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
a2food.mos
(!******************************************************
Mosel Example Problems
======================
file a2food.mos
```````````````
Food production for farm animals
Food must meet required content levels of nutritional
components (Proteins, Lipids, Fiber). Given the raw
materials available each day and daily demand to meet,
the objective is to determine how the Oat, Maize,
and Molasses should be blended to minimize the total cost.
Simple linear programming blending problem formulation includes
data with string indices and string formatting for solution printout.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002
*******************************************************!)
model "A-2 Animal Food Production"
uses "mmxprs"
declarations
FOOD = 1..2 ! Food types
COMP = 1..3 ! Nutritional components
RAW = {"oat", "maize", "molasses"} ! Raw materials
P: array(RAW,COMP) of real ! Composition of raw materials (in percent)
REQ: array(COMP) of real ! Nutritional requirements
AVAIL: array(RAW) of real ! Raw material availabilities
COST: array(RAW) of real ! Raw material prices
PCOST: array(set of string) of real ! Cost of processing operations
DEM: array(FOOD) of real ! Demands for food types
use: array(RAW,FOOD) of mpvar ! Quantity of raw mat. used for a food type
produce: array(FOOD) of mpvar ! Quantity of food produced
end-declarations
initializations from 'a2food.dat'
P REQ PCOST DEM
[AVAIL, COST] as 'RAWMAT'
end-initializations
! Objective function
Cost:= sum(r in RAW,f in FOOD) COST(r)*use(r,f) +
sum(r in RAW,f in FOOD|r<>"molasses") PCOST("grinding")*use(r,f) +
sum(r in RAW,f in FOOD) PCOST("blending")*use(r,f) +
sum(r in RAW) PCOST("granulating")*use(r,1) +
sum(r in RAW) PCOST("sieving")*use(r,2)
! Quantity of food produced corresponds to raw material used
forall(f in FOOD) sum(r in RAW) use(r,f) = produce(f)
! Fulfill nutritional requirements
forall(f in FOOD,c in 1..2)
sum(r in RAW) P(r,c)*use(r,f) >= REQ(c)*produce(f)
forall(f in FOOD) sum(r in RAW) P(r,3)*use(r,f) <= REQ(3)*produce(f)
! Use raw materials within their limit of availability
forall(r in RAW) sum(f in FOOD) use(r,f) <= AVAIL(r)
! Satisfy demands
forall(f in FOOD) produce(f) >= DEM(f)
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ", getobjval)
write("Food type"); forall(r in RAW) write(strfmt(r,9))
writeln(" protein lipid fiber")
forall(f in FOOD) do
write(strfmt(f,-9))
forall(r in RAW) write(strfmt(getsol(use(r,f)),9,2))
forall(c in COMP) write(" ",
strfmt(getsol(sum(r in RAW) P(r,c)*use(r,f))/getsol(produce(f)),3,2),"%")
writeln
end-do
end-model
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