### Abstract

Fixed charge transportation (FCT) problems addressed in literature assumed shipment between a source and a destination is fulfilled in a single lot. However, in reality the lot size may exceed the capacity of the carrier and hence the shipment needs to be executed by conducting more than one trip. This gives an increased fixed charge which is proportional to the number of trips performed. This paper proposes a special case of the FCT problem were the truck load constraint is considered and is referred as the fixed charge transportation problem with truck load constraints (FCT-TLC) problem. The objective considered in this problem is to minimize the total cost of transportation without violating the supply and demand constraints. The general FCT problem is classified as NP-hard and to solve this proposed problem with additional constraints, two metaheuristic algorithms are used. A Genetic Algorithm (GA) and a Simulated Annealing Algorithm (SAA) are proposed to solve the FCT-TLC problem and the performance of the algorithms is tested on twenty randomly generated problem instances. Detailed comparative study on the computational results obtained using GA and SAA are presented. Both metaheuristics show good results for solving the proposed problem. However, SAA outperformed GA for many problems with different truck load capacities. To test the performance of the proposed algorithms, comparison with approximate and lower bound solutions for the problem with a relaxed truck capacity constraint is also presented.

Original language | English |
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Journal | Annals of Operations Research |

Volume | 273 |

Issue number | 1-2 |

Pages (from-to) | 207-236 |

Number of pages | 30 |

ISSN | 0254-5330 |

DOIs | |

Publication status | Published - Feb 2019 |

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### Keywords

- Fixed charge
- Genetic algorithm
- Heuristics
- Simulated annealing algorithm
- Transportation problem
- Truck load capacity

### Cite this

*Annals of Operations Research*,

*273*(1-2), 207-236. https://doi.org/10.1007/s10479-017-2692-z