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Basic LP tasks: problem statement and solving; solution analysis

The first model (file chess.mos) is a small, introductory problem to modeling with Mosel that shows the basic features of the Mosel language:
  • formulation of a simple LP/IP problem
  • solving an optimization problem
  • solution printout
The second model (file chess2.mos) shows some more advanced features of Mosel, namely the data structures set and array:
  • formulating and solving a simple LP problem
  • defining a set of variables and an array of descriptions for the variables (to be used in the output printing)
Detailed solution information for MIP problems as may be required when performing sensitivity analysis, such as dual and reduced cost values (file chessfixg.mos) or ranging information for variables and constraints (file chessrng.mos), is not immediately available during or after the branch-and-bound search. The following procedure needs to be used to generate the sensitivity analysis data:
  1. Solve the MIP problem.
  2. Fix all discrete variables to their solution values.
  3. Re-solve the remaining LP problem.
  4. Retrieve the solution information.
Further explanation of this example: 'Mosel User Guide', Chapter 1 Getting started with Mosel and Section 8.1 Initializing sets, or the book 'Applications of optimization with Xpress-MP', Section 1.3 Solving the chess set problem.

Source Files
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  * Mosel Example Problems                              *
  * ======================                              *
  *                                                     *
  * file chess2.mos                                     *
  * ```````````````                                     *
  * Example for the use of the Mosel language           *
  * (Small LP-problem)                                  *
  *                                                     *
  * (c) 2008 Fair Isaac Corporation                     *
  *     author: S. Heipcke, 2001                        *

model Chess2                      ! Start a new model

uses "mmxprs"                     ! Load the optimizer library

 Allvars: set of mpvar            ! Set of all variables
 DescrV: array(Allvars) of string ! Descriptions of variables
 xs: mpvar                        ! Number of small chess sets to make
 xl: mpvar                        ! Number of large chess sets to make
 Allctrs: set of linctr           ! Set of all constraints
 DescrC: array(Allctrs) of string ! Descriptions of constraints
 Profit,mc_time,wood: linctr      ! Declaration of constraints: optional

! Define the variable and constraint descriptions. Since the arrays and
! the indexing sets are dynamic they grow with each new variable
! description added:
 DescrV(xs):= " Number of small chess sets"
 DescrV(xl):= " Number of large chess sets"

 DescrC(mc_time):= " Limit on available machine time"
 DescrC(wood):= " Limit on available wood"
 Profit:= 5*xs + 20*xl            ! Define the objective function

 mc_time:= 3*xs + 2*xl <= 400     ! Limit on available machine time
 wood:=      xs + 3*xl <= 200     ! Limit on available wood
 maximize(Profit)                 ! Solve the LP-problem

                                  ! Print out the solution
 writeln("Solution:\n Objective: ", getobjval)
 writeln(DescrV(xs), ":",xs.sol, ",", DescrV(xl), ":", xl.sol)
 writeln(" Constraint activity:")
 writeln(DescrC(mc_time), ":", mc_time.act, ",",
   DescrC(wood), ":", wood.act)


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