a b s t r a c tThis paper describes industrial aspects of combined inventory management and routing in maritime and road-based transportation, and gives a classification and comprehensive literature review of the current state of the research.The literature is contrasted with aspects of industrial applications from a constructive, but critical, viewpoint. Based on the status and trends within the field, future research is suggested with regard to both further development of the research area and industrial needs. By highlighting the industrial aspects, practitioners will hopefully see the benefit of using advanced decision support systems in complex situations related to combined inventory management and routing in their business. In addition, a classification and presentation of the research should help and motivate researchers to further focus on inventory management and routing challenges.

The purpose of this paper is to describe industrial aspects of combined fleet composition and routing in maritime and road-based transportation, and to present the current status of research in the form of a comprehensive literature review. With a backdrop of industrial aspects, a categorized survey of relevant literature since the first published papers in the 1950's is given. First, the literature review discusses some early seminal and application-oriented papers, presents a classification of problems, and then focuses on a basic definition of combined fleet composition and routing: the fleet size and mix vehicle routing problem. Three basic mathematical formulations from the literature are presented and compared. Further, the literature of extended and related problems is described and categorized. Surveys of application oriented research in road-based and maritime transportation conclude the review. Finally, we contrast the literature with aspects of industrial applications from a critical, but constructive stance. Major issues for future work are suggested.

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This paper presents a new deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows. The objective is to service, at minimal total cost, a set of customers within their time windows by a heterogeneous capacitated vehicle fleet. First, we motivate and define the problem. We then give a mathematical formulation of the most studied variant in the literature in the form of a mixed-integer linear program. We also suggest an industrially relevant, alternative definition that leads to a linear mixed-integer formulation. The suggested metaheuristic solution method solves both problem variants and comprises three phases. In Phase 1, high-quality initial solutions are generated by means of a savings-based heuristic that combines diversification strategies with learning mechanisms. In Phase 2, an attempt is made to reduce the number of routes in the initial solution with a new local search procedure. In Phase 3, the solution from Phase 2 is further improved by a set of four local search operators that are embedded in a deterministic annealing framework to guide the improvement process. Some new implementation strategies are also suggested for efficient time window feasibility checks. Extensive computational experiments on the 168 benchmark instances have shown that the suggested method outperforms the previously published results and found 167 best-known solutions. Experimental results are also given for the new problem variant.

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Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applications.

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