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

   file pricebrai.mos
   ``````````````````
   Modeling price breaks:
   All item discount pricing   
   
   This implementation represents the situation where we 
   buy a certain number of items and we get discounts on 
   all items that we buy if the quantity we buy lies in 
   certain price bands. We have three price bands. If we 
   buy a number of items in [0,B1) then for each item we 
   pay COST1, if the quantity we buy lies in [B1,B2) we 
   pay COST2 for each item. Finally if we buy an amount 
   in [B2,B3) then we pay an amount COST3 for each item. 
   This sort of pricing is called all item discount pricing.
   
   To model these item price breaks we use binary variables 
   b(i) which takes value 1 if we pay a unit cost of COST(i).
   We also define continuous decision variables x1, x2 and 
   x3 which represent the number of items bought at price 
   COST1, COST2, and COST3, respectively.

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

model "All item discount"
 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:: [ 1, 0.7, 0.5]
 
 forall(i in BREAKS) b(i) is_binary

(! Alternatively
 sum(i in BREAKS) B(i)*b(i) is_sos1
!) 

! 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 BREAKS) do
  B(i-1)*b(i) <= x(i);  x(i) <= B(i)*b(i)
 end-do

! The quantity bought lies in exactly one interval
 sum(i in BREAKS) b(i) = 1

! Solve the problem
 minimize(TotalCost)

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

end-model