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The repair kit problem with positive replenishment lead times and fixed ordering costs. (English) Zbl 1403.90046

Summary: The repair kit problem (RKP) concerns the determination of a set of items taken by a service engineer to perform on-site product support. Such a set is called a kit. Models developed in the literature have always ignored the lead times associated with delivering items to replenish the kit, thereby limiting the practical relevance of the proposed solutions. Motivated by a real life case, we develop a model with positive lead times to control the replenishment quantities of the items in the kit, and study the performance of (\(s, S\)) policies under a service objective. The choice for (\(s, S\)) policies is made in order to accommodate fixed ordering costs. We present a method to calculate job fill rates with exact expressions, and discuss a heuristic approach to optimize the reorder level and order-up-to level for each item in the kit. The empirical utility of the model is assessed on real world data from an equipment manufacturer and useful insights are offered to after-sales managers.

MSC:

90B05 Inventory, storage, reservoirs
90B25 Reliability, availability, maintenance, inspection in operations research
90C27 Combinatorial optimization
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References:

[1] Axsäter, S., Inventory control (2006), Springer: Springer New York, (2nd edition) · Zbl 1117.90042
[2] Bijvank, M.; Koole, G.; Vis, I. F.A., Optimising a general repair kit problem with a service constraint, European Journal of Operational Research, 204, 76-85 (2010) · Zbl 1178.90009
[3] Brumelle, S.; Granot, D., The repair kit problem revisited, Operations Research, 41, 994-1006 (1993) · Zbl 0797.90015
[4] Cohen, M. A.; Agrawal, N.; Agrawal, V., Winning in the aftermarket, Harvard Business Review, 84, 129-138 (2006)
[5] Gebauer, H.; Fleisch, E.; Friedli, T., Overcoming the service paradox in manufacturing companies, European Management Journal, 23, 14-26 (2005)
[6] Graves, S. C., A multiple-item inventory model with a job completion criterion, Management Science, 28, 1334-1337 (1982) · Zbl 0504.90026
[7] Guajardo, M.; Rönnqvist, M., Cost allocation in inventory pools of spare parts with service-differentiated demand classes, International Journal of Production Research, 53, 220-237 (2015)
[8] Heeremans, D.; Gelders, L. F., Multiple period repair kit problem with a job completion criterion: a case study, European Journal of Operational Research, 81, 239-248 (1995) · Zbl 0927.90017
[9] Lay, G., Servitization in industry (2014), Springer: Springer Heidelberg
[10] Mamer, J. W.; Smith, S. A., Optimising field repair kits based on job completion rate, Management Science, 28, 1328-1333 (1982) · Zbl 0502.90032
[11] Mamer, J. W.; Shogan, A. W., A constrained capital budgeting problem with applications to repair kit selection, Management Science, 33, 800-806 (1987)
[12] March, S. T.; Scudder, G. D., On optimizing field repair kits based on job completion rate, Management Science, 30, 1025-1028 (1984) · Zbl 0548.90023
[13] Saccani, N.; Visintin, F.; Mansini, R.; Colombi, M., Improving spare parts management for field services: a model and a case study for the repair kit problem, IMA Journal of Management Mathematics, 28, 185-204 (2017) · Zbl 1473.90010
[14] Silver, E. A.; Pyke, D. F.; Peterson, R., Inventory management and production planning and scheduling (1998), John Wiley & Sons: John Wiley & Sons New York, \((3^{rd}\) edition)
[15] Smith, S. A.; Chambers, J. C.; Shlifer, E., Optimal inventories based on job completion rate for repairs requiring multiple items, Management Science, 26, 849-854 (1980) · Zbl 0449.90023
[16] Song, J., On the order fill rate in a multi-item, base stock inventory system, Operations Research, 46, 831-845 (1998) · Zbl 0987.90011
[17] Syntetos, A. A.; Keyes, M.; Babai, M. Z., Demand categorisation in a European spare parts logistics network, International Journal of Operations & Production Management, 29, 292-316 (2009)
[18] Teunter, R. H., The multiple-job repair kit problem, European Journal of Operational Research, 175, 1103-1116 (2006) · Zbl 1142.90313
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