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
a4sugar.mos
(!******************************************************
Mosel Example Problems
======================
file a4sugar.mos
````````````````
Production of cane sugar
Sugar cane harvesting is highly mechanized, however, once
harvested the sugar content decreases rapidly through
fermentation. The sugar content of each wagon depends
on maturity of the sugar cane and where it was grown. A
production schedule for the current lot must be determined
so that it minimizes the total loss of sugar.
The problem formulation uses binary variables to assign wagons
to time slots and 'ceil' in the calculation of an upper bound
on the number of time slots needed.
(c) 2008-2022 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002, rev. Mar. 2022
*******************************************************!)
model "A-4 Cane sugar production"
uses "mmxprs", "mmsystem"
declarations
NW = 11 ! Number of wagon loads of sugar
NL = 3 ! Number of production lines
WAGONS = 1..NW
SLOTS = 1..ceil(NW/NL) ! Time slots for production
LOSS: array(WAGONS) of real ! Loss in kg/hour
LIFE: array(WAGONS) of real ! Remaining time per lot
DUR: integer ! Duration of the production
process: array(WAGONS,SLOTS) of mpvar ! 1 if wagon processed in slot,
! 0 otherwise
end-declarations
initializations from 'a4sugar.dat'
LOSS LIFE DUR
end-initializations
! Objective function
TotalLoss:= sum(w in WAGONS, s in SLOTS) s*DUR*LOSS(w)*process(w,s)
! Assignment
forall(w in WAGONS) sum(s in SLOTS) process(w,s) = 1
! Wagon loads per time slot
forall(s in SLOTS) sum(w in WAGONS) process(w,s) <= NL
! Limit on raw product life
forall(w in WAGONS) sum(s in SLOTS) s*process(w,s) <= LIFE(w)/DUR
forall(w in WAGONS, s in SLOTS) process(w,s) is_binary
! Solve the problem
minimize(TotalLoss)
! Solution printing
writeln("Total loss: ", getobjval)
forall(s in SLOTS) do
write("Slot ", s, ": ")
forall(w in WAGONS | getsol(process(w,s))>0)
write(formattext("wagon %2d (%3g) ", w, s*DUR*LOSS(w)))
writeln
end-do
end-model
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