Abstract
This paper studies a two-echelon dynamic lot-sizing model with demand time windows and early and late delivery penalties. The problem is motivated by third-party logistics and vendor managed inventory applications in the computer industry where delivery time windows are typically specified under a time definite delivery contract. Studying the optimality properties of the problem, the paper provides polynomial time algorithms that require O(T 3) computational complexity if backlogging is not allowed and O(T 5) computational complexity if backlogging is allowed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aggarwal, A. and Park, J.K. (1993). Improved algorithms for economic lot-size problems, Operations Research 41, 549–571.
Bitran, G.B., Magnanti, T.L. and Yanasse, H.H. (1984), Approximation methods for the uncapacitated dynamic lot size problem, Management Science 30, 1121–1140.
Bitran, G.B. and Yanasse, H.H. (1982), Computational complexity of the capacitated lot size problem, Management Science 28, 1174–1185.
Blackburn, J.D. and Millen, R.A. (1982), Improved heuristics for multistage requirements planning systems, Management Science 28, 44–56.
Bramel, J. and Simchi-Levi, D. (1997), The Logics of Logistics. Springer, New York.
Çetinkaya, S, and Lee, C.-Y. (2000). Stock replenishment and shipment scheduling for vendor managed inventory systems, Management Science 46, 217–232.
Chen, H.-D., Hearn, D.W. and Lee, C.-Y. (1994), A new dynamic programming algorithm for the single item capacitated dynamic lot size model, Journal of Global Optimization 4, 285–300.
Cheng, T.C.E. (1988), Optimal common due date with limited completion time deviation, Computers and Operations Research 15, 420–426.
Chung, C.S. and Lin. C.H.M. (1988), An O(T 2) algorithm for the NI/G/NI/ND capacitated lot size problem, Management Science 34, 420–426.
Crowston, W.B. and Wagner, M.H. (1973), Dynamic lot size models for multistage assembly systems. Management Science 20, 14–21.
Desrochers, M., Desrosiers, J. and Solomon, M. (1992), A new optimization algorithm for the vehicle routing problem with time windows, Operations Research 40, 342–254.
Diaby, M., and Martel, A. (1993), Dynamic lot sizing for multi-echelon distribution systems with purchasing and transportation price discounts, Operations Research 41, 48–59.
Dumas Y., Desrosiers, J. and Soumis, F. (1991), The pickup and delivery problem with time windows, European Journal of Operational Research 54, 7–22.
Federgruen, A. and Tzur, M. (1991), A Simple forward algorithm to solve general dynamic lot-sizing models with n periods in O(nlogn) or O(n) time, Management Science 37, 909–925.
Fisher, M.L., Jornsten, K.O. and Madsen, O.B.G. (1997), Vehicle routing with time windows: two optimization algorithms, Operations Research 45, 488–492.
Florian, M. and Klein, M. (1971), Deterministic production planning with concave costs and capacity constraints, Management Science 18, 12–20.
Jagannathan, R. and Rao, M.R. (1973), A class of deterministic production planning problems, Management Science 19, 1295–1300.
Kohl, N. and Madsen, O.B.G. (1997), An optimization algorithm for the vehicle routing problem with time windows based on lagrangian relaxation. Operations Research 45, 395–406.
Kraemer, F. and Lee, C.-Y. (1993), Common due window scheduling, Production and Operations Management 2, 262–275.
Lee, C.-Y. and Denardo, E.V. (1986), Rolling planning horizon: error bounds for the dynamic lot size model, Mathematics of Operations Research 11, 423–432.
Lee, C.-Y., Çetinkaya, S. and Jaruphongsa, W. (2003), A dynamic model for inventory lot sizing and outbound shipment scheduling at a third party warehouse, Operations Research 51, 735–747.
Lee, C.-Y., Çetinkaya, S. and Wagelmans, A.P.M. (2001), Dynamic lot-sizing model with demand time windows, Management Science 47, 1384–1395.
Liman, S.D. and Ramaswamy, S. (1994), Earliness-tardiness scheduling problem with a common delivery window, Operations Research Letters 15, 195–203.
Liman, S.D., Panwalkar, S.S. and Thongmee, S. (1996), Determination of common due window location in a single machine scheduling problem, European Journal of Operational Research 93, 68–74.
Love, S.F. (1973), Bounded production and inventory models with piecewise concave costs, Management Science 20, 313–318.
Shaw, D.X. and Wagelmans, A.P.M. (1998), Algorithm for single-item capacitated economic lot sizing with piecewise linear production costs and general holding costs. Management Science 44, 831–838.
Swoveland, C. (1975), A deterministic multi-period production planning model with piecewise concave production and holding-backlogging costs, Management Science 21, 1007–1013.
Wagelmans, A.P.M., Van Hoesel, S. and Kolen, A. (1992). Economic lot-sizing:an O (nlogn) 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.
Weng, M.X. and Ventura, J.A. (1994), Scheduling about a large common due date with tolerance to minimize mean absolute deviation of completion times, Naval Research Logistics 41, 843–851.
Zangwill, W.I. (1966), A deterministic multi-period production scheduling model with backlogging, Management Science 13, 105–119.
Zangwill, W.I. (1969), A backlogging model and a multi-echelon model of a dynamic economic lot size production system - a network approach, Management Science 15, 506–527.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jaruphongsa, W., Çetinkaya, S. & Lee, CY. A Two-Echelon Inventory Optimization Model with Demand Time Window Considerations. J Glob Optim 30, 347–366 (2004). https://doi.org/10.1007/s10898-004-6092-y
Issue Date:
DOI: https://doi.org/10.1007/s10898-004-6092-y