Providing an integrated multi-depot vehicle routing problem model with simultaneous pickup and delivery and package layout under uncertainty with fuzzy-robust box optimization method

This paper modeled and solved an integrated multi-depot vehicle routing problem (MDVRP) with simultaneous pickup and delivery (SPD) with package layout under unpredictable pickup, delivery, and transfer costs. The model described in this paper is divided into two stages. In the first stage, the SCA algorithm is used to optimize the package dimensions (a collection of commodities consumers need). The NSGA II and MOALO algorithms are used in the second stage to optimize the three objective functions of 1 simultaneously) minimizing total costs, 2) minimizing co2 emissions, and 3) minimizing the maximum working hours of drivers based on the optimal dimensions (length, width, and height) obtained from solving the first stage model. Determining the quantity and ideal location of possible warehouses, the best route for trucks to take to deliver and collect customer items, and the distribution of customers to warehouses are the key goals of the second stage. Since the model is unclear, the problem's uncertainty parameters are controlled using a novel fuzzy-robust box optimization (FRBO) technique. This technique, which combines the advantages of fuzzy programming with robust box-based optimization, produces excellent results when used to optimize objective functions. The numerical calculations in the numerical example show that the total network costs and CO2 emissions increased in the second stage in the presented model with an increasing uncertainty rate. At the same time, the maximum working hours of drivers decreased due to the shortened communication route and the number of vehicles increasing. Finally, the MOALO algorithm was used to resolve a case study at Safir Broadcasting Company because of its excellent efficiency in resolving the created model, the findings of which revealed the presence of 13 potential effective solutions. The quantity of greenhouse gas emissions rose by 1.11%, the overall expenditures climbed by 1.72%, and the number of hours that drivers worked fell by 11.98% when the uncertainty rate was raised from 0.5 to 0.7, according to research on the FRBO.