Survey on Ten Years of Multi-Depot Vehicle Routing Problems: Mathematical Models, Solution Methods and Real-Life Applications

A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

A reformulation strategy for mixed-integer linear bi-level programming problems

Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The solution of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort or cannot guarantee a global optimal solution. To overcome these issues, this paper proposes a two-step reformulation strategy in which the first part consists of reformulating the inner mixed-integer problem into a nonlinear one, while in the second step the well-known Karush-Kuhn-Tucker conditions for the nonlinear problem are formulated. This results in a mixed-integer nonlinear problem that can be solved with a global optimiser. The computational and numerical benefits of the proposed reformulation strategy are demonstrated by solving five examples from the literature

Rough-Cut Capacity Planning in Multimodal Freight Transportation Networks

A main challenge in transporting cargo for United States Transportation Command (USTRANSCOM) is in mode selection or integration. Demand for cargo is time sensitive and must be fulfilled by an established due date. Since these due dates are often inflexible, commercial carriers are used at an enormous expense, in order to fill the gap in organic transportation asset capacity. This dissertation develops a new methodology for transportation capacity assignment to routes based on the Resource Constrained Shortest Path Problem (RCSP). Routes can be single or multimodal depending on the characteristics of the network, delivery timeline, modal capacities, and costs. The difficulty of the RCSP requires use of metaheuristics to produce solutions. An Ant Colony System to solve the RCSP is developed in this dissertation. Finally, a method for generating near Pareto optimal solutions with respect to the objectives of cost and time is developed

An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

This paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approachThis publication has emanated from research conducted with the financial support of Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/228

An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems

Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust