INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. Hie quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough,margim, substandard and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Com pany 300 North 2eeb Road Ann Arbor. Ml 48106-1346 USA 313' 761-4700 800/521-0600 Order N u m b e r 9411996 Solving large scale location-spatial interaction models for retail analysis: A GIS-supported heuristic approach Lao, Yong, Ph.D. The Ohio State University, 1993 UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 SOLVING LARGE SCALE LOCATION-SPATIAL INTERACTION MODELS FOR RETAIL ANALYSIS: A GIS-SUPPORTED HEURISTIC APPROACH DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Yong Lao, B.A., M.A. The Ohio State University 1993 Dissertation Committee; Approved by M.E. 0'Kelly D.F. Marble & t Adviser L . A. Brown Department of Geography To My Family ii ACKNOWLEDGMENTS I would like to express my sincere appreciation to Dr. Morton O'Kelly for his advice and guidance throughout the dissertation research. His encouragement and support during my years of graduate study at Ohio State have been, and will continue to be my inspiration to work happier and harder. I am also deeply grateful to Dr. Duane Marble, who is always a source of valuable stimulations and insights. A special thank goes to Dr. Lawrence Brown for his great enthusiasm, help, and trust for my career development. The summer internship offered by ESRI is gratefully acknowledged. I am especially indebted with Dr. Jay Sandhu for his unfailing support during my work at ESRI. Thanks are also due to Mr. Paul Galimore and Mr. Xiaobo Zhang for their very useful suggestions on my Arc/Info work. To ny best friends, Zaiyong Gou, Lin Liu, Qin Tang, Deming Xiong, and Ling Li, words would never be enough to express my gratitude for your endless support of my professional pursuit, and for your everyday kindness and understanding. Finally, I dedicate this dissertation to my parents, Lao Keying and Liang Yan, my sister, Lao Jia, and ny uncle Lee Chu Hing, who are forever behind me with their love and trust. iii VITA February 8, 1967 ......... Born - Kunming, P. R. China 1984-1987 ................... Beijing University, Beijing, P. R. China 1988 .......................B.A., The Ohio State University, Columbus, Ohio 1990 ....................... M.A., The Ohio State University, Columbus, Ohio 1988-1993 ................... Teaching Associate, Department of Geography, The Ohio State University PUBLICATION 1991. M.E. O'Kelly and Y. Lao, "Mode choice in a hub-and- spoke network: a zero-one linear programming approach". Geographical Analysis. Vol.23, No.4, pp.283-297. FIELDS OF STUDY Major Field: Geography Studies in Location Analysis, Quantitative Methods, with Morton O'Kelly; Geographic Information Systems, with Duane Marble. iv TABLE OF CONTENTS DEDICATION ........................................ ii ACKNOWLEDGEMENTS.....................................iii VITA .............................................. iv LIST OF T A B L E S .................................. viii LIST OF FIGURES .................................. x LIST OF PLATES ...................................... xii INTRODUCTION............................ 1 CHAPTER PAGE I. INTRODUCTION .................................. 1 1.1 Problem Statement ........................ 1 1.2 Background of Research... ................. 2 1.2.1 Linking Location Allocation and Spatial Interaction ............... 3 1.2.2 Using Heuristic Algorithms ......... 5 1.2.3 Combining Location Analysis with GIS . 7 1.3 Research Organization .................... 8 II. LITERATURE R E V I E W ............................. 13 2.1 Introduction............................ 13 2.2 Location-Spatial Interaction (LSI) Models . 16 2.2.1 Spatial Interaction Based Allocation . 16 2.2.2 The LSI M o d e l s ................ 20 the cost minimizing approach . 21 the benefits maximizing approach . 23 the entropy maximizing approach . 25 2.2.3 Summary of LSI M o d e l i n g ...... 28 2.3 Heuristic Approaches toLocation-Allocation M o d e l i n g ................................ 29 2.3.1 General Heuristic Methods in Location Analysis ................. 