Mining and process industries
Description
| Problem name and type, features | Difficulty | Related examples |
| A‑1 | Production of alloys: Blending problem
formulation of blending constraints; data with numerical indices, solution printout, if-then, getsol | * | blending_graph.mos |
|---|
| A‑2 | Animal food production: Blending problem
formulation of blending constraints; data with string indices, as, formatted solution printout, use of getsol with linear expressions, strfmt | * | a1alloy.mos |
|---|
| A‑3 | Refinery : Blending problem
formulation of blending constraints; sparse data with string indices, dynamic initialization, union of sets | ** | a2food.mos |
|---|
| A‑4 | Cane sugar production : Minimum cost flow (in a bipartite graph)
mo
ceil, is_binary, formattext | * | e2minflow.mos, mincostflow_graph.mos |
|---|
| A‑5 | Opencast mining: Minimum cost flow
encoding of arcs, solving LP-relaxation only, array of set | ** | a4sugar.mos |
|---|
| A‑6 | Production of electricity: Dispatch problem
inline if, is_integer, looping over optimization problem solving | ** | |
|---|
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 6: Mining and process industries (blending problems)
Source Files
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Data Files
a5mine.mos
(!******************************************************
Mosel Example Problems
======================
file a5mine.mos
```````````````
Opencast mining
An opencast uranium mine is being prospected. 6 of
the 18 blocks contain uranium. To extract a block, 3
blocks of the level above it need to be extracted.
Blocks have varied extraction costs and each block
of uranium has a different market value. The objective
is to determine which blocks to extract to maximize
total benefit.
This model uses binary variables to indicate which
blocks will be extracted. There is also a two-dimensional
array to enforce the extraction order between layers.
A relaxed formulation of this constraint is commented out
for reference.
(c) 2008-2022 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002, rev. Mar. 2022
*******************************************************!)
model "A-5 Opencast mining"
uses "mmxprs"
declarations
BLOCKS = 1..18 ! Set of blocks
LEVEL23: set of integer ! Blocks in levels 2 and 3
COST: array(BLOCKS) of real ! Exploitation cost of blocks
VALUE: array(BLOCKS) of real ! Value of blocks
ARC: array(LEVEL23,1..3) of integer ! Arcs indicating order of extraction
extract: array(BLOCKS) of mpvar ! 1 if block b is extracted
end-declarations
initializations from 'a5mine.dat'
COST VALUE ARC
end-initializations
! Objective: maximize total profit
Profit:= sum(b in BLOCKS) (VALUE(b)-COST(b))* extract(b)
! Extraction order
! forall(b in LEVEL23) 3*extract(b) <= sum(i in 1..3) extract(ARC(b,i))
forall(b in LEVEL23)
forall(i in 1..3) extract(b) <= extract(ARC(b,i))
forall(b in BLOCKS) extract(b) is_binary
! Solve the problem
maximize(Profit)
! Solving LP relaxation only
! maximize(XPRS_LIN, Profit)
! Solution printing
declarations
WEIGHT: integer ! Weight of blocks
end-declarations
initializations from 'a5mine.dat'
WEIGHT
end-initializations
writeln("Total profit:", getobjval*WEIGHT)
write("Extract blocks")
forall(b in BLOCKS | getsol(extract(b))>0) write(" ", b)
writeln
end-model
| 
