无法找到可行的解决方案

Question

我正在Cplex中执行MIP代码。该问题具有可行的解决方案，但CPLEX解决方案不可行。而且，它并没有显示任何松弛，但是它放松了容量限制1和2。我认为它与运行配置有关，但我不知道问题出在什么地方。

模型如下：

//Parameters

//DKPCs
int I=...;
range DKPCs=1..I;

//Small DKPCs 
int S=...;
range SDKPCS=1..S;

//Big and Medium DKPCs

range BDKPCs=S+1..I;

//Depots
range Depots=1..2;

//Free capacity of depots
float Cj[Depots]=...;

//The unit storage cost of product i
float Hi[DKPCs]=...;

//Volume
float Vi[DKPCs]=...;

//The unit lost sale cost of product i
float Si[DKPCs]=...;

//The probability of selling product i if it were available in the DK depots

float Pi[DKPCs]=...;


//The initial inventory of consignment depot for product i
int Ki[DKPCs]=...;

// Total demand for product i in time period

int Di[DKPCs]=...;

int M=...;

//Decision Varaibles

//The assigned consignment capacity for product i
dvar int+ Yi[DKPCs];

//if product i is selected for consignment capacity
dvar boolean  Xi[DKPCs];

//if product i is available in the DK deopts in the problem time period
dvar boolean  Zi[DKPCs];

//Formulation
//Total Cost
dexpr float TotalStorageCost=sum (i in DKPCs)(Yi[i]+Ki[i]*Xi[i]-1/2*Di[i]*Xi[i])*Hi[i];
dexpr float TotalLostSaleCost=sum (i in DKPCs)(1-Zi[i])*(Di[i]-Ki[i])*Si[i]*Pi[i];
dexpr float TotalSmallProductsVolume= sum (i in SDKPCS)Vi[i]*Yi[i];
dexpr float TotalBigProductsVolume= sum (i in BDKPCs)Vi[i]*Yi[i];



minimize TotalStorageCost+TotalLostSaleCost;


subject to {

const1: forall (i in SDKPCS, j in 1..1){
                                                Vi[i]*Yi[i]<=Cj[1];}

const2: forall (i in BDKPCs, j in 2..2){
                                                Vi[i]*Yi[i]<=Cj[2];}

const3: forall (i in DKPCs){
                                                Yi[i]<=M*Xi[i];}

//const4: forall (i in DKPCs){                          
//                                              Ki[i]-Di[i]<=M*(1-Xi[i])-1;}

const5: forall (i in DKPCs){
                                                Ki[i]-Di[i]<=M*Zi[i]-1;}

const6: forall (i in DKPCs){                    
                                                Xi[i]*(Di[i]-Ki[i])<=Yi[i];}

const7: forall (i in DKPCs){                    
                                                Yi[i]<=M*Zi[i];}

const8: forall (i in DKPCs){
                                                (Di[i]-Ki[i])*Zi[i]<=M*Xi[i];}                                              

const9: forall (i in DKPCs){    
                                                Yi[i]>=0;}}

execute DISPLAY {
      writeln("TotalStorageCost=", TotalStorageCost);
      writeln("TotalLostSaleCost=",TotalLostSaleCost);
      writeln("TotalSmallProductsVolume=",TotalSmallProductsVolume);
      writeln("TotalBigProductsVolume=",TotalBigProductsVolume);

        }

并且数据如下：

 I=10;
 S=3;

Cj=[2,500];

Hi=[38  33  23  23  23  33  43  43  47  41];

Vi=[0.02    0.03    0.01    0.38    1.02    1.86    0.48    1.00    1.31    1.19];

Si=[63  81  174 119 157 177 125 101 97  176];

Pi=[0.83    0.69    0.10    0.07    0.51    0.20    0.92    0.60    0.32    0.33];

Ki=[20  24  13  22  16  24  13  12  20  13];


Di=[67  20  212 406 417 423 134 425 103 447];

M=999999999999999999;

Answer 1

的确。我的建议：关闭presolve。

添加

execute
{
  cplex.preind=0;
}

在模型的开头

加号，如果您使用datacheck 2

execute
{
  cplex.datacheck=2;
}

您会得到

CPLEX警告1041：在约束50中，变量'Xi（1）'具有一个 系数为1e + 18，请考虑使用指标。

因此，可以使用逻辑约束来代替使用大的M。

如果x是二进制决策变量，y是整数决策变量，则可以在OPL中编写

(x==(y>=7));