Resource allocation problems in supply chains

Resource Allocation Problems in Supply Chains This page intentionally left blank Resource Allocation Problems in Supply Chains By K Ganesh McKinsey & Company, Inc., Chennai, India R A Malairajan Anna University, Tuticorin, India Sanjay Mohapatra Xavier Institute of Management, Mumbai, India M Punniyamoorthy National Institute of Technology, Tiruchirappalli, India United Kingdom À North America À Japan India À Malaysia À China Emerald Group Publishing Limited Howard House, Wagon Lane, Bingley BD16 1WA, UK First edition 2015 Copyright r 2015 Emerald Group Publishing Limited Reprints and permissions service Contact: permissions@emeraldinsight.com No part of this book may be reproduced, stored in a retrieval system, transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without either the prior written permission of the publisher or a licence permitting restricted copying issued in the UK by The Copyright Licensing Agency and in the USA by The Copyright Clearance Center Any opinions expressed in the chapters are those of the authors Whilst Emerald makes every effort to ensure the quality and accuracy of its content, Emerald makes no representation implied or otherwise, as to the chapters’ suitability and application and disclaims any warranties, express or implied, to their use British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-1-78560-399-0 ISOQAR certified Management System, awarded to Emerald for adherence to Environmental standard ISO 14001:2004 Certificate Number 1985 ISO 14001 Abstract R esource Allocation (RA) involves the distribution and utilization of available resources in the system Because resource availability is usually scarce and expensive, it becomes important to find optimal solutions to such problems Thus, RA problems represent an important class of problems faced by mathematical programmers Conventionally, such RA problems have been modeled and solved for allocation in single-echelon Supply Chain (SC), single-objective allocation, and allocation with certainty of static input data, single-performance measure driven allocation, disintegrated allocation and routing both in strategic and operational levels Such models that consider the above assumptions/constraints are nominal models and their solutions are denoted nominal solutions However, in practice, these assumptions are rarely, if ever, true, which raises questions regarding the practicability and validity of the problems and solutions obtained under these assumptions The allocation problems focusing bi- or multiple objectives, dynamic allocation bases on dynamic input data and constraints, multiple performance driven allocation and integrated allocation and routing context are complex combinatorial problems which demand high computational time and effort for deriving compromised near-optimal/optimal solutions In this research, we study RA problems involving flow of resources over a typically, large-scale multi-echelon SC network in an optimal manner This research focuses on development of models and heuristics for six new and complex sub-classes of RA problems in SC network focusing bi-objectives, dynamic input data, and multiple performance measures based allocation and integrated allocation and routing with complex constraints This study considers six set of variants of the RA problems normally encountered in practice but have not been given attention to hitherto These variants of the classical RA are complex and pertaining to both manufacturing and service industry RA variant in bi-objective capacitated SC network, RA variant in bi-objective bound driven capacitated SC network, RA variant in multiple measures driven capacitated multi echelon SC network, RA variant in integrated decision and upper bound driven capacitated multi echelon SC network, RA variant in integrated decision and time driven capacitated multi echelon SC network, RA v vi ABSTRACT variant in integrated decision, bound and time driven capacitated multi echelon SC network are the new variants proposed in this research These variants have some applications that are of special interest, including those that arise in the areas of warehousing, transportation, logistics, and distribution These application domains have important economic value, and high importance is attached to achieve efficient solutions The Non-deterministic Polynomial (NP)-hardness of these problems mandates the use of heuristics/meta-heuristics as solution methodology to solve these complex variants Mathematical programming model, genetic algorithms, simulated annealing, simulation modeling, and decision-making models are used as solution methodologies to address these variants The solution methodologies are designed as unified methodology to solve the original or base variant of the proposed variants The proposed unified solution methodologies are evaluated by comparing it with published results using standard, derived, and randomly generated data sets In cases where benchmarks are not available, the published best results for the simpler versions of RA are used as substitutes for the lower bounds The solution methodologies performed exceedingly well in the evaluations, recording better or equally good results in comparison to the existing methodologies Keywords: Resource allocation problems; supply chain; mathematical programming model; heuristic; meta-heuristic; genetic algorithms; simulated annealing; simulated modeling Contents List of Tables xi List of Figures xiii List of Symbols and Abbreviations xv About the Authors xxi SECTION 1.1 1.2 1.3 1.4 Supply Chain Management Resource Allocation Problems in Supply Chain Motivation of Resource Allocation Problems 1.3.1 Resource Allocation Variant in Bi-Objective Capacitated Supply Chain Network 1.3.2 Resource Allocation Variant in Bi-Objective Bound Driven Capacitated