This research introduces a stochastic version of the multi-mode resource-constrained project scheduling problem (MRCPSP) and its mathematical model. In addition, an efficient multi-start iterated local search (MS-ILS) algorithm, capable of solving the deterministic MRCPSP, is adapted to deal with the proposed stochastic version of the problem. For its deterministic version, the MRCPSP is an NP-hard optimization problem that has been widely studied. The problem deals with a trade-off between the amount of resources that each project activity requires and its duration. In the case of the proposed stochastic formulation, the execution times of the activities are uncertain. Benchmark instances of projects with 10, 20, 30, and 50 activities from well-known public libraries were adapted to create test instances. The adapted algorithm proved to be capable and efficient for solving the proposed stochastic problem.

Background: Distribution systems often face the dual challenge of delivering products to customers and retrieving damaged items for repair, especially when the service center is separate from the depot. An optimized solution to this logistics problem produces benefits in terms of costs, greenhouse gas emissions, and disposal reduction. Methods: This research proposes a Capacitated Vehicle Routing Problem with Service Center (CVRPwSC) model to determine optimal routes involving customers, the depot, and the service center. AMPL-Gurobi was used to solve the model on adapted instances and new instances developed for the CVRPwSC. Additionally, a Variable Neighborhood Search (VNS) algorithm was implemented and compared with AMPL-Gurobi. Results: The model was applied to a real-world case study, achieving a 40% reduction in fuel costs, a reduction from 5 to 3 routes, and a sustainable logistics operations model with potential reductions of greenhouse gas emissions and item disposals. Conclusions: The main contribution of the proposal is a minimum-cost routing model integrating item returns for repair with customer deliveries, while the limitation is the exclusion of scenarios where return items exceed vehicle capacity. Finally, future research will enhance the CVRPwSC model by incorporating additional constraints and decision variables to address such scenarios.