Comparative analysis of different crossover structures for solving a periodic inventory routing problem

One of the most important challenges for a company is to manage its supply chain efficiently. One way to do this is to control and minimize its various logistics costs together to achieve an overall optimization of its supply network. One such system that integrates two of the most important logistics activities, namely inventory holding and transportation, is known as the inventory routing problem. Our replenishment network consists of a supplier that uses a single vehicle to distribute a single type of item during each period to a set of customers with independent and deterministic demand. The objectives considered are the management of supplier and customer inventories, the assignment of customers to replenishment periods, the determination of optimal delivery quantities to avoid customer stock-outs, the design and optimization of routes. A genetic algorithm (GA) is developed to solve our IRP. Different crossover structures are proposed and tested in two sets of reference instances. A comparison of the performance of different crossover structures was established. Then, it was used to find the most appropriate crossover structure that provides better results in a minor computation time. The obtained results prove the competitiveness of GAs compared to literature approaches, demonstrate the performance of our approach to best solve large scale instances and provide better solution quality in fast execution time.