CPLEX：如何在求和中使用数组？

Question

整数规划。 我尝试在 Cplex 中建模以下约束：

∑i ∑(τ=s-Dur(i)+1)to s x_(i,r,t,τ) ≤1, ∀r,∀t,∀s]

其中 x_(i,r,t,s) 是决策变量。 变量τ=s-Dur(i)+1 用作辅助变量。 无法对包含数组的总和进行建模。谢谢。

 range I = 1..operations;
 range J = 1..surgeons;
 range T = 1..timeBlock;
 range S = 1..timePeriod;
 range R = 1..room;

int Duration[I] =...;


//DVars
dvar int assignment[I][R][T][S] in 0..1;

//Objective function

maximize sum (i in I, r in R, t in T, s in S) (Duration[i] * assignment[i][r][t][s]);


// constraint
forall (r in R, t in T, s in S)
{
sum(i in I, s-Duration[i]+1 in s) (assignment[i][r][t][s-Dur[i]+1]) <= 1;
}

Answer 1

我会将您的约束重写为：

sum(i in I: s-Duration[i]+1 in S) (assignment[i][r][t][s-Duration[i]+1]) <= 1;

还有：

int operations=2;
int surgeons=3;
int timeBlock=2;
int timePeriod=2;
int room=4;
range I = 1..operations;
range J = 1..surgeons;
range T = 1..timeBlock;
range S = 1..timePeriod;
range R = 1..room;

int Duration[i in I] =i;


//DVars
dvar int assignment[I][R][T][S] in 0..1;

//Objective function

maximize sum (i in I, r in R, t in T, s in S) (Duration[i] * assignment[i][r][t][s]);

subject to
{
// constraint
forall (r in R, t in T, s in S)
{
sum(i in I: s-Duration[i]+1 in S) (assignment[i][r][t][s-Duration[i]+1]) <= 1;
}
}