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'producer_consumer' constraints: solving a resource-constrained project scheduling problem

Description
So-called 'producer_consumer' relations combine tasks that produce or consume quantities of the same non-renewable resource. Such problems may be modeled in two ways, namely
  • using 'producer_consumer' constraints (producer_consumer_alt.mos), or
  • using 'task' and 'resource' model objects that are configured correspondingly (producer_consumer.mos)
Further explanation of this example: 'Xpress Kalis Reference Manual'

producerconsumer.zip[download all files]

Source Files





producer_consumer_alt.mos

(!****************************************************************
   CP example problems
   ===================
   
   file producer_consumer_alt.mos
   ``````````````````````````````
   Resource-constrained project planning problem (construction of 
   a house) modeled with a producer-consumer constraint.

   *** This model cannot be run with a Community Licence *** 

   (c) 2008 Artelys S.A. and Fair Isaac Corporation
       Creation: 2007, rev. Mar. 2013
*****************************************************************!)
model "Cumulative Scheduling"  
 uses "kalis" 

 setparam("KALIS_DEFAULT_LB",0)
 setparam("KALIS_DEFAULT_UB",100)

 declarations
 ! Task indices
  Masonry = 1; Carpentry= 2; Roofing       = 3; Windows      = 4
  Facade  = 5; Garden   = 6; Plumbing      = 7; Ceiling      = 8
  Painting= 9; MovingIn =10; InitialPayment=11; SecondPayment=12
  BUILDTASKS = 1..10
  PAYMENTS = 11..12
  TASKS = BUILDTASKS+PAYMENTS
  TNAMES: array(TASKS) of string
  
  obj:cpvar                                ! Objective variable
  starts   : array(TASKS) of cpvar         ! Start times variables
  ends     : array(TASKS) of cpvar         ! Completion times
  durations: array(TASKS) of cpvar         ! Durations of tasks
  consos   : dynamic array(TASKS) of cpvar ! Res. consumptions
  sizes    : dynamic array(TASKS) of cpvar ! Consumption sizes
  prods    : dynamic array(TASKS) of cpvar ! Res. production
  sizep    : dynamic array(TASKS) of cpvar ! Production sizes
  Strategy : cpbranching                   ! Branching strategy
 end-declarations

 TNAMES:: (1..12)["Masonry", "Carpentry", "Roofing", "Windows",  
           "Facade", "Garden", "Plumbing", "Ceiling", "Painting", 
	   "MovingIn", "InitialPayment", "SecondPayment"]
 
! Setting the names of the variables
  forall(j in TASKS) do
    starts(j).name := TNAMES(j)+".start"
    ends(j).name := TNAMES(j)+".end"
    durations(j).name := TNAMES(j)+".duration"
  end-do

! Creating consumption variables
  forall(j in BUILDTASKS) do
    create(sizes(j))
    sizes(j).name := TNAMES(j)+".size"
    create(consos(j))
    consos(j).name := TNAMES(j)+".conso"
  end-do

! Setting durations of building tasks
 durations(Masonry) =7; durations(Carpentry)=3; durations(Roofing) =1
 durations(Windows) =1; durations(Facade)   =2; durations(Garden)  =1
 durations(Plumbing)=8; durations(Ceiling)  =3; durations(Painting)=2
 durations(MovingIn)=1

! Precedence constraints among building tasks
 starts(Carpentry) >= ends(Masonry)
 starts(Roofing)   >= ends(Carpentry)
 starts(Windows)   >= ends(Roofing)
 starts(Facade)    >= ends(Roofing)
 starts(Garden)    >= ends(Roofing)
 starts(Plumbing)  >= ends(Masonry)
 starts(Ceiling)   >= ends(Masonry)
 starts(Painting)  >= ends(Ceiling)
 starts(MovingIn)  >= ends(Windows)
 starts(MovingIn)  >= ends(Facade)
 starts(MovingIn)  >= ends(Garden)
 starts(MovingIn)  >= ends(Painting)

! Setting task consumptions
 consos(Masonry)  = 7; consos(Carpentry) = 3; consos(Roofing)  = 1 
 consos(Windows)  = 1; consos(Facade)    = 2; consos(Garden)   = 1 
 consos(Plumbing) = 8; consos(Ceiling)   = 3; consos(Painting) = 2 
 consos(MovingIn) = 1

! Production (amount) of payment tasks
 forall(j in PAYMENTS) do
  create(prods(j))
  prods(j).name := TNAMES(j)+".prod"
  create(sizep(j))
  sizep(j).name := TNAMES(j)+".sizep"
 end-do

! Payment data
 prods(InitialPayment)    = 20; prods(SecondPayment)     = 9
 durations(InitialPayment) = 1; durations(SecondPayment) = 1
 starts(InitialPayment)    = 0; starts(SecondPayment)    = 15


! Objective: makespan of the schedule
 obj = maximum({ ends(Masonry) , ends(Carpentry), ends(Roofing), 
         ends(Windows), ends(Facade), ends(Garden), ends(Plumbing),
	 ends(Ceiling), ends(Painting), ends(MovingIn)})

! Posting the producer_consumer constraint
 producer_consumer(starts,ends,durations,prods,sizep,consos,sizes)

! Setting the search strategy
 Strategy:= assign_var(KALIS_SMALLEST_MIN, KALIS_MIN_TO_MAX, starts)
 cp_set_branching(Strategy) 
 
! Find the optimal solution
 if cp_minimize(obj) then 
  writeln("Minimum makespan: ", obj.sol)
  forall(j in BUILDTASKS)
    writeln(TNAMES(j), ": ", starts(j).sol, " - ", ends(j).sol) 
 else
  writeln("No solution found")
 end-if

end-model


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