Cutting packing alonso bài toán cắt vật tư
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (2.28 MB, 58 trang )
Optimization methods for cutting
and packing problems
Maria Teresa Alonso Martinez
Universidad de Castilla-La Mancha, España
Where is UCLM?
Outline
• Introduction and classification
• Some problems
– Cutting Stock Problem:
– Strip Packing Problem:
• Future works
Column Generation
Branch & Bound
Cutting and packing problems?
If we were capable of solving this problems…
• Less production costs.
• Less waste of material
– Less natural resources consumption.
– Less pollution
• Waste,…
• Transport
– Less energy consumption.
/>
Cutting & Packing
Large
objects
¿Patterns?
Small objects
Stock sheets
Pieces
Characteristics
1. Dimensionality
/>
Characteristics
2. Type of assignment
Stock sheets
Pieces
All the pieces with minimum number of sheets
All the sheets with the maximum value of pieces
Characteristics
3. Type of small pieces
Identical pieces
Weakly heterogeneous
Strongly heterogeneous
Characteristics
4. Type of large objects
Identical pieces
Weackly heterogeneuos
Strongly heterogeneous
Irregular pieces
/>
Classification of problems
1. Dimension (1, 2, 3)
2. Objective
•
•
Maximize output ( fixed input)
Minimize input (fixed output)
3. Types of small objects (pieces, boxes,….)
•
•
•
Identical
Weakly heterogeneous
Strongly heterogeneous
4. Types of large objects (stock sheets, containers,….)
•
•
One object
Several objects (identical or different)
5. Shape of the small objects (pieces)
•
•
Rectangular
Irregular
Container loading
Dimension
Objective
Type of small objects
Type of large objects
Shape
3D
Output maximization
Weakly heterogeneous
One object
Rectangular
WHAT WAS RESEARCH?
Summary of research efforts
MAXIMIZE OUTPUT
SMALL
OBJECTS IDENTICAL
1995-2005
DIFFERENT
LARGE
OBJECTS
2006-2011
UNIQUE
FIXED
DIMENSIONS
IIPP
SLOPP/SKP
IDENTICAL
MILOPP/MIKP
DIFFERENT
MHLOPP/MHKP
MINIMIZE INPUT
SMALL
OBJECTS
LARGE
OBJECTS
IDENTICAL
WEAKLY
HETEROGENEOUS
SSSCSP
STRONGLY
HETEROGENEOUS
SBSBPP
FIXED
DIMENSIONS
DIFFERENT
LARGE OBJECT OF
VARIABLE DIMENSIONS
MSSCSP/RCSP
MBSBPP/RBPP
ODP
Summary of research efforts
MAXIMIZE OUTPUT
SMALL
OBJECTS
IDENTICAL
1995-2005
DIFFERENT
LARGE
OBJECTS
2006-2011
UNIQUE
FIXED
DIMENSIONS
IIPP
SLOPP/SKP
IDENTICAL
MILOPP/MIKP
DIFFERENT
MHLOPP/MHKP
MINIMIZE INPUT
SMALL
OBJECTS
LARGE
OBJECTS
IDENTICAL
WEAKLY
HETEROGENEOUS
SSSCSP
STRONGLY
HETEROGENEOUS
SBSBPP
FIXED
DIMENSIONS
DIFFERENT
LARGE OBJECT OF
VARIABLE DIMENSIONS
MSSCSP/RCSP
MBSBPP/RBPP
ODP
Summary of research efforts
MAXIMIZE OUTPUT
SMALL
