FICO
FICO Xpress Optimization Examples Repository
FICO Optimization Community FICO Xpress Optimization Home
Back to examples browserPrevious exampleNext example

Production planning under energy supply uncertainty

Description
Plan the production of liquid nitrogen and liquid oxygen for the next N periods subject to an Interruptible Load Contract (ILC) for the power supply. Formulation using a polyhedral uncertainty set.

Further explanation of this example: Whitepaper 'Robust Optimization with Xpress', Section 7 Production planning under energy supply uncertainty

robprodplan.zip[download all files]

Source Files

Data Files





prodplan_robust.mos

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

   file prodplan_robust.mos
   ````````````````````````
   Production planning of liquid gases under energy uncertainty

   (c) 2014 Fair Isaac Corporation
       author: P. Belotti, Apr. 2014, rev. Jun. 2015
*******************************************************!)

model robust_prodplan
  uses "mmrobust"

  parameters
    plan_data = "prodplan_robust.dat"
  end-parameters

  declarations
    NDAYS:    integer                      ! Planning horizon
    PERDAY:   integer                      ! Number of periods per day
    NPERIODS: integer                      ! Total number of periods

    PERIODS,PERIODS0: range                ! Time periods
    GASES: set of string                   ! Set of products

    PROD_CAP: array(GASES) of real         ! Production capacity every day
    INV_CAP:  array(GASES) of real         ! Inventory capacity
    INV_0:    array(GASES) of real         ! Initial inventory

    PROD_COST: real                        ! Production cost
    INV_COST:  real                        ! Inventory cost

    DEMAND: array (PERIODS, GASES) of real ! Demand of each gas every day

    MAX_NINTERR: integer                   ! Maximum number of interruptions
                                           ! (as per contract)
  end-declarations

!**** Initialize data ****
  initializations from plan_data
    NDAYS PERDAY
    PROD_CAP  INV_CAP
    PROD_COST INV_COST INV_0
    DEMAND
    MAX_NINTERR
  end-initializations

  NPERIODS := NDAYS * PERDAY
  PERIODS0 := 0..NPERIODS

!**** Problem formulation ****
  declarations
    produce:   array(PERIODS, GASES) of mpvar   ! Production every day
    inventory: array(PERIODS0, GASES) of mpvar  ! Inventory level every day,
                                                ! including initial level

    interruption: array(PERIODS) of uncertain   ! Is power cut at this time?
    RobProd: array(PERIODS, GASES) of robustctr ! Robust constraint dealing with uncertainty
  end-declarations

!**** Constraints ****

  ! Start inventory
  forall(g in GASES)
    inventory (0,g) = INV_0 (g)

  ! Inventory balance
  forall(t in PERIODS, g in GASES) do

    RobProd(t,g) :=  inventory(0,g) + sum(tp in PERIODS | tp <= t) 
      ((1 - interruption(tp)) * produce(tp,g) - DEMAND(tp,g)) >= 0

    inventory (0,g) + sum (tp in PERIODS | tp <= t) 
      (produce(tp,g) - DEMAND(tp,g)) <= inventory(t,g)

    inventory(t,g) <= INV_CAP(g)
    produce(t,g)   <= PROD_CAP(g)

  end-do

  ! Interruptions of production
  forall (t in PERIODS) do
    interruption (t) <= 1
    interruption (t) >= 0
  end-do

  sum(t in PERIODS) interruption (t) <= MAX_NINTERR
  interruption(1) = 0

!**** Solving ****
  setparam("robust_uncertain_overlap", true)

  ! Set verbosity level
  setparam("xprs_verbose", true)

  ! Objective function: total cost of production and storage
  minimize(sum (t in PERIODS, g in GASES) 
             (PROD_COST * produce (t,g) + INV_COST * inventory(t,g)))

!**** Solution reporting ****
  writeln("\nNumber of interruptions: ", MAX_NINTERR)
  writeln("\nOptimal solution has cost ", getobjval)

  COLWIDTH := 6

  forall(g in GASES) do

    writeln("\nProduction of ", g)

    write(strfmt ("Time",-COLWIDTH))
    forall(t in PERIODS0) write (strfmt(t,COLWIDTH))

    write("\n", strfmt("Dem",-2*COLWIDTH))
    forall(t in PERIODS) write(strfmt(DEMAND(t,g),COLWIDTH,1))

    write("\n", strfmt("Prod",-2*COLWIDTH))
    forall(t in PERIODS) write(strfmt (produce(t,g).sol,COLWIDTH,1))

    write("\n", strfmt("Inv*",-COLWIDTH))
    forall(t in PERIODS0) 
      write (strfmt(inventory(0,g).sol + 
            sum (tp in PERIODS | tp <= t)
              (produce(tp,g).sol - DEMAND(tp,g)),COLWIDTH,1))
    writeln("\n\nWorst-case interruptions for ", g, ": ")

    forall(t in PERIODS | getsol(interruption(t),RobProd(t,g)) > 0)
      write (t, " ")

    writeln
  end-do

end-model

Back to examples browserPrevious exampleNext example