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Delivery: Infeasibility analysis with IIS

A simple supply and demand network example demonstrating infeasibility analysis with IIS.
  • simple LP model
  • data input from file
  • retrieving IIS and printing out the names of all variables and constraints contained in the sets

Source Files
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Data Files


  Mosel Example Problems

  file delvriis.mos
  Transportation problem (infeasible data).
  Retrieving and printing IIS.

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, 2007, rev. Sep. 2018

model Delivery                      ! Start a new model
 uses "mmxprs","mmetc"              ! Load the optimizer and ETC libraries

 public declarations
  RSupp = 1..10                     ! Range of suppliers
  RCust = 1..7                      ! Range of customers
  VANCAP = 40                       ! Capacity on routes that use vans

  COST: array(RSupp,RCust) of real  ! Unit delivery cost on route supplier
                                    ! -> customer
  SUPPLY: array(RSupp) of real      ! Amount available from each supplier
  DEMAND: array(RCust) of real      ! Amount required by each customer
  IFVAN: array(RSupp,RCust) of integer    ! Non-zero if route uses vans
                                          ! instead of lorries

  flow: array(RSupp,RCust) of mpvar       ! Amount delivered from each
                                          ! supplier s to each customer c
  Demand: dynamic array(RCust) of linctr  ! Demand qty constraints
  Supply: dynamic array(RSupp) of linctr  ! Supply limit constraints

                                    ! Read data from file (dense format)
 diskdata(ETC_IN, "cost.dat", COST)
 diskdata(ETC_IN, "ifvan.dat", IFVAN)

                                    ! Assign some data arrays
! Supplier:     London  Luton  B'ham Bristl  Derby Stckpt   York
 SUPPLY:: (1..7)[140.0, 200.0,  50.0,  10.0, 400.0, 200.0,  20.0]
! Supplier:      Derby  Soton Scnthp
 SUPPLY:: (8..10)[90.0,  30.0,  12.0]

! Customer: London Livpol Doncst   York   Hull  Manchr Shffld
 DEMAND::  [1230.3, 560.4, 117.1, 592.8, 310.0, 1247.0,  86.0]

                                    ! Objective: Minimise total cost
 MinCost:= sum(s in RSupp,c in RCust) COST(s,c)*flow(s,c)

                                    ! Satisfy demand of each customer
 forall(c in RCust | c<=4)
   Demand(c):= sum(s in RSupp | s<=5) flow(s,c) >= DEMAND(c)
 forall(c in RCust | c>4)
   Demand(c):= sum(s in RSupp | s>5) flow(s,c) >= DEMAND(c)

                                    ! Keep within supply at each supplier
 forall(s in RSupp | s<=5)
   Supply(s):= sum(c in RCust | c<=4) flow(s,c) <= SUPPLY(s)
 forall(s in RSupp | s>5)
   Supply(s):= sum(c in RCust | c>4) flow(s,c) <= SUPPLY(s)

 forall(s in RSupp,c in RCust| IFVAN(s,c) <> 0) flow(s,c) <= VANCAP

 minimise(MinCost)                  ! Solve the LP-problem

! **** Print out the IIS ****
  V: set of mpvar
  C: set of linctr
  Ctype,Btype,Vtype: array(integer) of string
  BndType: dynamic array(mpvar) of integer
  CtrType: dynamic array(linctr) of integer
 Btype::([XPRS_IIS_LEQ, XPRS_IIS_GEQ, XPRS_IIS_RNG, XPRS_IIS_EQ])["upper bd","lower bd","range","fixed"]
         ["binary","integer","partial int","semi-cont","semi-cont int"]

 if getprobstat=XPRS_INF then
   getiis(0, V, C)                  ! Retrieve the IIS approximation
   writeln("IIS approximation")
   write("  variables: "); forall(v in V) write(getname(v), " "); writeln
   write("  constraints: "); forall(c in C) write(getname(c), " "); writeln
   getiis({},{})                    ! Generate all IIS
   numiis:= getparam("XPRS_NUMIIS") ! Retrieve the total number of IIS
   writeln("Total IIS:", numiis)
   forall(i in 1..numiis) do
     getiis(i, V, C)                ! Retrieve the i'th IIS
     delcell(BndType); getiis(i, BndType)
     delcell(CtrType); getiis(i, CtrType)
     writeln("IIS ", i)
     write("  variables: ")
     forall(v in V) write(getname(v), "[", Btype(getiissense(BndType(v))), 
       " ", Vtype(getiistype(BndType(v))), "] "); writeln
     write("  constraints: "); 
     forall(c in C) write(getname(c), "[", Ctype(CtrType(c)),"] "); writeln

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