethearting: Its Antecedents and Customer Consequences

This research is the first to examine service sweethearting, an illicit behavior that costs firms billions of dollars annually in lost revenues. Sweethearting occurs when frontline workers give unauthorized free or discounted goods and services to customer conspirators. The authors gather dyadic data from 171 service employees and 610 of their customers. The results from the employee data reveal that a variety of job, social, and remuneration factors motivate sweethearting behavior and several measurable employee traits suppress its frequency. The results from the customer data indicate that although sweethearting inflates a firms satisfaction, loyalty, and positive word-of-mouth scores by as much as 9%, satisfaction with the confederate employee fully mediates these effects. Thus, any benefits for customer satisfaction or loyalty initiatives are tied to a frontline worker that the firm would rather not employ. Marketing managers can use this study to recognize job applicants or company settings that are particularly prone to sweethearting and as the basis for mitigating a positive bias in key customer metrics.

A simulated annealing approach to the cyclic staff‐scheduling problem

This article presents the application of a simulated annealing heuristic to an NP-complete cyclic staff-scheduling problem. The new heuristic is compared to branch-and-bound integer programming algorithms, as well as construction and linear programming-based heuristics. It is designed for use in a continuously operating scheduling environment with the objective of minimizing the number of employees necessary to satisfy forecast demand. The results indicate that the simulated annealing-based method tends to dominate the branch-and-bound algorithms and the other heuristics in terms of solution quality. Moreover, the annealing algorithm exhibited rapid convergence to a low-cost solution. The simulated annealing heuristic is executed in a single program and does not require mathematical programming software.

Evaluating mixture modeling for clustering: recommendations and cautions.

This article provides a large-scale investigation into several of the properties of mixture-model clustering techniques (also referred to as latent class cluster analysis, latent profile analysis, model-based clustering, probabilistic clustering, Bayesian classification, unsupervised learning, and finite mixture models; see Vermunt & Magdison, 2002). Focus is given to the multivariate normal distribution, and 9 separate decompositions (i.e., class structures) of the covariance matrix are investigated. To provide a link to the current literature, comparisons are made with K-means clustering in 3 detailed Monte Carlo studies. The findings have implications for applied researchers in that mixture-model clustering techniques performed best when the covariance structure and number of clusters were known. However, as the information about the shape and number of clusters became unknown, degraded performance was observed for both K-means clustering and mixture-model clustering.

A morphing procedure to supplement a simulated annealing heuristic for cost‐ andcoverage‐correlated set‐covering problems

We report on the use of a morphing procedure in a simulated annealing (SA) heuristicdeveloped for set‐covering problems (SCPs). Morphing enables the replacement of columnsin solution with similar but more effective columns (morphs). We developed this procedureto solve minimum cardinality set‐covering problems (MCSCPs) containing columns whichexhibit high degrees of coverage correlation, and weighted set‐covering problems (WSCPs)that exhibit high degrees of both cost correlation and coverage correlation. Such correlationstructures are contained in a wide variety of real‐world problems including many scheduling,design, and location applications. In a large computational study, we found that the morphingprocedure does not degrade the performance of an SA heuristic for SCPs with low degreesof cost and coverage correlation (given a reasonable amount of computation time), and thatit improves the performance of an SA heuristic for problems with high degrees of suchcorrelations.

Cost analysis of alternative formulations for personnel scheduling in continuously operating organizations

Personnel-scheduling problems for continuously operating organizations have proven to be difficult to solve optimally. As a consequence, a number of alternative approaches have been devised for solving these problems. We provide computational results of a study of the staffing costs obtained using a prominent alternative formulation approach. The results demonstrate that excess staffing costs may result from the use of this approach. We subsequently develop a new local-search heuristic based on the simulated annealing algorithm to generate feasible integer personnel schedules in continuously operating organizations. The solution costs and computational effort associated with the new heuristic are shown to be generally superior to those of branch-and-bound integer programming.

A New Variable Weighting and Selection Procedure for K-means Cluster Analysis

A variance-to-range ratio variable weighting procedure is proposed. We show how this weighting method is theoretically grounded in the inherent variability found in data exhibiting cluster structure. In addition, a variable selection procedure is proposed to operate in conjunction with the variable weighting technique. The performances of these procedures are demonstrated in a simulation study, showing favorable results when compared with existing standardization methods. A detailed demonstration of the weighting and selection procedure is provided for the well-known Fisher Iris data and several synthetic data sets.

A Simulated Annealing Heuristic for a Bicriterion Partitioning Problem in Market Segmentation

K-means clustering procedures are frequently used to identify homogeneous market segments on the basis of a set of descriptor variables. In practice, however, market research analysts often desire both homogeneous market segments and good explanation of an exogenous response variable. Unfortunately, the relationship between these two objective criteria can be antagonistic, and it is often difficult to find clustering solutions that yield adequate levels for both criteria. The authors present a simulated annealing heuristic for solving bicriterion partitioning problems related to these objectives. A large computational study and an empirical demonstration reveal the effectiveness of the methodology. The authors also discuss limitations and extensions of the method.

Using Quadratic Assignment Methods to Generate Initial Permutations for Least-Squares Unidimensional Scaling of Symmetric Proximity Matrices

Combinatorial solution procedures for least-squares unidimensional scaling of symmetric proximity matrices frequently consist of two integrated processes: (a) the identification of a permutation of objects, and (b) the estimation of coordinate values on the continuum. These procedures typically require an initial permutation of objects. It is generally known that their final unidimensional scaling solutions are often very sensitive to these starting permutations, particularly when the number of objects is large (> 20). This paper demonstrates that, relative to random starting permutations, substantial improvements in final seriation quality and computational efficiency can be realized by using starting permutations obtained via solution to a quadratic assignment problem (QAP). Three methods-locally-optimal pairwise interchange (LOPI), simulated annealing (SA) and a hybrid (LOPI-SA)-were evaluated regarding their effectiveness and efficiency for solving the QAP. The results revealed that SA and LOPI-SA efficiently provided very good QAP solutions that subsequently led to good least-squares solutions.