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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'

assignmentgr.zip[download all files]

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)
 svgaddgroup("PersGraph", "Persons")
 svgaddgroup("ProjGraph", "Projects")
 svgaddgroup("AsgnGraph", "Assignments (preference-weighted)", SVG_GREY)
 
 forall(m in RP) do
  pos:=FACT*m
  svgaddpoint("PersGraph", 1*FACT, pos)
  svgaddtext("PersGraph", 1*FACT-0.02, pos-0.2, text(m))
  svgsetstyle(svggetlastobj, SVG_TEXTANCHOR, "end")
  a:=getsol(sum(p in RP) p*assign(m,p))
  svgaddline("AsgnGraph", 1*FACT, pos, 3*FACT, a*FACT)
  svgsetstyle(svggetlastobj, SVG_STROKEWIDTH, ceil(PREF(m,round(a))/2))
 end-do
 
 forall(p in RP) do
  pos:=FACT*p
  svgaddpoint("ProjGraph", 3*FACT, pos)
  svgaddtext("ProjGraph", 3*FACT+0.2, pos-0.2, string(p))
 end-do

 svgsave("assign.svg")
 svgrefresh
 svgwaitclose("Close browser window to terminate model execution.", 1)
end-model 

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