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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

burglar1.mos

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

file burglar1.mos
`````````````````
Knapsack problem

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

model "Burglar 1"
uses "mmxprs"

declarations
ITEMS = 1..8                   ! Index range 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

! Item:      1    2  3   4   5   6   7   8
VALUE :: [15, 100, 90, 60, 40, 15, 10, 1]
WEIGHT:: [ 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

```