Logistics of Facility Location and Allocation

LOGISTICS OF

FACILITY LOCATION

AND ALLOCATION

INDUSTRIAL ENGINEERING

A Series of Reference Books and Textbooks

1. Optimization Algorithms for Networks and Graphs, Edward Minieka

2. Operations Research Support Methodology, edited by Albert G.

Holzman

3. MOST Work Measurement Systems, Kjell B. Zandin

4. Optimization of Systems Reliability, Frank A. Tillman, Ching-Lai

Hwang, and Way Kuo

5. Managing Work-In-Process Inventory, Kenneth Kivenko

6. Mathematical Programming for Operations Researchers and Com￾puter Scientists, edited by Albert G. Holzman

7. Practical Quality Management in the Chemical Process Industry,

Morion E. Bader

8. Quality Assurance in Research and Development, George W.

Roberts

9. Computer-Aided Facilities Planning, H. Lee Hales

10. Quality Control, Reliability, and Engineering Design, BalbirS. Dhillon

11. Engineering Maintenance Management, Benjamin W. Niebel

12. Manufacturing Planning: Key to Improving Industrial Productivity,

Kelvin F. Cross

13. Microcomputer-Aided Maintenance Management, Kishan Bagadia

14. Integrating Productivity and Quality Management, Johnson Aimie

Edosomwan

15. Materials Handling, Robert M. Eastman

16. In-Process Quality Control for Manufacturing, William E. Barkman

17. MOST Work Measurement Systems: Second Edition, Revised and

Expanded, Kjell B. Zandin

18. Engineering Maintenance Management: Second Edition, Revised and

Expanded, Benjamin W. Niebel

19. Integrating Productivity and Quality Management: Second Edition, Re￾vised and Expanded, Johnson Aimie Edosomwan

20. Mathematical Programming for Industrial Engineers, edited by Morde￾cai Avriel and Boaz Go/any

21. Logistics of Facility Location and Allocation, D/7eep R. Sule

LOGISTICS OF

FACILITY LOCATION

AND ALLOCATION

DILEEP R. SUL

Louisiana Tech University

Ruston, Louisiana

MARCEL DEKKER, INC. NEW YORK • BASEL

ISBN: 0-8247-0493-2

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Preface

Facility location has long been a subject of interest among industrial engineers,

transportation engineers, management scientists, operations researchers, and

logistics personnel. Major contributors to the field have come from many sources,

but perhaps the largest single source has been well-trained mathematicians. As

such, most of the facility location research published in journals and books has

been mathematical in nature. Although the theorems and proofs that go along

with this research are very important for analyzing the subject matter, the

associated derivations and mathematical rigor can be intimidating to practicing

engineers and business executives. And the same is true with most undergraduate

and first-year graduate students, who may not be so mathematically inclined. Yet

facility location is an important subject with numerous practical applications, and

a happy medium must thus be found between theory and practice. Procedures that

can be easily understood have a higher probability of being used in real life.

This book outlines such procedures for various location and allocation

objectives. To facilitate understanding of concepts, each procedure is illustrated

by a problem and its solution. However, this is not a cookbook. There are

mathematical and logical foundations for the methods; these become apparent as

one follows the necessary steps of the procedures. The idea is to take out the

needless complexity and convey the solution procedure through simple steps. It is

helpful, but not necessary, for the reader to have had one course in operations

research. Many models are formulated as linear programming (LP) models to

illustrate the mathematical structure, but are solved by simpler, alternative

methods. For those with access to a computer program to solve LP problems,

the formulations may be used to verify the results obtained by these alternative

methods. Operations research techniques using the branch-and-bound algorithm,

iii

iv Preface

transportation algorithm, assignment algorithm, and dynamic programming are

illustrated before being used in location models.

The book is designed to cover most of the broad topics in location analysis

and can be used as a textbook as well as a reference book. The course can be a

one-semester course for advance undergraduate or early graduate students in

industrial engineering, management science, transportation science, logistics,

systems engineering, or related fields. The content of the book includes models

in which facilities may be placed anywhere in the plane (continuous location

theory), at some discrete locations (discrete models), or on a network (network

analysis).

The text has 12 chapters. The first is an introductory chapter; it also

presents an elementary but popular ranking method for location selection.

Chapter 2 presents some of the recent applications of fuzzy logic and the

analytical hierarchy procedure (AHP) in location selection. Some of these

procedures are long, but they can be computerized once the fundamentals are

understood.

