Discrete sequential search with group activities

Decision Sciences, Fall 2001 by Wagner, Bret J, Davis, Darwin J

Discrete Sequential Search with Group Activities*

ABSTRACT

Equipment failures can have significant implications in terms of cost and customer satisfaction. Reducing the time required to find the cause of a failure can provide large cost savings and help preserve customer goodwill. Single-item discrete sequential search models can be used to sequence the tasks in diagnostic search to minimize the expected time required to find the cause of the failure. We increase the utility of the single-item discrete sequential search model by developing a formulation that includes simple precedence relationships as well as sequence dependent relationships defined by group activities. This formulation can be applied to a number of other problems including determining the sequence for multiple quality control tests on an item, scheduling oil well workovers to maximize the expected increase in oil production, and sequencing tasks in a research project where there is a technological risk associated with each task.

Subject Areas: Integer/Binary Program, Linear Programming, and Search Theory.

INTRODUCTION

Equipment failures can have significant implications in terms of cost and customer service. For example, an electrical generator failure can cost as much as $15,000 per hour of downtime (Sweetser, 1998), and if the failure occurs during a peak demand period, it could lead to rolling blackouts that may have tremendous public relations impact. Similarly, in the transportation industry, failure of the transportation system (planes, trains, subways, cruise ships, etc.) can have significant impacts on large numbers of passengers. For example, a delayed flight early in the day can cause delays in all later flights that the plane is scheduled to service.

The time spent to determine the cause of a machine or system failure can be a significant portion of the total downtime. Because of the specialized and technical nature of machines and systems, maintenance personnel may determine the diagnostic sequence using judgment and intuition, producing sequences that may not have the shortest expected diagnostic time. In this paper, we extend the discrete sequential search problem to include sequence-dependent considerations so that it can be employed in a wider variety of diagnostic problems.

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Bret J. Wagner

Department of Management, Haworth College of Business, Western Michigan University, Kalamazoo, MI 49008-3806, email: bret.wagner@wmich.edu

Darwin J. Davis

Department of Business Administration, College of Business and Economics, University of Delaware, Newark, DE 19716-2710

* The authors would like to thank Dena Porter and Phil D'Eon of Casebank Technologies for providing the throttle stagger problem and for their support in the development of this manuscript.

Bret J. Wagner is an assistant professor in the Management Department at Western Michigan University. He received a BS in mechanical engineering from Michigan State University, a Master of Engineering Administration from George Washington University, and a PhD in operations management from Michigan State University. He has published papers in the Journal of Operations Management, European Journal of Operational Research, and Annals of Operations Research. His research interests include production planning and scheduling and simulation.

Darwin J. Davis is an assistant professor of operations management in the Department of Business Administration at the University of Delaware. He received a BA in mathematics from Utah State University, an MBA from the University of Delaware, and a PhD in operations management from Indiana University. He has published papers in Decision Sciences, European Journal of Operational Research, and Journal of Quality Technology. His research interests include cellular manufacturing, dual resource constrained systems, scheduling, quality, and mathematical programming.