×

zbMATH — the first resource for mathematics

Empty container management in a port with long-run average criterion. (English) Zbl 1112.90004
Summary: The empty container allocation problem in a port is related to one of the major logistics issues faced by distribution and transportation companies: the management of importing empty containers in anticipation of future shortage of empty containers or exporting empty containers in response to reduce the redundance of empty containers in this port. We considered the problem to be a nonstandard inventory problem with positive and negative demands at the same time under a general holding-penalty cost function and one-time period delay availability for full containers just arriving at the port. The main result is that there exists an optimal pair of critical policies for the discounted infinite-horizon problem via a finite-horizon problem, say \((U, D)\). That is, importing empty containers up to \(U\) when the number of empty containers in the port is less than \(U\), or exporting the empty containers down to \(D\) when the number of empty containers is more than \(D\), doing nothing otherwise. Moreover, we obtain the similar result over the average infinite horizon.

MSC:
90B05 Inventory, storage, reservoirs
90C40 Markov and semi-Markov decision processes
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Crainic, T.G; Laporte, G., Planning models for freight transportation, European journal of operational research, 97, 409-438, (1997) · Zbl 0919.90055
[2] Dejax, P.J.; Crainic, T.G., A review of empty flows and fleet management models in frieght transportation, Transportation science, 21, 227-247, (1987)
[3] Chih, K.C.K., A realtime dynamic optimal frieght car management simulation model of the multiple railroad, multicommodity temporal spatial network flow problem, ()
[4] Adamidou, E.A.; Kornhouser, A.L.; Koskosidis, Y.A., A game theoretic/network equilibrium solution approach for the railroad car management problem, Transportation research B, 27B, 237-252, (1993)
[5] Powell, W.B., Toward a unified modeling framework for real-time control of logistics, Military journal of operations research, 1, 4, (1995)
[6] Powell, W.B., A comparative review of alternative algorithms for the dynamic vehile allocation problem, (), 249-292
[7] Frantzeskakis, L.; Powell, W.B., A successive linear approximation procedure for stochastic dynamic vehicle allocation problems, Transportation science, 24, 40-57, (1990) · Zbl 0746.90044
[8] Powell, W.B.; Cheung, R.K., An algorithm for multistage dynamic networks with random arc capacities, with an application to dynamic fleet management, Operations research, 37, 12-29, (1996)
[9] Cheung, R.K.; Chen, C.Y., A two-stage stochastic network model and solution methods for the dynamic empty container allocation problem, Transportation science, 32, 142-162, (1998) · Zbl 0987.90515
[10] Lai, K.K.; Lam, K.K.; Chan, W.K., Shipping container logistics and allocation, Journal of the operational research society, 46, 687-697, (1995)
[11] Crainic, T.G.; Delorme, L., Dual-ascent procedure for multicommodity location-allocation problems with balancing requirements, Transportation science, 27, 90-101, (1993) · Zbl 0788.90043
[12] Gendron, B.; Crainic, T.G., A branch-and-bound algorithm for depot location and container fleet management, Location science, 3, 39-53, (1995) · Zbl 0917.90227
[13] Abrache, J.; Crainic, T.G.; Gendreau, M., A new decomposition algorithm for the deterministic dynamic allocation of empty containers, ()
[14] Park, C.S.; Noh, Y.D., A port simulation model for bulk cargo operations, Simulation, 48, 236-246, (1987)
[15] El Sheikh, A.A.; Paul, R.J.; Harding, A.S.; Balmer, D.W., A microcomputer-based simulation study of a port, Journal of the operational research society, 38, 673-681, (1987)
[16] Girgis, N.M., Optimal cash balance levels, Management science, 15, 130-140, (1968) · Zbl 0167.48302
[17] Eppen, G.D.; Fama, E.F., Cash balance and simple dynamic portfolio problems with proportional costs, International economic review, 10, 119-133, (1969) · Zbl 0212.24904
[18] Neave, E.H., The stochastic cash balance problem with fixed costs for increases and decreases, Management science, 16, 472-490, (1970) · Zbl 0193.19604
[19] Whisler, W.D., A stochastic inventory model for rented equipment, Management science, 13, 640-647, (1967)
[20] Marvel, H.P.; Peck, J., Demand uncertainty and returns policies, International economic review, 36, 691-714, (1995) · Zbl 0836.90019
[21] Pasternack, B.A., Optimal pricing and return policies for perishable commodities, Markeing science, 4, 166-176, (1985)
[22] Padmanabhan, V.; Png, I.P.L., Manufacturer’s returns policies and retail competition, Markeing science, 16, 81-94, (1997)
[23] Heyman, D.P.; Sobel, M.J., ()
[24] Heyman, D.P., Optimal disposal policies for a single-item inventory system with returns, Naval research logistics quarterly, 24, 385-405, (1977) · Zbl 0371.90034
[25] Teunter, R.H.; van der Laan, E., On the non-optimality of the average cost approach for inventory models with remanufacturing, International journal of production and economics, 79, 1, 67-73, (2002)
[26] Teunter, R.H., Economic ordering quantities for recoverable item inventory systems, Naval research logistics, 48, 6, 48-496, (2001) · Zbl 1009.90011
[27] Liu, J.Y.; Liu, K., Some problems about optimal policies of finite stage Markov decision programming, Military operations research, 2, 76-85, (1988), (in Chinese)
[28] Dong, Z.Q.; Liu, K., Structure of optimal policies for discounted semi-Markov decision programming with unbounded rewards, Scientia sinica, XXIX, 337-349, (1986) · Zbl 0618.90098
[29] Filar, J.A.; Vrieze, K., Competitive Markov decision processes, (1996), Springer New York · Zbl 0763.90093
[30] Chen, M.; Filar, J.A.; Liu, K., Semi-infinite Markov decision processes, Mathematical methods of operations research, 51, 115-137, (2000) · Zbl 0983.90071
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.