In this paper, we introduce a unified mathematical formulation for the Capacitated Vehicle Routing Problem (CVRP) and for the Capacitated Location Routing Problem (CLRP), adopting radiality constraints in order to guarantee valid routes and eliminate subtours. This idea is inspired by formulations already employed in electric power distribution networks, which requires a radial topology in its operation. The results show that the proposed formulation greatly improves the convergence of the solver.
A vehicle routing problem with time windows (VRPTW) is an important problem with many real applications in a transportation problem. The optimum set of routes with the minimum distance and vehicles used is determined to deliver goods from a central depot, using a vehicle with capacity constraint. In the real cases, there are other objective functions that should be considered. This paper considers not only the minimum distance and the number of vehicles used as the objective function, the customer’s satisfaction with the priority of customers is also considered. Additionally, it presents a new model for a bi-objective VRPTW solved by a revised multi-choice goal programming approach, in which the decision maker determines optimistic aspiration levels for each objective function. Two meta-heuristic methods, namely simulated annealing (SA) and genetic algorithm (GA), are proposed to solve large-sized problems. Moreover, the experimental design is used to tune the parameters of the proposed algorithms. The presented model is verified by a real-world case study and a number of test problems. The computational results verify the efficiency of the proposed SA and GA.
This paper introduces a new bi-objective vehicle routing problem that integrates the Open Location Routing Problem (OLRP), recently presented in the literature, coupled with the growing need for fuel consumption minimization, named Green OLRP (G-OLRP). Open routing problems (ORP) are known to be NP-hard problems, in which vehicles start from the set of existing depots and are not required to return to the starting depot after completing their service. The OLRP is a strategic-level problem involving the selection of one or many depots from a set of candidate locations and the planning of delivery radial routes from the selected depots to a set of customers. The concept of radial paths allows us to use a set of constraints focused on maintaining the radiality condition of the paths, which significantly simplifies the set of constraints associated with the connectivity and capacity requirements and provides a suitable alternative when compared with the elimination problem of sub-tours traditionally addressed in the literature. The emphasis in the paper will be placed on modeling rather than solution methods. The model proposed is formulated as a bi-objective problem, considering the minimization of operational costs and the minimization of environmental effects, and it is solved by using the epsilon constraint technique. The results illustrate that the proposed model is able to generate a set of trade-off solutions leading to interesting conclusions about the relationship between operational costs and environmental impact.
Perishability of platelets, uncertainty of donors’ arrival and conflicting views in platelet supply chain have made platelet supply chain planning a problematic issue. In this paper, mobile blood collection system for platelet production is investigated. Two mathematical models are presented to cover the bloodmobile collection planning problem. The first model is a multi-objective fuzzy mathematical programming in which the bloodmobiles locations are considered with the aim of maximizing potential amount of blood collection and minimizing the operational cost. The second model is a vehicle routing problem with time windows which studies the shuttles routing problem. To tackle the first model, it is reformulated as a crisp multi objective linear programming model and then solved through a fuzzy multi objective programming approach. Several sensitivity analysis are conducted on important parameters to demonstrate the applicability of the proposed model. The proposed model is then solved by using a tailored Simulated Annealing (SA) algorithm. The numerical results demonstrate promising efficiency of the proposed solution method.
This article paper presents a hybrid metaheuristic algorithm to solve the time-dependent vehicle routing problem with hard time windows. Time-dependent travel times are influenced by different congestion levels experienced throughout the day. Vehicle scheduling without consideration of congestion might lead to underestimation of travel times and consequently missed deliveries. The algorithm presented in this paper makes use of Large Neighbourhood Search approaches and Variable Neighbourhood Search techniques to guide the search. A first stage is specifically designed to reduce the number of vehicles required in a search space by the reduction of penalties generated by time-window violations with Large Neighbourhood Search procedures. A second stage minimises the travel distance and travel time in an ‘always feasible’ search space. Comparison of results with available test instances shows that the proposed algorithm is capable of obtaining a reduction in the number of vehicles (4.15%), travel distance (10.88%) and travel time (12.00%) compared to previous implementations in reasonable time.
Waste collection is an important municipal service that charges large expenditures to waste management (WM) system. In this study, a hierarchical structure is proposed in order to minimize total cost of waste collection routing problem. Moreover, in second stage destructive environmental effects of waste transportation are minimized concurrently through taking advantage of a road/rail transportation system. In the proposed multimodal transportation system, waste packs are transferred to final destination while travel time and risk of environmental threatening is minimized. The discussed problem is formulated mathematically in two stages. In the first stage, a household waste collection routing problem is formulated while, in second stage a multimodal transportation system is routed to transfer waste packs to final destination through roads and railroads. In order to solve the proposed NP hard models, an improved genetic algorithm is developed. Comparison of the obtained results with those of GAMS for small-size samples validates the proposed models.
Over the past three decades, the unified approach of the optimization of the logistic systems has become one of the most important aspects of optimizing the supply chain so that in recent decades it has had a large application in practice and has been used to increase the efficiency and effectiveness of the logistic fleet. The inter-urban transport networks by the terminals play an important role in logistic fleet and the goods distribution. In some cases, numbers of terminals face with an overload and others encounter with additional vehicles, which result delay in the load post and unnecessary car downtime. The present paper aims at modeling, scheduling and routing of the vehicles network and minimizing delays in order to create an optimal balance between the number of vehicles and the capacity of the car terminals to use the maximal capacity of vehicles. So that the multi-objective mathematical model is presented to quantify the regular transportation costs and to minimize the car downtime. The proposed model has two conflicting objectives where on tried to increase costs and the other decreases unused cars. Due to the high complexity of the problem, the multi-objective differential evolutionary algorithm (MODE) has been used. To prove the proposed algorithm, it has compared with the NSGA-II algorithm using four comparing indexes. The computational results show the superiority of the proposed algorithm.