Mark A. McKnew

Modeling co-located servers and dispatch ties in the hypercube model

Abstract Several spatially distributed queuing models, notably the hypercube models, have been developed for emergency vehicle service systems. None of these models specifically address the issue of dispatch preference ties that is commonly encountered in systems with co-located units; e.g. ambulance systems. A variation of the hypercube model that accommodates preference ties is developed and applied to the emergency medical system of Greenville County, S.C.

An application of multiattribute utility theory to the planning of emergency medical services

This research considers the problem of relating Emergency Medical Services (EMS) to patient outcome. The hypothesis is that response time alone may be misleading as an EMS performance criterion. This research uses methods for approximating multiattribute utility functions to consider both response time and on-the-scene care. The final result is an optimization problem where the response time and desired personnel requirements are decision variables. These are important inputs in the planning for Emergency Medical Services.

A goal programming workload balancing optimization model for ambulance allocation: An application to Shanghai, P.R.China

Abstract This research develops a workload balancing model that incorporates a preference list for a fixed number of ambulance stations and simple concepts of queuing theory into a mathematical programming formulation. The workload balancing model is demonstrated on actual operating data from the Emergency Medical Service (EMS) system of Shanghai, P.R. China. Results indicate that the model is able to minimize the workload imbalance among existing stations by assigning ambulance units on the basis of demand received by each station.

A quick and effective method for capacitated lot sizing with startup and reservation costs

Abstract We present a pure zerp-one integer programming model for determining single-item production lot sizes in capacitated “long production run” environments, where each production period is dedicated to a single product, and where production of a given item may extend over more than one production period. All costs, as well as capacity, are time-varying, and include startup (changeover), reservation (opportunity), holding, and production costs. Holding and production cost may also vary within a period. The problem setting is effectively the single-item subproblem of the “multiple product cycling” case. Our a model is efficient primarily because of variable elimination strategies associated with capacity limitations. Although our formulation makes two simplifying assumptions versus previous research, these did not significantly hamper model performance. Experimentation on problems from the literature yielded a 93% optimality frequency, with less than 60 pivots required for 20 period problems, a tremendous efficiency improvement over previous models. As such, the model represents an excellent and practical first step toward efficiently solving multiple product problems on an industrial scale.

On modeling the design of cellular manufacturing systems

A new optimization model is discussed for the design of cellular manufacturing systems. It is based on an integer programming formulation that updates some other models by eliminating redundant machine assignment and cost coefficients dependent on cell configuration. To reduce computational burdens, a simplified integer programming model and a decomposition algorithm are proposed. Several computer solutions were performed to evaluate the performance of the new model. The computational results are discussed.

Partial termination rule of Lagrangian relaxation for manufacturing cell formation problems

Abstract Mathematical programming models for manufacturing cell formation problems are primarily integer programming models with the special structure of being “multidivision problems”. Lagrangian relaxation has been one of the best decomposition approaches and enabled the solution of problems of practical size. This research develops a partial termination rule for the Lagrangian relaxation algorithm. While the existing algorithm solves all submodels in each iteration, the partial termination rule recognizes early termination of some submodels. This results in a substantial reduction of computation while generating the same solution. The new termination rule is proven mathematically. Thus, its applicability extends beyond the solution of the manufacturing cell formation problem.

A simple model for predicting the number of servers necessary to cover a region

Abstract A simple regression model is developed to estimate the number of servers necessary to cover a region. Data for the model were obtained within a research design that included five replications of 180 experimental conditions. A total of 300 rectangular regions were generated, and a set covering location problem was solved for each region using three distance metrics. Statistical results established coverage radius, compactness, and the number of nodes in the region to be significant factors. The resulting regression model was applied to a South Carolina county. Its estimates are seen to be very close to the number of units needed to cover. The model is shown to be a convenient technique for quickly estimating the number of servers while exhibiting an error distribution that is conservatively biased towards overestimation. This last property is desirable for public emergency services.