Modeling the arrival process at dry bulk terminals

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Modeling the arrival process at dry bulk terminals

• Delft University of Technology

Faculty 3ME, Transport Engineering Logistics
T.A. van Vianen, J.A. Ottjes and G. Lodewijks
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Content

• Arrival process
• Average port time
• Modeling arrival process
• Continuous quay layout or multiple berths
• Conclusions

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Arrival process (1)

• Typical performance indicator is the average
  ships waiting time
• Agreements between terminal operators and
  ship-owners are made about the maximum ships
  port time
• Demurrage costs have to be paid if ships stay
  longer in the port
• How much capacity must be installed at the quay
  side?

Ship unloading (Courtesy of J.Hiltermann)
Ship loading (Courtesy of Richards Bay Coal
Terminal)
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Arrival process (2)

• How to prevent that ships are queuing before
  getting serviced?

Ships waiting before servicing
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Content

• Arrival process
• Average port time
• Modeling arrival process
• Continuous quay layout or multiple berths
• Conclusions

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Average port time (1)

• Average port time is the average waiting time
  plus the average service time
• Ships interarrival time predominately determines
  the average waiting time
• Quay crane capacity and carriers tonnage
  determines the average service time

Waiting
Servicing
Arrival process
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Average port time (2)

• Existing literature about ships arrivals
• Ships do not generally arrive at their scheduled
  times because of bad weather conditions, swells
  and other natural phenomena during the sea
  journey as well as unexpected failures or
  stoppages (Jagerman and Altiok, 2003)
• Uncontrolled ship arrivals results in ship delays
  (Asperen, 2004)
• Ships interarrival times best approximated by a
  Poisson or Erlang-2 arrival process (UNCTAD,
  1985)
• An Erlang-2 distribution can be used to represent
  the service time distribution (UNCTAD, 1985 and
  Jagerman and Altiok, 2003)

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Average port time (3)

• But what is meant with Poisson or Erlang-2
  distributed interarrival times?
• In a Poisson and Erlang-2 arrival process,
  probability distributions express the probability
  of a ship arrival in a fixed interval of time

Poisson and Erlang-2 distributions for ships
interarrival times with an average of 10 hours
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Average port time (4)

• From 3 terminals, the arrival process was
  investigated to check real-world data with
  existing literature
• T1 single-user, import terminal
• T2 stevedore, import terminal
• T3 single-user, export terminal

Interarrival time distributions
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Average port time (5)

• Service time relates directly to the carriers
  tonnage

Real-world data does not correspond with the
suggested Erlang-2 distribution
Carriers tonnage distributions
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Content

• Arrival process
• Average port time
• Modeling arrival process
• Continuous quay layout or multiple berths
• Conclusions

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Modeling arrival process (1)

• Modeling of the arrival process based on Queuing
  Theory

Basic of a queuing system
Labeling of queuing models

• M/E2/2
• Interarrival times distributed according a
  Poisson (Markovian) arrival process
• Service times distributed according Erlang-2
  distribution
• 2 servers ? 2 berths where each berth is equipped
  with 1 quay crane

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Modeling arrival process (2)

• For single berth queuing systems, the impact of
  the several interarrival times distribution was
  investigated

Single berth queuing system
M/E2/1

• E2/E2/1

• D/E2/1

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Modeling arrival process (3)

• For multiple berths queuing systems, there are
  hardly mathematical expressions

Multiple berths queuing system
M/M/s
E2/E2/s ..
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Modeling arrival process (4)

• A discrete-event simulation model was developed

• CraneClass.Process
• MyDistGen.Start(Tnow)
• While True do
• Begin
• If IsInQueue(CraneIdleQ) then MyDistGen.Pause
• While IsInQueue(CraneIdleQ) do standby
• If MyDistGen.Status interrupted then
  MyDistGen.Resume(Tnow)
• If MyShip ltgtnil then
• Begin
• if MyShip.Tons gt 0 then
• Begin
• MyShip.TonsMyShip.Tons GrabTons
• Hold(Cranecycle)
• end
• if MyShip.Tons 0 then
• Begin
• If (IsInQueue(MyBerth.MyCranesQ)) and
  (MyBerth.MyCranesQ.Length gt 1) then
• Begin
• LeaveQueue(MyBerth.MyCranesQ)

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Modeling arrival process (5)

• For multiple berths queuing systems, the
  simulation model was used to determine the
  average ships waiting time

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Modeling arrival process (6)

• For multiple berths queuing systems, the
  simulation model was used to determine the
  average ships waiting time

Multiple berths queuing system

• (M/E2/1 1.75, M/E2/2 0.75, M/E2/3 0.58,
  M/E2/4 0.28)

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Modeling arrival process (7)

• Can analytical models be used for an accurate
  arrival process modeling?
• The simulation model was used to compare
  terminals real-world arrival data with
  analytical models

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Content

• Arrival process
• Average port time
• Modeling arrival process
• Continuous quay layout or multiple berths
• Conclusions

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Continuous quay layout or multiple berths (1)

1. Continuous quay layout
2. Multiple berths operation

Interarrival time distribution type NED
Bulk carriers tonnage distribution Table Input
Number of quay cranes - 4
Max. number of ships at the quay - 4
Quay crane capacity (free-digging) 3,000 t/h
Annual throughput Mt 20 50
Runtime of simulation years 5

• Simulation input

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Continuous quay layout or multiple berths (2)
Occupied quay length versus annual throughput
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Conclusions

• Serving ships on time and at correct speed is
  crucial for terminal operators
• Modeling the ships arrival process is required
  to design the terminals quay side
• The wilder the arrival pattern, the greater the
  average waiting time
• Modeling the arrival process must be based on
  Queuing Theory
• However, for multiple berths there are hardly
  analytical solutions and a discrete-event
  simulation is proposed
• For an accurate modeling, it is proposed to use a
  table distribution which represents the carriers
  tonnage instead of using analytical models for
  the service time distribution
• A continuous quay operation results in a higher
  annual throughput or less required quay length

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Thank you!