Abstract
We analyze a version of the Dynamic Lot Size (DLS) model where demands can be positive and negative and disposals of excess inventory are allowed. Such problems arise naturally in several applications areas, including retailing where previously sold items are returned to the point of sale and re-enter the inventory stream (such returns can be viewed as negative demands), and in managing kits of spare parts for scheduled maintenance of aircraft (where excess spares are returned to the depot), among other applications. Both the procurement of new items and the disposal of excess inventory decisions are considered within the framework of deterministic time-varying demands, concave holding, procurement and disposal costs and a finite time horizon (disposal of excess inventory at a profit is also allowed). By analyzing the structure of optimal policies, several useful properties are derived, leading to an efficient dynamic programming algorithm. The new model is shown to be a proper generalization of the classical Dynamic Lot Sizing Model, and the computational complexity of our algorithm is compared with that of the standard algorithms for the DLS model. Both the theoretical worst-case complexity analysis and a set of computational experiments are undertaken. The proposed methodology appears to be quite adequate for dealing with realistic-sized problems.
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References
Aggarwal, A. and Park, J.K. (1993) Improved algorithms for economic lot size problems. Operations Research, 41, 549–571.
Beltrán, J.L. (1998) On inventory models with salable returns. Ph.D.Dissertation, Faculty of Management, University of Toronto, Toronto, Canada.
Beltrán, J.L., Beyer, D., Krass, D. and Ramaswami, S. (1998) Stochastic inventory models with returns and delivery commitments.Working paper, Joseph L. Rotman School of Management, University of Toronto, Toronto, Canada.
Bahl, H.C., Ritzman, L.R. and Gupta, J.N.D. (1987) Determining lot sizes and resources requirements: a review. Operations Research, 35, 329–345.
Bensoussan, A., Crouhy, M. and Proth, J.M. (1983) Mathematical Theory of Production Planning, North Holland, Amsterdam, The Netherlands.
Chambers, M.L. and Eglese, R.W. (1986) Use of preview exercises to forecast demand for new lines in mail order. Journal of the Operational Research Society, 37, 267–273.
Chand, S. and Morton, T.E. (1982) Aperfect planning horizon procedure for a deterministic cash balance problem. Management Science, 28, 652–669.
Erickson, R.R., Monma, C.L. and Veinott, Jr., A.F. (1987) Send and split method for minimum concave costs network flows. Mathematics of Operations Research, 12(4), 634–664.
Federgruen, A. and Tzur, M. (1991) A simple forward algorithm to solve general dynamic lot sizing models with n periods O(n log n) or O(n) Time. Management Science, 37, 909–925.
Florian, M. Lenstra, J.K. and Rinnooy Kan, A.H.G. (1980) Deterministic production planning: algorithms and complexity. Management Science, 26, 669–679.
Graves, S.C. (1982) Using Lagrangian techniques to solve hierarchical production planning problems. Management Science, 28, 260–275.
Luss, H. (1982) Operations research and capacity expansion problems: a survey. Operations Research, 30, 907–947.
Manne, A.S. (1958) Programming of economic lot sizes. Management Science, 4, 115–135.
Thierry, M.C., Salomon, M., Van Nunen, J.A.E.E. and Van Wassenhove, L.N. (1995) Strategic production and operations management issues in product recovery management. California Management Review, 37, 114–135.
Van der Laan, E.A., Dekker, R., Ridder, A.A.N., and Salomon, M. (1994) An (s,Q) inventory model with remanufacturing Dynamic lot sizing with returning items and disposals 447 and disposal. International Journal of Production Economics (in press).
Veinott, Jr., A.F. (1969) Minimum concave-cost solutions of Leontief substitution models of multifacility inventory systems. Operations Research, 17, 262–291.
Wagelmans, A., Van Hoesel, S. and Kolen, A. (1992) Economic lot sizing: an O(n log n) algorithm that runs in linear time in the Wagner-Whitin case. Operations Research, 40, S145–S156.
Wagner, H.M. and Whitin, T.M. (1958) Dynamic version of the economic lot size model. Management Science, 5, 89–96.
Zangwill, W.I. (1966) Adeterministic multi-period production scheduling model with backlogging. Management Science, 12, 105–119.
Zangwill, W.I. (1968) Minimum concave cost flows in certain networks.Management Science, 14, 429–450.
Zangwill, W.I. (1969) Abacklogging model and a multi-echelon model of a dynamic economic lot size production system - a network approach. Management Science, 15, 506–527.
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Beltrán, J.L., Krass, D. Dynamic lot sizing with returning items and disposals. IIE Transactions 34, 437–448 (2002). https://doi.org/10.1023/A:1013554800006
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DOI: https://doi.org/10.1023/A:1013554800006