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Basic MIP tasks: binary variables; logic constraints

Description
We wish to choose among items of different value and weight those that result in the maximum total value for a given weight limit.
  • small MIP problem
  • alternative use of number-valued ranges and sets of strings for indexing variables and data
  • definition of binary variables
  • forall statement
  • formulation of logic constraints using indicators or advmod functionality (burglarl.mos)
Further explanation of this example: 'Mosel User Guide', Section 2.1 The burglar problem.


Source Files





burglar.mos

(!*******************************************************
  * Mosel Example Problems                              *
  * ======================                              *
  *                                                     *
  * file burglar.mos                                    *
  * ````````````````                                    *
  * Example for the use of the Mosel language           *
  * (Burglar problem)                                   *
  *                                                     *
  * (c) 2008 Fair Isaac Corporation                     *
  *     author: S. Heipcke, 2001                        *
  *******************************************************!)

model Burglar                       ! Start a new model

uses "mmxprs"                       ! Load the optimizer library

declarations
 Items=1..8                         ! Index range for items

 VALUE: array(Items) of real        ! Value of items
 WEIGHT: array(Items) of real       ! Weight of items
 WTMAX=102                          ! Max weight allowed for haul

 x: 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]
 
 MaxVal:= sum(i in Items) VALUE(i)*x(i)  ! Objective: maximize total value

                                    ! Weight restriction
 WtMax:= sum(i in Items) WEIGHT(i)*x(i) <= WTMAX 

 forall(i in Items) x(i) is_binary  ! All x are 0/1
  
 maximize(MaxVal)                   ! Solve the MIP-problem

                                    ! Print out the solution
 writeln("Solution:\n Objective: ", getobjval)
 forall(i in Items)  writeln(" x(", i, "): ", x(i).sol)

end-model

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