Loading and cutting problems
Description
| Problem name and type, features | Difficulty | Related examples |
| D‑1 | Wagon load balancing: Nonpreemptive scheduling on parallel machines | **** | |
|---|
| heuristic solution requiring sorting algorithm, formulation of maximin objective; nested subroutines: function returning heuristic solution value and sorting procedure, ceil, getsize, if-then, break, exit, all loop types (forall-do, repeat-until, while-do), setparam, qsort, cutoff value, loading a MIP start solution |
| D‑2 | Barge loading: Knapsack problem | ** | burglar1.mos, knapsack_graph.mos |
|---|
| incremental problem definition with 3 different objectives, procedure for solution printing |
| D‑3 | Tank loading: Loading problem | *** | |
|---|
| 2 objectives; data preprocessing, as, dynamic creation of variables, procedure for solution printing, if-then-else |
| D‑4 | Backing up files: Bin-packing problem | ** | binpacking_graph.mos |
|---|
| 2 versions of mathematical model, symmetry breaking; data preprocessing, ceil, range |
| D‑5 | Cutting sheet metal: Covering problem | * | g6transmit.mos, j2bigbro.mos |
|---|
| |
| D‑6 | Cutting steel bars for desk legs: Cutting-stock problem | ** | cutstock_graph.mos |
|---|
| set operation(s) on range sets, set of integer (data as set contents) |
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 9: Loading and cutting stock problems
Source Files
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Data Files
d5cutsh.mos
(!******************************************************
Mosel Example Problems
======================
file d5cutsh.mos
````````````````
Cutting of sheet metal
(2-dimensional cutting patterns)
A sheet metal shop cuts large pieces of sheet metal into
4 smaller sizes. There are 16 possible patterns that a
large sheet can be cut into. How can the incoming order
be met while using the smallest number of large sheets?
This mathematical model (formulated as a covering problem)
is very compact since the patterns have already been
pre-computed.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "D-5 Sheet metal cutting"
uses "mmxprs"
declarations
PATTERNS = 1..16 ! Set of cutting patterns
SIZES = 1..4 ! Set of sheet sizes
DEM: array(SIZES) of integer ! Demands for the different sizes
CUT: array(SIZES,PATTERNS) of integer ! Cutting patterns
use: array(PATTERNS) of mpvar ! Use of cutting patterns
end-declarations
initializations from 'd5cutsh.dat'
DEM CUT
end-initializations
! Objective: total number of sheets used
Sheets:= sum(p in PATTERNS) use(p)
! Satisfy demands
forall(s in SIZES) sum(p in PATTERNS) CUT(s,p)*use(p) >= DEM(s)
forall(p in PATTERNS) use(p) is_integer
! Solve the problem
minimize(Sheets)
! Solution printing
writeln("Total number of large sheets: ", getobjval)
write("Cutting patterns used: ")
forall(p in PATTERNS)
write( if(getsol(use(p)) > 0 , " " + p + ":" + getsol(use(p)), "") )
write("\nExemplaries of sheets sizes cut: ")
forall(s in SIZES)
write(s, ":", getsol(sum(p in PATTERNS) CUT(s,p)*use(p)), " ")
writeln
end-model
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