Simultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Ter
In this work, we focus on the integrated planning of the following problems faced within the context of seaside operations at container terminals: berth allocation, quay crane assignment, and quay crane scheduling. First, we formulate a new binary integer
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troduction There has been a considerable growth in the share of containerized trade in the world’s total dry cargo during the last 30 years. Therefore, the efficient management of seaport container terminals has become a crucial issue [2]. In this work, we concentrate on the integrated planning of seaside operations, which includes the berth allocation problem (BAP), quay crane assignment problem (CAP) and quay crane scheduling problem (CSP). Generally, BAP deals with the determination of the optimal berthing times and positions of vessels in container terminals. The focus of CSP, on the other hand, is mainly on the problem of determining an optimal handling sequence of vessels for the available cranes at the terminal. However, as can be realized, the assignment of the cranes to vessels has a direct effect on the processing times of the vessels. As a result, crane assignment decisions can be embedded within either BAP or CSP models. In this work we formulate two new MILP formulations integrating first BAP and CAP (BACAP), and then BAP, CAP, and CSP (BACASP). Both of them consider a continuous berth layout where vessels can berth at arbitrary positions within the range of the quay and dynamic vessel arrivals where vessels cannot berth before the expected arrival time. The crane schedule found by solving the BACASP formulation determines the specific crane allocation to vessels for every time period. These MILP models are the first models solved exactly rather than heuristically in the literature for relatively large instances. N. Aras (B) · Y. Türko˘gulları · Z. C. Ta¸skın · K. Altınel Bo˘gaziçi University, Istanbul, Turkey e-mail: [email protected] Y. Türko˘gulları e-mail: [email protected] Z. C. Ta¸skın e-mail: [email protected] K. Altınel e-mail: [email protected] S. Helber et al. (eds.), Operations Research Proceedings 2012, Operations Research Proceedings, DOI: 10.1007/978-3-319-00795-3_15, © Springer International Publishing Switzerland 2014
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2 Model Formulation The underlying assumptions of our models are given as follows. The planning horizon is divided into equal-sized time periods. The berth is divided into equal-sized berth sections. Each berth section is occupied by no more than one vessel in each time period. Each quay crane can be assigned to at most one vessel per time period. Each vessel has a minimum and maximum number of quay cranes that can be assigned to it. The service of a vessel by quay cranes begins upon that vessel’s berthing at the terminal, and it is not disrupted until the vessel departs. The number of quay cranes assigned to a vessel does not change during its stay at the berth, which is referred to as a time-invariant assignment [1]. Furthermore, the set of specific cranes assigned to a vessel is kept the same. By letting i the index of vessels, g the index of crane groups, j the index of berth sections, k the index of number of cranes, t the index of time g g periods, cl the index of the leftmost crane in group g, cr the index of the rightmost c
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