### Abstract

In this paper we address the issue of different mathematical models for the stochastic vehicle routing problem (SVRP). This problem is inherently much more difficult than the generic deterministic vehicle routing problem (VRP) for which optimal procedures can solve only small problems. Presently, we cannot even begin optimal solution procedures for the SVRP for any problem size exceeding 3 nodes. Thus, we need to examine modeling approaches to this problem in order to exploit the structure and solution properties. We present a multistate stochastic model for the SVRP. We prove that this model has an interesting minimal graph representation in which a SVRP solution corresponds to a Hamiltonian cycle. We also present a Markov decision model for the problem, concluding with a discussion of solution prospects and directions.

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

Pages (from-to) | 432-441 |

Number of pages | 10 |

Journal | European Journal of Operational Research |

Volume | 64 |

Issue number | 3 |

DOIs | |

State | Published - Feb 5 1993 |

Externally published | Yes |

### Fingerprint

### Keywords

- Routing
- Stochastic programming

### ASJC Scopus subject areas

- Management Science and Operations Research
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Modeling and Simulation
- Transportation
- Information Systems and Management

### Cite this

**Modeling vehicle routing with uncertain demands as a stochastic program : Properties of the corresponding solution.** / Dror, Moshe.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Modeling vehicle routing with uncertain demands as a stochastic program

T2 - Properties of the corresponding solution

AU - Dror, Moshe

PY - 1993/2/5

Y1 - 1993/2/5

N2 - In this paper we address the issue of different mathematical models for the stochastic vehicle routing problem (SVRP). This problem is inherently much more difficult than the generic deterministic vehicle routing problem (VRP) for which optimal procedures can solve only small problems. Presently, we cannot even begin optimal solution procedures for the SVRP for any problem size exceeding 3 nodes. Thus, we need to examine modeling approaches to this problem in order to exploit the structure and solution properties. We present a multistate stochastic model for the SVRP. We prove that this model has an interesting minimal graph representation in which a SVRP solution corresponds to a Hamiltonian cycle. We also present a Markov decision model for the problem, concluding with a discussion of solution prospects and directions.

AB - In this paper we address the issue of different mathematical models for the stochastic vehicle routing problem (SVRP). This problem is inherently much more difficult than the generic deterministic vehicle routing problem (VRP) for which optimal procedures can solve only small problems. Presently, we cannot even begin optimal solution procedures for the SVRP for any problem size exceeding 3 nodes. Thus, we need to examine modeling approaches to this problem in order to exploit the structure and solution properties. We present a multistate stochastic model for the SVRP. We prove that this model has an interesting minimal graph representation in which a SVRP solution corresponds to a Hamiltonian cycle. We also present a Markov decision model for the problem, concluding with a discussion of solution prospects and directions.

KW - Routing

KW - Stochastic programming

UR - http://www.scopus.com/inward/record.url?scp=0027908976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027908976&partnerID=8YFLogxK

U2 - 10.1016/0377-2217(93)90132-7

DO - 10.1016/0377-2217(93)90132-7

M3 - Article

VL - 64

SP - 432

EP - 441

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -