Paul A. Rubin

Paul A. Rubin
Michigan State University | MSU · Department of Management

Ph.D.

About

39
Publications
2,089
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944
Citations
Introduction
Paul A. Rubin is retired from the Department of Management, Eli Broad College of Business, Michigan State University. He does research in operations research, primarily in applications of discrete optimization.
Additional affiliations
May 2012 - present
Michigan State University
Position
  • Professor Emeritus

Publications

Publications (39)
Article
We consider the panel size management problem that aims to balance workloads among providers within a health care system, where the ratio of a primary care provider’s load to their own daily full capacity is used as a measure for overload or underload. While transferring patients from their existing providers to others is the means to achieve workl...
Article
Full-text available
The Sensor Location Partial and Full Observability Problems consist in determining the best placement of sensors on a network to allow partial or full observability of a given set of flows of interest in the network (i.e., either Origin–Destination flows, or route flows, or link flows, or a combination of them), respectively. We present the first e...
Article
We present an improved formulation for the maximum coverage patrol routing problem (MCPRP). The main goal of the patrol routing problem is to maximize the coverage of critical highway stretches while ensuring the feasibility of routes and considering the availability of resources. By investigating the structural properties of the optimal solution,...
Article
This article examines the problem of assigning individuals to teams to make the teams as similar as possible to each other across multiple attributes. This may be complicated by a variety of constraints, including restrictions on whether specific individuals can or should be assigned to the same team. The problem arises in multiple contexts, includ...
Article
Thesis (Ph. D.)--Michigan State University. Dept. of Mathematics, 1980. Includes bibliographical references (leaves 110-111). Microform. Ann Arbor, Mich. : Xerox University Microfilms, 1981. 1 microfilm reel ; 35 mm.
Article
Full-text available
We examined and compared short-rotation hybrid poplar investments using standard discounted cash flow and stochastic simulation. With stochastic simulation, triangular probability density functions were used to describe the values for three important uncertain factors: product price, product yield, and harvest and transport costs. We found that the...
Article
We address a toll pricing problem in which the objective is to minimize the number of required toll facilities in a transportation network while inducing drivers to make the most efficient collective use of the network. We formulate the problem as a mixed-integer programming model and propose a solution method using combinatorial Benders cuts. Comp...
Article
Keywords Introduction Models Pathologies Multiple Group Problems Methods See also References
Article
Keywords and Phrases Introduction Formulation Multiple Groups Methods See also References
Article
We examine a new algorithm developed by Kuzdrall and Britney [5] for locating the optimal order quantity in the presence of quantity discounts. Their algorithm, based on a model for the supplier's formulation of the price schedule, involves a regression analysis to identify the supplier's variable cost per unit and the fixed cost that the supplier...
Article
Linear programming discriminant analysis (LPDA) models are designed around a variety of objective functions, each representing a different measure of separation of the training samples by the resulting discriminant function. A separation failure is defined to be the selection of an “optimal” discriminant function which incompletely separates a pair...
Article
Recent simulation-based studies of linear programming models for discriminant analysis have used the Fisher linear discriminant function as the benchmark for parametric methods. This article reports experimental evidence which suggests that, while some linear programming models may match or even exceed the Fisher approach in classification accuracy...
Article
This paper introduces a method to increase productivity and competitiveness through an explicit formulation for sequence dependent production scheduling where the produced material will be cut into finished products. The formulation is then applied to a production scheduling problem typical of the paper industry. Results are contrasted with those p...
Article
We present a counterexample and correction to the contention by Xu and Li that the nonlinear Lagrangian dual problem they propose [Oper. Res. Lett. 30 (2002) 401] asymptotically has no duality gap.
Article
We propose a new nonparametric family of oscillation heuristics for improving linear classifiers in the two-group discriminant problem. The heuristics are motivated by the intuition that the classification accuracy of a separating hyperplane can be improved through small perturbations to its slope and position, accomplished by substituting training...
Article
The ability to determine the optimal frequencies and offsets for independent and unrestricted ordering cycles for multiple items can be very valuable for managing storage capacity constrained facilities in a supply chain. The complexity of this problem has resulted in researchers focusing on more tractable surrogate problems that are special cases...
Article
We reformulate branch-and-bound feature selection employing L<sub>∞</sub> or particular L<sub>p</sub> metrics, as mixed-integer linear programming (MILP) problems, affording convenience of widely available MILP solvers. These formulations offer direct influence over individual pairwise interclass margins, which is useful for feature selection in mu...
Article
