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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





burglari.mos

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

model "Burglar (index set)"         ! Start a new model

uses "mmxprs"                       ! Load the optimizer library

declarations
 Items={"camera", "necklace", "vase", "picture", "tv", "video",
        "chest", "brick"}           ! Index set 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

 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
 
 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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