Designing a locating-routing three-echelon supply chain network under uncertainty

PurposeIn 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/approachBy 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.FindingsAccording 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/implicationsSince 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 implicationsThe 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/valueAccording 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.