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
a3refine.mos
(!******************************************************
Mosel Example Problems
======================
file a3refine.mos
`````````````````
Refinery planning
A refinery produces butane, petrol, diesel oil, and heating oil
from two crudes. Four types of operations are necessary to
obtain these products: separation, conversion, upgrading, and
blending. Monthly demand must be met while certain levels of
octane value, vapor pressure, volatility, and sulfur content are
enforced by law. The objective is to minimize crude and production cost.
A much more involved linear programming blending problem
with two production stages that are related in complicated ways.
The implementation has sparse data with string indices that are
initialized dynamically from the input data file. A new set
'ALLPRODS' is defined as the union of several other sets.
(c) 2008-2022 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002, rev. Mar. 2022
*******************************************************!)
model "A-3 Refinery planning"
uses "mmxprs"
declarations
CRUDES: set of string ! Set of crudes
ALLPRODS: set of string ! Intermediate and final products
FINAL: set of string ! Final products
IDIST: set of string ! Products obtained by distillation
IREF: set of string ! Products obtained by reforming
ICRACK: set of string ! Products obtained by cracking
IPETROL: set of string ! Interm. products for petrol
IDIESEL: set of string ! Interm. products for diesel
IHO={"hogasoil", "hocrknaphtha", "hocrkgasoil"}
! Interm. products for heating oil
DEM: array(FINAL) of real ! Min. production
COST: array(set of string) of real ! Production costs
AVAIL: array(CRUDES) of real ! Crude availability
OCT, VAP, VOL: array(IPETROL) of real ! Octane, vapor pressure, and
! volatility values
SULF: array(IDIESEL) of real ! Sulfur contents
DIST: array(CRUDES,IDIST) of real ! Composition of crudes (in %)
REF: array(IREF) of real ! Results of reforming (in %)
CRACK: array(ICRACK) of real ! Results of cracking (in %)
end-declarations
initializations from 'a3refine.dat'
DEM COST OCT VAP VOL SULF AVAIL DIST REF CRACK
end-initializations
ALLPRODS:= FINAL+IDIST+IREF+ICRACK+IPETROL+IHO+IDIESEL
declarations
use: array(CRUDES) of mpvar ! Quantities used
produce: array(ALLPRODS) of mpvar ! Quantities produced
end-declarations
! Objective function
Cost:= sum(c in CRUDES) COST(c)*use(c) + sum(p in IDIST) COST(p)*produce(p)
! Relations intermediate products resulting of distillation - raw materials
forall(p in IDIST) produce(p) <= sum(c in CRUDES) DIST(c,p)*use(c)
! Relations between intermediate products
! Reforming:
forall(p in IREF) produce(p) <= REF(p)*produce("naphtha")
! Cracking:
forall(p in ICRACK) produce(p) <= CRACK(p)*produce("residue")
produce("crknaphtha") = produce("petcrknaphtha") +
produce("hocrknaphtha") + produce("dslcrknaphtha")
produce("crkgasoil") = produce("hocrkgasoil") + produce("dslcrkgasoil")
! Desulfurization:
produce("gasoil") = produce("hogasoil") + produce("dslgasoil")
! Relations final products - intermediate products
produce("butane") = produce("distbutane") + produce("refbutane") -
produce("petbutane")
produce("petrol") = sum(p in IPETROL) produce(p)
produce("diesel") = sum(p in IDIESEL) produce(p)
produce("heating") = sum(p in IHO) produce(p)
! Properties of petrol
sum(p in IPETROL) OCT(p)*produce(p) >= 94*produce("petrol")
sum(p in IPETROL) VAP(p)*produce(p) <= 12.7*produce("petrol")
sum(p in IPETROL) VOL(p)*produce(p) >= 17*produce("petrol")
! Limit on sulfur in diesel oil
sum(p in IDIESEL) SULF(p)*produce(p) <= 0.05*produce("diesel")
! Crude availabilities
forall(c in CRUDES) use(c) <= AVAIL(c)
! Production capacities
produce("naphtha") <= 30000 ! Reformer
produce("gasoil") <= 50000 ! Desulfurization
produce("residue") <= 40000 ! Cracker
! Satisfy demands
forall(p in FINAL) produce(p) >= DEM(p)
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Production costs: ", strfmt(getobjval,10,2))
forall(c in CRUDES) writeln(c, ": ", getsol(use(c)))
forall(p in ALLPRODS) writeln(p, ": ", getsol(produce(p)))
writeln("Petrol properties:")
writeln(" octane: ",
getsol(sum(p in IPETROL) OCT(p)*produce(p))/ getsol(produce("petrol")),
" vapor presure: ",
getsol(sum(p in IPETROL) VAP(p)*produce(p))/ getsol(produce("petrol")),
" volatility: ",
getsol(sum(p in IPETROL) VOL(p)*produce(p))/ getsol(produce("petrol")))
writeln("Sulfur in diesel oil: ",
getsol(sum(p in IDIESEL) SULF(p)*produce(p))/getsol(produce("diesel")) )
end-model
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