TRANSPORTATION SCIENCE Vol. 00, No. 0, Xxxxx 0000, pp. 000–000 issn 0041-1655 | eissn 1526-5447 | 00 | 0000 | 0001 INFORMS doi 10.1287/xxxx.0000.0000 c  0000 INFORMS Ship Scheduling and Network Design for Cargo Routing in Liner Shipping Richa Agarwal, ¨ Ozlem Ergun School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA. ragarwal@isye.gatech.edu, oergun@isye.gatech.edu A common problem faced by carriers in liner shipping is the design of their service network. Given a set of demand to be transported and a set of ports, a carrier wants to design service routes for his ships as eﬃciently as possible, using the underlying facilities. Furthermore, the proﬁtability of the service routes designed depends on the paths chosen to ship the cargo. We present an integrated model, a mixed integer linear program, to solve the ship scheduling and the cargo routing problems simultaneously. The proposed model incorporates relevant constraints, such as the weekly frequency constraint on the operated routes, and emerging trends, such as the transshipment of cargo between two or more service routes. To solve the mixed integer program, we propose algorithms that exploit the separability of the problem. More speciﬁcally, a greedy heuristic, a column generation based algorithm and a two phase Benders decomposition based algo- rithm is developed and their computational eﬃciency in terms of the solution quality and the computational time taken is discussed. An eﬃcient iterative search algorithm is proposed to generate good schedules for ships. Computational experiments are performed on randomly generated instances simulating real life with up to 20 ports and 100 ships. Our results indicate high percentage utilization of ships’ capacities and a signiﬁcant number of transshipments in the ﬁnal solution. Key words : maritime transportation; liner shipping; Benders decomposition Introduction Sea cargo is the freight carried by ships and it includes anything travelling by sea other than mail, persons and personal baggage. A global sea carrier is a person, business or organization that oﬀers transportation services via sea on a worldwide basis. A shipper is a person or company who is either the supplier or the owner of the cargo that is to be shipped. With rates for sea cargo transportation at approximately one-tenth of air freight rates, fewer accidents and less pollution maritime transportation is regarded as a cheap, safe and clean transportation mode, compared to other modes of transportation. Increasing globalization and inter-dependence of various world economies is leading to a tremendous positive growth in the sea cargo industry. International and domestic trade of many nations depend on this mode of transportation. According to American Association of Port Authorities (2006), in the United States, which is the largest trading nation in the world for both imports and exports - accounting for nearly 20% of world trade, sea cargo is responsible for moving over 99% of the international cargo. U.S. ports and waterways handle more than 2.5 billion tons of trade annually, and this volume is projected to double within the next ﬁfteen years. Increase in sea-borne trade worldwide has led to similar trends in the growth of the world ﬂeet. In 2005, world sea-borne trade increased to 7.11 billion tons of loaded goods (a 3.8 % annual growth rate) and the world ﬂeet expanded to 960.0 million deadweight tons (a 7.2% increase) (United Nations Conference on Trade and Development (2006)). Although the ﬂeet mix and size have changed over time considerably, the eﬃcient utilization of the ships remains to be one of the main determinants of a carrier’s proﬁtability. A ship involves a major capital investment, in millions of US dollars, and its daily operating costs can be in tens of thousands of dollars. Hence, development of optimization based decision support systems is necessary for eﬃcient ﬂeet management. 1