The Design of Production-Distribution Networks: A Mathematical Programming Approach

  • Alain Martel
Part of the Applied Optimization book series (APOP, volume 98)


This text proposes a mathematical programming approach to design international production-distribution networks for make-to-stock products with convergent manufacturing processes. Various formulations of the elements of production-distribution network design models are discussed. The emphasis is put on modeling issues encountered in practice which have a significant impact on the quality of the logistics network designed. The elements discussed include the choice of an objective function, the definition of the planning horizon, the manufacturing process and product structures, the logistics network structure, demand and service requirements, facility layouts and capacity options, product flows and inventory modeling, as well as financial flows modeling. Major contributions from the literature are reviewed and a number of new formulation elements are introduced. A typical model is presented, and the use of successive mixed-integer programming to solve it with commercial solvers is discussed. A more general version of the model presented and the solution method described were implemented in a commercial supply chain design tool which is now available on the market.


Logistics network design Supply chain engineering Location-allocation problems Capacity planning Technology selection Mathematical programming 


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  1. Ahmed, S., A. King and G. Parija 2001. A multi-stage stochastic integer programming approach for capacity expansion under uncertainty, The Stochastic Programming E-Print Series.Google Scholar
  2. Aikens, C.H. 1985. Facility Location Models for Distribution Planning, EJOR, 22, 263–279.zbMATHMathSciNetCrossRefGoogle Scholar
  3. Arntzen, B., G. Brown, T. Harrison and L. Trafton 1995. Global Supply Chain Management at Digital Equipment Corporation, Interfaces, 21-1, 69–93.Google Scholar
  4. Ballou, R.H. 1992. Business Logistics Management, 3rd ed., Prentice Hall.Google Scholar
  5. Ballou, R.H. 1994. Measuring transport costing error in customer aggregation for facility location, Transportation Journal, Lock Haven.Google Scholar
  6. Bhutta, K., F. Huq, G. Frazier and Z. Mohamed 2003. An Integrated Location, Production, Distribution and Investment Model for a Multinational Corporation, Int. Journal of Production Economics, 86, 201–216.CrossRefGoogle Scholar
  7. Birge, J.R. and F. Louveaux 1997. Introduction to Stochastic Programming, Springer.Google Scholar
  8. Brown, G., G. Graves and M. Honczarenko 1987. Design and Operation of a Multicommodity Production/Distribution System Using Primal Goal Decomposition, Management Science, 33-11, 1469–1480.Google Scholar
  9. Cohen, M., M. Fisher and R. Jaikumar 1989. International Manufacturing and Distribution Networks: A Normative Model Framework, in K. Ferdows ed. Managing International Manufacturing, Elsevier, 67–93.Google Scholar
  10. Cohen, M. and H. Lee 1989. Resource Deployment Analysis of Global Manufacturing and Distribution Networks, J. Mfg. Oper. Mgt., 2, 81–104.Google Scholar
  11. Cohen, M. and S. Moon 1990. Impact of Production Scale Economies, Manufacturing Complexity, and Transportation Costs on Supply Chain Facility Networks, J. Mfg. Oper. Mgt., 3, 269–292.Google Scholar
  12. Cohen, M. and S. Moon 1991. An integrated plant loading model with economies of scale and scope, EJOR, 50, 266–279.CrossRefzbMATHGoogle Scholar
  13. Cordeau, J-F., F. Pasin and M. Solomon 2002. An Integrated Model for Logistics Network Design, Les Cahiers du GERAD, G-2002-07.Google Scholar
