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Introductory examples

Description
Problem name and type, featuresDifficulty
approx Approximation: Piecewise linear approximation **
SOS-2, Special Ordered Sets, piecewise linear approximation of a nonlinear function, pwlin
burglar MIP modeling: Knapsack problem: 'Burglar' *
simple MIP model with binary variables, data input from text data file, array initialization, numerical indices, string indices, record data structure
chess LP modeling: Production planning: 'Chess' problem *
simple LP model, solution output, primal solution values, slack values, activity values, dual solution values
pricebrai All item discount pricing: Piecewise linear function ***
SOS-1, Special Ordered Sets, piecewise linear function, approximation of non-continuous function, step function, pwlin
pricebrinc Incremental pricebreaks: Piecewise linear function ***
SOS-2, Special Ordered Sets, piecewise linear function, step function


Further explanation of this example: 'Applications of optimization with Xpress-MP', Introductory examples (Chapters 1 to 5) of the book 'Applications of optimization with Xpress-MP'

mosel_app_intro.zip[download all files]

Source Files
By clicking on a file name, a preview is opened at the bottom of this page.
approx.mos[download]
approx2.mos[download]
burglar1.mos[download]
burglar2.mos[download]
burglari.mos[download]
burglar_rec.mos[download]
chess.mos[download]
chess2.mos[download]
pricebrai.mos[download]
pricebrai2.mos[download]
pricebrinc.mos[download]
pricebrinc2.mos[download]
pricebrinc3.mos[download]

Data Files
burglar.dat[download]
burglar2.dat[download]
burglar_rec.dat[download]




pricebrinc2.mos

(!******************************************************
   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
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