Abstract
The inventory of spare parts that a firm holds depends on the number of working parts and age of the equipment to be serviced, the expected failure rate associated with each working part, and the acceptable level of service. We model the problem of consolidation of spare parts to reduce overall inventory as an integer program with a nonlinear objective function. A linear reformulation of this model is obtained that helps solve some practical instances. A more compact implicit formulation is developed and solved using a specialized branch-and-price technique. We also demonstrate how this specialized branch-and-price technique is modified to devise a very effective heuristic procedure with a prespecifiable guarantee of quality of solution produced. This provides a practical and efficient methodology for maintenance spare consolidation.
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References
F. Barahona and R. Majhoub, “On the cut polytope, ” Mathematical Programming, vol. 36, pp. 157–173, 1986.
C. Barnhart, E.L. Johnson, G.L. Nemhauser, M.W.P. Savelsbergh, and P.H. Vance, “Branch-and-price: Column generation for huge integer programs, ” Operations Research, vol. 46, no. 3, pp. 316–329, 1998.
S. Chopra and M.R. Rao, “The partition problem, ” Mathematical Programming, vol. 59, pp. 87–116, 1993.
C.E. Ferreira, A. Martin, C.C. DeSouza, R. Weismantel, and L.A. Wolsey, “Formulations and valid inequalities for the node capacitated graph partitioning problem, ” Mathematical Programming, vol. 74, pp. 247–266, 1996.
C.E. Ferreira, A. Martin, C.C. De Souza, R. Weismantel, and L.A. Wolsey, “The node capacitated graph partitioning problem: A computational study, ” Mathematical Programming, Series B, vol. 81, pp. 229–256, 1998.
M. Grötschel and Y. Wakabayashi, “A cutting plane algorithm for a clustering problem, ” Mathematical Programming, Series B, vol. 45, pp. 59–96, 1989.
M. Grötschel and Y. Wakabayashi, “Facets of the clique partitioning polytope, ” Mathematical Programming, vol. 47, pp. 367–387, 1990.
E.L. Johnson, “Modeling and strong linear programs for mixed integer programming, ” in Algorithms and Model Formulations in Mathematical Programming, S.W. Wallace (Ed.), NATO ASI Series 51, 1989.
E.L. Johnson, A. Mehrotra, and G.L. Nemhauser, “Min-cut clustering, ” Mathematical Programming, vol. 62, pp. 133–151, 1993.
A. Mehrotra and M.A. Trick, “A column generation approach for graph coloring, ” INFORMS Journal on Computing, vol. 8, pp. 344–354, 1996.
A. Mehrotra and M.A. Trick, “Cliques and clustering: A combinatorial approach, ” Operations Research Letters, vol. 22, no. 1, pp. 1–12, 1997.
G.L. Nemhauser, M.W.P. Savelsbergh, and G.C. Sigismondi, “Minto, a mixed integer optimizer, ” Operations Research Letters, vol. 15, pp. 47–58, 1994.
J.C. Picard and H.D. Ratliff, “Minimum cuts and related problems, ” Networks, vol. 5, pp. 394–422, 1975.
J.M.W. Rhys, “A selection problem of shared fixed costs and network flows, ” Management Science, vol. 17, pp. 200–207, 1970.
D.M. Ryan and B.A. Foster, “An integer programming approach to scheduling, ” in Computer Scheduling of Public Transport Urban Passenger Vehicle and Crew Scheduling, A. Wren (Ed.), North Holland, Amsterdam, 1981, pp. 269–280.
M.W.P. Savelsbergh, “A branch-and-price algorithm for the generalized assignment problem, ” Operations Research, vol. 45, no. 6, pp. 831–841, 1997.
P.H. Vance, C. Barnhart, E.L. Johnson, and G.L. Nemhauser, “Solving binary cutting stock problems by column generation and branch-and-bound, ” Computational Optimization and Applications, vol. III, pp. 111–130, 1993.
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Mehrotra, A., Natraj, N. & Trick, M.A. Consolidating Maintenance Spares. Computational Optimization and Applications 18, 251–272 (2001). https://doi.org/10.1023/A:1011285220132
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DOI: https://doi.org/10.1023/A:1011285220132