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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
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
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

Data Files





burglar2.mos

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

   file burglar2.mos
   `````````````````
   Knapsack problem   

   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, Aug. 2002
*******************************************************!)

model "Burglar 2" 
 uses "mmxprs"

 declarations
  ITEMS: set of string           ! Set of items
  WTMAX = 102                    ! Maximum weight allowed
  VALUE: array(ITEMS) of real    ! Value of items
  WEIGHT: array(ITEMS) of real   ! Weight of items
 end-declarations

 initializations from 'burglar.dat'
  VALUE
  WEIGHT
 end-initializations

(! alternatively:
 initializations from 'burglar2.dat'
  [VALUE, WEIGHT] as 'KNAPSACK'
 end-initializations
!)

 declarations
  take: array(ITEMS) of mpvar    ! 1 if we take item i; 0 otherwise
 end-declarations

! Objective: maximize total value
 MaxVal:= sum(i in ITEMS) VALUE(i)*take(i) 

! Weight restriction
 sum(i in ITEMS) WEIGHT(i)*take(i) <= WTMAX

! All variables are 0/1
 forall(i in ITEMS) take(i) is_binary  

 maximize(MaxVal)                 ! Solve the MIP-problem

! Print out the solution
 writeln("Solution:\n Objective: ", getobjval)
 forall(i in ITEMS)  writeln(" take(", i, "): ", getsol(take(i)))
end-model

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