×

zbMATH — the first resource for mathematics

On optimal inventory control with independent stochastic item returns. (English) Zbl 1033.90002
Summary: To a growing extent companies take recovery of used products into account in their material management. One aspect distinguishing inventory control in this context from traditional settings is an exogenous inbound material flow. We analyze the impact of this inbound flow on inventory control. To this end, we consider a single inventory point facing independent stochastic demand and item returns. This comes down to a variant of a traditional stochastic single-item inventory model where demand may be both positive or negative. Using general results on Markov decision processes we show average cost optimality of an (\(s,S\))-order policy in this model. The key result concerns a transformation of the model into an equivalent traditional (\(s,S\))-model without return flows, using a decomposition of the inventory position. Traditional optimization algorithms can then be applied to determine control parameter values. We illustrate the impact of the return flow on system costs in a numerical example.

MSC:
90B05 Inventory, storage, reservoirs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Buchanan, D.J.; Abad, P.L., Optimal policy for a periodic review returnable inventory system, IIE transactions, 30, 1049-1055, (1998)
[2] Cohen, M.A.; Nahmias, S.; Pierskalla, W.P., A dynamic inventory system with recycling, Naval research logistics quarterly, 27, 2, 289-296, (1980) · Zbl 0441.90022
[3] Constantinides, G.M., Stochastic cash management with fixed and proportional transaction costs, Management science, 22, 12, 1320-1331, (1976) · Zbl 0343.90021
[4] Federgruen, A.; Zheng, Y.S., An efficient algorithm for computing an optimal (r,Q) policy in continuous review stochastic inventory systems, Operations research, 40, 808-813, (1992) · Zbl 0758.90021
[5] Fleischmann, M.; Bloemhof-Ruwaard, J.M.; Dekker, R.; van der Laan, E.; van Nunen, J.A.E.E.; Van Wassenhove, L.N., Quantitative models for reverse logistics: A review, European journal of operational research, 103, 1-17, (1997) · Zbl 0920.90057
[6] 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
[7] Heyman, D.P.; Sobel, M.J., Stochastic models in operations research, vol. 2, (1984), McGraw-Hill New York · Zbl 0531.90062
[8] Iglehart, D., Optimality of (s,S) policies in the infinite-horizon dynamic inventory problem, Management science, 9, 259-267, (1963)
[9] Inderfurth, K., Simple optimal replenishment and disposal policies for a product recovery system with leadtimes, OR spektrum, 19, 111-122, (1997) · Zbl 0889.90055
[10] Johansen, S.G., 1997. Computing optimal replenishment policies by structured policy iteration. Working Paper 97/4. University of Aarhus, Denmark · Zbl 0929.90002
[11] Kelle, P.; Silver, E.A., Forecasting the returns of reusable containers, Journal of operations management, 8, 1, 17-35, (1989)
[12] Meyn, S.P.; Tweedie, R.L., Markov chains and stochastic stability, (1993), Springer London · Zbl 0925.60001
[13] Moinzadeh, K.; Nahmias, S., A continuous review model for an inventory system with two supply modes, Management science, 34, 6, 761-773, (1988) · Zbl 0659.90038
[14] Muckstadt, J.A.; Isaac, M.H., An analysis of single item inventory systems with returns, Naval research logistics quarterly, 28, 237-254, (1981) · Zbl 0462.90021
[15] Nahmias, S., Managing repairable item inventory systems: A review, TIMS studies in the management sciences, 16, 253-277, (1981)
[16] Scarf, H., The optimality of (s,S) policies in the dynamic inventory problem, () · Zbl 0203.22102
[17] Sennott, L.I., Average cost optimal stationary policies in infinite state Markov decision processes with unbounded costs, Operations research, 37, 4, 626-633, (1989) · Zbl 0675.90091
[18] Silver, E.A.; Pyke, D.F.; Peterson, R., Inventory management and production planning and scheduling, (1998), John Wiley & Sons New York
[19] Simpson, V.P., Optimum solution structure for a repairable inventory problem, Operations research, 26, 2, 270-281, (1978) · Zbl 0377.90040
[20] Tijms, H., Stochastic models. an algorithmic approach, (1994), Wiley Chichester, UK · Zbl 0838.60075
[21] van der Laan, E.; Dekker, R.; Salomon, M., Product remanufacturing and disposal: A numerical comparison of alternative control strategies, International journal of production economics, 45, 489-498, (1996)
[22] van der Laan, E.; Salomon, M., Production planning and inventory control with remanufacturing and disposal, European journal of operational research, 102, 264-278, (1997) · Zbl 0955.90018
[23] van der Laan, E.; Salomon, M.; Dekker, R.; Van Wassenhove, L., Inventory control in hybrid systems with remanufacturing, Management science, 45, 5, 733-747, (1999) · Zbl 1231.90066
[24] Zheng, Y.-S., A simple proof for optimality of (s,S) policies in infinite-horizon inventory systems, Journal of applied probability, 28, 802-810, (1991) · Zbl 0747.90032
[25] Zheng, Y.-S.; Federgruen, A., Finding optimal (s,S) policies is about as simple as evaluating a single policy, Operations research, 39, 4, 654-665, (1991) · Zbl 0749.90024
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.