(!*******************************************************
Mosel Example Problems
======================
file prodplan_robust.mos
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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
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