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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





c5fiber.mos

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

   file c5fiber.mos
   ````````````````
   Planning the production of fiberglass
   
   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Nov. 2017
*******************************************************!)

model "C-5 Fiberglass"
 uses "mmxprs"

 declarations   
  NODES: range                           ! Production and demand nodes
                                         ! odd numbers: production capacities
                                         ! even numbers: demands

  ARC: dynamic array(NODES,NODES) of real   ! Cost of flow on arcs
  WEIGHT: array(NODES) of integer           ! Node weights (capacities/demand)

  flow: dynamic array(NODES,NODES) of mpvar ! Flow on arcs
 end-declarations

 initializations from 'c5fiber.dat'
  ARC WEIGHT
 end-initializations

 forall(m,n in NODES | exists(ARC(m,n))) create(flow(m,n))

! Objective: total cost of production and storage
 Cost:= sum(m,n in NODES | exists(ARC(m,n))) ARC(m,n)*flow(m,n)

! Satisfy demands (flow balance constraints)
 forall(n in NODES | isodd(n)=FALSE)
  if(n>2, flow(n-2,n), 0) + flow(n-1,n) = 
   if(n<getlast(NODES), flow(n,n+2), 0) + WEIGHT(n)

! Production capacities
 forall(n in NODES | isodd(n)) flow(n,n+1) <= WEIGHT(n)

! Solve the problem
 minimize(Cost)
 
! Solution printing
 writeln("Total cost: ",getobjval)
 write("Week")
 forall(t in 1..integer(getlast(NODES)/2)) write(strfmt(t,5))
 write("\nProd.")
 forall(n in NODES | isodd(n)) 
  write(strfmt(getsol(sum(m in NODES) flow(n,m)),5))
 write("\nStock")
 forall(n in NODES | not(isodd(n))) 
  write(strfmt(getsol(sum(m in NODES) flow(n,m)),5))
 writeln

end-model

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