HEURISTIC ALGORITHMS FOR 3D MULTIPLE BIN SIZED BIN PACKING PROBLEM

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HEURISTIC ALGORITHMS FOR 3D MULTIPLE BIN SIZED
BIN PACKING PROBLEM

• Gürdal Ertek Kemal Kiliç

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Motivation

• A major automobile manufacturer located in Bursa,
  Turkey
• Urgent order packaging
• Everyday...
• gt80 service dealers submit their urgent orders.
• orders pooled in an information system until
  300pm.
• foreman decides approximate number and sizes of
  boxes needed for each order.
• workers start picking the requested items and
  packing them into adequately sized boxes.
• by 500 p.m., trucks of a 3rd party logistics
  firm collect the boxes to deliver them to their
  destinations.

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Motivation

• Selection of appropriate boxes
• 300pm two experienced foremen spend 20 minutes
  on a PC.
• decide on and record the choice of boxes for each
  order.
• goal minimize the posterior extra work of
  reallocating the items between boxes
• Goal of Warehouse Managers
• development and implementation of a decision
  support system
• help the foremen in their decision making to
  eliminate item reallocation

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The DSS

• Operate in real-time
• Metaheuristic algorithm to make the decisions
• how many boxes are used of each box type
• how each item is placed in its box
• Objective
• minimization of the total cost of the boxes used
• Our Study
• proposal of three alternative algorithms that can
  serve as the solution engine
• their comparison with respect to objective
  function value and running time performance

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Packing Problems

• The DSS basically solves multiple number of
  packing problems for each order.
• Loading of a set of items (objects) into a set of
  boxes (containers)
• Optimize a performance criterion under various
  constraints.
• Becoming more popular
• barcode and RFID technologies
• investments in IT infrastructures
• companies now have access to the necessary data
  for improving packing processes.

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Problem Definition

• A set of rectangular objects (items)
• each with height , width , and depth

• Packed into a set of larger rectangular
  objects (boxes)
• each with height , width , and
  depth
• and cost

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Problem Definition

• Objective
• Minimize the total cost of boxes that are used
• Allocating all the items into boxes without
  overlap
• Decisions
• types of boxes to be used
• number of boxes of each type
• boxes that each item will go into
• position of each item in each box
• Assumptions
• Only orthogonal arrangements of items
• Allow items to be rotated around all three axis

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Packing Literature

• Cutting and packing problems over a thousand
  paper (Since Gilmore and Gomory, 60s)
• Three reasons
• Wide range of applications in industry
• Supply chain logistics cutting metal sheets,
  loading containers with boxes
• Computer science memory allocation of processors
• Finance capital budgeting
• NP-hard problems
• Diversity of real world problems
• Even small nuances in the objective function or
  the packing/ cutting constraints result in new
  problem structures

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Packing Literature

• Over a thousand papers published on related
  problems. Three typologies are proposed
• Dyckhoff and Finke (1992)
• review of 308 papers prior to 1992
• Dimensionality (1D,2D,3D,ND), kind of assignment,
  assortment of large objects, assortment of small
  objects our paper (3 /V a selection of objects
  and all items/ Different sizes of boxes / Many
  items many size)
• Wäscher et al. (2006)
• improved typology
• review of 413 papers between 1994-2004
• 3D MBSBPP

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Relevant Literature

• Closely Related Studies 3D Multiple
  Heterogeneous Large Objects Placement Problem
• Ivancic et al. (1989)
• assuming smaller objects have limited number of
  possible types
• few preassigned patterns
• Brunetta and Grégoire (2005)
• only 15 items
• packing at a biscuit factory
• Martello et al. (2000) 3D Single Bin Size BPP

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Methodology

• Greedy Algorithm (G)
• Filtered Beam Search Algorithm (BS)
• Tree Search based implicit enumeration algorithm
  (TS) (depth-first)

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Greedy Algorithm (G)

• While there are objects that are not packed into
  a box...
• A single sized bin container loading problem
  (SSBCLP) is solved independently for each
  different box size (Pisinger), and the best box
  is selected according to a dispatching index
• Objects that are assigned to a box are deleted
  from the waiting list.

Cost per volume of box j
Filling ratio
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Beam Search Algorithm (BS)

• At each level of the branch bound search tree
• A single sized bin container loading problem
  (SSBCLP) is solved independently for each
  different box size (Pisinger), and the best f
  solutions (box selections) are filtered according
  to a local evaluation function
• From among these f boxes, best b are selected
  according to a global evaluation function

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Beam Search Algorithm (BS)

• Global Evaluation Function The total cost of the
  boxes of the solution that is obtained by
  applying the greedy algorithm to the non-pruned
  nodes

f 3 b 2
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Beam Search Algorithm (BS)

• Algorithms coded with C
• MS Visual Studio .NET environment
• Experiments run on a PC
• Intel Centrino 1700 Mhz processor and 512 MB of
  RAM
• Subroutine of our program
• C implementation of Prof. David Pisinger's
  algorithm for container loading (CLA)
• Item sizes generated randomly within given
  bounds.
• Box costs
• 10 random instances of 3x3 9 experimental
  conditions (number of orders x size of items

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Experimental Results
9 July, 2007
Euro 2007, Praha
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Experimental Results
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Experimental Results
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Conclusion

• Theoretical Contributions
• Presenting the 3D-MBSBPP problem within a real
  world context
• typology by Wäscher et al. (2006)
• Developing and implementing solution algorithms
  for the problem
• Presenting computational results to compare the
  algorithms

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Conclusion

• Practical Contributions
• Reducing cost of boxes
• Eliminating posterior reallocation of items into
  boxes, i.e. labor savings
• Eliminating dependency on experienced foremen
• Pilot study for the much larger problem of
  packing regular orders
• Enable the computation of best box types and
  dimensions based on historical data, further cost
  reduction and space reduction

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Further Challenges

• Physical constraints (items that might harm,
  might be harmed, etc...)
• Validation of the methodology by comparing the
  foreman decisions and the DSS
• Convince the upper management the usefulness of
  DSS
• Apply the DSS to regular orders as well
• Different dispatching indices
• Optimum box sizes historical demand data

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Thank You !