(52h) Time Window Based Berth and Yard Allocation Planning of Container Vessels | AIChE

(52h) Time Window Based Berth and Yard Allocation Planning of Container Vessels


Xu, J. - Presenter, Lamar University
Qu, H., Lamar University
Xu, Q., Lamar University
Transshipment of container vessels has been playing a significant role in international sea freight transport. Over the past several years, a reduction in the productivity of port has been observed due to inefficient usage of the available resources. Amongst all the operations, the most important is an optimal berth allocation of the ship and yard allocation for the containers. The berth location of ships and the yard location of containers are inter-dependent on each other. Also container vessels might arrive earlier or later than their nominal arrival time due to all kinds of uncertainties during port operations. Conventional berth allocation and planning models have difficulties to handle the uncertainty of vessel arrival while constructing a nominal berth plan or nominal berth allocation. However, in reality, the delay of a single vessel might interrupt the entire schedule and make it very difficult or even impossible to recover. And terminal operators strive to optimize the berth and yard allocation planning so as to minimize the travel distance of all containers. Because long travel distance not only causes high cost of carriers but also has a potential threat to the loading and discharging operations at the quayside. So, it is crucial to consider these two planning problems in an integrated manner.

Mathematical optimization has been used to improve the operational capability of port terminals using various realistic constraints. An integrated model of berth and yard template planning is developed for transshipment hubs [1]. But a weighted sum of berth-side and yard-side cost is utilized in the objective, and yard crane contention during the unloading activities has not been considered in the model. A joint planning problem for berth and yard allocation in transshipment terminals has also been developed using multi-cluster stacking strategy [2]. However, the two objectives are linearly combined by assigning each a weight which disregards that they are of different units. Existing publications are either focused on planning problem without considering realistic flexible arrival and departure time windows or using fixed maximal deviation from nominal arrival time [3].

The goal of this study is to optimally use the resources on the quay. For instance, making the most of quay cranes and minimizing total carrier transportation cost. A time window-based berth and yard allocation planning problem has been developed. Flexible arrival and departure time windows have to be taken into account specifically as control variables. We consider the simultaneous berth allocation and yard planning problem at a tactical level. This implies that certain decisions have already been made at a strategic level. We also assume that an optimal layout of the yard has been determined. And the number of storage blocks as well as their sizes and locations are known. We allow transshipment not only from vessel to storage block, but also from storage block to vessel. And containers can only be loaded or discharged when the vessel is berthing in the terminal.

The problem consists of two parts, first is the berth allocation planning model, which we called BAP model. BAP model is a MIP model and the objective function is to minimize total operational cost while satisfying all the transportation demand and operation constraints. The second part is the berth and yard allocation planning model, which we called BAYAP model. The berthing and departure time of each vessel are results of BAP model, which based on the expected amount of containers to be handled and the necessary quay and crane capacity to do so. These results can serve as an input to the following BAYAP model. The BAYAP model is a MINLP model and the objective function is to minimize total carrier transportation cost. Commercial solvers such as CPLEX, BARON, and ANTIGONE have been employed to obtain the optimal solution of the developed planning models. After solving the BAYAP model, we can get the optimal schedule of containers transshipment. Computational results of the case study demonstrate the efficacy of the developed planning model.


  1. Zhen, L., E.P. Chew, and L.H. Lee, An Integrated Model for Berth Template and Yard Template Planning in Transshipment Hubs. Transportation Science, 2011. 45(4): p. 483-504.
  2. Tao, Y. and C.-Y. Lee, Joint planning of berth and yard allocation in transshipment terminals using multi-cluster stacking strategy. Transportation Research Part E: Logistics and Transportation Review, 2015. 83: p. 34-50.
  3. Hendriks, M.P.M., E. Lefeber, and J.T. Udding, Simultaneous berth allocation and yard planning at tactical level. OR Spectrum, 2013. 35(2): p. 441-456.