On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

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

The two-echelon capacitated vehicle routing problem: models and math-based heuristics

Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed

Routing Applications in Newspaper Delivery

-The goal of this report is to give an up-to-date account of routing applications in the newspaper business. We describe the newspaper supply chain, and focus on the “last mile” distribution that has been advocated as an application of arc routing in the literature. A literature survey is provided, followed by a discussion of the arc routing model and its adequacy to newspaper applications. A more general and normally more adequate model: The Node, Edge, and Arc Routing Problem, is discussed. Characteristics of routing problems in carrier delivery are presented, together with a case study from the development of a web-based route design and revision system. Finally, summary, conclusions, and prospects for the future are given

Modeling a four-layer location-routing problem

Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations

Internalizing negative externalities in vehicle routing problems through green taxes and green tolls

Road freight transportation includes various internal and external costs that need to be accounted for in the construction of efficient routing plans. Typically, the resulting optimization problem is formulated as a vehicle routing problem in any of its variants. While the traditional focus of the vehicle routing problem was the minimization of internal routing costs such as travel distance or duration, numerous approaches to include external factors related to environmental routing aspects have been recently discussed in the literature. However, internal and external routing costs are often treated as competing objectives. This paper discusses the internalization of external routing costs through the consideration of green taxes and green tolls. Numeric experiments with a biased-randomization savings algorithm, show benefits of combining internal and external costs in delivery route planning.Peer Reviewe