Traffic and transportation are of essential importance for the global economy and society. Growing need of transportation and limitation of fossil fuel imply that economical use of transportation resources is critical and will become increasingly important in the future. Simultaneously enterprises are forced to reduce costs and save resources to increase their competitiveness in the global markets. Optimization models and computational solution methods have been developed to manage and control complex systems arising in traffic, transportation and logistics. However, such problems often become very difficult and cannot be solved to optimality with today’s technologies. New models and methods are needed to be able to compute better solutions for practical use. The modeling and solution approaches are often based on mathematical programming and complemented with heuristic methods.

The primary objective of this special issue is to examine the methodological and research issues in optimization of logistics, traffic and transportation systems, focusing on the latest developments in modeling and optimization methods. For this special issue six articles have been selected for publication after a thorough peer-review according to the standards of the FSM journal.

1 Papers in the special issue

The first paper by Rune Larsen, Marco Pranzo and Andrea D’Ariano addresses susceptibility of optimal train schedules considering stochastic disturbances and their effects in railway traffic. The research question is to assess the degree of sensitivity of various rescheduling algorithms to variations in process times. Computational results are based on a complex and densely occupied Dutch railway area where train delays are computed based on statistical distributions, and dwell and running times of trains are subject to additional stochastic variations.

Delay management and train scheduling have been studied by Twan Dollevoet, Francesco Corman, Andrea D’Ariano and Dennis Huisman in the second paper as well. Delay management determines which connections should be maintained in case of a delayed feeder train. The authors propose an optimization approach that iteratively solves a macroscopic delay management model on the one hand, and a microscopic train scheduling model on the other hand. The macroscopic model determines which connections to maintain and proposes a disposition timetable. This disposition timetable is then validated microscopically for a bottleneck station of the network, proposing a feasible schedule of railway operations. The iterative optimization framework is evaluated using real-world instances around Utrecht in the Netherlands.

The distribution process of heating oil typically involves solving vehicle routing problems on a daily basis. The paper written by Eric Prescott-Gagnon, Guy Desaulniers and Louis-Martin Rousseau presents heuristic methods for such an oil delivery vehicle routing problem. The authors consider rich vehicle routing problems that may involve heterogeneous vehicle fleet, multiple depots, intra-route replenishments, time windows, driver shifts and optional customers. Three metaheuristics have been developed, namely, a tabu search algorithm, a large neighborhood search (LNS) heuristic based on the tabu search heuristic, and another LNS heuristic based on a column generation heuristic. Computational results obtained on instances derived from a real-world dataset are presented.

The paper by Tiantang Liu, Zhibin Jiang and Na Geng studies the multi-depot heterogeneous fleet capacitated arc routing problem (MDHCARP). This is a problem with rather rare research in the past, but with many applications in real life. The MDHCARP extends the capacitated arc routing problem by considering both the multi-depot case and limited heterogeneous fleet constraints. The authors propose a genetic local search algorithm for the MDHCARP. Computational results are presented that show the superiority of the proposed algorithm compared to existing approaches.

The fifth article is written by Ilse Louwerse, Jos Mijnarends, Ineke Meuffels, Dennis Huisman and Hein Fleuren, and it studies scheduling movements in the network of an express service provider. Transportation of shipments in the network is organized via depots and hubs, where depots are local sorting centers that take care of the collection and delivery of the parcels at the customers, and hubs are used to consolidate the transportation between the depots. The paper addresses the scheduling of all movements in an express network at minimum cost. The problem is divided into two subproblems, and a column generation approach and a local search algorithm are used to solve them.

The scheduling of passenger elevators in a building is an online optimization problem, where the data describing the optimization task become available over time. The paper by Benjamin Hiller, Torsten Klug and Andreas Tuchscherer in the special issue considers scheduling of elevator groups such that short waiting and travel times for the passengers are obtained. The authors present an exact reoptimization algorithm that uses column generation techniques and adopts a Branch & Bound method to solve the column generation problems.

2 Concluding remarks

This special issue has greatly benefited from the cooperation among the authors, reviewers, and editors. We would like to express our sincere thanks to the reviewers for their excellent and timely refereeing. Last, but not least, we thank all authors for their contributions which made this special issue possible.