Multiple replenishment orders in a continuous-review inventory system with lost sales
Operations Research LettersPublished 1 April 2002
Esmail Mohebbi, M. J. M. Posner
Citations27
SJR quartileQ2
SJR score0.44
SNIP0.68
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The stationary distribution of the on-hand inventory is derived using a level-crossing methodology and this distribution is then used to formulate an exact expression for the long-run average cost per unit time.
Abstract
For a continuous-review inventory system with lost sales, non-unit-sized demand, multiple replenishment orders outstanding, and split deliveries, we derive the stationary distribution of the on-hand inventory using a level-crossing methodology. This distribution is then used to formulate an exact expression for the long-run average cost per unit time. Some numerical results are also presented.
Keywords
Business, Management and Accounting
Operations ResearchPoisson Arrivals See Time Averages
1,247 Citations1982Ronald W. Wolff
This paper presents a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.
Management ScienceSole Versus Dual Sourcing in Stochastic Lead-Time (s, Q) Inventory Models
231 Citations1991Ranga V. Ramasesh, J. Keith Ord +2 more
Operations ResearchLevel Crossings in Point Processes Applied to Queues: Single-Server Case
142 Citations1977Percy H. Brill, M. J. M. Posner
This paper introduces a new methodology for obtaining the stationary waiting time distribution in single-server queues with Poisson arrivals by exploiting the observation that the stationary density of the virtual waiting time can be interpreted as the long-run average rate of downcrossings of a level in a stochastic point process.
Communications in Statistics Stochastic ModelsCharacterizations of generalized hyperexponential distribution functions
117 Citations1987Robert F. Botta, Carl M. Harris +1 more
Journal of the Operational Research SocietyStock Control with Two Suppliers and Normal Lead Times
112 Citations1981D. Sculli, Steve Wu
The results indicate that the reorder level required to give a specific probability of no stock-out during replenishment is lower when using two suppliers simultaneously.
Naval Research Logistics (NRL)Safety stock reduction by order splitting
97 Citations1990Péter Kelle, Edward A. Silver
European Journal of Operational ResearchOptimal ordering policies with two suppliers when lead times and demands are all stochastic
75 Citations1993Hon‐Shiang Lau, Long-Geng Zhao
European Journal of Operational ResearchDetermining optimal order splitting and reorder level for N-supplier inventory systems
72 Citations1999Dayani Sedarage, Okitsugu Fujiwara +1 more
This paper develops a mathematical model describing the multiple-supplier single-item inventory systems, where the item acquisition lead times of suppliers and demand arrival are random, and backorder is allowed.
Naval Research Logistics (NRL)Sole sourcing versus dual sourcing under stochastic demands and lead times
66 Citations1994Chi Chiang, W.C. Benton
Naval Research Logistics (NRL)A continuous-review inventory system with lost sales and variable lead time
41 Citations1998Esmail Mohebbi, M. J. M. Posner
Operations ResearchApproximate Order Quantities and Reorder Points for Inventory Systems Where Orders Arrive in Two Shipments
35 Citations1989Kamran Moinzadeh, Hau L. Lee
An inventory system where orders may arrive in two shipments, that is, the first shipment of the order may contain only part of the items ordered, while the rest of theitems arrive in a second shipment, is considered.
Lecture notes in economics and mathematical systemsStochastic Processes and their Applications
34 Citations1991Martin J. Beckmann, M.N. Gopalan +1 more
Journal of the Operational Research SocietyReducing Inventory Costs by Order Splitting in the Sole Sourcing Environment
31 Citations1996Chi Chiang, Wen‐Chyuan Chiang
Journal of the Operational Research SocietyAre More Suppliers Better?
28 Citations1995Yuanming Guo, Ram Ganeshan
European Journal of Operational ResearchNumerical analysis of a continuous-review lost-sales inventory model where two orders may be outstanding
17 Citations1992Roger M. Hill
Journal of the Operational Research SocietyAre more suppliers better?: generalising the Guo and Ganeshan procedure
12 Citations2000K. K. Geetha, K. K. Achary
The procedure is based on using the Generalised Lambda Distribution (GLD) to approximate the lead time distribution and has the advantage that the computations involved are very simple and can be used for any continuous unimodal leading time distribution.
International Journal of Production EconomicsContinuous review lost sales inventory models where two orders may be outstanding
9 Citations1994Roger M. Hill
Lecture notes in economics and mathematical systemsA Lost Sales Inventory System with Multiple Reorder Levels
6 Citations1991S. Kalpakam, G. Arivarignan
Journal of the Operational Research SocietyApproximate analysis of the delivery splitting model
6 Citations2000Frank Janssen, A.G. de Kok +1 more
It is shown that for the supplier considerable cost savings can be obtained by using the concept of delivery splitting, although the motivation and the practical implementation can be different for buyer and supplier.
Operations Research LettersAn inventory system with multiple replenishment scheduling
5 Citations1994Liao Ching-Jong, Wen-Hwa Yang
An inventory system in which more than on replenishment of an item are triggered whenever the inventory level drops to the order point or lower is considered, which minimizes the sum of the expected holding and shortage costs.