Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand

J.J.A. Moors, L.W.G. Strijbosch

Research output: Working paperDiscussion paperOther research output

366 Downloads (Pure)

Abstract

For the familiar (R; s; S) inventory control system only approximate expressions exist for the fill rate, i.e. the fraction of demand that can be satisfied from stock.Best-known are the approximations derived from renewal theory by Tijms & Groenevelt (1984), holding under specific conditions; in particular, S ¡ s should be reasonably large.They considered, more specifically, the cases of normally and gamma distributed demand.Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued parameters, while lead time is constant.This formula is checked through extensive simulations; besides, detailed comparisons are made with Tijms & Groenevelt's approximation.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages20
Volume2001-32
Publication statusPublished - 2001

Publication series

NameCentER Discussion Paper
Volume2001-32

Keywords

  • demand
  • inventory control
  • simulation

Cite this

Moors, J. J. A., & Strijbosch, L. W. G. (2001). Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand. (CentER Discussion Paper; Vol. 2001-32). Tilburg: Operations research.
Moors, J.J.A. ; Strijbosch, L.W.G. / Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand. Tilburg : Operations research, 2001. (CentER Discussion Paper).
@techreport{c967aa9cb4fa40749fbfc1f64940cb37,
title = "Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand",
abstract = "For the familiar (R; s; S) inventory control system only approximate expressions exist for the fill rate, i.e. the fraction of demand that can be satisfied from stock.Best-known are the approximations derived from renewal theory by Tijms & Groenevelt (1984), holding under specific conditions; in particular, S ¡ s should be reasonably large.They considered, more specifically, the cases of normally and gamma distributed demand.Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued parameters, while lead time is constant.This formula is checked through extensive simulations; besides, detailed comparisons are made with Tijms & Groenevelt's approximation.",
keywords = "demand, inventory control, simulation",
author = "J.J.A. Moors and L.W.G. Strijbosch",
note = "Pagination: 20",
year = "2001",
language = "English",
volume = "2001-32",
series = "CentER Discussion Paper",
publisher = "Operations research",
type = "WorkingPaper",
institution = "Operations research",

}

Moors, JJA & Strijbosch, LWG 2001 'Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand' CentER Discussion Paper, vol. 2001-32, Operations research, Tilburg.

Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand. / Moors, J.J.A.; Strijbosch, L.W.G.

Tilburg : Operations research, 2001. (CentER Discussion Paper; Vol. 2001-32).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand

AU - Moors, J.J.A.

AU - Strijbosch, L.W.G.

N1 - Pagination: 20

PY - 2001

Y1 - 2001

N2 - For the familiar (R; s; S) inventory control system only approximate expressions exist for the fill rate, i.e. the fraction of demand that can be satisfied from stock.Best-known are the approximations derived from renewal theory by Tijms & Groenevelt (1984), holding under specific conditions; in particular, S ¡ s should be reasonably large.They considered, more specifically, the cases of normally and gamma distributed demand.Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued parameters, while lead time is constant.This formula is checked through extensive simulations; besides, detailed comparisons are made with Tijms & Groenevelt's approximation.

AB - For the familiar (R; s; S) inventory control system only approximate expressions exist for the fill rate, i.e. the fraction of demand that can be satisfied from stock.Best-known are the approximations derived from renewal theory by Tijms & Groenevelt (1984), holding under specific conditions; in particular, S ¡ s should be reasonably large.They considered, more specifically, the cases of normally and gamma distributed demand.Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued parameters, while lead time is constant.This formula is checked through extensive simulations; besides, detailed comparisons are made with Tijms & Groenevelt's approximation.

KW - demand

KW - inventory control

KW - simulation

M3 - Discussion paper

VL - 2001-32

T3 - CentER Discussion Paper

BT - Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand

PB - Operations research

CY - Tilburg

ER -

Moors JJA, Strijbosch LWG. Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand. Tilburg: Operations research. 2001. (CentER Discussion Paper).