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Assignment

Description
A set of projects is assigned to persons with the objective to maximize the overall satisfaction. A preference rating per person and project is given. In this model formulation the solution to the LP problem is integer, there is no need to define the decision variables explicitly as binaries.

Further explanation of this example: Similar problems: 'Applications of optimization with Xpress-MP', Section 11.1 'Flight connections at a hub', Section 14.1 'Assigning personnel to machines', Section 8.6 'Assignment of production batches to machines'

Source Files

assignment_graph.mos

```(!*********************************************************************
Mosel Example Problems
======================

file assignment.mos
```````````````````
TYPE:         Assignment problem
DIFFICULTY:   1
FEATURES:     simple LP problem, graphical representation of results
DESCRIPTION:  A set of projects is assigned to persons with the
objective to maximize the overall satisfaction.
A preference rating per person and project is given.
In this model formulation the solution to the LP problem
is integer, there is no need to define the decision
variables explicitly as binaries.
FURTHER INFO: Similar problems:
`Applications of optimization with Xpress-MP',
Section 11.1 `Flight connections at a hub',
Section 14.1 `Assigning personnel to machines'
Section 8.6 `Assignment of production batches to machines'

(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Feb. 2004, rev. Sep. 2017
**********************************************************************!)

model Assignment
uses "mmxprs", "mmsvg"

declarations
NP = 5                                ! Number of persons/projects
RP = 1..NP                            ! Set (range) of persons/projects
PREF: array(RP,RP) of integer         ! Preference values

assign: array(RP,RP) of mpvar         ! Assignment person-project
end-declarations

PREF:: [1, 2, 3, 5, 4,
3, 2, 5, 4, 1,
3, 4, 1, 5, 2,
4, 3, 2, 5, 1,
2, 3, 5, 4, 1]

! Objective function: maximize satisfaction
Satisfaction:= sum(m,p in RP) PREF(m,p)*assign(m,p)

! One person per project
forall(p in RP) OnePersProj(p):= sum(m in RP) assign(m,p)=1

! One project per person
forall(m in RP) OneProjPers(m):= sum(p in RP) assign(m,p)=1

! Solve the problem
maximize(Satisfaction)

! Solution printing
writeln("Total satisfaction score: ", getobjval)
forall(m in RP)
writeln("Person ", m, ": project ", getsol(sum(p in RP) p*assign(m,p)) )

! Solution drawing
FACT:=5
svgsetgraphscale(FACT)
svgsetgraphviewbox(0,0,30,NP*FACT+5)

forall(m in RP) do
pos:=FACT*m
svgsetstyle(svggetlastobj, SVG_TEXTANCHOR, "end")
a:=getsol(sum(p in RP) p*assign(m,p))
svgsetstyle(svggetlastobj, SVG_STROKEWIDTH, ceil(PREF(m,round(a))/2))
end-do

forall(p in RP) do
pos:=FACT*p