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Production planning under demand uncertainty

Description
Planning the production of several types of drinking glasses for the next N weeks subject to uncertain demand (formulated via scenarios) or uncertain resource capacity limits (polyhedral uncertainty).

Further explanation of this example: Whitepaper 'Robust Optimization with Xpress', Section 3 Production planning under demand uncertainty

robc2glass.zip[download all files]

Source Files

Data Files





c2glass_robust.mos

(!******************************************************
   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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