### Abstract

We consider a discrete state, discrete decision epoch inventory replenishment control problem under supply uncertainty. We assume that there is no backlogging, the single period demand d is deterministic, and once an item is placed in inventory, it will not perish. If a units of the product are ordered, then α units are placed into inventory with probability P(α{pipe}a), where ∑_{α=0}^{a}P(α{pipe}a) = 1. Let z=d-x, where x is the current inventory level. For the infinite horizon, total discounted cost criterion, we present conditions that guarantee that an optimal replenishment policy δ ^{*} is such that δ ^{*}(z)=0 for z≤0, δ ^{*}(z)≥z≥0, and δ ^{*}(z)-z is monotonically non-decreasing for z≥0. Such a "staircase" structure has a simple parametric description, which can help to accelerate value iteration and policy iteration.

Original language | English |
---|---|

Pages (from-to) | 581-592 |

Number of pages | 12 |

Journal | Annals of Operations Research |

Volume | 208 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Sep 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Inventory systems
- Markov decision processes
- Periodic review
- Random yields
- Supply uncertainty

### ASJC Scopus subject areas

- Decision Sciences(all)
- Management Science and Operations Research

### Cite this

*Annals of Operations Research*,

*208*(1), 581-592. https://doi.org/10.1007/s10479-011-0929-9

**Inventory replenishment control under supply uncertainty.** / Cheong, Tae Su; White, Chelsea C.

Research output: Contribution to journal › Article

*Annals of Operations Research*, vol. 208, no. 1, pp. 581-592. https://doi.org/10.1007/s10479-011-0929-9

}

TY - JOUR

T1 - Inventory replenishment control under supply uncertainty

AU - Cheong, Tae Su

AU - White, Chelsea C.

PY - 2013/9/1

Y1 - 2013/9/1

N2 - We consider a discrete state, discrete decision epoch inventory replenishment control problem under supply uncertainty. We assume that there is no backlogging, the single period demand d is deterministic, and once an item is placed in inventory, it will not perish. If a units of the product are ordered, then α units are placed into inventory with probability P(α{pipe}a), where ∑α=0aP(α{pipe}a) = 1. Let z=d-x, where x is the current inventory level. For the infinite horizon, total discounted cost criterion, we present conditions that guarantee that an optimal replenishment policy δ * is such that δ *(z)=0 for z≤0, δ *(z)≥z≥0, and δ *(z)-z is monotonically non-decreasing for z≥0. Such a "staircase" structure has a simple parametric description, which can help to accelerate value iteration and policy iteration.

AB - We consider a discrete state, discrete decision epoch inventory replenishment control problem under supply uncertainty. We assume that there is no backlogging, the single period demand d is deterministic, and once an item is placed in inventory, it will not perish. If a units of the product are ordered, then α units are placed into inventory with probability P(α{pipe}a), where ∑α=0aP(α{pipe}a) = 1. Let z=d-x, where x is the current inventory level. For the infinite horizon, total discounted cost criterion, we present conditions that guarantee that an optimal replenishment policy δ * is such that δ *(z)=0 for z≤0, δ *(z)≥z≥0, and δ *(z)-z is monotonically non-decreasing for z≥0. Such a "staircase" structure has a simple parametric description, which can help to accelerate value iteration and policy iteration.

KW - Inventory systems

KW - Markov decision processes

KW - Periodic review

KW - Random yields

KW - Supply uncertainty

UR - http://www.scopus.com/inward/record.url?scp=84883055595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883055595&partnerID=8YFLogxK

U2 - 10.1007/s10479-011-0929-9

DO - 10.1007/s10479-011-0929-9

M3 - Article

AN - SCOPUS:84883055595

VL - 208

SP - 581

EP - 592

JO - Annals of Operations Research

JF - Annals of Operations Research

SN - 0254-5330

IS - 1

ER -