Multi-echelon open location-routing problem with time window and mixed last-mile delivery for optimizing food supply chains

The pandemic experience made online grocery shopping the new normal. The perishable and Fast-Moving Consumer Goods (FMCG) supply chain should be adjusted to extend their distribution capabilities and adapt to the new business environment. This study introduces the Three-Echelon Open Location-Routing Problem with Time Windows (3E-OLRPTW) with simultaneous home delivery and store pickup services for optimizing last-mile delivery operations. A Mixed-Integer Non-Linear Programming (MINLP) formulation and an improved metaheuristic, the Hybrid Genetic Algorithm (HGA), are developed using a customized local search method. The objective is to minimize total operating costs while accounting for the time window and capacity constraints. Numerical experiments are conducted to evaluate the performance of the developed solution method, comparing it with the improved hybrid variants of the Genetic Algorithm (GA), Artificial Bee Colony (ABC), Simulated Annealing (SA), and Imperialist Competitive Algorithm (ICA) algorithms. Statistical tests confirm that the HGA algorithm outperforms the benchmarks in terms of solution quality and convergence.