Michael W. Carter

Recent Developments in Practical Course Timetabling

Course timetabling is a multi-dimensional NP-Complete problem that has generated hundreds of papers and thousands of students have attempted to solve it for their own school. In this paper, we describe the major components of the course timetabling problem. We discuss some of the primary types of algorithms that have been applied to these problems. We provide a series of tables listing papers in refereed journals that have either implemented a solution or tested their algorithm on real data. We made no attempt to provide a qualitative comparison. We restricted our presentation to a description of the types of technique used and the size of problem solved We have not included commercial software vendors.

Recent Developments in Practical Examination Timetabling

In 1986, Carter published a survey of papers on practical examination timetabling, in the intervening years, there have been a number of new applications, and several innovative techniques have been attempted. In this paper, we will classify the algorithms, discuss their reported results and try to draw some conclusions on the state of the art. We have not attempted to perform any experimental comparisons on the different methods.

A goal programming approach to strategic resource allocation in acute care hospitals

Abstract This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Torontos Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.

The hot strip mill production scheduling problem: A tabu search approach

Abstract The Hot Strip Mill Production Scheduling Problem is a hard problem that arises in the steel industry when scheduling steel coil production. It can be modeled as a generalization of the Prize Collecting Traveling Salesman Problem with multiple and conflicting objectives and constraints. In this paper we formulate this problem as a mathematical program and propose a heuristic method to determine good approximate solutions. The heuristic is based on Tabu Search and a new idea called “Cannibalization”. Computational results on production data from Dofasco are presented and analyzed. Comparison with actual production schedules indicates that the proposed method could produce significantly better schedules.

Scheduling emergency room physicians.

This paper introduces the problem of scheduling emergency room physicians. We interviewed physicians from six hospitals in the greater Montreal, Canada area, in order to understand the emergency room scheduling problem. Extracting the real scheduling problem is difficult because physician working conditions are based on informal mutual cooperation which is usually not documented. We present the characteristics of the scheduling problem and the scheduling techniques currently used in the six emergency rooms we analyzed. Using the scheduling problems of Charles-Lemoyne Hospital and the Jewish General Hospital, we show how to modify a hospitals existing scheduling rules to develop techniques which produce better schedules and reduce the time needed to build them.

A nonlinear optimization approach for solving facility layout problems

Abstract Facility layout research has many subproblems for which optimization models can be developed. Although modeling these problems is often simple, the resulting large size of these models can make solution by decision makers very difficult. This paper is concerned with the development of new heuristics to be used as aids in finding good solutions to the facility layout problem. In particular, nonlinear programming (NLP) techniques are developed that minimize the material handling cost. Descriptions of the problems to be solved are presented along with the formulations of the NLP models to be optimized and the methods used to solve them. Also presented are computational results and a comparison of these results to those of other layout algorithms. The heuristics developed are shown to produce solutions comparable to, and in many cases better than, those of other algorithms. The approach is particularly effective for problems with unequal-size departments. As well, the models are shown to be computationally practical for solving real-world problems.

When is the classroom assignment problem hard

The classroom assignment (or hotel room or interval scheduling) problem is to assign classes, which meet at different time intervals, to rooms. Two classes may not meet simultaneously in the same room, nor may a class meet in two different rooms. Thousands of colleges and secondary schools face this problem every semester. There has been some confusion as to how hard this problem is. Many colleges claim that it is easy, while others complain that it is next to impossible. In the literature, some authors claim or conjecture polynomial time algorithms, while others develop heuristic approaches. The goal of this paper is to resolve the confusion by identifying cases where the problem will be easy and others where it will be hard. We focus on the kinds of cases that schedulers are apt to encounter in practice.

An Analysis Of Emergency Room Wait Time Issues Via Computer Simulation

AbstractThis paper describes a study undertaken at the Children’s Hospital of Eastern Ontario to quantify issues surrounding the delivery of primary care through the hospital’s emergency room. The project centres on a discrete event simulation model of the emergency room used to investigate issues contributing to wait time. Results indicate that patient wait time is affected by the availability of staff physicians and the amount of time physicians are required to spend engaged in the education of medical residents. Based on the recommendations of the study, the hospital’s administration has implemented a fast track facility for treating patients with minor injuries and has increased the number of physician hours in the emergency room.

The indefinite zero-one quadratic problem

Abstract A method is described for transforming an indefinite 0–1 quadratic programming problem into an equivalent positive definite problem of precisely the same size. Several variations of the basic transformation are incorporated in a branch and bound algorithm. This technique is combined with a system of analytical bounds on the variables. Computational results on several hundred random test problems with up to 30 variables demonstrate that the (polynomial bounded) transformation together with the bounds are sufficient to solve many large indefinite problems.

Tutorial on constructing a red blood cell inventory management system with two demand rates

Abstract Many countries face the situation where demand for blood products is growing faster than donor recruitment, so the efficient management of available blood supplies is of great economic and social importance. Historically, blood models dealt with two main issues—expiration of blood products with a limited shelf life vs. minimizing blood inventory shortages. Advances in blood storage technologies have resulted in extended shelf lives for some blood products, as well as the ability to use substitute, synthetic blood products at an additional cost. Moreover, prior models do not support multiple demand levels and priorities, where demand for non-urgent blood products can be restricted in event of low inventory levels. The work described in this paper revisits a queuing model and using level crossing techniques, determines an optimal policy to support modeling trade-offs between the following criteria: multiple demand levels (emergency and discretionary), service levels, costs, as well as the traditional objectives of minimizing shortages and expiration (matching supply and demand). Using simulation, the model was compared with current control techniques and demonstrated to be effective using real data obtained from Canadian Blood Services.