30 2.3.2 New Heuristic Approaches ......... 35 2.3.3 The Evaluation of Heuristic Methods . 42 v 2.3.4 Summary of Heuristic Approaches . 43 2.4 GIS Supported Visual Interactive Modeling . 44 2.4.1 Interactive Visualization ......... 46 2.4.2 Interactive Optimization ........... 50 2.4.3 GIS Supported Visual Interactive Modeling........................... 51 2.4.4 Summary of GIS Supported Visual Interactive Modeling ........ .... 54 2.5 Summary and C o n c l u s i o n .................... 55 III. MODEL DEVELOPMENT AND SOLUTION PROCEDURE ........ 57 3.1 Introduction.............................. 57 3.2 Model Development .......................... 57 3.2.1 Model A s s u m p t i o n s ................. 57 3.2.2 Model Formulation ................. 60 3.2.3 Model Complexity................... 65 3.3 Solution Strategies ........................ 66 3.3.1 Initialization..................... 69 random start ................... 69 interactive start ............. 70 the greedy heuristic ............ 71 the voting heuristic ........... 74 3.3.2 Search............................. 84 the vertex substitution method . 85 tabu s e a r c h ..................... 87 the hashing s t r a t e g y ............ 92 3.3.3 Evaluation and Improvement......... 96 lagrangian relaxation and subgradient search ............. 96 interactive evaluation .......... 101 3.4 Summary and C o n c l u s i o n ...................... 103 IV. DESIGN AND IMPLEMENTATION OF THE GIS PROTOTYPE . 105 4.1 Introduction............................ 105 4.2 System Design ............................... 107 4.2.1 Data Requirement..................... 108 4.2.2 Functional Requirement........... Ill 4.2.3 User Interface D e s i g n ............... 113 4.3 System Inplementation....................... 120 4.3.1 Database Construction ............. 120 4.3.2 The Menu Structure................... 125 4.3.3 Integration of Arc/Info and LSI M o d e l ............................133 4.4 Summary and Conclusion ...................... 146 V. R E S U L T S ..................................... 148 5.1 Introduction................................ 148 5.2 Solution Quality ........................ 149 vi 5.2.1 Problem Desi g n ....................... 149 5.2.2 The Primal Versus the D u a l ....... 150 5.3 Solution Dynamics...................... 155 5.3.1 The Average Trip L e n g t h .......... 156 5.3.2 The Cost Effectiveness............ 160 5.3.3 The Location and Spatial Interaction Pattern ............. 162 5.4 Computational Experience ............... 172 5.4.1 Run Time A n a l y s i s ................ 172 5.4.2 The Memory Requirement............ 179 5.5 Summary and C o n c l u s i o n ..................... 181 VI. CONCLUSION.......................................184 6.1 Research S u m m a r y ...........................184 6.2 Contributions.............................. 192 6.3 Directions for Further Research ............ 194 6.3.1 Vertical Development............. 195 6.3.2 Horizonal Devel o p m e n t........... 199 BIBLIOGRAPHY ...................................... 202 vii LIST OF TABLES PAGE Major Survey Articles on Location Analysis 14 Published Books on Location Analysis . 15 An Example of the Allocation Table ....... 41 Data of the Sample Network ............... 68 The Initial Solution Using Random Start . 69 The Initial Solution Using Interactive Start 71 The Result of Using Step One of Greedy Add 72 The Result of Using Step Two of Greedy Add 73 The Node Centrality Index of the Sample Network .................................. 76 The Result of Applying Voting Rule Two to the Sample Network ....................... 77 The Accessibility Index of the Sample Network 77 The Voting Process of Rule Number Three . 80 Comparison of Initialization Strategies . 82 The Degree of Cut Provided by Different Tabu Strategies ........................... 91 The Hash Table for the Sample Problem . 95 Functional Process within the Modeling Module 118 The Coverage and Info Files for the City of Redlands ..................... 124 The Menu Structure of GRALSIM ............. 126 Solutions of the First Set LSI Problem . 151