This paper focuses on the continuous location-routing problem that comprises of the location of multiple depots from a given region and determining the routes of vehicles assigned to these depots. The objective of the problem is to design the delivery system of depots and routes so that the total cost is minimal. The standard location-routing problem considers a finite number of possible locations. The continuous location-routing problem allows location to infinite number of locations in a given region and makes the problem much more complex. We present a genetic algorithm that tackles both location and routing subproblems simultaneously.

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Distribution of the goods from a producer to a customer is one of the most important tasks of transportation. This paper focuses on the usage of genetic algorithms (GA) for optimizing problems in transportation, namely vehicle routing problem (VRP). VRP falls in the field of NP-hard problems, which cannot be solved in polynomial time. The problem was solved using genetic algorithm with two types of crossover, both including and leaving-out elitism, setting variable parameters of crossover and mutation probability, as well as prevention of creating invalid individuals. The algorithm was programmed in Matlab, tested on real world problem of spare parts distribution for garages, while the results were compared with another heuristic method (Clarke-Wright method). Genetic algorithm provided a better solution than the heuristic Clarke-Wright method.

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In this paper, we focus on the optimization of the system of the spare parts distribution for authorized garages in the Czech Republic. A spare parts market belongs to one of the key elements of the car industry. However, it has to adapt to still higher requirements on accuracy, speed and minimum error rate of the deliveries with keeping the costs at its minimum at the same time. The distribution of products from depots to customers is a practical and challenging problem in logistics that opens a significant space for application of software products.The design of optimal routes of vehicles from two depots can be formulated in combinatorial optimization as a multi-depot vehicle routing problem.The goal of a multi-depot vehicle routing problem is to design routes that start and end in one of the depots and visit a subset of customers in a specific sequence. Every customer has to be visited on one of the routes and the total costs for the delivery should be minimal.Vehicle routing problems belong to the class of NP-hard problems which means that there is no efficient algorithm for finding optimal solution available. To find a solution in an efficient way, we propose an approximate method based on a genetic algorithm.