Skip to main content
    • Aa
    • Aa

Modeling Stochastic Lead Times in Multi-Echelon Systems

  • E. B. Diks (a1) and M. C. van der Heijden (a2)

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

2.R. Anupindi , T.E. Morton & D. Pentico (1996). The nonstationary stochastic lead-time inventory problem: Near-myopic bounds, heuristics, and testing. Management Science 42: 124129.

3.V.N. Bhat (1993). Approximation for the variance of the waiting time in a GI/G/l queue. Microelectronics and Reliability 33: 19972002.

5.R. Ehrhardt (1984). (s, S) policies for a dynamic inventory model with stochastic lead time. Operations Research 32: 121132.

6.A.A. Fredericks (1982). A class of approximations for the waiting time distribution in a GI/G/l queueing system. Bell System Technical Journal 61: 295325.

7.M.F. Friedman (1984). On a stochastic extension of the EOQ formula. European Journal of Operational Research 17: 125127.

8.D. Gross & A. Soriano (1969). The effect of reducing leadtime on inventory levels-simulation analysis. Management Science 16: B61B76.

11.R. Heuts & J. de Klein (1995). An (s, q) inventory model with stochastic and interrelated lead times. Naval Research Logistics 42: 839859.

12.R.S. Kaplan (1970). A dynamic inventory model with stochastic lead times. Management Science 16: 491507.

15.S. Nahmias (1979). Simple approximations for a variety of dynamic leadtime lost-sales inventory models. Operations Research 27: 904924.

16.G.P. Sphicas (1982). On the solution of an inventory model with variable lead times. Operations Research 30: 404410.

17.G.P. Sphicas & F. Nasri (1984). An inventory model with finite-range stochastic lead times. Naval Research Logistics Quarterly 31: 609616.

19.C.E. Vinson (1972). The cost of ignoring lead time unreliability in inventory theory. Decision Sciences 3: 87105.

20.W. Whitt (1982). Refining diffusion approximations for queues. Operations Research Letters 1: 165169.

21.C.A. Yano (1987). Stochastic leadtimes in two-level distribution-type networks. Naval Research Logistics 34: 831843.

22.P. Zipkin (1986). Stochastic leadtimes in continuous-time inventory models. Naval Research Logistics Quarterly 33: 763774.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Probability in the Engineering and Informational Sciences
  • ISSN: 0269-9648
  • EISSN: 1469-8951
  • URL: /core/journals/probability-in-the-engineering-and-informational-sciences
Please enter your name
Please enter a valid email address
Who would you like to send this to? *