(!******************************************************
Mosel Example Problems
======================
file c2glass_robust.mos
```````````````````````
Planning the production of glasses
- Robust against demand scenarios or workers' absence -
Based on c2_glass.mos (Mar 2002)
(c) 2014 Fair Isaac Corporation
author: S. Heipcke, Apr. 2014
*******************************************************!)
model "C-2 Glass production (scenarios)"
uses "mmrobust"
parameters
DATAFILE="c2glass_scen.dat"
IF_SCEN = true !false
IF_WORK = false !true
end-parameters
declarations
WEEKS: range ! Planning period
PRODS: range ! Set of products
SCEN: range ! Demand scenarios
CAPW,CAPM: integer ! Capacity of workers and machines
CAPS: integer ! Storage capacity
SCENDEM: array(SCEN,PRODS,WEEKS) of integer ! Demand per product & week
CPROD: array(PRODS) of integer ! Production cost per product
CSTOCK: array(PRODS) of integer ! Storage cost per product
ISTOCK: array(PRODS) of integer ! Initial stock levels
FSTOCK: array(PRODS) of integer ! Min. final stock levels
TIMEW,TIMEM: array(PRODS) of integer ! Worker and machine time per unit
SPACE: array(PRODS) of integer ! Storage space required by products
ABSENCE: dynamic array(WEEKS) of real ! Max. absence (hours)
produce: array(PRODS,WEEKS) of mpvar ! Production of products per week
store: array(PRODS,WEEKS) of mpvar ! Amount stored at end of week
absent: dynamic array(WEEKS) of uncertain ! Absence of personnel
demand: dynamic array(PRODS,WEEKS) of uncertain ! Uncertain demand
SCENDATA: array(SCEN,set of uncertain) of real ! Aux. data structure
end-declarations
initializations from DATAFILE
CAPW CAPM CAPS SCENDEM CSTOCK CPROD
ISTOCK FSTOCK TIMEW TIMEM SPACE ABSENCE
end-initializations
! Objective: sum of production and storage costs
Cost:=
sum(p in PRODS, t in WEEKS) (CPROD(p)*produce(p,t) + CSTOCK(p)*store(p,t))
if IF_SCEN then
! Demand scenarios
forall(p in PRODS, t in WEEKS | sum(s in SCEN) SCENDEM(s,p,t)>0)
create(demand(p,t))
forall(s in SCEN, p in PRODS, t in WEEKS | SCENDEM(s,p,t)>0)
SCENDATA(s, demand(p,t)):= SCENDEM(s,p,t)
scenario(SCENDATA)
! Stock balances
forall(p in PRODS, t in WEEKS) do
store(p,t) <= if(t>1, store(p,t-1), ISTOCK(p)) + produce(p,t) - demand(p,t)
store(p,t) >= if(t>1, store(p,t-1), ISTOCK(p)) + produce(p,t) -
max(s in SCEN) SCENDEM(s,p,t)
end-do
setparam("ROBUST_UNCERTAIN_OVERLAP", true)
else
forall(p in PRODS, t in WEEKS)
store(p,t) =
if(t>1, store(p,t-1), ISTOCK(p)) + produce(p,t) - SCENDEM(1,p,t)
end-if
! Final stock levels
forall(p in PRODS) store(p,WEEKS.last) >= FSTOCK(p)
if IF_WORK then
! Limit on total absence (uncertainty set)
forall(t in WEEKS) create(absent(t))
sum(t in WEEKS) absent(t) <= 0.05*CAPW*WEEKS.size
forall(t in WEEKS) absent(t) <= ABSENCE(t)
forall(t in WEEKS) absent(t) >= 0
setparam("ROBUST_UNCERTAIN_OVERLAP", true)
end-if
! Capacity constraints
forall(t in WEEKS) do
if IF_WORK then
sum(p in PRODS) TIMEW(p)*produce(p,t) <= CAPW -absent(t) ! Workers
else
sum(p in PRODS) TIMEW(p)*produce(p,t) <= CAPW/1.1 ! Workers
end-if
sum(p in PRODS) TIMEM(p)*produce(p,t) <= CAPM ! Machines
sum(p in PRODS) SPACE(p)*store(p,t) <= CAPS ! Storage
end-do
! Solve the problem
minimize(Cost)
! Solution printing
if getprobstat<>XPRS_OPT then
writeln("No solution found."); exit(1)
end-if
writeln("Total cost: ",getobjval)
writeln("Production plan:")
write(" Week")
forall(t in WEEKS) write(strfmt(t,7))
writeln
forall(p in PRODS) do
write(p,": Prod. ")
forall(t in WEEKS) write(strfmt(getsol(produce(p,t)),7,1))
writeln
write(" Store ")
forall(t in WEEKS) write(" (", if( store(p,t).sol>0,
strfmt(getsol(store(p,t)),4,1), " - "), ")")
writeln
end-do
writeln("\nCapacities used:")
writeln("Week",strfmt("Workers",8),strfmt("Machines",9),strfmt("Space",7))
forall(t in WEEKS)
writeln(strfmt(t,2),
strfmt(ceil(getsol(sum(p in PRODS) TIMEW(p)*produce(p,t))),8),
strfmt(getsol(sum(p in PRODS) TIMEM(p)*produce(p,t)),10,2),
strfmt(getsol(sum(p in PRODS) SPACE(p)*store(p,t)),9,2) )
end-model
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