### M. Sc. Moustafa El-Ashry

# The Fleet-Sizing-and-Allocation Problem: Models and Solution Approaches

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### Hinweis

Bitte nutzen Sie beim Zitieren immer folgende Url:

**http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200701915**

### Kurzfassung in Englisch

Transportation is one of the most vital services in modern society. It makes most of the other functions of society possible. Real transportation systems are so large and complex that in order to build the science of transportation systems it will be necessary to work in many areas, such as: Modeling, Optimization and Simulation. We are interested in solutions for the so-called fleet-sizing-and-allocation problem (FSAP). Fleet sizing and allocation problems are one of the most interesting and hard to solve logistic problems. A fleet sizing and allocation problem consists of two interdependent parts. The fleet sizing problem is to determine a number of transportation units that optimally balances service requirements against the cost of purchasing and maintaining the transportation units. The allocation problem is dealing with the repositioning of transportation units to serve future transportation demand.

To make the fleet sizing and allocation problem a little bit more tractable we concentrate on logistic systems with a special hub-and-spoke structure. We start with a very simple fleet sizing of one-to-one case. This case will cause us to focus attention on several key issues in fleet sizing. Afterwards, the generalization of the one-to-one system is the one-to-many system. As a simple example can serve the continuous time situation where a single origin delivers items to many destinations. For the case that items are produced in a deterministic production cycle and transportation times are stochastic. We also studied a hub-and-spoke problem with continuous time and stochastic demand. To solve this problem, based on Marginal Analysis, we applied queueing theory methods.

The investigation of the fleet-sizing-and-allocation problem for hub-and-spoke systems is started for a single-period, deterministic-demand model. In that the model hub has to decide how to use a given number of TU’s to satisfy a known (deterministic) demand in the spokes. We consider two cases:

1. Renting of additional TU’s from outside the system is not possible, 2. Renting of additional TU’s from outside the system is possible. For each case, based on Marginal Analysis, we developed a simple algorithm, which gives us the cost-minimal allocation. Since the multi-period, deterministic demand problem is NP-hard we suggest to use Genetic Algorithms. Some building elements for these are described.

For the most general situation we also suggest to use simulation optimization. To realize the simulation optimization approach we could use the software tool “Calculation Assessment Optimization System” (CAOS). The idea of CAOS is to provide a software system, which separates the optimization process from the optimization problem. To solve an optimization problem the user of CAOS has to build up a model of the system to which the problem is related. Furthermore he has to define the decision parameters and their domain. Finally, we used CAOS for two classes of hub-and-spoke system: 1. A single hub with four spokes, 2. A single hub with fifty spokes. We applied four optimizers – a Genetic Algorithm, Tabu Search, Hybrid Parallel and Hybrid Serial with two distributions (Normal Distribution and Exponential Distribution) for a customer interarrival times and their demand.

### weitere Metadaten

Schlagwörter | Fleet sizing |

Schlagwörter | Genetic Algorithm |

Schlagwörter | Hub-and-spoke system |

Schlagwörter | Modeling and simulation |

Schlagwörter | Queueing model |

Schlagwörter | Transportation system |

Schlagwörter | simulation optimization |

SWD Schlagworte | Modellierung |

SWD Schlagworte | Simulation |

SWD Schlagworte | Transportsystem |

DDC Klassifikation | 004 |

Institution(en) | |

Hochschule | TU Chemnitz |

Fakultät | Fakultät für Informatik |

Betreuer | Prof. Dr. rer. nat. habil. Dr. oec. Peter Köchel |

Gutachter | Prof. Dr. rer. nat. habil. Dr. oec. Peter Köchel Prof. Dr. Knut Richter Prof. Dr. Peter Gluchowski |

Dokumententyp | Dissertation |

Sprache | Englisch |

Tag d. Einreichung (bei der Fakultät) | 19.09.2007 |

Tag d. Verteidigung / Kolloquiums / Prüfung | 23.11.2007 |

Veröffentlichungsdatum (online) | 26.11.2007 |

persistente URN | urn:nbn:de:bsz:ch1-200701915 |