Supply Chain Network 1.3.3 Resource Allocation Variant in Multiple Measures Driven Capacitated Multi-Echelon Supply Chain Network 1.3.4 Resource Allocation Variant in Integrated Decision and Upper Bound Driven Capacitated Multi-Echelon Supply Chain Network 1.3.5 Resource Allocation Variant in Integrated Decision and Time Driven Capacitated Multi-Echelon Supply Chain Network 1.3.6 Resource Allocation Variant in Integrated Decision, Bound and Time Driven Capacitated Multi-Echelon Supply Chain Network Scope of the Present Study SECTION 2.1 2.2 Introduction Literature Review Resource Allocation Problem Review of the RA Variants Addressed in Current Research 2.2.1 Bi-Objective Generalized Assignment Problem 2.2.2 Multi-Commodity Network Flow Problem 2.2.3 Multiple Measures Resource Allocation Problem 1 7 8 9 10 10 13 13 14 14 15 21 vii viii CONTENTS 2.2.4 2.2.5 2.2.6 2.3 2.4 Mixed Capacitated Arc Routing Problem Employee Routing Problem Vehicle Routing Problem with Backhauls with Time Windows Observations and Research Gap Summary SECTION 3.1 3.2 3.3 3.4 Bi-Objective Resource Allocation Problem with Varying Capacity Solution Methodology to Solve BORAPVC 3.2.1 Mathematical Programming Model for BORAPVC 3.2.2 Simulated Annealing with Population Size Initialization through Neighborhood Generation for GAP and BORAPVC Computational Experiments and Results Conclusion SECTION 4.1 4.2 4.3 4.4 4.5 5.2 Bi-Objective Bound Driven Capacitated Supply Chain Network Bi-Objective Resource Allocation Problem with Bound and Varying Capacity Solution Methodology to Solve IRARPUB 4.2.1 Recursive Function Inherent Genetic Algorithm (REFING) for MCNF and BORAPBVC Computational Experiments and Results 4.3.1 Performance of Solution Methodology Case Study Demonstration 4.4.1 Problem Identification and Discussion 4.4.2 Formulation of the Problem 4.4.3 Model Testing 4.4.4 Analysis of Results and Discussion 4.4.5 Managerial Implications 4.4.6 Summary for Case Study Conclusion SECTION 5.1 Bi-Objective Capacitated Supply Chain Network Multiple Measures Driven Capacitated Multi-Echelon Supply Chain Network Multiple Measures Resource Allocation Problem for Multi-Echelon Supply Solution Methodology for MMRAPMSC 24 26 30 35 36 37 37 39 39 40 43 47 49 49 54 54 58 58 59 62 66 68 72 72 72 73 75 75 76 Contents 5.2.1 5.3 5.4 5.5 Simulation Modeling with Multiple Performances Measures (SIMMUM) for MMRAPMSC 5.2.2 Model Descriptions 5.2.3 SIMMUM Model Assumptions 5.2.4 Decision Variables in SIMMUM 5.2.5 Multiple Performance Measures of Multi-Echelon Supply Chain 5.2.6 SIMMUM Model Initialization 5.2.7 SIMMUM Model Execution 5.2.8 Output of SIMMUM Model 5.2.9 SIMMUM Model Implementation Simulation Model Experimentations and Results Case Study for Inventory and Purchasing Policy 5.4.1 Procurement Policy for all “A” Class Items 5.4.2 Inventory Policy for all “A” Class Items 5.4.3 Procurement and Inventory Policy for all “B” “C” Class Items Conclusion ix SECTION 6.1 6.2 6.3 6.4 6.5 Integrated Resource Allocation and Routing Problem with Upper Bound 6.1.1 Constraints 6.1.2 Assumptions of IRARPUB Problem Solution Methodology to Solve IRARPUB 6.2.1 Dijkstra’s Algorithm and Local Search Inherent Genetic Algorithm (DIALING) for MCARP and IRARPUB 6.2.2 Parameter Settings for DIALING Computational Experiments and Results 6.3.1 Performance of Solution Methodology Case Study for IRARPUB Conclusion SECTION 7.1 7.2 Integrated Decision and Upper Bound Driven Capacitated Multi-Echelon Supply Chain Network Integrated Decision and Time Driven Capacitated Multi-Echelon Supply Chain Network Integrated Resource Allocation and Routing Problem with Time Window Solution Methodology to Solve IRARPTW 7.2.1 Clustering Inherent Genetic Algorithm (CLING) for VRPTW and IRARPTW 76 77 78 79 80 81 81 82 85 86 90 91 92 93 94 97 97 99 99 100 100 108 108 109 111 113 115 115 116 117 160 RESOURCE ALLOCATION PROBLEMS IN SUPPLY CHAINS periodic bases (or) as and when required The incorporation of “What if” rules in the system may enhance the utility of the current study As an extension of the study, large-sized problems can also be solved with the suggested solution methodologies Incorporating additional constraints such as multiple objectives and multiple depots can also be thought of development of various other metaheuristics such as particle swarm optimization, tabu search, memetic algorithm, and ant colony optimization can be a potential future work Bibliography Aarts, C., & Lenstra, J (1997) Local search in combinatorial optimization New York, NY: Wiley Agarwal, R., & Ergun, O (2008) Mechanism design for a multicommodity flow game in service network alliances Operations Research Letters, 36(5), 520À524 Amaya, A., Langevin, A., & Trepanier, M (2007) The capacitated arc routing problem with refill points Operations Research Letters, 35(1), 45À53 Amiri, A., & Pirkul, H (1997) New formulation and relaxation to solve a concavecost network flow problem Journal of Operations Research Society, 48, 278À287 Amponsah, S K., & Salhi, S (2004) The investigation of a class of capacitated arc routing problems: The collection of garbage in developing countries Waste Management, 24(7), 711À721 Assad, A A (1978) Multicommodity network flows — A survey Networks, 8(1), 37À91 Assad, A A., & Golden, B L (1995) Arc routing methods and applications In M O Ball, T L Magnanti, C L Monma, & G L Nemhauser (Eds.), Handbooks in operations research and management science (Vol 8, pp 375À483) Network Routing Amsterdam: Elsevier Science Publishers Azadeh, A., Allahverdiloo, M., & Shirkouhi, S N (2011) A computer simulation model for analysing performance of inventory policy in multi-product mode in twoechelon supply chain International Journal of Logistics systems and Management, 8(1), 66À85 Babonneau, F., Merle, O D., & Vial, J P (2004) Solving large scale linear multi commodity flow problems with an