FICO Xpress Optimization Examples Repository: 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:

Solve the MIP problem.
Fix all discrete variables to their solution values.
Re-solve the remaining LP problem.
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.

(!******************************************************* * 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 declarations 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 end-declarations ! 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) end-model