workforce3.m
function workforce3() % Copyright 2021, 狗万app足彩Gurobi Optimization, LLC % %分配工人轮班;每个工作人员可能在某%的特定日子可用，也可能不可用。如果问题无法解决，则放宽模型%，以确定哪些约束不能满足，以及它们需要放宽多少%。% define data nshift = 14;nWorkers = 7;nVars = nshift * nWorkers;={转变“Mon1”;“Tue2”;“Wed3”;“Thu4”; 'Fri5'; 'Sat6'; 'Sun7'; 'Mon8'; 'Tue9'; 'Wed10'; 'Thu11'; 'Fri12'; 'Sat13'; 'Sun14'}; Workers = {'Amy'; 'Bob'; 'Cathy'; 'Dan'; 'Ed'; 'Fred'; 'Gu'}; pay = [10; 12; 10; 8; 8; 9; 11]; shiftRequirements = [3; 2; 4; 4; 5; 6; 5; 2; 2; 3; 4; 6; 7; 5]; availability = [ 0 1 1 0 1 0 1 0 1 1 1 1 1 1; 1 1 0 0 1 1 0 1 0 0 1 0 1 0; 0 0 1 1 1 0 1 1 1 1 1 1 1 1; 0 1 1 0 1 1 0 1 1 1 1 1 1 1; 1 1 1 1 1 0 1 1 1 0 1 0 1 1; 1 1 1 0 0 1 0 1 1 0 0 1 1 1; 1 1 1 0 1 1 1 1 1 1 1 1 1 1 ]; % Build model model.modelname = 'workforce3'; model.modelsense = 'min'; % Initialize assignment decision variables: % x[w][s] == 1 if worker w is assigned % to shift s. Since an assignment model always produces integer % solutions, we use continuous variables and solve as an LP. model.ub = ones(nVars, 1); model.obj = zeros(nVars, 1); for w = 1:nWorkers for s = 1:nShifts model.varnames{s+(w-1)*nShifts} = sprintf('%s.%s', Workers{w}, Shifts{s}); model.obj(s+(w-1)*nShifts) = pay(w); if availability(w, s) == 0 model.ub(s+(w-1)*nShifts) = 0; end end end % Set-up shift-requirements constraints model.sense = repmat('=', nShifts, 1); model.rhs = shiftRequirements; model.constrnames = Shifts; model.A = sparse(nShifts, nVars); for s = 1:nShifts for w = 1:nWorkers model.A(s, s+(w-1)*nShifts) = 1; end end % Save model gurobi_write(model,'workforce3_m.lp'); % Optimize params.logfile = 'workforce3_m.log'; result = gurobi(model, params); % Display results if strcmp(result.status, 'OPTIMAL') % The code may enter here if you change some of the data... otherwise % this will never be executed. printsolution(result, Shifts, Workers) else if strcmp(result.status, 'INFEASIBLE') penalties.lb = inf(nVars, 1); penalties.ub = inf(nVars, 1); penalties.rhs = ones(nShifts, 1); feasrelax = gurobi_feasrelax(model, 0, false, penalties, params); result = gurobi(feasrelax.model, params); if strcmp(result.status, 'OPTIMAL') printsolution(result, Shifts, Workers); fprintf('Slack value:\n'); for j = nVars+1:length(result.x) if result.x(j) > 0.1 fprintf('\t%s, %g\n', feasrelax.model.varnames{j}, result.x(j)); end end else fprintf('Unexpected status %s\n',result.status); end else % Just to handle user interruptions or other problems fprintf('Unexpected status %s\n',result.status); end end end function printsolution(result, Shifts, Workers) % Helper function to display results nShifts = length(Shifts); nWorkers = length(Workers); fprintf('The optimal objective is %g\n', result.objval); fprintf('Schedule:\n'); for s = 1:nShifts fprintf('\t%s:', Shifts{s}); for w = 1:nWorkers if result.x(s+(w-1)*nShifts) > 0.9 fprintf('%s ', Workers{w}); end end fprintf('\n'); end end