active set strategy and Proximal-ACCPM Working Paper Balakrishnan, A., & Graves, S C (1989) A composite algorithm for a concave-cost network flow problem Networks, 19(2), 175À202 Baldacci, R., & Maniezzo, V (2006) Exact methods based on node-routing formulations for undirected arc routing problems Networks, 47(1), 52À60 Ball, M O., Magnanti, T L., Monma, C L., & Nemhauser, G L (1995) Network routing Amsterdam: Elsevier Science Balram, S (2005) Study of self — Stopping PDMOSA and performance measure in multi objective optimization Computers & Chemical Engineering, 29(5), 1131À1147 Bautista, J., Fernandez, E., & Pereira, J (2008) Solving an urban waste collection problem using ants heuristics Computers & Operations Research, 35(9), 3020À3033 Bektas, T., & Elmastas, S (2007) Solving school bus routing problems through integer programming Journal of the Operational Research Society, 58(12), 1599À1604 161 162 BIBLIOGRAPHY Belenguer, J M., & Benavent, E (1998) The capacitated arc routing problem: Valid inequalities and facets Computational Optimization and Applications, 10(2), 165À187 Belenguer, J M., & Benavent, E (2003) A cutting plane algorithm for the capacitated arc routing problem Computers & Operations Research, 30(5), 705À728 Belenguer, J M., Benavent, E., Lacomme, P., & Prins, C (2006) Lower and upper bounds for the mixed capacitated arc routing problem Computers & Operations Research, 33(12), 3363À3383 Belotti, P (2005) Multicommodity network design with survivability constraints: Some models and algorithms, PhD Book 4OR: A Quarterly Journal of Operations Research, 3(1), pp 79À81 Benavent, E., Campos, V., Corberan, A., & Mota, E (1992) The capacitated arc routing problem: Lower bounds Networks, 22(7), 669À690 Bennett, B T., & Gazis, D C (1972) School bus routing by computer Transportation Research, 6(4), 17À25 Ben-Tal, A., & Nemirovski, A (2000) Robust solutions of linear programming problems contaminated with uncertain data Mathematical Programming, 88(3), 411À424 Bentall, H B., & Stent, A F (2001) A scheduling model for a high speed containership service: A hub and spoke short — Sea application International Journal of Maritime Economics, 3(3), 262À277 Beullens, P., Muyldermans, L., Cattrysse, D., & Van Oudheusden, D (2003) A guided local search heuristic for the capacitated arc routing problem European Journal of Operational Research, 147(3), 629À643 Biswas, S., & Narahari, Y Object oriented modeling and decision support for supply chains Electronic Enterprises Laboratory, Computer Science and Automation, Indian Institute of Science, Bangalore, India Bodin, L D., Golden, B L., Assad, A A., & Ball, M O (1983) Computers and operations research Special Issue on the Routing and Scheduling of Vehicles and Crews, 10(2), 63À211 Book binder, J H., & Cakanyildirim, M (1999) Random lead times and expedited orders in (Q, r) inventory systems European Journal of Operational Research, 115(2), 300À313 Bowerman, R., Hall, B., & Calamai, P (1995) A multi-objective optimization approach to urban school bus routing: Formulation and solution method Transportation Research Part A: Policy and Practice, 29(2), 107À123 Brauer, K., & Backholer, C (2009) A strategic view of transportation management in automotive supply networks International Journal of Automotive Technology and Management, 9(1), 69À86 Calitz, C (2008) Optimal routing of waste collection vehicles, Research Report, University of Pretoria Casco, D O., Golden, B L., & Wasil, E A (1988) Vehicle routing with backhauls: Models, algorithms, and case studies In Golden & Assad (Eds.), Vehicle routing: Methods and studies (pp 127À147) Section Amsterdam: Elsevier Science Publishers Chan, Y., Carter, W B., & Burnes, M D (2001) A multiple-depot, multiple-vehicle, location-routing problem with stochastically processed demands Computers & Operations Research, 28(8), 803À826 Chancellor, A (1988) Snack food companies haul more than chips The Journal of Commerce and Commercial, 10, 35À52 Bibliography Chandra, C., & Grabis, J (2009) A goal model-driven supply chain design International Journal of Data Analysis Techniques and Strategies, 1(3), 224À241 Chiang, W., & Russell, R (1997) A reactive tabu search metaheuristic for the vehicle routing problem with time windows INFORMS Journal on Computing, 9(4), 417À430 Christodoulou, S E (2010) Traffic modeling and college-bus routing using entropy maximization Journal of Transportation Engineering, 136(2), 102À109 Christopher, M (2005) Managing risk in the supply chain In Logistics and supply chain management (pp 231À258) Harlow: Prentice-Hall Clarke, G., & Wright, J (1964) Scheduling of vehicles from a central depot to a number of delivery points Operations Research, 12(4), 568À581 Corbera, A., Mota, E., & Salazar, J J (2003) Some recent contributions to routing and location problems Networks, 42(2), 109À113 Corberan, A., Fernandez, E., Laguna, M., & Marti, R (2002) Heuristic solutions to the problem of routing school buses with multiple objectives Journal of Operation Research Society, 53(4), 427À435 Corberan, A., Mejia, G., & Sanchis, J M (2003) New results on the mixed general routing problem Operation Research, 53(2), 363À376 Corberan, A., Romero, A., & Sanchis, J M (2003) The mixed general routing polyhedron Mathematical Programming, 96(1), 103À137 Crainic, T G., Frangioni, A., & Gendron, B (2001) Bundle-based relaxation methods for multicommodity capacitated fixed charge network design problems Discrete Applied Mathematics, 112(1À3), 73À99 Croxton, K L., Gendron, B., & Magnanti, T L (2003) A comparison of mixedinteger programming models for non convex piecewise linear cost minimization problems Management Science, 49(9), 1268À1273 Cullen, F H., Jarvis, J J., & Ratliff, H D (1981) Set partitioning based heuristics for interactive routing Networks, 11(2), 125À143 Deif, I., & Bodin, L (1984) Extension of