Florida International University FIU Digital Commons FIU Electronic Theses and Dissertations University Graduate School 3-25-2010 Branch and Price Solution Approach for Order Acceptance and Capacity Planning in Make-to- Order Operations Siddharth D. Mestry Florida International University, [email protected] Martha A. Centeno Florida International University, [email protected] Jose A. Faria Florida International University, [email protected] Purushothaman Damodaran Northern Illinois University, [email protected] Chen Chin-Sheng Florida International University, [email protected] Follow this and additional works at: http://digitalcommons.fiu.edu/etd Recommended Citation Mestry, Siddharth D.; Centeno, Martha A.; Faria, Jose A.; Damodaran, Purushothaman; and Chin-Sheng, Chen, "Branch and Price Solution Approach for Order Acceptance and Capacity Planning in Make-to-Order Operations" (2010). FIU Electronic Theses and Dissertations. Paper 145. http://digitalcommons.fiu.edu/etd/145 This work is brought to you for free and open access by the University Graduate School at FIU Digital Commons. It has been accepted for inclusion in FIU Electronic Theses and Dissertations by an authorized administrator of FIU Digital Commons. For more information, please contact [email protected]. FLORIDA INTERNATIONAL UNIVERSITY Miami, Florida BRANCH AND PRICE SOLUTION APPROACH FOR ORDER ACCEPTANCE AND CAPACITY PLANNING IN MAKE-TO-ORDER OPERATIONS A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in INDUSTRIAL AND SYSTEMS ENGINEERING by Siddharth D. Mestry 2010 To: Dean Amir Mirmiran College of Engineering and Computing This dissertation, written by Siddharth D. Mestry, and entitled Branch and Price Solution Approach for Order Acceptance and Capacity Planning in Make-to-Order Operations, having been approved in respect to style and intellectual content, is referred to you for judgment. We have read this dissertation and recommend that it be approved. _______________________________________ Martha A. Centeno _______________________________________ José A. Faria _______________________________________ Purushothaman Damodaran, Co-Major Professor _______________________________________ Chin-Sheng Chen, Co-Major Professor Date of Defense: March 25, 2010 The dissertation of Siddharth D. Mestry is approved. _______________________________________ Dean Amir Mirmiran College of Engineering and Computing _______________________________________ Interim Dean Kevin O’Shea University Graduate School Florida International University, 2010 ii © Copyright 2010 by Siddharth D. Mestry All rights reserved iii DEDICATION I dedicate this dissertation to my wife Vrunda and to my parents for their tremendous patience and understanding. Without their support, the completion of this work would not have been possible. And, to my son Arav for giving me the strength to push myself to the limits of my capabilities and potential, to help me see the light at the end of the tunnel, to believe in the future with all our dreams fulfilled. iv ACKNOWLEDGMENTS I am greatly indebted to Dr. Purush Damodaran for being an excellent academic advisor, and a tremendous mentor. He has not only helped me in my scholastic pursuits but has also given me valuable guidance in personal matters. I owe him this dissertation and much more. I would like to thank Dr. Chin-Sheng Chen for the confidence he showed in my capabilities, for his practical insights and for sharing his limitless knowledge with me. I will forever remember the discussions which we had in his office. A special thanks to Dr. Martha Centeno for being an excellent teacher and for inculcating in me the qualities to be one. I appreciate Dr. Jose Faria’s valuable inputs in improving this Dissertation. v ABSTRACT OF THE DISSERTATION BRANCH AND PRICE SOLUTION APPROACH FOR ORDER ACCEPTANCE AND CAPACITY PLANNING IN MAKE-TO-ORDER OPERATIONS by Siddharth D. Mestry Florida International University, 2009 Miami, Florida Professor Chin-Sheng Chen, Co-Major Professor Professor Purushothaman Damodaran, Co-Major Professor The increasing emphasis on mass customization, shortened product lifecycles, synchronized supply chains, when coupled with advances in information system, is driving most firms towards make-to-order (MTO) operations. Increasing global competition, lower profit margins, and higher customer expectations force the MTO firms to plan its capacity by managing the effective demand. The goal of this research was to maximize the operational profits of a make-to-order operation by selectively accepting incoming customer orders and simultaneously allocating capacity for them at the sales stage. For integrating the two decisions, a Mixed-Integer Linear Program (MILP) was formulated which can aid an operations manager in an MTO environment to select a set of potential customer orders such that all the selected orders are fulfilled by their deadline. The proposed model combines order acceptance/rejection decision with detailed scheduling. Experiments with the formulation indicate that for larger problem sizes, the computational time required to determine an optimal solution is prohibitive. This vi formulation inherits a block diagonal structure, and can be decomposed into one or more sub-problems (i.e. one sub-problem for each customer order) and a master problem by applying Dantzig-Wolfe’s decomposition principles. To efficiently solve the original MILP, an exact Branch-and-Price algorithm was successfully developed. Various approximation algorithms were developed to further improve the runtime. Experiments conducted unequivocally show the efficiency of these algorithms compared to a commercial optimization solver. The existing literature addresses the static order acceptance problem for a single machine environment having regular capacity with an objective to maximize profits and a penalty for tardiness. This dissertation has solved the order acceptance and capacity planning problem for a job shop environment with multiple resources. Both regular and overtime resources is considered. The Branch-and-Price algorithms developed in this dissertation are faster and can be incorporated in a decision support system which can be used on a daily basis to help make intelligent decisions in a MTO operation. vii TABLE OF CONTENTS CHAPTER PAGE 1. INTRODUCTION .......................................................................................................... 1 1.1. Background ............................................................................................................. 1 1.2. Research Problem.................................................................................................... 6 1.3. Research Objective.................................................................................................. 7 1.4. Significance of the Research Problem .................................................................. 10 1.5. Dissertation Structure ............................................................................................ 11 2. LITERATURE REVIEW ............................................................................................. 12 2.1. Order acceptance with dynamic arrivals ............................................................... 12 2.2. Order acceptance with static arrivals .................................................................... 17 2.3. Applications of column generation in scheduling ................................................. 19 2.4. Summary ............................................................................................................... 19 3. MATHEMATICAL FORMULATION ........................................................................ 21 3.1. Problem characteristics ......................................................................................... 21 3.2. Assumptions .......................................................................................................... 22 3.3. Mathematical model .............................................................................................. 22 3.4. “What-if” scenario analysis using the MTO formulation ..................................... 27 3.5. Computational runtime analysis ............................................................................ 34 4. BRANCH AND PRICE ALGORITHM ....................................................................... 38 4.1. Theory of Branch-and-Price Algorithm ................................................................ 38 4.2. Decomposition of the MTO model ....................................................................... 45 4.3. Solution approach for solving sub-problem .......................................................... 46 4.4. Greedy heuristic for initial solution to RMP ......................................................... 54 4.5. Branching in Branch and Price algorithm ............................................................. 55 4.5.1. Definition of an integer feasible solution to RMP ...................................... 55 4.5.2. Branching strategies .................................................................................... 58 4.5.3. Lagrangian bounds ...................................................................................... 61 4.5.4. Node Selection ............................................................................................ 63 4.6. Experimentation .................................................................................................... 64