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

   file e4deliver.mos
   ``````````````````
   Heating oil delivery (Traveling Salesman Problem)

   Heating oil is delivered from a refinery to 6 clients.
   Which routes should be schedules so that all clients
   receive their deliveries with the minimal total km
   driven by the tanker trucks?

   This problem formulation defines constraints to eliminate
   infeasible subtours. It introduces '|' to limit the index
   tuples that are enumerated in 'forall' loops or in sums. 
   An additional set of constraints can be added as model cuts.
   These must be declared as 'linctr' and are specified
   using 'setmodcut'.

   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)

model "E-4 Oil delivery"
 uses "mmxprs"

 declarations
  NS = 7
  SITES = 1..NS                       ! Set of locations, 1=refinery
  CLIENTS = 2..NS

  DEM: array(SITES) of integer        ! Demands
  DIST: array(SITES,SITES) of integer ! Distances between locations
  CAP: integer                        ! Lorry capacity

  prec: array(SITES,SITES) of mpvar   ! 1 if i immediately precedes j,
                                      ! 0 otherwise
  quant: array(CLIENTS) of mpvar      ! Quantity delivered up to i
 end-declarations

 initializations from 'e4deliver.dat'
  DEM DIST CAP
 end-initializations

! Objective: total distance driven
 Length:= sum(i,j in SITES | i<>j) DIST(i,j)*prec(i,j)

! Enter and leave every city only once (except the depot)
 forall(j in CLIENTS) sum(i in SITES| i<>j) prec(i,j) = 1
 forall(i in CLIENTS) sum(j in SITES| i<>j) prec(i,j) = 1

! If i is the first client of a tour, then quant(i)=DEM(i)
 forall(i in CLIENTS) quant(i) <= CAP + (DEM(i)-CAP)*prec(1,i)

! If j comes just after i in a tour, then quant(j) is greater than the
! quantity delivered during the tour up to i plus the quantity to be
! delivered at j (to avoid loops and keep capacity limit of the tanker)
 forall(i,j in CLIENTS| i<>j) quant(j) >= quant(i) + DEM(j) - CAP +
                           CAP*prec(i,j) + (CAP-DEM(j)-DEM(i))*prec(j,i)

! Additional constraints:
! If i is not the first client of a tour, quant(i) is larger than the sum
! of the quantities to deliver to i and to his predecessor on the tour
(!
 declarations
  ModCut: array(CLIENTS) of linctr
 end-declarations

 forall(i in CLIENTS) do
  ModCut(i):= quant(i) >= DEM(i) + sum(j in SITES| i<>j) DEM(j)*prec(j,i)
  setmodcut(ModCut(i))
 end-do
!)

 forall(i in CLIENTS) do
  quant(i) <= CAP
  quant(i) >= DEM(i)
 end-do
 
 forall(i,j in SITES | i<>j) prec(i,j) is_binary

! Uncomment the following line to see the Optimizer log
! setparam("XPRS_VERBOSE",true)

! Solve the problem
 minimize(Length)

! Solution printing
 writeln("Total distance: ", getobjval)
 forall(i in CLIENTS | getsol(prec(1,i))>0) do
  ct:=DEM(i)
  writeln(1, " -> ", i)
  p:=i
  while(p<>1) do
   n:= round(sum(j in SITES) j*getsol(prec(p,j)))
   writeln(p, " -> ", n)
   ct+=DEM(n)
   p:=n
  end-do
  writeln("Quantity delivered: ", ct)
 end-do

end-model