the clarke and wright algorithm for solving the vehicle routing problem with backhauling In A E Kidder (Ed.), Proceedings of the Babson conference on software uses in transportation and logistics management, Babson Park, MA (pp 75À96) Desrochers, M., & Solomon, M (1992) A new optimization algorithm for the vehicle routing problem with time windows Operations Research, 40(2), 342À354 Dhanalakshmi, R., Parthiban, P., Arunkumar, T., & Dominic, P D D (2009) Modelling of single sourcing, multiperiod, multivendor, multibuyer based VMI International Journal of Enterprise Network Management, 3(2), 165À180 Dhanalakshmi, R., Parthiban, P., Ganesh, K., & Arunkumar, T (2009) Genetic algorithm to solve multi-period, multi-product, Bi-echelon supply chain network design problem International Journal of Information Systems and Supply Chain Management, 2(4), 24À42 Dror, M (2000) Arc routing: Theory, solutions and applications Boston, MA: Kluwer Academic Publishers Duhamel, C., & Potvin, J (1997) A tabu search heuristic for the vehicle routing problem with backhauls and time windows Transportation Science, 31(1), 49À59 Edwin Romeijn, H., & Morales, D R (2000) A class of greedy algorithms for the generalized assignment problems Discrete Applied Mathematics, 103(3), 209À235 163 164 BIBLIOGRAPHY Eglese, R W., & Letchford, A N (2000) Polyhedral theory for arc routing problems In M Dror (Ed.), Arc routing: Theory, solutions and applications (pp 199À230) Boston, MA: Kluwer Academic Publishers Eiselt, H A., Gendreau, M., & Laporte, G (1995a) Arc routing problems, Part I: The Chinese postman problem Operations Research, 43(2), 231À242 Eiselt, H A., Gendreau, M., & Laporte, G (1995b) Arc routing problems, Part II: The rural postman problem Operations Research, 43(3), 399À414 Fayazbakhsh, K., & Razzazi, M (2008) Coordination of a Multi-Commodity supply chain with Multiple members using flow networks, Second international conference on the digital society, IEEE Computer Society Figliozzi, M A (2009) Planning approximations to the average length of vehicle routing problems with time window constrains Transportation Research Part B: Methodological, 43(4), 438À447 Fisher, M L., & Jaikumar, R (1978) A decomposition algorithm for large-scale vehicle routing Working Paper Wharton Department of Decision Sciences, University of Pennsylvania Fisher, M L., & Jaikumar, R (1981) A generalized assignment heuristic for vehicle routing Networks, 11(2), 109À124 Frangioni, A., & Gendron, B (2009) 0À1 reformulations of the multicommodity capacitated network design problem Discrete Applied Mathematics, 157(6), 1229À1241 Gabrel, V., Knippel, A., & Minoux, M (1999) Exact solution of multicommodity network optimization problems with general step cost functions Operations Research, 25(1), 15À23 Gabrel, V., Knippel, A., & Minoux, M (2003) A comparison of heuristics for the discrete cost multicommodity network optimization problem Journal of Heuristics, 9(5), 429À445 Gabrel, V., & Minoux, M (1997) LP relaxations better than convexification for multicommodity network optimization problems with step-increasing cost functions Acta Mathematica Vietnamica, 22(1), 128À145 Gamst, M., Jensen, P N., Pisinger, D., & Plum, C (2010) Two- and three-index formulations of the minimum cost multicommodity k-splittable flow problem European Journal of Operational Research, 202(1), 82À89 Gavish, B., & Graves, S C (1978) The traveling salesman problem and related problems Working Paper Operation Research Center, Massachusetts Institute of Technology Gavish, B., & Graves, S C (1982) Scheduling and routing in transportation and distribution systems: Formulations and new relaxations Working Paper Graduate School of Management, University of Rochester Gelinas, S (1991) Fabrication de tournees avec rechargement (in French, Construction of Backhaul Routes) Unpublished master’s book, Ecole Polytechnique, Montreal Gelinas, S., Desrochers, M., Desrosiers, J., & Solomon, M (1995) A new branching strategy for time constrained routing problems with application to backhauling Annals of Operations Research, 61, 91À109 Gendron, B., & Crainic, T G (1993) Parallel implementations of a branch and bound algorithm for multicommodity location with balancing requirements INFOR, 31(3), 151À165 Geoffrion, G., & Graves, G (1974) Multicommodity distribution system design by Benders decomposition Management Science, 20(5), 822À844 Bibliography Ghatee, M., & Hashemi, S M (2009) Some concepts of the fuzzy multicommodity flow problem and their application in fuzzy network design Mathematical and Computer Modelling, 49(5À6), 1030À1043 Ghiani, G., Guerreiro, F., Improta, G., & Musmanno, R (2005) Waste collection in Southern Italy: Solution of a real-life arc routing problem International Transactions in Operational Research, 12(2), 135À144 Ghiani, G., Improta, G., & Laporte, G (2001) The capacitated arc routing problem with intermediate facilities Networks, 37(3), 134À143 Gillett, B., & Miller, L (1974) A heuristic algorithm for the vehicle dispatch problem Operations Research, 22, 340À349 Goetschalckx, M., & Jacobs, B C (1989) The vehicle routing problem with backhauls European Journal of Operational Research, 42(1), 39À51 Golden, B., & Skiscim, C (1986) Using simulated annealing to solve routing and location problems Naval Research Logistics, 33(2), 261À279 Golden, B L (1975) A minimum-cost multicommodity network flow problem concerning imports and exports Networks, 5(4), 331À356 Golden, B L., & Assad, A A (1988) Vehicle routing: Methods and studies New York, NY: Elsevier Science Publishers Golden, B L., Baker, E K., Alfaro, J L., & Schaffer, J R (1985) The vehicle routing problem with backhauling: Two approaches Working Paper College of Business and Management, University of Maryland Golden, B L., Dearmon, J S., & Baker, E K (1983) Computational experiments with algorithms for a class