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Introductory examples

Description
approx burglar chess Problem name and type, features Difficulty Approximation: Piecewise linear approximation ** SOS-2, Special Ordered Sets, piecewise linear approximation of a nonlinear function 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 LP modeling: Production planning: 'Chess' problem * simple LP model, solution output, primal solution values, slack values, activity values, dual solution values All item discount pricing: Piecewise linear function *** SOS-1, Special Ordered Sets, piecewise linear function, approximation of non-continuous function, step function 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'

Source Files

Data Files

burglar_rec.mos

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

file burglar_rec.mos
````````````````````
Use of records.

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

model "Burglar (records)"
uses "mmxprs"

declarations
WTMAX = 102                    ! Maximum weight allowed
ITEMS = {"camera", "necklace", "vase", "picture", "tv", "video",
"chest", "brick"}     ! Index set for items

I: array(ITEMS) of record
VALUE: real                   ! Value of items
WEIGHT: real                  ! Weight of items
end-record
take: array(ITEMS) of mpvar    ! 1 if we take item i; 0 otherwise
end-declarations

initializations from 'burglar_rec.dat'
I
end-initializations

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

! Weight restriction
sum(i in ITEMS) I(i).WEIGHT*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

```