Voyage allocation and fuelling decisions in shipping

Abstract

The thesis considers the following two types of problems in shipping viz.(i) Allocation of planned voyages to ships and Iii) Cargo mix cum fuelling decisions. The first problem considers deploying of different classes of ships available with SCI to undertake a set of planned voyages with date of departure, amount of cargo to be carried, steaming distance and the average number of days of stay at ports, The ships in each class are assumed to be homogeneous with respect to speed, capacity etc. In resolving this problem it is assumed that the capacity of the ship assigned to a voyage should be sufficient to carry the cargo enroute. Our criterion is one of minimizing the total fuel consumed. The second problem is that of deciding how much fuel and cargo should be shipped through each port to a ship assigned to a scheduled route as prices of fuel vary from one port to another. A judicious purchase of fuel requirements would result in reducing the expenditure on fuel consumption. These two problems together result in reducing the expenditure on fuel consumption since we know the amount of cargo to be shipped on each voyage and the prices of fuel at each port on the route. Three different types of formulations are considered for voyage allocation problem. All of these are 0-1 Integer Programming Problems. The first one is based upon the idea of finding a sailing schedule for each ship. Here a ship’s sailing schedule consists of a set of voyages undertaken by a ship such that each voyage occupies a specific position in the sequence of voyages undertaken by a ship. The second problem is a set partitioning problem with side constraints. The size of both these formulations makes solution procedures such as branch and bound, cutting plane methods etc. impracticable with the available computations facilities. The third formulation is an Integer Programming Problem defined over a set of networks. This is based upon the concept of partitioning the set of voyages into disjoint sets such that they can be undertaken by the ships available in that class. A branch and bound type of algorithm is developed for solving the last formulation. Here branching scheme is based upon Dilworth’s Decomposition theorem. Three types of bounds are defined and the last two bounds are obtained by solving mincost flow problems. Some computational experience with the algorithm is given. The second problem is a linear programming problem. An efficient algorithm is developed for solving large sized problems with hand.