Ship routing and scheduling with cargo coupling and synchronization constraints q Henrik Andersson a , Jon M. Duesund a , Kjetil Fagerholt a,b,⇑ a Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Alfred Getz veg 3, NO-7491 Trondheim, Norway b Norwegian Marine Technology Research Institute (MARINTEK), POB 4125 Valentinlyst, NO-7450 Trondheim, Norway article info Article history: Received 15 February 2011 Received in revised form 21 June 2011 Accepted 1 July 2011 Available online 19 July 2011 Keywords: Ship routing and scheduling Synchronization Path-flow abstract The purpose of this paper is to introduce and solve a planning problem faced by shipping companies operating in a special segment of tramp shipping called project shipping. Project shipping differs from other more traditional tramp segments because the cargoes are more unique and usually transported on a one-time basis. The special nature of the cargoes complicates the routing and scheduling. For instance, a cargo can be part of a process facility, but the shipping company cannot transport it unless other parts of the same facility are transported as well, even though these parts may have different ori- gins. This creates an additional coupling constraint between the cargoes. In addition, the different parts might require synchronized delivery within some time window. We present a mathematical formulation for the problem and propose three alternative solution methods based on path flow formulations and a priori column generation. In one of the solution methods this is combined with a scheme for relaxing the complicating synchronization constraints and reintroducing them dynamically when needed. Computa- tional results show that we are able to find optimal solutions to problems based on data obtained from a shipping company. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Maritime shipping represents the most important source of transportation in international trade, and its share of the total glo- bal trade has been estimated to lie between 65% and 85% (UNCTAD, 2007). Basically seaborne shipping has a monopoly in transporting large quantities of goods between continents. Acquisitions of new ships represent a huge capital investment, and thus it is crucial for shipping companies to utilize their fleets in the best possible way. Most companies rely on manual planning of fleet schedules, which usually works reasonably well due to experienced planners. How- ever, in the last couple of decades there have been many mergers and acquisitions with the result that fleets have become larger and the scheduling more complex. Thus optimization based meth- ods might have a great potential for improving fleet routing and scheduling. Lawrence (1972) discusses three general modes of maritime shipping; industrial, liner and tramp shipping. Industrial operators own the transported cargo, and thus focus on minimizing their tra- vel costs. Liner ships resemble bus lines and follow published itin- eraries and schedules, and the demand will depend on the routes and schedules. Tramp ships operate like a taxi and follow the car- goes that are available in the market. Tramp companies often enter contracts of affreightment (COAs) for some cargoes, and then try to maximize their profit by carrying optional spot cargoes. The differ- ent cargoes must be picked up at their loading port and delivered to their corresponding unloading ports, often within specified time windows. This paper presents a routing and scheduling problem for a spe- cial segment within tramp shipping referred to as project shipping, and relates to the real planning problem for a shipping company. This segment is also known as heavy duty and heavy lifting, and dif- fers from other more traditional tramp segments like tankers and dry bulk because the cargoes are more unique and usually trans- ported on a one-time basis, like for instance parts of a process facil- ity, reactors, yachts and train sets. These cargoes give rise to special stowage challenges, and a project shipping company might need an engineering unit in order to calculate the possibility of trans- porting their cargoes due to shape, stability, sea fastening, weight and lifting. The special nature of the cargoes also complicates the routing and scheduling. For instance, a cargo can be part of a process facility, but the shipping company cannot transport it unless other parts of the same facility are transported as well, even though these parts may have different origins. This creates an additional coupling constraint between the cargoes. In addition, the different parts might require synchronized delivery within some time window. Thus many of the cargoes cannot be evaluated individually, but rather as groups or projects. For the remainder of the paper this problem will be denoted as the project shipping problem. 0360-8352/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2011.07.001 q This manuscript was processed by Area Editor Maged M. Dessouky. ⇑ Corresponding author at: Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Alfred Getz veg 3, NO-7491 Trondheim, Norway. Tel.: +47 73 59 56 80/7; fax: +47 73 59 55 75. E-mail addresses: kjetil.fagerholt@marintek.sintef.no, kjetil.fagerholt@iot. ntnu.no (K. Fagerholt). Computers & Industrial Engineering 61 (2011) 1107–1116 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie