是否可以在 CPLEX 中对 MILP 执行灵敏度分析？

Question

我正忙着尝试在 CPLEX IDE 中对我的 MILP 问题执行灵敏度分析。我在我的代码中收到一个错误，因为它回复说此脚本不适用于 MILP 问题。

有人知道另一种进行（部分）敏感性分析的方法吗？或者知道我的代码有什么问题吗？

这是我用来查找约束的松弛变量的代码。

Mod

int Time = ...;
int Prod = ...;

 range T=0..Time;
 range J=1..Prod;

 // Parameters
 int d [T][J] = ...; // demand in period t  
 int K[J]  = ...; // fixed order cost in period t 
 int h  = ...; // unit holding cost in period t 
 int p  = ...; // fixed cost of increasing WH size in period t
 int q  = ...; // fixed cost of increasing WH size in period t
 int e  = ...; // variable cost of increasing WH size in period t
 int c  = ...; // variable cost of decreasing WH size in period t
 int r  = ...;  // WH rental cost per unit in period t 
 
dvar int+ x[T][J]; //order quantity in period t 
dvar int+ i[T][J]; //inventory lvl at the end of period t 
dvar int+ w[T]; // warehouse size at the end of period t 
dvar int+ u[T]; // warehouse size expansion at beginning of period t 
dvar int+ v[T]; // warehouse size contraction at beginning of period t 
dvar boolean y[T][J]; // binary variable for ordering in period t     dvar int+ y[T][J];             //// this constraint assumes that only 1 order can be placed in t 
dvar boolean z1[T]; // binary variable for WH expansion in period t 
dvar boolean z2[T]; // binary variable for WH contraction in period t 
 
 //objecTive funcTion
dexpr int Cost = sum(t in T,j in J)
(K[j]*y[t][j]+h*i[t][j]+p*z1[t]+e*u[t]+q*z2[t]+c*v[t]+r*w[t]);
 
minimize Cost;

//constraints

subject to {

forall(t in 1..Time, j in J) {
  
c1: i[t-1][j] + x[t][j] - d[t][j] == i[t][j];    //Inventory balance constraint


c2: w[t-1] + u[t] - v[t] == w[t];   //warehouse balance constraint


c3:sum(j in J)i[t][j] <= w[t];   // inventory should be max. the warehouse level


c4:x[t][j] <= (sum(t1 in t..Time)d[t1][j])*y[t][j];  // dtT Cumulative demand from t to end T 


c5:u[t] <= (sum(t in T)d[t][j])*z1[t]; // Total demand from 1 to T * z1  u[t] <= dtot*z1[t];


c6:v[t] <= (sum(t in T)d[t][j])*z2[t]; // Total demand from 1 to T  *z2   v[t] <= dtot*z2[t]; or v[t] <= (sum(t in T,j in J)d[t][j])*z2[t];

c7:w[t] <= 14000; // WH max available capacity 

c8:x[t][1] <= 8000; // production capacity prod 1 in a period t 
c9:x[t][2] <= 9000; // production capacity prod2 in a period t 

c10:i[0][1]==100;   // initial inv prod 1
c11:i[0][2]==500;   // initial inv prod 2
c12:w[0]==1000;  //initial warehouse size 
}   
}
//display solution identifier

// Post Processing Code
execute {
   if(cplex.getCplexStatus()==1){ 
  writeln("Slack variable for c1=",c1.slack);
  writeln("Slack variable for c2=",c2.slack);
  writeln("Slack variable for c3=",c3.slack);
  writeln("Slack variable for c4=",c4.slack);
  writeln("Slack variable for c5=",c5.slack);
  writeln("Slack variable for c6=",c6.slack);
  writeln("Slack variable for c7=",c7.slack);
  writeln("Slack variable for c8=",c8.slack);
  writeln("Slack variable for c9=",c9.slack);
  writeln("Slack variable for c10=",c10.slack);
  writeln("Slack variable for c11=",c11.slack);
  writeln("Slack variable for c12=",c12.slack); 
}
else {
   writeln("Solution not found");
 }  
}

数据

Time=4;
Prod=2;


 d = [[0,0],[1500,500],[4000,2000],[200,3000],[2000,2000]];
 K = [100000,200000]; // ordering costs
 h = 1; // holding costs 
 p = 300; // fixed cost increasing size
 q = 300; // fixed cost decreasing size
 e = 1; // variable costs per unit increase
 c = 2; // variable cost per unit decrease
 r = 4; // WH rent costs

Answer 1

您遇到错误，因为 c1 是约束数组而不是约束。

如果你写

//display solution identifier

range T1=1..Time;

// Post Processing Code
execute {
   if(cplex.getCplexStatus()==1){ 
  for (t in T1) for ( j in J)  writeln("Slack variable for c1=",c1[t][j].slack);
 
}
else {
   writeln("Solution not found");
 }  
}

相反，你会得到一个漂亮的显示

是否可以在 CPLEX 中对 MILP 执行灵敏度分析？

Is it possible to perform a sensitivity analysis in CPLEX fo a MILP?

analysis

cplex

slack

mixed-integer-programming