apis/examples_matlab_control/CutstockModel_8m_source.html

classdef CutstockModel < handle


    properties (SetAccess = private)

        widths

        raw_width

        demand

        width

        pat_rep

        ws

        cutstock_data

        dbout

        opt

        job

    end


    methods


        function obj = CutstockModel(ws)


            obj.ws = ws;

            obj.opt = ws.addOptions();


            obj.cutstock_data = obj.ws.addDatabase('gdxincname');


            obj.opt.defines('gdxincname', 'gdxincname');

            obj.opt.defines('dbOut1', 'dbOut1');

            obj.opt.solveLink = gams.control.options.SolveLink.LoadLibrary;


            obj.widths = obj.cutstock_data.addSet('i', 'widths');

            obj.raw_width = obj.cutstock_data.addParameter('r', 'raw width');

            obj.demand = obj.cutstock_data.addParameter('d', 'demand', obj.widths);

            obj.width = obj.cutstock_data.addParameter('w', 'width', obj.widths);


            obj.job = obj.ws.addJobFromString(obj.modelSource());

        end


        function run(obj, output)

            if ~obj.cutstock_data.checkDomains()

                error('Domain Errors in Cutstock Database');

            end


            if isempty(output)

                obj.job.run(obj.opt, false, obj.cutstock_data);

            else

                obj.job.run(obj.opt, output, false, obj.cutstock_data);

            end

            obj.dbout = obj.ws.addDatabaseFromGDX([obj.opt.getDefinitionOf('dbOut1'), '.gdx']);

            obj.pat_rep = obj.dbout.getParameter('patrep');

        end


        function model = modelSource(obj)

            model = {

            '$Title Cutting Stock - A Column Generation Approach (CUTSTOCK,SEQ=294)     '

            '                                                                           '

            '$ontext                                                                    '

            'The task is to cut out some paper products of different sizes from a       '

            'large raw paper roll, in order to meet a customer''s order. The objective  '

            'is to minimize the required number of paper rolls.                         '

            '                                                                           '

            'P. C. Gilmore and R. E. Gomory, A linear programming approach to the       '

            'cutting stock problem, Part I, Operations Research 9 (1961), 849-859.      '

            '                                                                           '

            'P. C. Gilmore and R. E. Gomory, A linear programming approach to the       '

            'cutting stock problem, Part II, Operations Research 11 (1963), 863-888.    '

            '$offtext                                                                   '

            '                                                                           '

            'Set  i    widths                                                           '

            'Parameter                                                                  '

            '    r    raw width                                                         '

            '    w(i) width                                                             '

            '    d(i) demand ;                                                          '

            '                                                                           '

            '$if not set gdxincname $abort ''no include file name for data file provided'''

            '$gdxin %gdxincname%                                                        '

            '$load r i w d                                                              '

            '$gdxin                                                                     '

            '                                                                           '

            '* Gilmore-Gomory column generation algorithm                              '

            '                                                                           '

            'Set  p        possible patterns  /p1*p1000/                                '

            '     pp(p)    dynamic subset of p                                          '

            'Parameter                                                                  '

            '    aip(i,p) number of width i in pattern growing in p;                    '

            '                                                                           '

            '* Master model                                                             '

            'Variable xp(p)     patterns used                                           '

            '         z         objective variable                                      '

            'Integer variable xp; xp.up(p) = sum(i, d(i));                              '

            '                                                                           '

            'Equation numpat    number of patterns used                                 '

            '         demand(i) meet demand;                                            '

            '                                                                           '

            'numpat..     z =e= sum(pp, xp(pp));                                        '

            'demand(i)..  sum(pp, aip(i,pp)*xp(pp)) =g= d(i);                           '

            '                                                                           '

            'model master /numpat, demand/;                                             '

            '                                                                           '

            '* Pricing problem - Knapsack model                                         '

            'Variable  y(i) new pattern;                                                '

            'Integer variable y; y.up(i) = ceil(r/w(i));                                '

            '                                                                           '

            'Equation defobj                                                            '

            '         knapsack knapsack constraint;                                     '

            '                                                                           '

            'defobj..     z =e= 1 - sum(i, demand.m(i)*y(i));                           '

            'knapsack..   sum(i, w(i)*y(i)) =l= r;                                      '

            '                                                                           '

            'model pricing /defobj, knapsack/;                                          '

            '                                                                           '

            '* Initialization - the initial patterns have a single width                '

            'pp(p) = ord(p)<=card(i);                                                   '

            'aip(i,pp(p))$(ord(i)=ord(p)) = floor(r/w(i));                              '

            '*display aip;                                                              '

            '                                                                           '

            'Scalar done  loop indicator /0/                                            '

            'Set    pi(p) set of the last pattern; pi(p) = ord(p)=card(pp)+1;           '

            '                                                                           '

            'option optcr=0,limrow=0,limcol=0,solprint=off;                             '

            '                                                                           '

            'While(not done and card(pp)<card(p),                                       '

            '    solve master using rmip minimizing z;                                  '

            '    solve pricing using mip minimizing z;                                  '

            '                                                                           '

            '* pattern that might improve the master model found?                       '

            '  if(z.l < -0.001,                                                         '

            '     aip(i,pi) = round(y.l(i));                                            '

            '     pp(pi) = yes; pi(p) = pi(p-1);                                        '

            '  else                                                                     '

            '     done = 1;                                                             '

            '  );                                                                       '

            ');                                                                         '

            'display ''lower bound for number of rolls'', master.objval;                '

            '                                                                           '

            'option solprint=on;                                                        '

            'solve master using mip minimizing z;                                       '

            '                                                                           '

            'Parameter patrep Solution pattern report                                   '

            '        demrep Solution demand supply report;                              '

            '                                                                           '

            'patrep(''# produced'',p) = round(xp.l(p));                                 '

            'patrep(i,p)$patrep(''# produced'',p) = aip(i,p);                           '

            'patrep(i,''total'') = sum(p, patrep(i,p));                                 '

            'patrep(''# produced'',''total'') = sum(p, patrep(''# produced'',p));       '

            '                                                                           '

            'demrep(i,''produced'') = sum(p,patrep(i,p)*patrep(''# produced'',p));      '

            'demrep(i,''demand'') = d(i);                                               '

            'demrep(i,''over'') = demrep(i,''produced'') - demrep(i,''demand'');        '

            '                                                                           '

            'display patrep, demrep;                                                    '

            '$if not set dbOut1 $abort ''no file name for out-database 1 file provided'''

            'execute_unload ''%dbOut1%'', patrep;                                       '

            '                                                                           '};

            model = sprintf('%s\n', model{:});

        end


    end


end