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
d6cutbar.mos
(!******************************************************
Mosel Example Problems
======================
file d6cutbar.mos
`````````````````
Cutting of steel bars into school desk legs
(1-dimensional cutting patterns)
A company produces school desks of various heights. The
legs are all cut from steel bars of 1.5 or 2 meters. How
should an order be produced to minimize the trim loss?
Note that each length of steel bars has a unique set of
patterns. The total set of patterns is the union of these
two sets. This problem also uses a 'set of integer' which is
more general than a 'range [of integer]'.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "D-6 Cutting steel bars"
uses "mmxprs"
declarations
PAT1 = 1..6; PAT2 = 7..12 ! Sets of cutting patterns
PATTERNS = PAT1 + PAT2 ! Set of all cutting patterns
SIZES: set of integer ! Desk heights
DEM: array(SIZES) of integer ! Demands for the different heights
CUT: array(PATTERNS,SIZES) of integer ! Cutting patterns
LEN: array(range) of integer ! Lengths of original steel bars
use: array(PATTERNS) of mpvar ! Use of cutting patterns
end-declarations
initializations from 'd6cutbar.dat'
DEM CUT LEN
end-initializations
! Objective: total loss
Loss:= sum(p in PAT1) LEN(1)*use(p) + sum(p in PAT2) LEN(2)*use(p) -
sum(s in SIZES) 4*DEM(s)*s
! Satisfy demands
forall(s in SIZES) sum(p in PATTERNS) CUT(p,s)*use(p) >= 4*DEM(s)
forall(p in PATTERNS) use(p) is_integer
! Solve the problem
minimize(Loss)
! Solution printing
writeln("Loss: ", getobjval, "cm")
write("Short bars: ", getsol(sum(p in PAT1) use(p)))
writeln(", long bars: ", getsol(sum(p in PAT2) use(p)))
write("Cutting patterns used:")
forall(p in PATTERNS)
write( if(getsol(use(p)) > 0 , " " + p + ":" + getsol(use(p)), "") )
write("\nNumbers of legs cut: ")
forall(s in SIZES)
write(s, ":", getsol(sum(p in PATTERNS) CUT(p,s)*use(p)), " ")
writeln
end-model
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