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PRESENTATION AT GRADUATE STUDENT DAY, 2012 

 INTER-BLOCK YARD CRANE SCHEDULING

AT A MARINE CONTAINER TERMINAL

byOmor Sharif, Nathan Huynh, Mashrur Chowdhury, Jose

Vidal

Paper submitted to International Journal of Transportation Science and

Technology

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A VERY BRIEF REVIEW OF A CONTAINER TERMINAL!

• An interface between ocean and land transport• Containers are loaded/unloaded to/from a ship• Operation involves a large number of decisions• Capacity Constraints, Environmental Concerns etc

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RESEARCH PROBLEM AND MOTIVATION

• Container Yard and Yard Crane (YC)• A container yard is made up of several blocks of

containers• Workload varies among blocks during operational

hours• Efficiency of YCs impacts truck waiting/ship waiting

time• Assign/relocate YCs among blocks to finish most work • Known as Interblock YC Scheduling Problem

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MODEL ASSUMPTIONS

• Total operational hours is divided in several planning periods

• A workload forecast for blocks is known at start (time-units)

• At most two cranes work at a block at the same time• At most one transfer per planning period• Other operations will not introduce delay• 10 minutes transfer time for each longitudinal block

traveled

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INITIAL ASSIGNMENT OF YARD CRANES

High to low work volume• Sort blocks in decreasing order of initial work volume (IWb)• Assign NCb

max cranes to each block starting from topmost item

Crane at each block • If nc = nb, assign one crane per block.• If nc < nb, sort blocks in decreasing IWb , assign cranes.• If nc > nb, first assign one crane per block, then sort in

decreasing IWb . Reduce transfers • Assign cranes to reduce future transfers.• Based on pass/fail of a series of iequalites.• A four step approach

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THREE PRINCIPAL PARAMETERS

Extra capacity of a crane

• E (c) = Tc × NCbinitial − IWb

Amount of help needed by a block

• H (b) = IWb − Tc × NCbcurrent

Transfer time

• TTcod

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PREFERENCE FUNCTIONS FOR BLOCK AND CRANE AGENTS

Minimum transfer time • Transfer time of a crane from origin to destination block

Positive difference • Extra Capacity of a crane – Help needed by a block –

Transfer time

Absolute difference • abs (Extra Capacity of a crane – Help needed by a block

– Transfer time)

Absolute difference squared distance• abs (Extra Capacity of a crane – Help needed by a block

– Transfer time2)

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AN ALGORITHM TO ASSIGN CRANES TO BLOCKS

Crane proposing version

Block proposing version • …

1. Each crane j proposes to first block i from its preference list2. Each block i receiving more than qi proposals, ‘holds’ the most preferred qi cranes and rejects all others.n. Each crane j rejected at step n − 1 removes the block i rejecting the crane from its preference list. Then the rejected crane j makes a new proposal to its next most preferred block i who hasn’t yet rejected it. Go to step n − 1.

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IMPLEMENTATION

• Multi-agent simulation GUI• Implemented in NETLOGO• Stationary block and Mobile crane agents

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DESIGN OF EXPERIMENTS

Parameter Value UnitNumber of blocks

10, 20, 30 Nos

Number of cranes

1 or 1.5 × Number of blocks Nos

Length of planning period

240 Minutes

Work volume (1) Moderate (2) Heavy (3) Above capacity

Minutes 

Initial assignment

(1) Crane at each block (2) High to low work volume (3) Reduce transfers

-

Preference strategy

(1) Minimum transfer time (2) Absolute difference (3) Positive difference (4) Absolute inverse squared distance

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AlgorithmVersion

(1) Blocks proposing (2) Cranes proposing

-

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RESULTS

Percentage incomplete work volume: Case I - average number of cranes per block = 1.0

Number of Blocks     10

      20

      30

 

Number of Cranes     10

      20

      30

Work Volume M H  AC M H   AC M H   AC

Minimum Transfer Time 0 0.13 11.34

0 0.10 11.14

0 0.12 11.28

Absolute difference 0 0.16 12.16

0 0.13 12.09

0 0.11 12.16

Positive difference 0 0 13.55

0 0.05 13.08

0 0.04 12.86

Absolute difference squared distance

0 0.13 11.80

0 0.08 11.69

0 0.10 11.81

Mathematical Program 0 0 10.57

0 0 10.57

0 0 10.60

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RESULTS (CONTD..)

Percentage incomplete work volume: Case II - average number of cranes per block = 1.5

Number of Blocks   10     20     30 

Number of Cranes   15     30     45

Work Volume M H AC M H AC M H AC

Minimum Transfer Time 0 0.02 9.79 0 0.20 10.00

0 0.48 10.04

Absolute difference 0 0.07 10.19

0 0.18 10.45

0 0.43 10.48

Positive difference 0 0.14 10.40

0 0.53 10.73

0 1.00 10.71

Absolute difference squared distance

0 0.01 10.06

0 0 10.31

0 0.01 10.38

Mathematical Program 0 0 9.69 0 0 9.77 0 0 9.79

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CONCLUDING REMARKS

• In ‘medium’ condition all work can be finished • In ‘heavy’ condition the percentage incomplete is 1% or

less• In ‘above capacity’ condition the percentage remaining is

within 3% of the lower bound.• Scalable; a test case with 30 blocks can be solved within 3

seconds

• Consider relocating cranes multiple time• Include forecasts for multiple planning periods • Solve integrated problems involving other related

decisions

Summary of Findings

Future Work

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Thank You

Questions ?

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A SAMPLE EXAMPLE