Chapters 3 and 4 are associated with continuous location problems for a

single facility. A facility can be located to optimize the number of different

objectives; the optimal location in each case may not be the same. Chapter 3

addresses the objective of minimizing the travel cost, called the minisum

problem. Based on the mathematical expression for travel cost, a number of

different procedures are applicable. Chapter 4 incorporates objectives such as

minimizing the maximum distance, the circle covering problem, working with an

undesirable facility location, and linear path facility development.

Chapter 5 addresses placement of multiple facilities in a continuous

location problem. Unfortunately, it is not a direct extension of a single facility

location problem and requires some effort. This chapter also discusses the

machine layout models for efficient material flow analysis.

Chapter 6 is a basic location-allocation model that initiates discrete

location analysis. The objective is to select from among the known locations

the required number of locations to place facilities, and then allocate customers to

receive service from one of these facilities to minimize cost.

Chapter 7 describes facility location in network-based problems. These

problems are typical in transportation planning and other such applications in

which travel is permitted only by a path represented on the network. The chapter

describes, for example, where to place a competitive facility or how to develop a

transportation hub.

Chapter 8 describes the procedures in tour development. In many instances

the objective is to develop efficient routes for deliveries and collections of

customer orders. This is a logistical problem of connecting different customers

in sequence to minimize transportation cost. The procedures illustrated in this

chapter accommodate many different modes of operation.

Preface v

Chapter 9 deals with data changes due to such factors as shifts in demand

pattern or foreseen changes in the use of the facilities. Changes are time￾dependent; we often have to decide the initial location of the facility, and

then when and where to move the facility to respond to changing costs and

demands.

Chapter 10 addresses simultaneous facility location or, as popularly called

in the literature, a quadratic assignment problem. Besides the well-known branch￾and-bound procedure, a few easy-to-apply heuristics are explained that lead to a

good, often optimal, solution.

Chapter 11 introduces transportation network-related problems, as it

mainly applies the transportation algorithm to minimize nonlinear transportation

costs as well as the maximum response time from a source to a destination in a

transportation network.

Chapter 12 describes new location-allocation modes in a production

environment. It describes which locations to select if there is a fixed cost for a

location, if the cost of production varies from location to location, or if there is an

advantage associated with a large-scale production at one place. It also discusses

the machine or facility capacity selection procedure based on the various costs

associated with machines of different capacity. It is an interesting chapter, and

although the procedures seem lengthy at first glance, they can be easily grasped if

the example solutions are followed.

An instructor should have no problem in developing a facility location

course by selecting appropriate chapters that he or she feels are suitable for the

class. Chapters 1,2,7, and 11 are independent and require no previously acquired

information from other chapters.

Dileep R. Sule

Acknowledgments

I would like to thank a number of students in my facilities location class who

suffered through an incomplete manuscript while it was being developed and

made some useful suggestions for improvement. My special thanks to Rahul

Joshi and Kedar Panse, who spent many days (and nights) developing some of the

topics. Their efforts are sincerely appreciated. My thanks also to Advait Damle,

Vikram Patel, and Amol Damle for proofreading the final copy.

Important suggestions were also made by Horst Eiselt, Trevor Hale, and

Vedat Verier, who served as reviewers. Although not all the suggestions could be

incorporated, the book has benefited greatly from their comments. I thank these

reviewers for their time and effort.

The staff of Marcel Dekker, Inc., especially acquisitions editor John

Corrigan and production editor Michael Deters, were very helpful in production

of the book, and I thank them for their support.

And finally, to my wife, Ulka, and my children, Sangeeta and Sandeep, my

thanks for their support during this proejct.

vii

Contents

Preface iii

Part I Introduction and Qualitative Methods

1. Introduction and the Traditional Approach 3

2. Fuzzy Logic and the Analytical Hierarchy Procedure 21

Part II Basic Quantitative Models

3. Single-Facility Minisum Location 59

4. Alternative Objectives in Single-Facility Location 91

5. Multiple Facility Location 123

6. Basic Location-Allocation Model 159

7. Network Facility Location 179

Part III Tour Development Models

8. Logistics in Tour Development 227

Part IV Additional Quantitative Models

9. Dynamic Facility Locations 283

10. Simultaneous Facility Location 323

11. Transportation Network Problems 373

12. Allocation-Selection Models in the Production Environment 397

Bibliography 447

Index 455

ix

PART I_________

Introduction and Qualitative

Methods