  14. Daskin, M. 1995. Network and Discrete Location, Wiley Inter-Science.Google Scholar
  15. Dogan K. and M. Goetschalckx 1999. A Primal Decomposition Method for the Integrated Design of Multi-Period Production-Distribution Systems, IIE Trans., 31, 1027–1036.CrossRefGoogle Scholar
  16. Eppen, G., R. Kipp Martin and L. Schrage 1989. A Scenario Approach to Capacity Planning, Operations Research, 37-4, 517–527.Google Scholar
  17. Everett, G., A. Philpott and G. Cook 2000. Capital Planning Under Uncertainty at Fletcher Challenge Canada, Proceedings of 32th Conference of ORSNZ.Google Scholar
  18. Everett, G., S. Aoude and A. Philpott 2001. Capital Planning in the Paper Industry using COMPASS, Proceedings of 33th Conference of ORSNZ.Google Scholar
  19. Fabrycky, W. and P. Torgersen 1966. Operations Economy, Prentice-Hall.Google Scholar
  20. Fine, C.H. 1993. Developments in Manufacturing Technology and Economic Evaluation Models, in: S. Graves, A. Rinnooy Kan and P. Zipkin, eds., Logistics of Production and Inventory, Handbooks in Operations Research and Management Science, vol 4, North-Holland.Google Scholar
  21. Fleischmann, B. 1993. Designing Distribution Systems with Transport Economies of Scale, EJOR, 70, 31–42.zbMATHCrossRefGoogle Scholar
  22. Francis, R.L., L.F. McGinnis and J.A. White 1992. Facility Layout and Location, 2nd ed., Prentice-Hall.Google Scholar
  23. Freidenfelds, J. 1981. Capacity Expansion, North-Holland.Google Scholar
  24. Geoffrion, A. and G. Graves 1974. Multicommodity Distribution System Design by Benders Decomposition, Man. Sci., 20, 822–844.MathSciNetzbMATHGoogle Scholar
  25. Geoffrion, A. and R. Powers 1995. 20 Years of Strategic Distribution System Design: An Evolutionary Perspective, Interfaces, 25-5, 105–127.Google Scholar
  26. Glover, F., G. Jones, D. Karney, D. Klingman and J. Mote 1979. An Integrated Production, Distribution, and Inventory-Planning System, Interfaces, 9-5, 21–35.Google Scholar
  27. Hill, T. 1999. Manufacturing Strategy, 3rd ed, McGraw-Hill/Irwin.Google Scholar
  28. Huchzermeier, A. and M. Cohen 1996. Valuing Operational Flexibility under Exchange Rate Risk, Operations Research, 44-1, 100–113.Google Scholar
  29. Kim, D. and P.M. Pardalos 2000. Dynamic Slope Scaling and Trust Interval Techniques for Solving Concave Piecewise Linear Network Flow Problems, Networks, 35-3, 216–222.MathSciNetCrossRefGoogle Scholar
  30. Kogut, B. and N. Kalatilaka 1994. Operating Flexibility, Global Manufacturing and the Option Value of a Multinational Network, Management Science, 40-1, 123–139.Google Scholar
  31. Lakhal, S., A. Martel, M. Oral, and B. Montreuil 1999. Network Companies and Competitiveness: A Framework for Analysis, EJOR, 118-2, 278–294.CrossRefGoogle Scholar
  32. Lakhal, S., A. Martel, O. Kettani and M. Oral 2001. On the Optimization of Supply Chain Networking Decisions, EJOR, 129-2, 259–270.MathSciNetCrossRefGoogle Scholar
  33. Li, S. and D. Tirupati 1994. Dynamic Capacity Expansion Problem with Multiple Products: Technology Selection and Timing of Capacity Additions, Operations Research, 42-5, 958–976.Google Scholar
  34. Luss, H., Operations Research and Capacity Expansion Problems: A Survey, Operations Research, 30,5, 1982, 907–947.zbMATHMathSciNetCrossRefGoogle Scholar
  35. Martel, A. and U. Vankatadri 1999. Optimizing Supply Network Structures Under Economies of Scale, IEPM Conference Proceedings, Glasgow, Book 1, 56–65.Google Scholar
  36. Martel, A. 2002. Conception et gestion de chaînes logistiques, Manuel de formation, Université Laval.Google Scholar
  37. Mazzola, J. and R. Schantz 1997. Multiple-Facility Loading Under Capacity-Based Economies of Scope, Nav. Res. Log., 44, 1997, 229–256.MathSciNetCrossRefzbMATHGoogle Scholar
