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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]




burglari.mos

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

   file burglari.mos
   `````````````````
   Knapsack problem
   -- Using string indices --   
  -- Using string indices --

   A burglar considers eight items that have different values
   and weights. He wants to take a group of items that maximizes
   the total value while the total weight is not more than the
   maximum 'WTMAX' he can carry.

   This IP model represents the so-called knapsack problem where
   binary decision variable 'take(i)' takes value 1 if item 'i'
   is taken; 0 otherwise. This implementation illustrates the
   use of string indices having the data embedded in the model file.

   (c) 2008 Fair Isaac Corporation
       author: R.C. Daniel, Jul. 2002
*******************************************************!)

model "Burglar 1 (index set)" 
 uses "mmxprs"
  
 declarations
  ITEMS = {"camera", "necklace", "vase", "picture", "tv", "video", 
           "chest", "brick"}     ! Set for items
  WTMAX = 102                    ! Maximum weight allowed
  
  VALUE: array(ITEMS) of real    ! Value of items
  WEIGHT: array(ITEMS) of real   ! Weight of items
  
  take: array(ITEMS) of mpvar    ! 1 if we take item i; 0 otherwise
 end-declarations

 VALUE("camera")  := 15;  WEIGHT("camera")  :=  2
 VALUE("necklace"):=100;  WEIGHT("necklace"):= 20
 VALUE("vase")    := 90;  WEIGHT("vase")    := 20
 VALUE("picture") := 60;  WEIGHT("picture") := 30
 VALUE("tv")      := 40;  WEIGHT("tv")      := 40
 VALUE("video")   := 15;  WEIGHT("video")   := 30
 VALUE("chest")   := 10;  WEIGHT("chest")   := 60
 VALUE("brick")   :=  1;  WEIGHT("brick")   := 10

(! Alternative data initialization:
  VALUE :: (["camera", "necklace", "vase", "picture", "tv", "video", 
             "chest", "brick"])[15, 100, 90, 60, 40, 15, 10, 1]
  WEIGHT:: (["camera", "necklace", "vase", "picture", "tv", "video", 
             "chest", "brick"])[ 2,  20, 20, 30, 40, 30, 60, 10]
!)

! 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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