### Abstract

In many applications it is necessary to find a minimum weight assignment that satisfies one or several additional resource constraints. For example, consider the problem of assigning persons to jobs where each assignment utilizes at least two scarce resources and the resource utilization is dependent on the person and the type of task. A practical situation where the above might occur is a slaughter house where the "cutters" are assigned to different cut patterns. In this case the resources are the time, the cost and the productivity measured in terms of quality and amount of the end products. In this paper we study the resource constrained assignment problem and derive several classes of valid inequalities based on the properties of the knapsack and assignment polytopes. We also present an algorithm that uses both the linear programming and the Lagrangean relaxation of the original problem in order to solve the separation problem. Some computational experiments are presented.

Original language | English (US) |
---|---|

Pages (from-to) | 175-191 |

Number of pages | 17 |

Journal | Discrete Applied Mathematics |

Volume | 26 |

Issue number | 2-3 |

DOIs | |

State | Published - Jan 1 1990 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*26*(2-3), 175-191. https://doi.org/10.1016/0166-218X(90)90099-X

**Resource constrained assignment problems.** / Aboudi, Ronny; Jørnsten, Kurt.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 26, no. 2-3, pp. 175-191. https://doi.org/10.1016/0166-218X(90)90099-X

}

TY - JOUR

T1 - Resource constrained assignment problems

AU - Aboudi, Ronny

AU - Jørnsten, Kurt

PY - 1990/1/1

Y1 - 1990/1/1

N2 - In many applications it is necessary to find a minimum weight assignment that satisfies one or several additional resource constraints. For example, consider the problem of assigning persons to jobs where each assignment utilizes at least two scarce resources and the resource utilization is dependent on the person and the type of task. A practical situation where the above might occur is a slaughter house where the "cutters" are assigned to different cut patterns. In this case the resources are the time, the cost and the productivity measured in terms of quality and amount of the end products. In this paper we study the resource constrained assignment problem and derive several classes of valid inequalities based on the properties of the knapsack and assignment polytopes. We also present an algorithm that uses both the linear programming and the Lagrangean relaxation of the original problem in order to solve the separation problem. Some computational experiments are presented.

AB - In many applications it is necessary to find a minimum weight assignment that satisfies one or several additional resource constraints. For example, consider the problem of assigning persons to jobs where each assignment utilizes at least two scarce resources and the resource utilization is dependent on the person and the type of task. A practical situation where the above might occur is a slaughter house where the "cutters" are assigned to different cut patterns. In this case the resources are the time, the cost and the productivity measured in terms of quality and amount of the end products. In this paper we study the resource constrained assignment problem and derive several classes of valid inequalities based on the properties of the knapsack and assignment polytopes. We also present an algorithm that uses both the linear programming and the Lagrangean relaxation of the original problem in order to solve the separation problem. Some computational experiments are presented.

UR - http://www.scopus.com/inward/record.url?scp=38249020928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249020928&partnerID=8YFLogxK

U2 - 10.1016/0166-218X(90)90099-X

DO - 10.1016/0166-218X(90)90099-X

M3 - Article

AN - SCOPUS:38249020928

VL - 26

SP - 175

EP - 191

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 2-3

ER -