The use of price to influence a buyer's purchasing behavior and thus improve supply chain coordination has received considerable attention. The vendor and buyer are independent economic entities, each maximizing its own profit. We consider the case of a buyer with fixed annual demand, independent of cost. The vendor's objective is to set a price sc...
Article
In this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations. The constraints take the form of upper bounds on positively weighted linear combinations of order size, dollar volume, unit price a...
Article
Full-text available
Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. This paper considers the problem of scheduling a single machine for minimizing total tardiness in a sequence dependent setup environment. The comparative performance of branch-and-bou...
Article
Soltysik and Yarnold propose, as a method for two-group multivariate optimal discriminant analysis (MultiODA), selecting a linear discriminant function based on an algorithm by Warmack and Gonzalez. An important assumption underlying the Warmack–Gonzalez algorithm is likely to be violated when the data in the discriminant training samples are discr...
Article
Research into the accuracy of mixed integer programming models for discrimination and classification, and the efficacy of heuristics developed for them, has been hampered by the inability to solve to optimality problems with moderate to large sample sizes. We present encouraging preliminary results for a decomposition approach that allows solution...
Article
Work on scheduling in the presence of squence dependent setup times has generally focused on minimizing the total setup time (or cost) or minimizing the makespan of a set of jobs. We explore the problem of sequencing to minimize the total tardiness of a set of jobs in a single-stage process where setup times are sequence dependent. In particular, w...
Article
In this article we investigate situations where the buyer is offered discounted price schedules from alternative vendors. Given various discount schedules, the buyer must make the best buying decision under a variety of constraints, such as limited storage space and restricted inventory budgets. Solutions to this problem can be utilized by the buye...
Article
In this article we investigate situations where the buyer is offered discounted price schedules from alternative vendors. Given various discount schedules, the buyer must make the best buying decision under a variety of constraints, such as limited storage space and restricted inventory budgets. Solutions to this problem can be utilized by the buye...
Article
The relationship between supplier and customer in the United States is gradually changing from adversarial to cooperative. The potential benefits of collaborative negotiation typically have been developed only in highly specialized or unique operating situations. This article demonstrates the general superiority of cooperative negotiation, from the...
Article
Mixed-integer programming models for the two-group discriminant problem appear to be more promising, in terms of accuracy, than are linear programming models, but at a substantial computational cost. This paper poses a particular mixed-integer model and suggests heuristics, based on linear programming, for obtaining suboptimal but “good” solutions...
Article
The ‘maximize minimum distance’ (MMD) linear programming model for the two group discriminant problem has been noted to produce occasionally a trivial (identically zero) discriminant function, one which classifies all observations into a single category. In tests against other methods, both parametric and nonparametric, MMD has fared poorly. In thi...
Article
Using an interrupted time series design, this paper examined long-term changes in the magnitude and trend of productivity following the introduction of nonmanagerial incentive payment. Analyses of three 114-month data series from a unionized iron foundry revealed a strong asymptotic increase in productivity without corresponding increases in labor...
Article
An alternative to using acceptance-rejection methods to generate a sample of points distributed uniformly over a region is to employ a random walk over that region. The sequence of points generated by a random walk has been shown, under certain easily satisfied conditions, to be a realization of a vector-valued discrete parameter Markov process, an...
Article
This paper proposes a new approach to formulating fuzzy priorities in a goal programming problem. The proposed methodology remedies certain shortcomings of the composite membership function approach discussed in previous works [7, 10]. The principal advantage of the proposed method is that it leads to a formulation in which tradeoffs between goals...
Article
An algorithm is presented for generating pseudorandom variates distributed uniformly over an arbitrary convex polytope in a Euclidean space of arbitrary dimension. Many commonly used methods for generating uniform variates require that the polytope be expressed as the solution set of a system of linear inequalities; the algorithm presented here req...
Article
This paper discusses the implementation of an algorithm due to Sreedharan [8] for the minimization, subject to linear constraints, of an objective function composed of the sum of a piecewise-affine, convex function with a smooth, strictly convex function. Successful techniques for two subproblems arising in the algorithm, a projection problem and a...
Article
A proposed characterization of the set of reciprocal fuzzy relation matrices is shown to be incorrect, and the correct dimension of the set is computed.

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Projects (3)
Project
Find a minimal set of locations for traffic sensors (counting vehicles) to ensure full knowledge of the traffic volume on a road network. Sensors are deployed at nodes (not on arcs), and there is an assumption that the "turning ratios" for all arcs are known in advance.
Project
Develop an optimization model for allocating patients to primary care providers (spanning multiple practice locations) to level the loads on the providers.