盒包裝的Gurobi C＃優化

Question

我有三個產品和五盒：

var products = new string[] { "A", "B", "C"}; 
var boxes = new string[] { "1", "2", "3" ,"4","5"}; 

和尺寸是：

double[,] boxDimensions = new double[,] 
          {{8}, 
          {15}, 
          {30}, 
          {40}, 
          {50}}; 

double[,] productDimensions = new double[,] 
         { { 5 }, 
          { 10 }, 
          { 20 } }; 

我想選擇與所有的產品將被安裝在minumum體塊

我寫了下面的代碼，我知道我應該添加約束來選擇只有他們一個框。 但它不工作（給不可行的溶膠）與當前狀態。 代碼如下可供選擇：

感謝提前4侑幫助，

static void Main() 
     { 
      try 
      { 

       var products = new string[] { "A", "B", "C" }; 
       var boxes = new string[] { "1", "2", "3", "4", "5" }; 

       double[,] boxDimensions = new double[,] {{8}, 
              {15}, 
              {30}, 
              {40}, 
              {50}}; 

       double[,] productDimensions = 
        new double[,] { { 5 }, 
            { 5 }, 
            { 20 }}; 

       // Model 
       GRBEnv env = new GRBEnv(); 
       GRBModel model = new GRBModel(env); 
       model.Set(GRB.StringAttr.ModelName, "box"); 

       // Box decision variables: open[p] == 1 if box i is choosen. 
       GRBVar[] open = new GRBVar[boxes.Length]; 
       for (int i = 0; i < boxes.Length; i++) 
       { 
        open[i] = model.AddVar(0, 1, boxDimensions[i, 0], GRB.BINARY, boxes[i]); 
       } 

       GRBVar[] x = new GRBVar[products.Length]; 

       for (int j = 0; j < products.Length; j++) 
       { 
        x[j] = model.AddVar(productDimensions[j, 0], productDimensions[j, 0], 0, GRB.CONTINUOUS, products[j]); 
       } 


       // The objective is to minimize the total fixed and variable costs 
       model.Set(GRB.IntAttr.ModelSense, 1); 

       // Update model to integrate new variables 
       model.Update(); 
       GRBLinExpr lhs = 0.0; 
       GRBLinExpr rhs = 0.0; 
       // Production constraints 
       // Note that the right-hand limit sets the production to zero if 
       // the plant is closed 
       // Constraint: assign exactly shiftRequirements[s] workers 
       // to each shift s 
       for (int s = 0; s < products.Length; ++s) 
       { 
        lhs.AddTerm(1.0, x[s]); 
       } 

       for (int w = 0; w < boxes.Length; w++) 
       { 
        rhs.AddTerm(boxDimensions[w, 0], open[w]); 
       } 

       model.AddConstr(lhs <= rhs, "BoxConstraint"); 

       model.GetEnv().Set(GRB.IntParam.Method, GRB.METHOD_BARRIER); 

       // Solve 
       model.Optimize(); 

       // Print solution 
       int status = model.Get(GRB.IntAttr.Status); 
       if (status == GRB.Status.UNBOUNDED) 
       { 
        Console.WriteLine("The model cannot be solved " 
         + "because it is unbounded"); 
        return; 
       } 
       if (status == GRB.Status.OPTIMAL) 
       { 
        Console.WriteLine("The optimal objective is " + 
         model.Get(GRB.DoubleAttr.ObjVal)); 
        return; 
       } 
       if ((status != GRB.Status.INF_OR_UNBD) && 
        (status != GRB.Status.INFEASIBLE)) 
       { 
        Console.WriteLine("Optimization was stopped with status " + status); 
        return; 
       } 

       // Dispose of model and env 
       model.Dispose(); 
       env.Dispose(); 

      } 
      catch (GRBException e) 
      { 
       Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message); 
      } 
     } 

注：我給簡單的問題（1D），其實我真正的問題是3D的問題。在這種情況下，我只考慮產品和盒子的長度，但在實際中我應該考慮寬度和高度。

Answer 1

您的編寫模型的一般方法是可以的。儘管如此，對於x，您將下限和上限設置爲固定x的相同值。此外，我想知道爲什麼你讓Gurobi使用Barrier方法。我不確定在您正在使用的MIP設置中這是否正確。