The {Q,r) Inventory System With An Unreliable Supplier

AbstractThis paper examines the impact on operating costs of having an unreliable supplier in a continuous review, fixed order quantity (Q) — reorder point (r) inventory system. We assume Poisson demand and exponentially distributed lengths of the supplier’s on and off periods. On (off) periods represent time lengths during which the supplier is able (unable) to fill new orders. Any unsatisfied demand is assumed to be lost. We analyze two situations. The first has a negligible lead time but allows the number of outstanding orders, each of a fixed size Q, to be arbitrary. The second situation, on the other hand, has a constant lead time but there the number of outstanding orders is restricted to at most one. In each case, exact expressions necessary to find the average cost minimizing (Q, r) pair are developed and several numerical examples are solved. Computational results show the cost function to be well behaved and suggest that ignoring supply uncertainty or approximate modeling can be relatively very ...

[1]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2]  Joel Weisman,et al.  Introduction to optimization theory , 1973 .

[3]  Colin E. Bell,et al.  Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server , 1971, Oper. Res..

[4]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[5]  A. Seidmann,et al.  Production lot sizing with machine breakdowns , 1992 .

[6]  Michael H. Rothkopf,et al.  Reliability and Inventory in a Production-Storage System , 1979 .

[7]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[8]  H. D. Miller,et al.  The Theory Of Stochastic Processes , 1977, The Mathematical Gazette.

[9]  Leonard Kleinrock,et al.  Queueing Systems: Volume I-Theory , 1975 .

[10]  M. Parlar,et al.  Future supply uncertainty in EOQ models , 1991 .

[11]  David Perry,et al.  Inventory models of future supply uncertainty with single and multiple suppliers , 1996 .

[12]  Hung-Po Chao,et al.  Inventory Policy in the Presence of Market Disruptions , 1987, Oper. Res..

[13]  Kamran Moinzadeh,et al.  Analysis of a production/inventory system subject to random disruptions , 1997 .

[14]  S. Sethi,et al.  Planning for surprise: water resources development under demand and supply uncertainty. I. the general model , 1989 .

[15]  Søren Glud Johansen,et al.  Optimal and approximate (Q, r) inventory policies with lost sales and gamma-distributed lead time , 1993 .