The topics covered by the papers can be roughly categorized as belonging to: fleet management or scheduling (5 papers), container operations (4 papers), facility location-routing problem (11 papers), and supply chain management (6 papers). Furthermore, a number of the papers tackle combined decision problems, found in a large variety of contexts. Several papers address liner shipping, sustainable supply chains, or even container repositioning.

Likewise, the solution approaches are widely varied with a large minority using hybrid metaheuristics or heuristics to address the problems. Papers address game theory or constraint logic programming and a large variety of nature-inspired meta-heuristics (e.g., particle swarm optimization, genetic algorithms, and ant colony optimization). A simplified overview of the most common approaches can be seen in Fig. 1.

Fig. 1
figure 1

The solution approaches applied in this special issue

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The real-life problems addressed are rather large, typically NP-hard, and have to be solved on a continuous basis as part of the operations of companies. The solution approaches therefore often include heuristics and the use of hybrid optimization to find good quality solutions in short computational time. Despite the complexity, several papers propose exact solution approaches under certain conditions. This simply serves to illustrate that there are many relevant approaches to solve problems and improve our insight into these complex issues.

Of the eleven facility location and routing papers, seven employ heuristics algorithms to solve the routing problem, three focus on exact algorithms, and one is a systematic literature review. Among the seven heuristics algorithms papers, Penna, Subramanian, Ochi, Vidal, and Prins propose a hybrid metaheuristic that combines an iterated local search with variable neighborhood descent for solution improvement, and a set partitioning formulation to exploit the memory of the past search. Asefi, Lim, Maghrebi, and Shahparvari present a mixed-integer linear programming (MILP) model, solved by a hybrid variable neighborhood search and simulated annealing algorithm, to minimize the total cost of the integrated solid waste management system. Chen, Tian, and Yao develop a hybrid heuristic integrating distance-based clustering approach, mutation operation, and a relocate exchange method for a location–routing–inventory problem in food distribution networks. Armas, Keenan, Juan, and McGarraghy create two different novel approaches to solve the time capacitated arc routing problem. One is a savings-based heuristic, and the other is a metaheuristic integrating a biased-randomized version of the aforementioned heuristic with a simulated annealing framework. Yao, Chen, Song, and Yang employ ant colony optimization, adopting a scanning strategy and crossover operation to improve the performance in solving the fresh seafood delivery routing problem. Shan, Yan, Chen, Zheng, Yao, and Fu propose a heuristic to optimize selection of the location of new chain stores by maximizing the benefit on the principle of the Nash equilibrium. Balaji, Nilakantan, Nielsen, Jawahar, and Ponnambalam utilize a genetic algorithm and a simulated annealing algorithm to solve the fixed charge transportation problem with truck load constraints. Besides these seven papers on heuristics, three other papers focus on exact algorithms. Chami, Manier, and Manier work on a lexicographic approach to deal with the proposed mono-objective model to solve the selective pickup and delivery problem with time windows and paired demands. Sitek and Wikarek present an optimization model and its implementation using a hybrid approach for the capacitated vehicle routing problem with pick-up and alternative delivery. Xie, Wu, and Boyles study a new traffic network equilibrium problem with continuously distributed bounds on path weights and develop a linear approximation algorithm. The remaining paper is a systematic literature review by Vega-Mejía, Montoya-Torres, and Islam, focusing on recent optimization developments in integrated packing and routing problems.

Four container operations papers address different aspects of the ocean container transportation system. Yang, Lee, Liu, and Zheng study the carrier–shipper contracting issue under asymmetric information and propose a proportion requirement policy to mutually benefit both sides in contract negotiation. Ma, Chung, Chan, and Cui develop a novel multicontinuous berth layout approach and a mixed integer linear programming formulation for the berth and yard planning problem in a container terminal. Poo and Yip formulate the empty container repositioning (ECR) problem, propose an ECR policy, and analyze its impact on the profit of a container transport system. Zhen, Yu, Wang, and Sun develop a particle swarm optimization based solution method to solve the proposed mixed-integer programming model on quay crane and yard truck scheduling in a container terminal.

Five fleet management and scheduling papers cover some interesting real world applications. Harbering, Ranade, Schmidt, and Sinnen consider the single-track train scheduling problem and develop a lower bound on the makespan of the problem that can give an easy solution method in some special cases. Cheaitou and Cariou study the greening of maritime transportation and develop a multi-objective model to address the trade-off between profit maximization, CO2 emissions, and SOx emissions. Their model is tested on the trans-Pacific and Europe–Far East markets. Konur and Geunes formulate a mixed-integer-nonlinear model of an integrated districting, fleet composition, and inventory planning problem for a multiretailer distribution system. They develop a column generation based heuristic approach as its solution. Bocewicz, Banaszak, and Nielsen study a transportation network of various heterogeneous AGVs in a multiproduct manufacturing system and propose a solution to assign the AGVs to transportation tasks considering fuzzy operation time constraints. Zhang, Wang, Sun, and Yu propose an optimization method for the tourist sightseeing bus scheduling problem, considering the passenger demand split in multiple transport modes between a self-driving and a sightseeing bus.

Finally, six papers study transportation issues in supply chain management and present a variety of new solution methods and applications. Govindan, Agarwal, Darbari, and Jha propose an integrated supply chain network model to study the evaluation and selection of forward distribution partners as well as third party reverse logistic providers, to emphasize the sustainability aspect of an electronic manufacturing company. Kaur and Singh propose that, because of various uncertainties, a supply chain has to be flexible; and they propose a flexible procurement framework to allocate order quantities to preferred suppliers and carriers in a global supply chain. Darbari, Kannan, Agarwal, and Jha design a closed loop supply chain network for an Indian laptop manufacturer, modelled as a MILP problem with fuzzy goals of minimizing environmental impact and maximizing net profit and social impact, subject to fuzzy demand and capacity constraints. Poudel, Quddus, Marufuzzaman, Bian, and Burch V present a two-stage stochastic programming model to manage a biomass co-firing supply chain network, which takes the congestion effect into account. Paul, Asian, Goh, and Torabi study the recovery problem after a sudden disruption considering not only the delivery delay but also fractional quantity loss during the delay, and propose three different heuristic solutions to solve such a problem. The final paper is a literature review by Soheilirad, Govindan, Mardani, Zavadskas, Nilashi, and Zakuan that presents a comprehensive review of data envelopment analysis models in supply chain management studies.

Looking at the papers collected here, we cannot help but feel they illustrate both the complexity of the problems found within operations research as applied to transportation and some of the best ideas addressing these challenges. We are extremely satisfied with the quality of the papers accepted and would like to extend thanks to the authors for their high-quality contributions and prompt replies and revisions to the papers. However, the biggest thanks we reserve for the numerous reviewers who have diligently worked to ensure that the papers are of the highest quality. Last but not least, our special thanks go to Prof. Endre Boros for encouraging us to organize this special issue and to Katie D’Agosta for her great support facilitating the entire publication process.