OBJECTS IDENTICAL
1995-2005
DIFFERENT
LARGE
OBJECTS
2006-2011
UNIQUE
FIXED
DIMENSIONS
IIPP
SLOPP/SKP
IDENTICAL
MILOPP/MIKP
DIFFERENT
MHLOPP/MHKP
MINIMIZE INPUT
SMALL
OBJECTS
LARGE
OBJECTS
IDENTICAL
WEAKLY
HETEROGENEOUS
SSSCSP
STRONGLY
HETEROGENEOUS
SBSBPP
FIXED
DIMENSIONS
DIFFERENT
LARGE OBJECT OF
VARIABLE DIMENSIONS
MSSCSP/RCSP
MBSBPP/RBPP
ODP
Summary of research efforts
MAXIMIZE OUTPUT
SMALL
OBJECTS IDENTICAL
1995-2005
DIFFERENT
LARGE
OBJECTS
2006-2011
UNIQUE
FIXED
DIMENSIONS
IIPP
SLOPP/SKP
IDENTICAL
MILOPP/MIKP
DIFFERENT
MHLOPP/MHKP
MINIMIZE INPUT
SMALL
OBJECTS
LARGE
OBJECTS
IDENTICAL
WEAKLY
HETEROGENEOUS
SSSCSP
STRONGLY
HETEROGENEOUS
SBSBPP
FIXED
DIMENSIONS
DIFFERENT
LARGE OBJECT OF
VARIABLE DIMENSIONS
MSSCSP/RCSP
MBSBPP/RBPP
ODP
Summary of research efforts
MAXIMIZE OUTPUT
SMALL
OBJECTS IDENTICAL
1995-2005
DIFFERENT
LARGE
OBJECTS
2006-2011
UNIQUE
FIXED
DIMENSIONS
IIPP
SLOPP/SKP
IDENTICAL
MILOPP/MIKP
DIFFERENT
MHLOPP/MHKP
MINIMIZE INPUT
SMALL
OBJECTS
LARGE
OBJECTS
IDENTICAL
WEAKLY
HETEROGENEOUS
SSSCSP
STRONGLY
HETEROGENEOUS
SBSBPP
FIXED
DIMENSIONS
DIFFERENT
LARGE OBJECT OF
VARIABLE DIMENSIONS
MSSCSP/RCSP
MBSBPP/RBPP
ODP
Summary of research efforts
MAXIMIZE OUTPUT
SMALL
OBJECTS IDENTICAL
c3
c4
DIFFERENT
1995-2005
LARGE
OBJECTS
2006-2011
UNIQUE
FIXED
DIMENSIONS
IIPP
IDENTICAL
c1
DIFFERENT
SLOPP/SKP
MILOPP/MIKP
c2
MHLOPP/MHKP
MINIMIZE INPUT
SMALL
OBJECTS
LARGE
OBJECTS
IDENTICAL
WEAKLY
HETEROGENEOUS
SSSCSP
STRONGLY
HETEROGENEOUS
SBSBPP
FIXED
DIMENSIONS
DIFFERENT
LARGE OBJECT OF
VARIABLE DIMENSIONS
MSSCSP/RCSP
MBSBPP/RBPP
ODP
Summary of research efforts
MAXIMIZE OUTPUT
SMALL
OBJECTS IDENTICAL
1995-2005
DIFFERENT
LARGE
OBJECTS
2006-2011
UNIQUE
FIXED
DIMENSIONS
IIPP
SLOPP/SKP
IDENTICAL
MILOPP/MIKP
DIFFERENT
MHLOPP/MHKP
MINIMIZE INPUT
SMALL
OBJECTS
LARGE
OBJECTS
IDENTICAL
WEAKLY
HETEROGENEOUS
SSSCSP
STRONGLY
HETEROGENEOUS
SBSBPP
FIXED
DIMENSIONS
DIFFERENT
LARGE OBJECT OF
VARIABLE DIMENSIONS
MSSCSP/RCSP
MBSBPP/RBPP
ODP
AN EXAMPLE
The two-dimensional guillotine cutting stock
problem
• Given a set of stock sheets, with known dimensions and costs
• and a set of pieces, with known dimensions and demands
The two-dimensional guillotine cutting stock
problem
• The problem is:how many sheets to cut? and in which way to cut
them?
• to satisfy the demands of pieces completely with minimum cost of
sheets
Something easy:
One-dimensional problem
• We have 2 types of bars: 120 y 100 cm.
(unlimited quantities)
• Demand:
– 60 pieces of 80 cm.
– 40 pieces of 50 cm.
– 75 pieces of 30 cm.
• Costs:
$3 bar of 120 cm
$2.5 bar of 100 cm
+ $0.5 each cut
