The range of applications of RPAs in various industries indicates that their increased usage could reduce operational costs and time. Remotely piloted aircraft systems (RPASs) can be deployed quickly and effectively in numerous distribution systems and even during a crisis by eliminating existing problems in ground transport due to their structure and flexibility. Moreover, they can also be useful in data collection in damaged areas by correctly defining the condition of flight trajectories. Hence, defining a framework and model for better regulation and management of RPAS-based systems appears necessary; a model that could accurately predict what will happen in practice through the real simulation of the circumstances of distribution systems. Therefore, this study attempts to propose a multi-objective location-routing optimization model by specifying time window constraints, simultaneous pick-up and delivery demands, and the possibility of recharging the used batteries to reduce, firstly, transport costs, secondly, delivery times, and thirdly, estimated risks. Furthermore, the delivery time of the model has been optimized to increase its accuracy based on the uncertain conditions of possible traffic scenarios. It is also imperative to note that the assessment of risk indicators was conducted based on the Specific Operations Risk Assessment (SORA) standard to define the third objective function, which was conducted in a few previous studies. Finally, it shows how the developed NSGA-II algorithm in this study performed successfully and reduced the objective function by 31%. Comparing the obtained results using an NSGA-II meta-heuristic approach, through the rigorous method GAMS, indicates that the results are valid and reliable.

Purpose: In the present research, location and routing problems, as well as the supply chain, which includes manufacturers, distributor candidate sites and retailers, are explored. The goal of addressing the issue is to reduce delivery times and system costs for retailers so that routing and distributor location may be determined.Design/methodology/approach: By adding certain unique criteria and limits, the issue becomes more realistic. Customers expect simultaneous deliveries and pickups, and retail service start times have soft and hard time windows. Transportation expenses, noncompliance with the soft time window, distributor construction, vehicle purchase or leasing, and manufacturing costs are all part of the system costs. The problem's conceptual model is developed and modeled first, and then General Algebraic Modeling System software (GAMS) and Multiple Objective Particle Swarm Optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGAII) algorithms are used to solve it in small dimensions.Findings: According to the mathematical model's solution, the average error of the two suggested methods, in contrast to the exact answer, is less than 0.7%. In addition, the performance of algorithms in terms of deviation from the GAMS exact solution is pretty satisfactory, with a divergence of 0.4% for the biggest problem (N = 100). As a result, NSGAII is shown to be superior to MOSPSO.Research limitations/implications: Since this paper deals with two bi-objective models, the priorities of decision-makers in selecting the best solution were not taken into account, and each of the objective functions was given an equal weight based on the weighting procedures. The model has not been compared or studied in both robust and deterministic modes. This is because, with the exception of the variable that indicates traffic mode uncertainty, all variables are deterministic, and the uncertainty character of demand in each level of the supply chain is ignored.Practical implications: The suggested model's conclusions are useful for any group of decision-makers concerned with optimizing production patterns at any level. The employment of a diverse fleet of delivery vehicles, as well as the use of stochastic optimization techniques to define the time windows, demonstrates how successful distribution networks are in lowering operational costs.Originality/value: According to a multi-objective model in a three-echelon supply chain, this research fills in the gaps in the link between routing and location choices in a realistic manner, taking into account the actual restrictions of a distribution network. The model may reduce the uncertainty in vehicle performance while choosing a refueling strategy or dealing with diverse traffic scenarios, bringing it closer to certainty. In addition, two modified MOPSO and NSGA-II algorithms are presented for solving the model, with the results compared to the exact GAMS approach for medium- and small-sized problems.