Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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A Study on Developing an Integrated Model of Facility Location Problems and Safety Stock Optimization Problems in Supply Chain Management

공급사슬관리에서 생산입지선정 문제와 안전재고 최적화 문제의 통합모형 개발에 관한 연구

  • 조건 (전남대학교 경영학부, 경영연구소)
  • Published : 2006.03.01
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Abstract

Given a bill of materials (BOM) tree T labeled by the breadth first search (BFS) order from node 0 to node n and a general network ${\Im}=(V,A)$, where V={1,2,...,m} is the set of production facilities and A is the set of arcs representing transportation links between any of two facilities, we assume that each node of T stands for not only a component. but also a production stage which is a possible stocking point and operates under a periodic review base-stock policy, We also assume that the random demand which can be achieved by a suitable service level only occurs at the root node 0 of T and has a normal distribution $N({\mu},{\sigma}^2)$. Then our integrated model of facility location problems and safety stock optimization problem (FLP&SSOP) is to identify both the facility locations at which partitioned subtrees of T are produced and the optimal assignment of safety stocks so that the sum of production cost, inventory holding cost, and transportation cost is minimized while meeting the pre-specified service level for the final product. In this paper, we first formulate (FLP&SSOP) as a nonlinear integer programming model and show that it can be reformulated as a 0-1 linear integer programming model with an exponential number of decision variables. We then show that the linear programming relaxation of the reformulated model has an integrality property which guarantees that it can be optimally solved by a column generation method.

Keywords

References

  1. Balinski, M.L. and P. Wolfe, 'On Benders Decomposition and a Plant Location Problem,' Working paper ARO-27, Mathematica, Inc., Princeton, New Jersey, 1963
  2. Barcelo, J. and J. Casanovas, 'A Heuristic Lagrangean Algorithm for the Capacitated Plant Location Problem,' European Journal of Operational Research, Vol.15(1984), pp. 212-226 https://doi.org/10.1016/0377-2217(84)90211-X
  3. Barnhart, C., E.L. Johnson, G.L. Nemhauser, M.W.P. Savelsbergh, P.H. Vance, 'Branchand- price：Column Generation for Solving Huge Integer Programs,' Operations Research, Vol.46(1998), pp.316-329 https://doi.org/10.1287/opre.46.3.316
  4. Cho, G., 'A Pseudopolynomial-time Algorithm for Solving a Capacitated Subtree of a Tree Problem in a Telecommunication System,' Journal of the Korean Institute of Industrial Engineers, Vol.22, No.3(1996), pp.485-498
  5. Cho, G., 'An Efficient Algorithm for an Uncapacitated Facility Location Problem on a Tree Structured Network,' DAEHAN Journal of Business, Vol.18(1998), pp.97-109
  6. Conn, A.R. and G. Cornuejols, 'A Projection Method for the Uncapacitated Facility Location Problem,' CS-87-19, Computer Science Department, University of Waterloo, 1987
  7. Cornuejols, G. and J.M. Thizy, 'Some Facets of the Simple Plant Location Polytope,' Mathematical Programming, Vol. 23(1982), pp. 50-74 https://doi.org/10.1007/BF01583779
  8. Graves, S.C. and S.P. Willems, 'Optimizing Strategic Safety Stock Placement in Supply Chains,' Manufacturing & Service Operations Management, Vol.2, No.1(2000), pp. 68-83 https://doi.org/10.1287/msom.2.1.68.23267
  9. Holmberg, K., M. Ronqvist, and D. Yuan, 'An Exact Algorithm for the Capacitated Facility Location Problems with Single Sourcing,' European Journal of Operational Research, Vol.113(1999), pp.544-559 https://doi.org/10.1016/S0377-2217(98)00008-3
  10. Inderfurth, K., 'Safety Stock Optimisation in Multi Stage Inventory Systems,' International Journal of Production Economics, Vol.24(1991), pp.103-113
  11. Klincewicz, J. and H. Luss, 'A Lagrangian Relaxation Heuristic for Capacitated Facility Location with Single-source Constraints,' Journal of Operational Research Society, Vol.37(1986), pp.495-500 https://doi.org/10.2307/2582672
  12. Magnanti, T.L. and R.T. Wong, 'Accelerated Benders Decomposition：Algorithmic Enhancement and Model Selection Criteria,' Operations Research, Vol.29(1981), pp.464- 484 https://doi.org/10.1287/opre.29.3.464
  13. Mirchandani, P.B. and R.L. Francis, Discrete Location Theory, John Wiley and Sons, Inc. New York, U.S.A, 1990
  14. Pirkul, H., 'Efficient Algorithm for the Capacitated Concentrator Location Problem,' Computers and Operations Research, Vol. 14(1987), pp.197-208 https://doi.org/10.1016/0305-0548(87)90022-0
  15. Savelsbergh, M., 'A Branch-and-Price Algorithm for the Generalized Assignment Problem,' Operations Research, Vol.45(1997), pp.831-841 https://doi.org/10.1287/opre.45.6.831
  16. Shaw, D.X., 'Reformulation and Column Generation for Several Telecommunication Network Design Problems, Technical Report, School of Industrial Engineering, Purdue University, West Lafayette, IN47907, U.S.A., 1993
  17. Shen, Z.M., C. Coullard, and M.S. Daskin, 'A Joint Location-inventory Model,' to appear in Transportation Science, 2001
  18. Simpson, K.F., 'In-process Inventories,' Operations Research, Vol.6(1958), pp.863- 873 https://doi.org/10.1287/opre.6.6.863
  19. Sridharan, R., 'A Lagrangian Heuristic for the Capacitated Plant Location Problem with Single Source Constraints,' European Journal of Operational Research, Vol.66 (1993), pp.305-312 https://doi.org/10.1016/0377-2217(93)90219-D