of routing problems Computers and Operations Research, 10(1), 47À59 Golden, B L., & Wong, R T (1981) Capacitated arc routing problems Networks, 11(3), 305À315 Gouveia, L., Mourao, M C., & Pinto, L S (2010) Lower bounds for the mixed capacitated arc routing problem Computers and Operations Research, 37(4), 692À699 Haddadi, S., & Ouzia, H (2004) Effective algorithm and heuristic for the generalized assignment problem European Journal of Operational Research, 153(1), 184À190 Haimovich, M., & Rinnooy Kan, A H G (1985) Bounds and heuristics for capacitated routing problems Mathematics of Operations Research, 10(4), 527À542 Hajri Gabouj, S (2003) A fuzzy genetic multiobjective optimization algorithm for a multi level generalized assignment problem IEEE Transactions on Systems, Man, and Cybernetics, 33(2), 214À224 Han, C., & Damrongwongsiri, M (2005) Stochastic modeling of a two-echelon multiple sourcing supply chain system with genetic algorithm Journal of Manufacturing Technology Management, 16(1), 87À108 Haouari, M., Aissaoui, N., & Mansour, F Z (2009) Network flow-based approaches for integrated aircraft fleeting and routing European Journal of Operational Research, 193(2), 591À599 Hertz, A., Laporte, G., & Mittaz, M (2000) A tabu search heuristic for the capacitated arc routing problem Operations Research, 48(1), 129À135 Holland, J H (1975) Adaptation in natural and artificial systems Ann Arbor, MI: University of Michigan Press Holmberg, K., & Yuan, D (2003) A multi commodity network flow problem with side constraints on path solved by column generation INFORMS Journal on Computing, 15(1), 42À57 165 166 BIBLIOGRAPHY Homberger, J., Gehring, H., Hagen, F., Wirtschaftsinformatik, L., Hagen, D., & Deutschland, B (1999) Two evolutionary meta-heuristics for the vehicle routing problem with time windows INFORMS Journal on Computing, 37, 297À318 Hou, J., Zeng, A Z., & Lindu, Z (2009) A coordinated revenue-sharing contract for a two-stage supply chain with linear stepwise inventory holding costs International Journal of Information Systems and Supply Chain Management, 2(4), 1À23 Irnich, S (2008) Solution of real-world postman problems European Journal of Operational Research, 190(1), 52À67 Ismail, Z., & Yunos, N M (2010) Reactive tabu search approach for scheduling solid waste collection problems Australian Journal of Basic and Applied Sciences, 4(10), 5171À5177 Iwan, V., Zailani, S., & Nyoman, P (2009) Supply chain risk management: Literature review and future research International Journal of Information Systems and Supply Chain Management, 2(1), 16À33 Jacobs, B C., & Goetschalckx, M (1993) The vehicle routing problem with backhauls: Properties and solution algorithms Technical report MHRC-TR-88À13, Georgia Institute of Technology, Atlanta, Georgia John, H H (1975) Adaptation in natural and artificial systems Ann Arbor, MI: University of Michigan Press Jordan, W C (1987) Truck backhauling on networks with many terminals Transportation Research-B, 21B(3), 183À193 Jordan, W C., & Burns, L D (1984) Truck back hauling on two terminal networks Transportation Research-B, 18B(6), 487À503 Kannan, G., Senthil, P., Sasikumar, P., & Vinay, V P (2008) A nelder and mead methodology for solving small fixed-charge transportation problems International Journal of Information Systems and Supply Chain Management, 1(4), 60À72 Kattan, I A., & Khudairi, T A (2010) Simulation of inventory control system in a supply chain using RFID International Journal of Information Systems and Supply Chain Management, 3(1), 68À86 Kearney, A T (1984) Measuring and improving productivity in physical distribution, a report prepared for the national council of physical distribution management, NCPDM, Oak Brook, IL Kennington, J (1978) A survey of linear cost multicommodity network flows Operations Research, 26(2), 209À236 Kimemia, J., & Gershwin, S (1976) Complex materials handling and assembly systems Network Flow Optimization in Flexible Manufacturing System are Intuitively Pleas, 2(2), 834À839 Kirkpatrick, S., Gelatt, C D., Jr., & Vecchi, M P (1983) Optimization by simulated annealing Science, 220(4598), 671À680 Kontoravdis, G., & Bard, J (1995) A GRASP for the vehicle routing problem with time windows ORSA Journal on Computing, 7(1), 10À23 Lacomme, P., Prins, C., & Erif, W R (2005) Evolutionary algorithms for periodic arc routing problems European Journal of Operational Research, 165(2), 535À553 Lacomme, P., Prins, C., & Ramdane, C W (2001) A genetic algorithm for the capacitated arc routing problem and its extensions In E J W Boers, et al (Eds.), Applications of evolutionary computing, lecture notes in computer science 2037 (pp 473À483) Berlin: Springer Lacomme, P., Prins, C., & Ramdane, C W (2003) An integer linear model for general arc routing problems Working Paper Universite Technologie de Troyes Bibliography Lacomme, P., Prins, C., & Ramdane, C W (2004) Competitive memetic algorithms for arc routing problems Research Report LOSI-2001-01, University of Technology of Troyes, France, 2001 Annals of Operations Research, 131, 159À185 Lacomme, P., Prins, C., & Sevaux, M (2006) A genetic algorithm for a bi-objective capacitated arc routing problem Computers and Operation Research, 33(12), 3473À3493 Ledesma, J R., & Gonzalez, J J S (2012) Solving school bus routing using the multiple vehicle travelling purchaser problem: A branch-and-Cut approach Computers and Operation Research, 39(2), 391À404 Leighton, T., Makedon, F., Plotkin, S., Stein, C., Tardos, E., & Tragoudas, S (1991) Fast approximation algorithms for multicommodity flow problems Proceedings of the 23rd annual symposium on theory of computing (pp 101À111) Lenstra, J., & Kan, A R (1981) Complexity of vehicle routing and scheduling problems Networks, 11(2), 221À227 Li, J., Chu, F., & Prins, C (2009) Lower and upper bounds for a capacitated plant location problem with