workforce4_vb.vb
'版权所有2018，Gurobi O狗万app足彩ptimization，LLC''分配工人转移;每个工人可能会或可能无法在某个日子上使用。我们使用帕累托优化来解决模型：“首先，我们最小化了松弛的线性总和。然后，我们限制了“懈怠的总和”，我们最大限度地减少了一个二次目标，即“尝试平衡工人之间的工作量。导入系统导入Gurobi类Workforce4_vb共享子主（）尝试“示例数据”一组天数和工人Dim班幻灯片作为字符串（）= new字符串（）{mon1“，”tue2“，”wed3“，”thu4“，_“Fri5”，“SAT6”，“Sun7”，“Mon8”，_“Tue9”，“Wed10”，“星期四”，_“Fri12”，“SAT13”，“Sun14”} Dimer Workers作为String（）= newstring（）{amy“，”bob“，”cathy“，”dan“，_”ed“，”fred“，”gu“，”gu“}暗中nshifts作为整数= shifts.length昏暗nworkers作为整数= workers.length'每个Shift昏暗的工作人员需要双（）= new double（）= new double（）{3,2,4,4,5,6，_ 5,2,2,3,4,6，_ 7,5}'工人可用性：0如果工作人员不可用的换档暗淡可用性作为双（，）=新的Double（，）{_ {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}，_ {0,0,1，1,1，1， 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}} ' Model Dim env As New GRBEnv() Dim model As New GRBModel(env) model.ModelName = "assignment" ' Assignment variables: x(w)(s) == 1 if worker w is assigned ' to shift s. This is no longer a pure assignment model, so we ' must use binary variables. Dim x As GRBVar(,) = New GRBVar(nWorkers - 1, nShifts - 1) {} For w As Integer = 0 To nWorkers - 1 For s As Integer = 0 To nShifts - 1 x(w, s) = model.AddVar(0, availability(w, s), 0, _ GRB.BINARY, _ Workers(w) & "." & Shifts(s)) Next Next ' Add a new slack variable to each shift constraint so that the ' shifts can be satisfied Dim slacks As GRBVar() = New GRBVar(nShifts - 1) {} For s As Integer = 0 To nShifts - 1 slacks(s) = _ model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, _ Shifts(s) & "Slack") Next ' Variable to represent the total slack Dim totSlack As GRBVar = model.AddVar(0, GRB.INFINITY, 0, _ GRB.CONTINUOUS, "totSlack") ' Variables to count the total shifts worked by each worker Dim totShifts As GRBVar() = New GRBVar(nWorkers - 1) {} For w As Integer = 0 To nWorkers - 1 totShifts(w) = _ model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, _ Workers(w) & "TotShifts") Next Dim lhs As GRBLinExpr ' Constraint: assign exactly shiftRequirements(s) workers ' to each shift s, plus the slack For s As Integer = 0 To nShifts - 1 lhs = 0 lhs.AddTerm(1.0, slacks(s)) For w As Integer = 0 To nWorkers - 1 lhs.AddTerm(1.0, x(w, s)) Next model.AddConstr(lhs = shiftRequirements(s), Shifts(s)) Next ' Constraint: set totSlack equal to the total slack lhs = 0 For s As Integer = 0 To nShifts - 1 lhs.AddTerm(1.0, slacks(s)) Next model.AddConstr(lhs = totSlack, "totSlack") ' Constraint: compute the total number of shifts for each worker For w As Integer = 0 To nWorkers - 1 lhs = 0 For s As Integer = 0 To nShifts - 1 lhs.AddTerm(1.0, x(w, s)) Next model.AddConstr(lhs = totShifts(w), "totShifts" & Workers(w)) Next ' Objective: minimize the total slack model.SetObjective(1.0*totSlack) ' Optimize Dim status As Integer = _ solveAndPrint(model, totSlack, nWorkers, Workers, totShifts) If status <> GRB.Status.OPTIMAL Then Exit Sub End If ' Constrain the slack by setting its upper and lower bounds totSlack.UB = totSlack.X totSlack.LB = totSlack.X ' Variable to count the average number of shifts worked Dim avgShifts As GRBVar = model.AddVar(0, GRB.INFINITY, 0, _ GRB.CONTINUOUS, "avgShifts") ' Variables to count the difference from average for each worker; ' note that these variables can take negative values. Dim diffShifts As GRBVar() = New GRBVar(nWorkers - 1) {} For w As Integer = 0 To nWorkers - 1 diffShifts(w) = _ model.AddVar(-GRB.INFINITY, GRB.INFINITY, 0, _ GRB.CONTINUOUS, Workers(w) & "Diff") Next ' Constraint: compute the average number of shifts worked lhs = 0 For w As Integer = 0 To nWorkers - 1 lhs.AddTerm(1.0, totShifts(w)) Next model.AddConstr(lhs = nWorkers * avgShifts, "avgShifts") ' Constraint: compute the difference from the average number of shifts For w As Integer = 0 To nWorkers - 1 model.AddConstr(totShifts(w) - avgShifts = diffShifts(w), _ Workers(w) & "Diff") Next ' Objective: minimize the sum of the square of the difference ' from the average number of shifts worked Dim qobj As GRBQuadExpr = New GRBQuadExpr For w As Integer = 0 To nWorkers - 1 qobj.AddTerm(1.0, diffShifts(w), diffShifts(w)) Next model.SetObjective(qobj) ' Optimize status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts) If status <> GRB.Status.OPTIMAL Then Exit Sub End If ' Dispose of model and env model.Dispose() env.Dispose() Catch e As GRBException Console.WriteLine("Error code: " & e.ErrorCode & ". " & e.Message) End Try End Sub Private Shared Function solveAndPrint(ByVal model As GRBModel, _ ByVal totSlack As GRBVar, _ ByVal nWorkers As Integer, _ ByVal Workers As String(), _ ByVal totShifts As GRBVar()) As Integer model.Optimize() Dim status As Integer = model.Status solveAndPrint = status If (status = GRB.Status.INF_OR_UNBD) OrElse _ (status = GRB.Status.INFEASIBLE) OrElse _ (status = GRB.Status.UNBOUNDED) Then Console.WriteLine("The model cannot be solved because " & _ "it is infeasible or unbounded") Exit Function End If If status <> GRB.Status.OPTIMAL Then Console.WriteLine("Optimization was stopped with status " _ & status) Exit Function End If ' Print total slack and the number of shifts worked for each worker Console.WriteLine(vbLf & "Total slack required: " & totSlack.X) For w As Integer = 0 To nWorkers - 1 Console.WriteLine(Workers(w) & " worked " & _ totShifts(w).X & " shifts") Next Console.WriteLine(vbLf) End Function End Class