  38. Owen, S. and M. Daskin 1998. Strategic Facility Location: A Review, EJOR, 111, 423–447.CrossRefzbMATHGoogle Scholar
  39. Paquet, M., A. Martel and B. Montreuil 2003. A manufacturing network design model based on processor and worker capabilities, Proceedings of the International Conference on Industrial Engineering and Production Management, Quebec.Google Scholar
  40. Paquet, M., A. Martel and G. Desaulniers 2004. Including Technology Selection Decisions in Manufacturing Network Design Models, International Journal of Computer Integrated Manufacturing, 17-2, 117–125.CrossRefGoogle Scholar
  41. Philpott, A., and G. Everett 2001. Supply Chain Optimisation in the Paper Industry. Annals of Operations Research, 108 1): 225–237.CrossRefzbMATHGoogle Scholar
  42. Pirkul, H. and V. Jayaraman 1996. Production, Transportation, and Distribution Planning in a Multi-Commodity Tri-Echelon System, Transp. Science, 30-4, 291–302.Google Scholar
  43. Pomper, C. 1976. International Investment Planning: An Integrated Approach, North-Holland.Google Scholar
  44. Porter, M. 1985. Competitive Advantage, Free Press.Google Scholar
  45. Rajagopalan, S. and A. Soteriou 1994. Capacity Acquisition and Disposal with Discrete Facility Sizes, Management Science, 40-7, 903–917.Google Scholar
  46. Revelle, C.S. and G. Laporte 1996. The Plant Location Problem: New Models and Research Prospects, Oper. Res., 44-6, 864–874.Google Scholar
  47. Rosenfield, D., R. Shapiro and R. Bohn 1985. Implications of Cost-Service Trade-offs on Industry Logistics Structures, Interfaces, 15-6, 48–59.Google Scholar
  48. Shapiro, J., V. Singhal and S. Wagner 1993. Optimizing the Value Chain, Interfaces, 23-2, 102–117.Google Scholar
  49. Shapiro, J. 2001. Modeling the Supply Chain, Brooks/Cole Publishing Company.Google Scholar
  50. Shulman, A. 1991. An Algorithm for Solving Dynamic Capacitated Plant Location Problems with Discrete Expansion Sizes, Operations Research, 39-3, 423–436.CrossRefGoogle Scholar
  51. Sule, D. 2001. Logistics of Facility Location and Allocation, Marcel Dekker Inc.Google Scholar
  52. Trigeorgis, L. 1996. Real Options, MIT Press.Google Scholar
  53. Verter, V. and C. Dincer 1992. An integrated evaluation of facility location, capacity acquisition, and technology selection for designing global manufacturing strategies, EJOR, 60, 1–18.CrossRefzbMATHGoogle Scholar
  54. Verter, V. and C. Dincer 1995. Facility Location and Capacity Acquisition: An Integrated Approach, Nav. Res. Log., 42.Google Scholar
  55. Vidal, C. and M. Goetschalckx 1997. Strategic Production-Distribution Models: A Critical Review with Emphasis on Global Supply Chain Models, EJOR, 98, 1–18.CrossRefzbMATHGoogle Scholar
  56. Vidal, C. and M. Goetschalckx 2001. A Global Supply Chain Model with Transfer Pricing and Transportation Cost Allocation, EJOR, 129, 134–158.CrossRefzbMATHGoogle Scholar
  57. Vila, D., A. Martel and R. Beauregard 2004. Designing Logistics Networks in Divergent Process Industries: A Methodology and its Application to the Lumber Industry, Working Paper DT-2004-AM-5, Centor, Université Laval, Québec.Google Scholar
  58. Vila, D., A. Martel and R. Beauregard 2005. Taking Market Forces into Account in the Design of Production-distribution Networks: A Positioning by Anticipation Approach, International Conference on Industrial Engineering and Systems Management Proceedings, Marrakech, Morocco.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Alain Martel
    • 1
  1. 1.Network Organization Technology Research Center (CENTOR)Université LavalQuébecCanada

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