multicommodity flow Computers & Operations Research, 36(11), 3019À3030 Li, L Y O., & Fu, Z (2002) The school bus routing problem: A case study The Journal of the Operational Research Society, 53(5), 552À558 Li, X Y., Aneja, Y P., & Baki, F (2010) An ant colony optimization metaheuristic for single-path multicommodity network flow problems Journal of the Operational Research Society, 61(9), 1340À1355 Lin, S., & Kernighan, B (1973) An effective heuristic algorithm for the traveling salesman problem Operations Research, 21(2), 498À516 Lin, Y (2006) A two-commodity multistate flow network with capacity weight varying with edges, nodes and types of commodity Applied Mathematics and Computation, 183(1), 142À151 Liu, K., & Zhang, Z (2008) Channel competition and selection in a capacitated multi-channel distribution system International Journal of Logistics Systems and Management, 4(5), 596À616 Longo, H., Poggi de Aragao, M., & Uchoa, E (2006) Solving capacitated arc routing problems using a transformation to the CVRP Computers and Operations Research, 33(6), 1823À1837 Magnanti, T L (1981) Combinatorial optimization and vehicle fleet planning: Perspectives and prospects Networks, 11(2), 179À213 Mahamani, A., Prahlada Rao, K., & Pandurangadu, V (2008) The development of a simulation-based approach to optimise the inventory policy in a single-echelon supply chain: A case study International Journal of Data Analysis Techniques and Strategies, 1(2), 173À192 Makipaa, M (2008) On cooperative inter-organisational relationships: Historical grounds and levels of cooperation International Journal of Enterprise Network Management, 2(2), 105À122 Maniezzo, V (2004) Algorithms for large directed CARP instances: Urban solid waste collection operational support Technical Report UBLCS-2004-16, Department of Computer Science, University of Bologna, Italy Mathirajan, M., Manoj, K., & Ramachandran, V (2011) A design of distribution network and development of efficient distribution policy International Journal of Logistics systems and Management, 9(1), 108À137 McBride, R D (1998) Advances in solving the multi-commodity flow problem Interfaces, 28(2), 32À41 167 168 BIBLIOGRAPHY Melachrinoudis, E., & Min, H (2000) Dynamic relocation and phase-out of a hybrid, two-echelon, hybrid plant/warehousing facility: A multiple objective approach European Journal of Operational Research, 123(1), 1À15 Min, H., Current, J., & Schilling, D (1992) The multiple depot vehicle routing problem with backhauling Journal of Business Logistics, 13(1), 259À288 Min, H., & Guo, Z (2010) Developing bi-level equilibrium models for the global container transportation network from the perspectives of multiple stakeholders International Journal of Logistics systems and Management, 6(4), 362À379 Min, H., Ko, H J., & Lim, C S (2009) Designing the global inland transportation network International Journal of Logistics systems and Management, 5(5), 457À472 Min, H., & Melachrinoudis, E (1999) The relocation of a hybrid manufacturing and distribution facility from supply chain perspectives: A case study Omega, 27(1), 75À85 Min, H., & Zhou, G (2002) Supply chain modeling: Past, present and future Computers & Industrial Engineering, 43(1À2), 231À249 Minoux, M (1981) Optimum synbook of a network with non-simultaneous multicommodity flow requirements Annals of Discrete Mathematics 11, 59, 269À277 Minoux, M (2001) Discrete cost multicommodity network optimization problems and exact solution methods Annals of Operations Research, 106, 19À46 Moreira, L M., Oliveira, J F., Gomes, A M., & Ferreira, J S (2007) Heuristics for a dynamic rural postman problem Computers & Operations Research, 34(11), 3281À3294 Mourao, M C., & Almeida, M T (2000) Lower-bounding and heuristic methods for a refuse collection vehicle routing problem European Journal of Operational Research, 121(2), 420À434 Mourao, M C., & Amado, L (2005) Heuristic method for a mixed capacitated arc routing problem: A refuse collection application European Journal of Operational Research, 160(1), 139À153 Mulvey, J M., Vanderbei, R J., & Zeinos, S A (1981) Robust optimization of large-scale systems Operations Research, 43(34), 56À59 Newton, R., & Thomas, W (1969) Design of school bus route by computer Economic Planning Sciences, 3(1), 75À85 Newton, R M., & Thomas, W H (1974) Bus routing in a multi-school system Computers and Operations Research, 1(2), 213À222 Nilsson, D (1999) SHAM — A simulation model for designing straw fuel delivery systems Part 1: Model description Biomass & Bio Energy, 16(1), 25À28 Nobert, Y., & Picard, J C (1996) An optimal algorithm for the mixed Chinese postman problem Networks, 27(2), 95À108 Onaga, A., & Kakusho, O (1971) On feasibility conditions of multicommodity flows in networks IEEE Transactions on Circuit Theory CT, 18(4), 425À429 Or, I (1976) Traveling salesman type combinatorial problems and their relation to the logistics of blood banking PhD dissertation, Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL Orr, A (1989) Spartan looks down the road U S Distribution Journal, (February), 43À48 Osorio, M A., & Laguna, M (2003) Logic cuts for multilevel generalized assignment problems European Journal of Operational Research, 151(1), 238À246 Bibliography Ozdaglar, A E., & Bertsekas, D P (2003, June) Optimal solution of integer multicommodity flow problems with application in optical networks Proceedings of symposium on global optimization, Santorini, Greece Paksoy, T., & Cavlak, E B (2011) Development and optimization of a new linear programming model for production/distribution network of an edible vegetable oils manufacturer International Journal of Logistics Systems and Management, 9(1), 1À21 Panagiotakopoulos, D (1976) Multi-commodity multi-transformed network flows with an application Management Science, 22(8), 874À882 Park, J., & Kim, B I (2010) The school bus routing