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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
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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