We present a modification of three existing methods for finding a basic feasible solution for Capacitated transportation problem. To obtain an optimal solution, eht simplex algorithm for bounded variables is applied. Special properties of transportation problem help us to operate each step of simplex algorithm directly on the transportation tableau. At last, numerical examples are represented to illustrate our method.

Hub location-routing problem is a practical subject in the last decades. This study considers a many-to-many hub location-routing problem where the best locations of hubs and tours for each hub are determined with simultaneous pickup and delivery. First, an optimization model is proposed to minimize the total sum of fixed costs of locating hubs, the costs of handling, traveling, assigning, and transportation costs. To find practical solutions, the hubs have constrained capacity, in which single allocations can service every node to the hubs. What is more, the balancing requisites are imposed on the network by allocating the appropriate number of demand nodes to the hubs. Then the problem is solved using GAMS software for small-size instances of the problem. Due to the NP-hard nature of the problem, the proposed optimization model is solved by the Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). For the problem instances, the comparative results indicate that GA has a better performance compared to ICA, and incorporating capacity and balancing considerations can influence the reduction of costs of the investigated network.

In this paper, we develop a Capacitated location-covering model considering interval values for demand and service parameters. We also consider flexibility on distance standard for covering demand nodes by the servers. We use the satisfaction degree to represent the constraint of service capacity. The proposed model belongs to the class of mixed integer programming models. Our model can be reduced to the p-median problem in polynomial time so it is NP-Hard. A genetic algorithm is proposed to solve the developed model and experimental results of solving the model are presented.

The vehicle routing problem with the capacity constraints was considered in this paper. It is quite difficult to achieve an optimal solution with traditional optimization methods by reason of the high computational complexity for large-scale problems. Consequently, new heuristic or metaheuristic approaches have been developed to solve this problem. In this paper, we constructed a new heuristic algorithm based on the tabu search and adaptive large neighborhood search (ALNS) with several specifically designed operators and features to solve the Capacitated vehicle routing problem (CVRP). The effectiveness of the proposed algorithm was illustrated on the benchmark problems.The algorithm provides a better performance on largescaled instances and gained advantage in terms of CPU time.In addition, we solved a real-life CVRP using the proposed algorithm and found the encouraging results by comparison with the current situation that the company is in.

Capacitated p-median problem (CPMP) is a well-known facility location problem, in which p Capacitated facility points are selected to satisfy n demand points in such a way that the total assigned demand to each facility does not exceed its capacity. Minimizing the total sum of distances between each demand point and its nearest facility point is the objective of the problem. Developing an efficient solution method for the problem has been a challenge during last decades in literature. In this paper, a hybrid met heuristic called GACO is developed to find high quality and fast solutions for the CPMP. The GACO combines elements of genetic algorithm and ant colony optimization' met heuristics. Computational results on standard test problems show the robustness and efficiency of the algorithm and confirm that the proposed method is a good choice for solving the CPMP.

This paper proposes an integer linear mathematical formulation for Vehicle Routing problem (VRP), where the capital cost for deploying each vehicle is minimized together with other on-link transportation costs. The model has been formulated as a multi-commodity network flow model with capacity constraints. It is well known that the computational complexity to this type of problems is NP-hard. Thus, the ACO algorithm, which has been known to be a powerful meta-heuristic algorithm for solving VRPs in large networks, has been adapted to solve the problem. Although the ACO algorithm has repeatedly been used to solve the Capacitated VRP, it has a drawback that cannot consider the capital cost of each vehicle along with other operational costs of the vehicles (associated with the total distance traveled within a day) in its initial form. More specifically, naturally it assumes that each vehicle returns to the depot if it becomes full or the demand finishes, each met first; this paper seeks to propose an adapted ACO algorithm in which this assumption is released. To assess the capability of the proposed model in large-scale networks, the case study of Mashhad city, consisting of 253 traffic analysis zones and over than 3800 links, has been considered. Results show that the proposed algorithm converges to near-to-optimal solutions within two seconds of cpu time, which is encouraging.

In this paper, a heuristic solution approach to the single source Capacitated facility location problem is considered. As a first step, a local search method is designed to perform quick simple moves in the solution structure. Then, the greedy manner of the local search is combined by Simulated Annealing meta-heuristic. Such a careful combination would allow escaping local optima with the aim of more diversified search capabilities. The method, then makes use of acceleration mechanisms to enhance search process. Here, we combine the algorithm with two different acceleration mechanisms namely consecrating mechanism and parallelizing mechanism. Such a combination will define two different versions of the mentioned search strategy based on simulated annealing meta-heuristic. Computational results obtained over the existing standard benchmark instances, not only demonstrate the superiority of the proposed method over the best existing ones, but also announce the method as an effective practical tool to tackle the problem.