problem: A review European Journal of Operational Research, 202(2), 311À319 Pearn, W L., Assad, A., & Golden, B L (1987) Transforming arc routing into node routing problems Computers and Operations Research, 14(4), 285À288 Pia, A D., & Filippi, C (2006) A variable neighborhood descent algorithm for a real waste collection problem with mobile depots International Transactions in Operational Research, 13(2), 125À141 Piramuthu, S (2005) Knowledge-based framework for automated dynamic supply chain configuration European Journal of Operational Research, 165(1), 219À230 Potvin, J., & Bengio, S (1996) The vehicle routing problem with time windows, part II: Genetic search INFORMS Journal on Computing, 8(2), 165À172 Potvin, J., Kervahut, T., Garcia, B., & Rousseau, J (1996) The vehicle routing problem with time windows, part I: Tabu search INFORMS Journal on Computing, 8(2), 158À164 Pradhananga, R., Hanaoka, S., & Sattayaprasert, W (2011) Optimisation model for hazardous material transport routing in Thailand International Journal of Logistics Systems and Management, 9(1), 22À42 RamKumar, P N., & Sivakumar, A I (2011) On solving the capacitated hub routing problem International Journal of Logistics Systems and Management, 8(4), 392À402 Rees, L P., Clayton, E R., & Taylor III, B W (1987) A linear goal programming model of a multi-period, multi-commodity network flow problem Journal of Business Logistics, 8(1), 117À140 Reeves, C (1993) Modern heuristic techniques for combinatorial problems Oxford: Blackwell Scientific Publications Ronald, H B (1999) Business logistics management (4th ed.) Upper Saddle River, NJ: Prentice-Hall Russell, R (1995) Hybrid heuristics for the vehicle routing problem with time windows Transportation Science, 29(2), 156À166 Russell, R., & Igo, W (1979) An assignment routing problem Networks, 9(1), 1À17 Saban, K., & Mawhinney, J (2010) The strategic role of human collaboration in supply chain management International Journal of Information Systems and Supply Chain Management, 3(1), 43À57 Sabri, E H., & Beamon, B M (2000) A multi-objective approach to simultaneous strategic and operational planning in supply chain design The International Journal of Management Science, 28(5), 581À598 Saen, R F (2010) A new look at selecting third-party reverse logistics providers International Journal of Information Systems and Supply Chain Management, 3(1), 58À67 169 170 BIBLIOGRAPHY Salim, H., & Quzia, H (2004) Effective algorithm and heuristic for the generalised assignment problem European Journal of Operational Research, 153(1), 184À190 Saxena, A., Ducq, Y., Malairajan, R A., & Sivakumar, P (2010) Simulation-based decision-making scenarios in dynamic supply chain International Journal of Enterprise Network Management, 4(2), 166À182 Saxena, A., & Wadhwa, S (2008) Flexible configuration for seamless supply chains: A decision knowledge sharing focus Journal of Robotics and Computer Integrated Manufacturing, 25(4À5), 839À852 Schittekat, P., Sevaux, M., & Sorensen, K (2006) A mathematical formulation for a school bus routing problem Service Systems and Service Management, 2, 1552À1557 Seifi, A A., Safaei, N., & Assadi, P (2011) A heuristic approach for periodic vehicle routing problem: A case study International Journal of Logistics Systems and Management, 8(4), 425À443 Shen, S Y (1999) Time window constrained vehicle routing problems Ph.D Dissertation, National Chiao Tung University, R.O.C Shen, Z M (2007) Integrated supply chain design models: A survey and future research directions Journal of Industrial and Management Optimization, 3(1), 1À27 Smith, S A., Agrawal, N., & Tsay, A A (2002) Decision support system for a retail supply chain planning for private-label merchandise with multiple vendors Santa Clara, CA: Santa Clara University Solomon, M (1983) Vehicle routing and scheduling with time window constraints: Models and algorithms Ph.D Dissertation, University of Pennsylvania Solomon, M (1987) Algorithms for the vehicle routing and scheduling problem with time window constraints Operations Research, 35(2), 254À265 Solomon, M., & Desrosiers, J (1988) Time window constrained routing and scheduling problems Transportation Science, 22(1), 1À13 Souza, L V D., & Siquerira, P H (2010) Heuristic method applied to the optimization school bus transportation routes: A real case (No 1, Vol 32, pp 247À256) Berlin: Springer-Verlag Sujatha, R (2011) Role of intelligent agents in facilitating information flow in supply chain management International Journal of Logistics Systems and Management, 9(2), 229À237 Taillard, E., Badeau, P., Gendreau, M., Guertin, F., & Potvin, J (1997) A tabu search heuristic for the vehicle routing problem with soft time windows Transportation Science, 31(2), 170À186 Teng, C X., Yao, F M., & Hu, X W (2007) Study on multi-commodity flow supply chain network equilibrium model with random demand Systems Engineering — Theory & Practice, 27(10), 77À83 Thomas, H., Charles, E., & Stein, C (2001) Dijkstra’s algorithm In Introduction to algorithms (No 3, Vol 24, pp 595À601) New York, NY: McGraw-Hill Toth, P., & Vigo, D (1996) A heuristic algorithm for the vehicle routing problem with backhauls In L Bianco & P Toth (Eds.), Advanced methods in transportation analysis: Proceedings of the 2nd TRISTAN conference Berlin: Springer Towill, D R (1991) Supply chain dynamics International Journal of Computer Integrated Manufacturing, 4(4), 197À208 Towill, D R., Naim, M., & Wikner, J (1992) Industrial dynamics simulation models in the design of supply chains International Journal of Physical Distribution and Logistics Management, 22(5), 3À13 Bibliography Ulusoy, G (1985) The fleet size and mixed problem for the capacitated arc routing problem European Journal of Operational Research, 22, 329À337 Vaidyanathan, B., Jha, K C., & Ahuja, R K (2007) Multicommodity network flow approach to the