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
d2ship.mos
(!******************************************************
Mosel Example Problems
======================
file d2ship.mos
```````````````
Choice of wheat load for a ship
A shipper has 7 clients that wish to ship wheat. Each has
varying quantities of lots, size of lots, shipping price,
and transport costs. How can the shipper maximize profit?
Three incrementally defined problems are solved in series.
Each introduces a new constraint while still maximizing profit.
Procedure "printsol" is used to print the different
solutions depending on which problem is solved.
(c) 2008-2022 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)
model "D-2 Ship loading"
uses "mmxprs"
forward procedure printsol(num:integer)
declarations
CLIENTS = 1..7 ! Set of clients
AVAIL: array(CLIENTS) of integer ! Number of lots per client
SIZE: array(CLIENTS) of integer ! Lot sizes
PRICE: array(CLIENTS) of integer ! Prices charged to clients
COST: array(CLIENTS) of integer ! Cost per client
PROF: array(CLIENTS) of integer ! Profit per client
CAP: integer ! Capacity of the ship
loadqty: array(CLIENTS) of mpvar ! Lots taken from clients
end-declarations
initializations from 'd2ship.dat'
AVAIL SIZE PRICE COST CAP
end-initializations
forall(c in CLIENTS) PROF(c):= PRICE(c) - COST(c)*SIZE(c)
Profit:= sum(c in CLIENTS) PROF(c)*loadqty(c)
! Limit on the capacity of the ship
sum(c in CLIENTS) SIZE(c)*loadqty(c) <= CAP
! Problem 1: unlimited availability of lots at clients
maximize(Profit)
printsol(1)
! Problem 2: limits on availability of lots at clients
forall(c in CLIENTS) loadqty(c) <= AVAIL(c)
maximize(Profit)
printsol(2)
! Problem 3: lots must be integer
forall(c in CLIENTS) loadqty(c) is_integer
maximize(Profit)
printsol(3)
!-----------------------------------------------------------------
! Solution printing
procedure printsol(num:integer)
writeln("Problem ", num, ": profit: ", getobjval)
forall(c in CLIENTS)
write( if(getsol(loadqty(c))>0 , " " + c + ":" + getsol(loadqty(c)), ""))
writeln
end-procedure
end-model
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