Jeff Goldberg

A Hamiltonian path approach to reordering the part-machine matrix for cellular manufacturing

The formation of machine and part groups is a central issue in the design of cellular manufacturing systems. The part-machine incidence matrix has formed the basis of several techniques for cell formation. In this paper, we propose formulating machine and part ordering as a Hamiltonian Path Problem. Similarity coefficients are used to form a distance measure for machines and parts. The resulting solutions are shown to be better than those obtained from binary clustering on a set of test problems.

Validating and applying a model for locating emergency medical vehicles in Tuczon, AZ

Abstract This paper deals with the problem of locating emergency medical vehicles in Tuczon, AZ. The model is based on a general service time approximation model for spatially distributed queueing systems. Provisions for unequal vehicle utilizations, stochastic travel times, and multiple call classes are included. The model is tailored for emergency medical systems that experience low vehicle utilizations. Validation of the model using the Tucson system is discussed in detail. The predictive ability of the model is demonstrated by comparing model output with actual system data. The model has been used to evaluate potential changes in the paramedic services provided by the Tucson Emergency Medical System and two cases are discussed.

Locating Emergency Vehicle Bases When Service Time Depends on Call Location

This paper deals with the problem of locating emergency vehicles in an urban area. We formulate an optimization model that extends previous work by allowing stochastic travel times, unequal vehicle utilizations, various call types, and service times that depend on call location. The basis of the model is a procedure for approximating the performance of spatially distributed queueing systems. In previous work the model has been validated using data from the Tucson Emergency Medical Services (EMS). We test the computational effectiveness of pairwise interchange heuristics on 192 test problems. Demand and service time components of the test data are generated using characteristics of the Tucson data set. For these test problems, simple pairwise interchange techniques yield reasonable solutions with little computational effort. Also, solutions obtained from the model differ from those generated using methods previously presented in the literature.

DETERMINING THE NUMBER OF KANBANS IN MULTI-ITEM JUST-IN-TIME SYSTEMS

Kanbans (cards) are one means of controlling just-in-time production systems. The Kanbans serve as production authorization orders and essentially become the information system. The presence of a production ordering Kanban for a specific part type constitutes an instruction to the workcenter to produce a “container” of that part. In this chapter we assume workcenters produce multiple part types and address the issue of the number of Kanbans needed for each part type. Our objective is to minimize the sum of inventory holding and backorder cost. A stochastic model is formulated. Steady-state results are derived for several operating environments and results and validated by simulation.

Methods for solving nonlinear equations used in evaluating emergency vehicle busy probabilities

In this paper we present two iterative methods for solving a model to evaluate busy probabilities for Emergency Medical Service (EMS) vehicles. The model considers location dependent service times and is an alternative to the mean service calibration method; a procedure, used with the Hypercube Model, to accommodate travel times and location-dependent service times. We use monotonicity arguments to prove that one iterative method always converges to a solution. A large computational experiment suggests that both methods work satisfactorily in EMS systems with low ambulance busy probabilities and the method that always converges to a solution performs significantly better in EMS systems with high busy probabilities.

A note on the effect of neighborhood structure in simulated annealing

Abstract The simulated annealing method is a neighborhood search algorithm that can be used as a heuristic for many combinatorial problems. Recent research has concentrated on the viability of the approach and the appropriate algorithm parameter settings to use in implementation. In this note we consider a problem specific parameter; the neighborhood structure. We motivate the importance of considering the neighborhood by appealing to results on the convergence rate of simulated annealing and previous empirical results. We test several neighborhood structures on four different problems: the traveling salesman problem, the quadratic assignment problem, the quadratic selection problem and the stochastic quadratic selection problem. Our results suggest that for these problem classes and the particular annealing schedule used, small neighborhoods are better.

Module design with substitute parts and multiple vendors

Abstract In this paper, we present a model to design a single standard module when many parts can satisfy a particular technical requirement and parts may be purchased from a variety of vendors. The model attempts to minimize the total fixed costs for using vendors and parts, and the total variable costs for parts. Technical requirements for the set of products are modeled by requiring a miniml number of parts from each substitution group in each product. Also, life cycle demand must be met. We present an algorithm and a heuristic to solve the model. We include initial computational results that demonstrate that the heuristic performs well on the problems tested.

ECONOMIC OPTIMIZATION IN PRODUCT DESIGN

Worldwide competition and rapid technological innovation have revitalized interest in efficient techniques for product design for quality and manufacturability. The Japanese approach, popularized by G. Taguchi, uses outcomes of statistical experiments to select settings for design parameters which yield desirable process mean and variance. In this paper we present mathematical models for incorporating the results of statistical performance models along with production costs into product design models. The objective of the models is to minimize the sum of quality loss, material and production costs. Costs are assumed to be functions of the design parameters. Statistical experiments are employed to aid in the development of quality performance models. Pertinent constraints include limits on the bias of the process mean and variance. The proposed approach permits a more general environment and utilizes a more direct, economic objective as compared to the Taguchi method. A product design example is presented.

Technical Note—A Polynomial Algorithm for the Equal Capacity p-Center Problem on Trees

The uncapacitated p -center problem has been shown to be NP-Hard for the case of a general network, yet polynomial algorithms exist for the case of a tree network. We extend the results for trees to include the case where each center can serve a limited number of customers and show that the capacitated p -center problem on trees can be solved in polynomial time when the capacities are identical. The algorithm consists of solving a capacitated covering problem and then using search routines to find the optimal domination radius. We show that the addition of center capacities to either the vertex center problem or the absolute center problem requires a multiplicative factor of O ( n ) more work, relative to that required for the uncapacitated problems, to solve the related covering problems ( n is the number of vertices in the tree).

Using student conative behaviors and technical skills to form effective project teams

Throughout much of the past century, manufacturing efficiencies were gained by constructing systems from independently designed and optimized tasks. Theories and practice have extolled the virtues of team-based practices that rely on human flexibility and empowerment to improve system performance. The formation of teams requires the consideration of innate tendencies and interpersonal skills as well as technical skills. In this paper, we discuss an experiment that was run for developing effective student teams. We used the Kolbe Index to help ensure that student conative tendencies are considered along with technical skills. We then developed and solved mathematical programming models to form effective teams. The method can easily be moved to an industrial setting.