Some stochastic inventory models with deterministic variable lead time. (English) Zbl 0933.90005

Summary: We determine optimal reduction in the procurement lead time duration for some stochastic inventory models, jointly with the optimal ordering decisions. The models are developed with complete and partial information about the lead time demand distribution. The stochastic models analyzed in this paper are the classical continuous and periodic review models with a mixture of backorders and lost sales and the base stock model. For each of these models we provide sufficient conditions for the uniqueness of the optimal operating policy. We also develop algorithms for solving these models and provide illustrative numerical examples.


90B05 Inventory, storage, reservoirs
Full Text: DOI


[1] Ben-Daya, M; Raouf, A, Inventory models involving lead time as a decision variable, J. oper. res. soc., 45, 579-582, (1994) · Zbl 0805.90037
[2] Burgin, T.A, The gamma distribution and inventory control, Oper. res. quart., 26, 507-525, (1975) · Zbl 0326.90019
[3] C. Das, Explicit formulas for the order size and reorder point in certain inventory problems, Naval Res. Logist. Quart. 23 (1976) 25-30 · Zbl 0332.90014
[4] Das, C, Approximate solution to the (Q, r) inventory model for gamma lead time demand, Management sci., 22, 1043-1047, (1976) · Zbl 0326.90020
[5] Das, C, Effect of lead time on inventory: A static analysis, Oper. res. quart., 26, 273-282, (1975) · Zbl 0325.90018
[6] Foote, B; Kebriaei, N; Kumin, H, Heuristic policies for inventory ordering problems with long and randomly varying lead time, J. oper. management, 7, 115-124, (1988)
[7] Gallego, G, A minmax distribution free procedure for the (Q, r) inventory model, Oper. res. lett., 11, 55-60, (1992) · Zbl 0764.90025
[8] Gallego, G; Moon, I, The distribution free newsboy problem: review and extension, J. oper. res. soc., 44, 825-834, (1993) · Zbl 0781.90029
[9] G. Hadley, T.M. Whitin, Analysis of Inventory Systems, Prentice-Hall, Englewood Cliffs, NJ, 1963 · Zbl 0133.42901
[10] F.S. Hillier, G.J. Lieberman, Introduction to Operations Research, 6th edition, McGraw-Hill, New York, 1995 · Zbl 0155.28202
[11] L.A. Johnson, D.C. Montgomery, Operations Research in Production Planning, Scheduling, and Inventory Control, Wiley, New York, 1974
[12] Liao, C.J; Shyu, C.H, An analytical determination of lead time with normal demand, Internat. J. oper. prod. management, 11, 72-78, (1991)
[13] S. Love, Inventory Control, McGraw-Hill, New York, 1979
[14] Magson, D, Stock control when the lead time cannot be considered constant, J. oper. res. soc., 44, 825-834, (1993)
[15] Montgomery, D.C; Bazara, M.S; Keswani, A.K, Inventory models with mixture of backorders and lost sales, Naval res. logist. quart., 20, 255-263, (1973) · Zbl 0262.90020
[16] I. Moon, The effect of lead time reduction in a continuous review inventory model, Working paper, Department of Industrial Engineering, Pusan National University, 1977
[17] Moon, I; Gallego, G, Distribution free procedures for some inventory models, J. oper. res. soc., 45, 651-658, (1994) · Zbl 0920.90050
[18] Moon, I; Choi, S, The distribution free newsboy problem with balking, J. oper. res. soc., 46, 537-542, (1995) · Zbl 0830.90039
[19] Ouyang, L.Y; Yeh, N.C; Wu, K.S, Mixture inventory models with backorders and lost sales for variable lead time, J. oper. res. soc., 47, 829-832, (1996) · Zbl 0856.90041
[20] H. Scarf, A min – max solution of an inventory problem, in: K. Arrow, S. Karlin, H. Scarf (Eds.), Studies in the Mathematical Theory of Inventory and Production, Stanford University Press, Stanford, CA, 1958
[21] E.A. Silver, R. Peterson, Decision Systems for Inventory Management and Production Planning, Wiley, New York, 1985
[22] H.M. Wagner, Principles of Operations Research, 2nd edition, Prentice-Hall, Englewood Cliffs, NJ, 1975
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.