Purpose:  The purpose of this study is the well-known Heterogeneous Fleet Vehicle Routing Problem (HVRP) is one of the developed problems of vehicle routing, which involves optimizing a set of routes for a fleet of vehicles with different costs and capacities. Methods: HVRP is usually modeled as a single objective that aims to minimize overall transportation costs (total fixed costs and costs commensurate with total distance). Results: These vehicles are located in the central depot and serve customers’ demands. Implications: In this case, the number of vehicles available (of any type) may be limited.

In this article, equipment overhaul is considered in a multi-stage flow shop scheduling problem. In this problem, the equipments are disassembled in the first stage, overhaul and repairs are done on the equipment in parallel workshops in the second stage, and the assembly operation is done in parallel workshops in the third stage. Considering a three-stage overhaul with parallel machines in the second and third stages is new in the overhaul industry. The sequence of equipment processing is determined in the first stage, as well as the allocation and sequence of equipment in the second and third stages should be done in such a way that the total completion time of jobs is minimized. Unlike most articles, the sequence of processing jobs is not the same in all stages and changes with the use of decoding. For the next innovation: in order to solve the problem, a new mathematical model is presented. Two new improved algorithms, Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) are presented to solve the problem in large dimensions. By using the shortest processing time (SPT) heuristic, these two algorithm have been improved and Hybrid GA (HGA) and Hybrid PSO (HPSO) algorithms have been presented. In order to achieve better results with the current conditions, the parameters setting is done by one-way analysis of variance (ANOVA). Finally, it is possible to improve the performance of the equipment by applying the discussed issues.