### Abstract

We consider a periodic-review base stock inventory system with partial backorders. At the beginning of each period t of a T period problem, an order of size q_{t} is placed for delivery one period later. As the stochastic demand is realized, as much as possible of it is filled immediately from the inventory on-hand. If the realized demand exceeds the inventory on-hand, up to q_{t}–k_{t} units of excess demand are backordered to be filled from the pipeline inventory or future orders. The on-order quantity k_{t} denotes the reservation quantity held back for use in subsequent periods. The case k_{t}=q_{t} yields the full lost sales model while the case k_{t}=−∞ yields the full backorder model.

Language | English (US) |
---|---|

Pages | 315-322 |

Number of pages | 8 |

Journal | Operations Research Letters |

Volume | 45 |

Issue number | 4 |

DOIs | |

State | Published - Jul 1 2017 |

### Fingerprint

### Keywords

- Backorders
- Base-stock system
- Inventory
- Lost sales
- Optimal policy
- Stochastic demand

### ASJC Scopus subject areas

- Software
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics

### Cite this

*Operations Research Letters*,

*45*(4), 315-322. DOI: 10.1016/j.orl.2017.04.007

**A finite-horizon inventory system with partial backorders and inventory holdback.** / Xu, Yanyi; Bisi, Arnab; Dada, Maqbool.

Research output: Contribution to journal › Article

*Operations Research Letters*, vol 45, no. 4, pp. 315-322. DOI: 10.1016/j.orl.2017.04.007

}

TY - JOUR

T1 - A finite-horizon inventory system with partial backorders and inventory holdback

AU - Xu,Yanyi

AU - Bisi,Arnab

AU - Dada,Maqbool

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We consider a periodic-review base stock inventory system with partial backorders. At the beginning of each period t of a T period problem, an order of size qt is placed for delivery one period later. As the stochastic demand is realized, as much as possible of it is filled immediately from the inventory on-hand. If the realized demand exceeds the inventory on-hand, up to qt–kt units of excess demand are backordered to be filled from the pipeline inventory or future orders. The on-order quantity kt denotes the reservation quantity held back for use in subsequent periods. The case kt=qt yields the full lost sales model while the case kt=−∞ yields the full backorder model.

AB - We consider a periodic-review base stock inventory system with partial backorders. At the beginning of each period t of a T period problem, an order of size qt is placed for delivery one period later. As the stochastic demand is realized, as much as possible of it is filled immediately from the inventory on-hand. If the realized demand exceeds the inventory on-hand, up to qt–kt units of excess demand are backordered to be filled from the pipeline inventory or future orders. The on-order quantity kt denotes the reservation quantity held back for use in subsequent periods. The case kt=qt yields the full lost sales model while the case kt=−∞ yields the full backorder model.

KW - Backorders

KW - Base-stock system

KW - Inventory

KW - Lost sales

KW - Optimal policy

KW - Stochastic demand

UR - http://www.scopus.com/inward/record.url?scp=85019347942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019347942&partnerID=8YFLogxK

U2 - 10.1016/j.orl.2017.04.007

DO - 10.1016/j.orl.2017.04.007

M3 - Article

VL - 45

SP - 315

EP - 322

JO - Operations Research Letters

T2 - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 4

ER -