This document discusses emerging techniques for berth allocation and quay crane scheduling at port container terminals. It examines approaches like mixed integer programming and genetic algorithms. Mixed integer programming models are used to minimize the makespan of handling all container ships by determining optimal berth allocation and quay crane scheduling. A genetic algorithm represents berth allocation as a chromosome sequence and uses steps like crossover and mutation to obtain near-optimal solutions for the integrated berth allocation and quay crane scheduling problem. Both methods provide effective solutions but genetic algorithms are needed because the problem is NP-complete.

1. Emerging Techniques in Berth Allocation
and Quay Crane Scheduling at Port
Container Terminals
Kriti Srivastava

2. Objective: To understand the relationship between berth
allocation and quay crane scheduling at port container terminals. To
examine approaches like Mixed Integer Programming and Genetic
Algorithm, their effectiveness and efficiency in solving the studied
problem.
Introduction: The handling time of a container ship at a berth,
which is a vital factor in berth allocation, is related to the quay
crane schedule for the container ship at the berth. However, most
of the research work study berth allocation and quay crane
scheduling independently. In recent years, the focus has shifted to
Integrated Berth Allocation and Quay Crane Scheduling in which the
handling time of a container ship at a berth is obtained from a quay
crane scheduling model.
• Berth Allocation:
• Berth allocation is to determine the berthing time and
position of every container ship considering some
factors:
• Length and draft of each container ship
• Arrival time of each container ship
• Number of containers to be unloaded and
loaded
• Storage location of outbound containers to be
loaded onto the corresponding container ship
• Quay Crane Scheduling
• Quay cranes are operated on the same tracks and thus
cannot cross over each other.
• Only 1 quay crane can work on a ship bay at any
time and a quay crane usually moves to the next
assigned ship bay until it completes the current
one.
• The average processing time of a ship bay is
about 3 hours and the travel time of a quay
crane between two ship bays is about 1 minute.
Methodology:
1. Mixed Integer Programming Model
• Dynamic berth allocation model based on discrete
locations: The objective function minimizes the
makespan of handling all container ships, which is the
latest completion time among all container ships.
• Quay crane scheduling with non-crossing constraints.
The objective function minimizes the handling time of
container ships at berth.
Assumptions:
• Each berth can handle only one container ship at a
time until the container ship is completed.
• The handling time of a container ship at a berth
depends on the quay crane schedule for the container
ship.
• Container ships can arrive at a port container terminal
during the planning horizon and no container ship can
be handled before it arrives.
• The number of quay cranes at each berth is fixed.
• Quay cranes are operated on the same tracks and thus
cannot cross over each other.
• Only one quay crane can work on a ship bay at a time
until it completes the ship bay.
• Compared with the processing time of a ship bay by a
quay crane, the travel time of a quay crane between
two ship bays is small and hence it is not considered.
Limitation:
Integrated Berth allocation and Quay Crane Scheduling
Problem (IBAQCSP) is NP-complete, and thus there exists
no polynomial time algorithm for the exact solution to the
IBAQCSP unless P = NP. Hence heuristic algorithms are
needed to obtain near optimal solutions for the problem
Fig1: Port Operation overview
Fig2: Berth Allocation and QC arrangement at Port
Fig3: Quay Crane Scheduling
Journal Ref: Der-Horng Lee & Hui Qiu Wang (2010) Integrated discrete berth allocation and quay crane scheduling in port container terminals, Engineering Optimization | Taylor and Francis
Lee et.al Quay crane scheduling with non-interference constraints in port container terminals | Transportation Research Part E 44 (2008) | Elsevier Ltd

3. 2. Genetic Algorithm:
A chromosome of the GA represents a sequence of container
ships. Based on the sequence of container ships represented by
the chromosome, a berth allocation can be constructed using
the following procedure.
• Step 1 Based on the current completion time of each berth
to finish its already allocated container ships and the arrival
time of the first unassigned container ship in the
chromosome, determine which berths can handle this
container ship immediately. If there is no idle berth when
this container ship arrives, go to Step 2.1. Otherwise, go to
Step 3.1.
• Step 2.1 If there is only one berth with the earliest
completion time, this container ship has to wait. Allocate it
to this berth. Then, delete this container ship from the
chromosome, update the completion time of the assigned
berth, and go to Step 4. If there are two or more berths with
the earliest completion time, go to Step 2.2.
• Step 2.2 If there is only one berth with the largest number
of quay cranes, this container ship has to wait. Allocate it to
this berth. Then, delete this container ship from the
chromosome, update the completion time of the assigned
berth, and go to Step 4. If there are two or more berths with
the largest number of quay cranes, go to Step 2.3.
• Step 2.3 This container ship has to wait. Allocate it to the
berth with the smallest number. Then, delete this container
ship from the chromosome, update the completion time of
the assigned berth, and go to Step 4.
• Step 3.1 If there is only one idle berth, allocate this
container ship this berth. Then, delete this container ship
from the chromosome, update the completion time of the
assigned berth, and go to Step 4. If there are two or more
idle berths, go to Step 3.2.
• Step 3.2 If there is only one idle berth with the largest
number of quay cranes, allocate this container ship to this
berth. Then, delete this container ship from the
chromosome, update the completion time of the assigned
berth, and go to Step 4. If there are two or more idle berths
with the largest number of quay cranes, go to Step 3.3.
• Step 3.3 Allocate this container ship to the idle berth with
the smallest number. Then, delete this container ship from
the chromosome, update the completion time of the
assigned berth, and go to Step 4.
• Step 4 If there are unassigned container ships in the
chromosome, go to Step 1; otherwise, go to End.
• Fitness Evaluation:
• Crossover: Refer Fig4
• Mutation: Random selection and swapping of chromosomes
applied.
Note: When updating the completion time of the
assigned berth in the aforementioned procedure, the
handling time of this container ship at the assigned
berth is obtained from an approximation algorithm for
the quay crane scheduling with non-crossing constraints
problem.
Conclusion: The proposed genetic algorithm to obtain near
optimal solutions for the IBAQCSP has been performed using
computational Experiments and has been effective and efficient
in solving the IBAQCSP.
Fig4: Crossover
Journal Ref: Yang et.al Computers & Industrial Engineering 56 (2009) A quay crane dynamic scheduling problem by hybrid evolutionary algorithm for berth allocation planning | Elsevier Ltd
Agostinho Agra, Maryse Oliveira (2017) MIP approaches for the integrated berth allocation and quay crane assignment and scheduling problem | European Journal of Operational Research | Elsevier Ltd
Further Research Areas:
• Relative position formulation(RPF) for the berth
allocation.
• Discretization of the time and space variables to
avoid the big-M constraints included in the RPF.