railroad crew-scheduling problem IBM Journal of Research and Development, 51, 325À344 Vanany, I., Zailani, S., & Pujawan, N (2009) Supply chain risk management: Literature review and future research International Journal of Information Systems, 2(1), 16À33 Wadhwa, S., Saxena, A., & Chan, F T S (2008) A framework for flexibility in dynamic supply chain management International Journal of Production Research, 46(6), 1373À1404 Wang, G., Huang, S H., & Dismukes, J P (2004) Product-driven supply chain selection using integrated multi-criteria decision-making methodology International Journal of Production Economics, 91(1), 1À15 Wang, L., & Prabhu, V (2009) A stochastic perturbation algorithm for inventory optimization in supply chains International Journal of Information Systems and Supply Chain Management, 2(3), 1À18 Wikner, J., Towill, D R., & Naim, M (1991) Smoothing supply chain dynamics International Journal of Production Economics, 22(3), 231À248 Wohlk, S (2008) A decade of capacitated arc routing In B Golden, S Raghavan, & E Wasil (Eds.), The vehicle routing problem-latest advances and new challenges Berlin: Springer Wu, D., & Olson, D L (2008) The challenges and expectations for enterprises International Journal of Enterprise Network Management, 18, 5À20 Xanthopoulos, A., & lakovou, E (2010) A strategic methodological optimisation framework for the design of a reverse logistics network with forward supply channel synergies International Journal of Logistics systems and Management, 7(2), 165À183 Yadav, S R., Ghorpade, A., Mahajan, C., Tiwari, M K., & Shankar, R (2009) Optimising a logistics system with multiple procurements and warehousing using endosymbiotic evolutionary algorithm International Journal of Logistics systems and Management, 5(1À2), 154À175 Yan, S., & Chen, H L (2002) A scheduling model and a solution algorithm for inter-city carriers Transportation Research Part A: Policy and Practice, 36(9), 805À825 Yano, C A., Chan, T J., Richter, L., Culter, T., Murty, K G., & McGettigan, D (1987) Vehicle routing at quality stores Interfaces, 17(2), 52À63 Zhou, G., Min, H., & Gen, M (2003) A genetic algorithm approach to the bi-criteria allocation of customers to warehouses International Journal of Production Economics, 86(1), 35À45 171 This page intentionally left blank Index “A” Class, 91À93 ABC Analysis, 92À94 Analytic hierarchy, 17 Ant colony, 21, 160 Augmented simultaneous, 31 “B” class, 92, 93À94 Backhauls with Time windows, 30À35 Bi-Objective, 5, 7À8, 11, 14À15, 25, 35, 37À39, 49À54, 155, 156 BORAPVC, 8, 38, 39À43, 44, 45, 47, 156, 157 Bound and time driven capacitated, 10, 11, 35, 127À153, 155, 156 Bound and Time Window, 10, 127À129, 156 Bullwhip effect, 86, 87, 88, 89 “C” class, 92, 93À94 Capacitated supply chain, 7À8, 37À47, 49À73, 155, 156 Chromosome representation, 104, 118 CLING, 117À121, 122, 123, 124, 125, 158, 159 Clustering inherent, 117, 158 Constraints, 3, 5, 6, 7, 10, 13, 16, 20, 21, 24, 25, 26, 27, 29, 33, 36, 37, 38, 49, 52, 62, 63, 65, 67, 72, 73, 93, 98, 99, 100, 104, 114, 117, 125, 128, 134, 142, 152, 153, 157, 158, 159, 160 Critical Processes, 138 Cycle crossover, 57 Decision Support System, 17, 129, 151À152, 159 Delivery nodes, 129 DIALING, 100À108, 109, 110, 111, 113, 114, 123, 158 Dijkstra’s Algorithm, 100À108, 158 Directed graph, 99, 101 Distribution Processes, 140 Dump cost, 98, 99 Edge cost, 98 Employee Routing, 26À30 Heuristics, 5, 11, 16, 17, 19, 21, 25, 28, 29, 31, 34, 35, 36, 37, 73, 101, 102, 103, 104, 118, 133, 134, 155, 156, 159 Integrated decision, 9À11, 35, 97À114, 115À125, 127À153, 155, 156 Integrated Resource Allocation, 9, 10, 97À100, 115À116, 127À129, 156 Inversion Mutations, 108 IRARPTW, 10, 116À122, 124, 125, 156, 158, 159 IRARPUB, 9, 54À58, 98, 99À108, 111À113, 114, 156, 158 Iteration number, 41, 57 173 174 INDEX Managerial Implications, 72 Milk processing, 136, 139, 140 Min Max Inventory, 90 Mixed Capacitated Arc, 24À26 MMRAPMSC, 9, 75, 76À86, 94, 156, 157 Model Testing, 68À71 Motivation, 7À10, 36, 100 Multi echelon supply chain, 8À10, 75À95, 115À125, 127À153 Multi-Commodity Network, 15À21, 72 Multiple measures, 8À9, 11, 21À23, 35, 75À95, 155, 156 Multiple Measures Resource Allocation, 8, 21À23, 75À76, 156 Neighborhood generation, 41, 56, 104 Network arcs, 51 Order taking, 140, 142 Organization Structure, 137 Packaging, 137, 138, 139 Patient distribution system, 17, 62À63, 69 Procurement, 90, 91À92, 93À94, 136, 140, 141 Recursive function, 54, 157 REFING, 54À58, 59, 60, 61, 73, 157 Refuse collection, 24, 28, 97 Resource allocation, 4, 5À11, 13À36, 37À39, 49À54, 75, 97, 98, 115, 127, 128, 155, 156, 159 SAPING, 39, 40À43, 43, 44, 45, 46, 47, 157 SIMMUM, 76À77, 78À79, 81À86, 158 Simulated Annealing, 14, 15, 34, 42, 157 Solid Waste Management, 9, 10, 99, 111, 112, 116 Supply chain, 1À11, 16, 18, 21, 22, 23, 31, 32, 35, 36, 39, 43, 50, 55, 59, 60, 75, 76, 77, 78, 79, 80, 81, 85, 86, 87, 89, 90, 94, 95, 97, 98, 112, 141, 142, 152, 155, 157, 158, 159 Tabu search, 17, 24, 34, 35, 160 Time driven capacitated, 9À11, 35, 115À125, 127, 128, 155, 156 Two point crossover, 54, 56, 100, 102, 104, 106, 107, 117, 120, 121, 157, 158, 159 Upper bound driven capacitated, 9, 11, 35, 97À114, 155, 156 VRPTW, 33, 34, 35, 115, 116, 117À121, 122, 123, 124, 125, 134, 135, 153, 158, 159 .. .Resource Allocation Problems in Supply Chains This page intentionally left blank Resource Allocation Problems in Supply Chains By K Ganesh McKinsey & Company, Inc., Chennai, India R A... 1.4 Supply Chain Management Resource Allocation Problems in Supply Chain Motivation of Resource Allocation Problems 1.3.1 Resource Allocation Variant in Bi-Objective Capacitated Supply Chain Network... lines, warehouses, etc are involved RESOURCE ALLOCATION PROBLEMS IN SUPPLY CHAINS Supply Chain Decisions Temporal Strategic Tactical Operational Functional Sourcing Location Allocation Routing