A bi-objective berth allocation formulation to account for vessel handling time uncertainty
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A bi-objective berth allocation formulation to account for vessel handling time uncertainty Mihalis M. Golias Department of Civil Engineering and Center for Intermodal Freight Transportation Studies, University of Memphis, Memphis, Tennessee 38152, USA. E-mail: [email protected]
A b s t r a c t In this article we formulate the berth allocation problem as a bi-objective mixed-integer programming problem with the objective to maximize berth throughput and reliability of the schedule under the assumption that vessel handling times are stochastic parameters, being a function of other stochastic parameters (that is, quay crane breakdowns, quay-to-yard transport vehicle productivity, yard congestion, and so on). A combination of an exact algorithm, a Genetic Algorithms-based heuristic and a Monte Carlo simulation are proposed as the solution approach for the resulting problem. Based on a number of simulation experiments, it is shown that the proposed modeling approach is effective and outperforms berth allocation solutions where reliability is not considered. Maritime Economics & Logistics (2011) 13, 419–441. doi:10.1057/mel.2011.21
Keywords: marine container terminals; berth allocation; optimization; meta-heuristics
Introduction The berth allocation problem (BAP) deals with the assignment of vessels to berth space in container terminals. Among the models found in the literature, there are four most frequently observed cases: (a) discrete versus continuous berthing space; (b) static versus dynamic vessel arrivals; (c) static versus dynamic vessel handling times; and (d) variable vessel arrivals. In the discrete r 2011 Macmillan Publishers Ltd. 1479-2931 Maritime Economics & Logistics Vol. 13, 4, 419–441 www.palgrave-journals.com/mel/
Golias
problem, the quay is viewed as a finite set of berths (for example, Imai et al, 2007). In the continuous problem, vessels can berth anywhere along the quay (for example, Lee et al, 2010). The majority of the published research considers the discrete case (Bierwirth and Meisel, 2009). In the static arrival problem, all the vessels to be served are already in the port at the time scheduling begins, whereas in the dynamic arrival problem not all the vessels to be scheduled for berthing have arrived, though arrival times are known in advance. The majority of the published research in berth allocation considers the latter case. In the static handling time problem, vessel handling times are considered as an input (for example, Imai et al, 2001), whereas in the dynamic handling problem, vessel handling is a variable; usually a function of the quay cranes that will operate on the vessel and the distance of the vessels’ berthing position from a location in the yard (for example, Imai et al, 2008; Legato et al, 2009). Finally, in the last case (for example, Golias et al, 2009a) vessel arrival times are considered as variables and are optimized. Technical restrictions such as berthing draft, inter-vessel and end-berth clearance distance are further assumptions that have been adopted in
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