### Abstract

The classical shortest route problem in networks assumes deterministic arc weights and a utility (or cost) function that is linear over path weights for route evaluation. When the environment is stochastic and the "traveler's" utility function for travel attributes is nonlinear, we define "optimal paths" that maximize the expected utility. We review the concepts of temporary and permanent preferences for comparing a traveler's preference for available subpaths. It has been shown before that when the utility function is linear or exponential, permanent preferences prevail and an efficient Dijkstra-type algorithm [3] is available that determines the optimal path. In this paper an exact procedure is developed for determining an optimal path when the utility function is quadratic-a case where permanent preferences do not always prevail. The algorithm uses subpath comparison rules to establish permanent preferences, when possible, among subpaths of the given network. Although in the worst case the algorithm implicitly enumerates all paths (the number of operations increasing exponentially with the size of the network), we find, from the computational experience reported, that the number of potentially optimal paths to evaluate is generally manageable.

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

Pages (from-to) | 365-381 |

Number of pages | 17 |

Journal | Computers and Operations Research |

Volume | 12 |

Issue number | 4 |

DOIs | |

State | Published - 1985 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems and Management
- Management Science and Operations Research
- Applied Mathematics
- Modeling and Simulation
- Transportation

### Cite this

*Computers and Operations Research*,

*12*(4), 365-381. https://doi.org/10.1016/0305-0548(85)90034-6

**Optimal paths in probabilistic networks : A case with temporary preferences.** / Mirchandani, Pitu; Soroush, Hossein.

Research output: Contribution to journal › Article

*Computers and Operations Research*, vol. 12, no. 4, pp. 365-381. https://doi.org/10.1016/0305-0548(85)90034-6

}

TY - JOUR

T1 - Optimal paths in probabilistic networks

T2 - A case with temporary preferences

AU - Mirchandani, Pitu

AU - Soroush, Hossein

PY - 1985

Y1 - 1985

N2 - The classical shortest route problem in networks assumes deterministic arc weights and a utility (or cost) function that is linear over path weights for route evaluation. When the environment is stochastic and the "traveler's" utility function for travel attributes is nonlinear, we define "optimal paths" that maximize the expected utility. We review the concepts of temporary and permanent preferences for comparing a traveler's preference for available subpaths. It has been shown before that when the utility function is linear or exponential, permanent preferences prevail and an efficient Dijkstra-type algorithm [3] is available that determines the optimal path. In this paper an exact procedure is developed for determining an optimal path when the utility function is quadratic-a case where permanent preferences do not always prevail. The algorithm uses subpath comparison rules to establish permanent preferences, when possible, among subpaths of the given network. Although in the worst case the algorithm implicitly enumerates all paths (the number of operations increasing exponentially with the size of the network), we find, from the computational experience reported, that the number of potentially optimal paths to evaluate is generally manageable.

AB - The classical shortest route problem in networks assumes deterministic arc weights and a utility (or cost) function that is linear over path weights for route evaluation. When the environment is stochastic and the "traveler's" utility function for travel attributes is nonlinear, we define "optimal paths" that maximize the expected utility. We review the concepts of temporary and permanent preferences for comparing a traveler's preference for available subpaths. It has been shown before that when the utility function is linear or exponential, permanent preferences prevail and an efficient Dijkstra-type algorithm [3] is available that determines the optimal path. In this paper an exact procedure is developed for determining an optimal path when the utility function is quadratic-a case where permanent preferences do not always prevail. The algorithm uses subpath comparison rules to establish permanent preferences, when possible, among subpaths of the given network. Although in the worst case the algorithm implicitly enumerates all paths (the number of operations increasing exponentially with the size of the network), we find, from the computational experience reported, that the number of potentially optimal paths to evaluate is generally manageable.

UR - http://www.scopus.com/inward/record.url?scp=0021855448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021855448&partnerID=8YFLogxK

U2 - 10.1016/0305-0548(85)90034-6

DO - 10.1016/0305-0548(85)90034-6

M3 - Article

AN - SCOPUS:0021855448

VL - 12

SP - 365

EP - 381

JO - Surveys in Operations Research and Management Science

JF - Surveys in Operations Research and Management Science

SN - 0305-0548

IS - 4

ER -