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

   file pricebrinc2.mos
   ````````````````````
   Incremental pricebreaks formulated with 
   binary variables   

   This model represents the situation where we buy a certain
   number of items and we get discounts incrementally. The
   unit cost for items between 0 and B1 is C1, whereas items
   between B1 and B2 cost C2 each, and items between B2 and
   B3 cost C3 each.

   We model the incremental price breaks by using binary
   decision variables. Binary variable 'b(i)' takes value 1
   if we have bought any items at a unit cost of 'COST(i)'.
   Decision variables 'x(i)' is the number of items bought at
   price 'COST(i)'.

   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, Sep. 2006
*******************************************************!)

model "Incremental pricebreaks (binaries)"
 uses "mmxprs"
 
 declarations
  NB = 3                                ! Number of price bands
  BREAKS = 1..NB
  COST: array(BREAKS) of real           ! Cost per unit
  x: array(BREAKS) of mpvar             ! Number of items bought at a price
  b: array(BREAKS) of mpvar             ! Indicators of price bands
  B: array(0..NB) of real               ! Break points of cost function 
 end-declarations
 
 DEM:= 150                              ! Demand
 B::  [0, 50, 120, 200]
 COST:: [0.8, 0.5, 0.3]
 
 forall(i in BREAKS) b(i) is_binary

! Objective: total price
 TotalCost:= sum(i in BREAKS) COST(i)*x(i)  

! Meet the demand
 sum(i in BREAKS) x(i) = DEM 

! Lower and upper bounds on quantities
 forall(i in 1..NB-1) (B(i)-B(i-1)) * b(i+1) <= x(i)
 forall(i in BREAKS)  x(i) <= (B(i)-B(i-1)) * b(i)

! Sequence of price intervals
 forall(i in 1..NB-1) b(i) >= b(i+1)

! Solve the problem
 minimize(TotalCost)

! Solution printing
 writeln("Objective: ", getobjval, 
         " (avg price per unit: ", getobjval/DEM, ")")
 forall(i in BREAKS) 
  writeln("x(", i, "): ", getsol(x(i)), " (price per unit: ", COST(i), ")")

end-model