Background: The Capacitated Vehicle Routing Problem (CVRP) is one of the most important transportation problems in logistics and supply chain management. The standard CVRP considers a fleet of vehicles with homogeneous capacity that depart from a warehouse, collect products from (or deliver products to) a set of customer locations (points) and return to the same warehouse. However, the operation of carrier companies and third-party transportation providers may follow a different network flow for collection and delivery. This may lead to non-optimal route planning through the use of the standard CVRP.Objective: To propose a model for carrier companies to obtain optimal route planning.Method: A Capacitated Vehicle Routing Problem for Carriers (CVRPfC) model is used to consider the distribution scenario where a fleet of vehicles depart from a vehicle storage depot, collect products from a set of customer points and deliver them to a specific warehouse before returning to the vehicle storage depot. Validation of the model’s functionality was performed with adapted CVRP test problems from the Vehicle Routing Problem LIBrary. Following this, an assessment of the model’s economic impact was performed and validated with data from a real carrier (real instance) with the previously described distribution scenario.Results: The route planning obtained through the CVRPfC model accurately described the network flow of the real instance and significantly reduced its distribution costs.Conclusion: The CVRPfC model can thus improve the competitiveness of the carriers by providing better fares to their customers, reducing their distribution costs in the process.

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.

The global supply chain relies on road, land, and air transport, significantly contributing to greenhouse gas emissions. Various measures have been proposed to reduce these emissions, including energy taxes, environmentally friendly vehicles, and optimized transportation loads. Current optimization mainly considers fixed loads and vehicle types to reduce CO₂ emissions. However, dynamic loads in distribution networks and their interactions with factors like distance and vehicle type have not been studied. The present work contributes by (a) extending a vehicle routing problem (VRP) database to include vehicle type and load size data; (b) developing a mathematical model for emissions based on traveled distance, vehicle type, and load size; (c) creating a multivariate database of the emissions considering optimal routing; and (d) analyzing the database to identify key factors influencing emissions. A factorial analysis determined that vehicle type, load size, and traveled distance are the main factors associated with CO₂ emissions. By coding and rearranging the database considering three levels for each main factor, a 3^k full factorial design was developed to analyze the interactions of these factors and their effect on CO₂ emissions. The results of the analyses corroborate that optimizing vehicle utilization and minimizing routes, which depend on optimal load, distribution routes, and infrastructure planning, are recommended actions to reduce emissions.

This paper presents the analytical controllable workspace boundaries of a crane-type cable-based robot with purely translational motions. The underconstrained cable robot is composed of eight cables which support the weight of a mobile platform, restricting its motions into the vertical plane of a static platform. The analytic equations are developed so that its workspace fulfills the tensionable condition for a given set of minimum and maximum tension limits. The all-tensionable workspace is obtained by analyzing slackness conditions with constant orientation of the mobile platform and by solving the all-positive cable tension redundancy. The minimum two-norm cable tension formulation results in a quadratic equation which admits a minimum value by equaling its derivative to zero.