×

Redistributing stock in library systems with a depot. (English) Zbl 1458.90146

Summary: Public library organizations often utilize depots for carrying out shipments to libraries in case of stock-outs and for storing low demand rental items at low cost. Similar systems may be employed by rental companies for other rental products such as tools, DVDs, and jewelry. Since shipments deplete the depot’s inventory, stock must be taken back from the libraries in order to deal with future shipment requests. These shipment and take-back operations are carried out periodically, e.g., daily or weekly. This work focuses on optimizing the decisions for shipments and take-backs. We model the system by means of a Markov decision process and investigate its optimal policy for various problem instances. For the take-back decision, we distinguish between so-called threshold, reactive, and preventive take-backs. We use the insights from the MDP to develop a three-phase take-back heuristic. In experiments, our heuristic performs within 1% on average from the optimal solution. For settings with a large number of libraries, it is shown that an acceptable performance can be achieved by setting a base-stock level at the depot and taking back sufficient stock from the libraries to achieve this level.

MSC:

90B06 Transportation, logistics and supply chain management
90C59 Approximation methods and heuristics in mathematical programming

Software:

MCQueue
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Axsäter, S.; Howard, C.; Marklund, J., A distribution inventory model with transshipments from a support warehouse, IIE Trans., 45, 3, 309-322, (2013)
[2] Dell’Amico, M.; Iori, M.; Novellani, S.; Stützle, T., A destroy and repair algorithm for the bike sharing rebalancing problem, Comput. Oper. Res., 71, 1, 149-162, (2016) · Zbl 1349.90082
[3] Ernst, A.; Gavriliouk, E.; Marquez, L., An efficient Lagrangean heuristic for rental vehicle scheduling, Comput. Oper. Res., 38, 1, 216-226, (2011) · Zbl 1231.90188
[4] George, D.; Xia, C., Fleet-sizing and service availability for a vehicle rental system via closed queueing networks, Eur. J. Oper. Res., 211, 1, 198-207, (2011) · Zbl 1218.90038
[5] Kemeny, J.; Snell, J., Finite Markov chains, (1976), Springer Berlin · Zbl 0328.60035
[6] Köchel, P., Order optimisation in multi-location models with hub-and-spoke structure, Int. J. Prod. Econ., 108, 1, 368-387, (2007)
[7] Li, Z.; Tao, F., On determining optimal fleet size and vehicle transfer policy for a car rental company, Comput. Oper. Res., 37, 2, 341-350, (2010) · Zbl 1175.90227
[8] Muckstadt, J.; Thomas, L., Are multi-echelon inventory methods worth implementing in systems with low-demand-rate items?, Manage. Sci., 26, 5, 483-494, (1980)
[9] Song, D.; Carter, J., Optimal empty vehicle redistribution for hub-and-spoke transportation systems, Nav. Res. Logist., 55, 2, 156-171, (2008) · Zbl 1152.90343
[10] Taguchi, G., Introduction to quality engineering: designing quality into products and processes, (1986), Asian Productivity Organization Tokyo
[11] Tijms, H., A first course in stochastic models, (2003), John Wiley & Sons Chichester · Zbl 1088.60002
[12] Van der Heide, G., Inventory Control for Multi-location Rental Systems, (2015), Ph.D. Thesis. University of Groningen
[13] Van der Heide, G.; Roodbergen, K., Transshipment and rebalancing policies for library books, Eur. J. Oper. Res., 228, 2, 447-456, (2013) · Zbl 1317.90184
[14] Van Wijk, A.; Adan, I.; Van Houtum, G., Optimal allocation policy for a multi-location inventory system with a quick response warehouse, Operat. Res. Lett., 41, 3, 305-310, (2013) · Zbl 1286.90015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.