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Planning problems

Description
Problem name and type, featuresDifficulty
C‑1 Planning the production of bicycles: Production planning (single product) ***
modeling inventory balance; inline if, forall-do
C‑2 Production of drinking glasses: Multi-item production planning **
modeling stock balance constraints; inline if, index value 0
C‑3 Material requirement planning: Material requirement planning (MRP) **
working with index (sub)sets, dynamic initialization, finalize, create, as
C‑4 Planning the production of electronic components: Multi-item production planning **
modeling stock balance constraints; inline if
C‑5 Planning the production of fiberglass: Production planning with time-dependent production cost ***
representation of multi-period production as flow; encoding of arcs, exists, create, isodd, getlast, inline if
C‑6 Assignment of production batches to machines: Generalized assignment problem *


Further explanation of this example: 'Applications of optimization with Xpress-MP', Chapter 8: Production planning

mosel_app_3.zip[download all files]

Source Files

Data Files





c2glass.mos

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

   file c2glass.mos
   ````````````````
   Planning the production of glasses
   
   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002
*******************************************************!)

model "C-2 Glass production"
 uses "mmxprs"

 declarations   
  NT = 12                              ! Number of weeks in planning period
  WEEKS = 1..NT 
  PRODS = 1.. 6                        ! Set of products

  CAPW,CAPM: integer                   ! Capacity of workers and machines
  CAPS: integer                        ! Storage capacity
  DEM: array(PRODS,WEEKS) of integer   ! Demand per product and per 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
  
  produce: array(PRODS,WEEKS) of mpvar ! Production of products per week
  store: array(PRODS,WEEKS) of mpvar   ! Amount stored at end of week
 end-declarations

 initializations from 'c2glass.dat'
  CAPW CAPM CAPS DEM CSTOCK CPROD ISTOCK FSTOCK TIMEW TIMEM SPACE
 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))

! Stock balances
 forall(p in PRODS, t in WEEKS)
  store(p,t) = if(t>1, store(p,t-1), ISTOCK(p)) + produce(p,t) - DEM(p,t)

! Final stock levels
 forall(p in PRODS) store(p,NT) >= FSTOCK(p)

! Capacity constraints
 forall(t in WEEKS) do
  sum(p in PRODS) TIMEW(p)*produce(p,t) <= CAPW     ! Workers
  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
 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))
  writeln
  write("   Store ")
  forall(t in WEEKS) write(strfmt("("+getsol(store(p,t))+")",7))
  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(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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