This paper presents a hybrid grasshopper optimization algorithm using a novel decoder and local search to solve instances of the open vehicle routing problem with capacity and distance constraints. The algorithm's decoder first defines the number of vehicles to be used and then it partitions the clients, assigning them to the available routes. The algorithm performs a local search in three neighborhoods after decoding. When a new best solution is found, every route is locally optimized by solving a traveling salesman problem, considering the depot and clients in the route. Three sets containing a total of 30 benchmark problems from the literature were used to test the algorithm. The experiments considered two cases of the problem. In the first, the primary objective is to minimize the total number of vehicles and then the total distance to be traveled. In the second case, the total distance traveled by the vehicles is minimized. The obtained results showed the algorithm's proficient performance. For the first case, the algorithm was able to improve or match the best-known solutions for 21 of the 30 benchmark problems. For the second case, the best-known solutions for 18 of the 30 benchmark problems were found or improved by the algorithm. Finally, a case study from a real-life problem is included.
This paper presents a new combinatorial optimization problem, the inventory routing problem with priorities, and a fixed heterogeneous fleet. In this problem, a particular set of customers has to be served before the rest of the customers using vehicles with different capacities. The problem is inspired by the current situation faced by a specialized gas distribution company in the northeast region of Mexico. The company produces and distributes three main products, although this paper focuses only on the oxygen distribution problem. The company delivers oxygen to industrial customers, as well as hospitals and other medical facilities. Due to Mexican government regulations, the company requires prioritizing deliveries to hospitals and medical facilities over its industrial customers. Therefore, the company is obliged to satisfy the customers demand considering inventory levels and priority constraints while minimizing the inventory and routing cost. An integer programming model is proposed to solve the problem. The model minimizes the total distribution cost while considering inventory level, priority constraints, and a fixed fleet of vehicles with different capacities. Finally, computational experiments were carried out using benchmark instances to validate the correctness of the proposed model and to analyze the effect of priorities on the total distribution cost. Finally, actual customers of the company were selected to show the effectiveness of the proposed model to solve real-world problems.
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