CPLEX/OPL 模型 - 具有子集索引的约束

Question

我目前正在使用 IBM ILOG CPLEX Optimization Studio 对 CPLEX/OPL 模型进行编程。我在使用包含子集并依赖于另一个 parameter/variable 的总和或索引时遇到问题，例如检查以下约束：NB 2,3,4,8).

任何人都可以帮助我正确地合并这些约束吗？

请查找附件中的源代码：

  //Parameter

int maxblock=...;                   //number of blocks (I)
int maxprodfam=...;             //number of product families (J)
int maxprod=...;                    //number of products (P)
int maxdemand=...;                  //number of demand elements (K)

range blocks=1..maxblock;
range prodfam=1..maxprodfam;
range products=1..maxprod;
range demandelements=1..maxdemand;

int startalpha[blocks]=...;     //earliest start time of block i
int endalpha[blocks]=...;       //latest completion time of block i
int prodtime[products]=...;     //unit production time for product p (a)
int minorsetup[products]=...;   //minor setup time per sub-lot of product p (s)
int majorsetup[prodfam]=...;        //major setup time for product family j (S)
int demand[products]=...;           //demand elements (d)

//Variablen

dvar int+ x[blocks][demandelements];    //quantity of demand element k satisfied from production in block i (x)
dvar boolean y[blocks][prodfam];        //product family assessment to blocks (y)
dvar boolean q[blocks][products];       //product assessment to blocks 
dvar boolean o[blocks];             //activation of blocks (e.g. if a prodfam is assignes to it)
dvar int+ alpha[blocks];                //start time block
dvar int+ duration[blocks];         //duration of block

 //Modell

minimize
alpha[maxblock]+duration[maxblock]; //objective function (minimize the makespan)

subject to {
 forall(i in blocks)
   NB1: //one product family assigned to each block
    sum(j in prodfam)
      y[i][j]==o[i];

 forall(i in blocks, j in prodfam)
   NB2: //production sub-lots
    sum(p in products(j))q[i][p]<=y[i][j]*abs(products(j));

 forall(i in blocks, k in demandelements(i))
   NB3: //product flow from block i into demand element k
    x[i][k]<=demand[k]*q[i][p(k)];

 forall(i in blocks)
   NB4: //block schedule
    duration[i]==sum(j in prodfam)majorsetup[j]*y[i][j]
    +sum(p in products)minorsetup[p]*q[i][p]
    +sum(k in demandelements(i))alpha[p(k)]*x[i][k];

 forall(i in 2..maxblock)
   NB5: //block starts when other block finished
    alpha[i]>=alpha[i-1]+duration[i-1];

 forall(i in blocks)
   NB6: //time window earliest start
    alpha[i]>=startalpha[i]*o[i];

 forall(i in blocks)
   NB7: //time window latest completion
    alpha[i]+duration[i]<=endalpha[i];

 forall(k in demandelements)
   NB8: //matching output and demand
    sum(i in blocks(k))x[i][k]==demand[k];
}

Answer 1

不清楚你的问题是什么，但我猜你的问题是与约束 2 中的 products(j) 之类的东西建模有关。尝试对这些使用集合 - 所以在中创建一组产品集合每个产品系列。作为安装的一部分提供的 OPL 示例中有这方面的示例。例如，在 examples\opl\models\AssemblySequencing\Sequence 模型中我们有

{string} computer[AllComputers] = ...;

所以你可以做类似的事情，例如

{int} productsInFamily[prodfam] = ...;

编辑：使用新结构...尝试类似的方法：

 forall(i in blocks, j in prodfam)
   NB2: //production sub-lots
    sum(p in productsInFamily[j])q[i][p]<=y[i][j]*abs(products(j));

还有许多其他方法可以实现这种数据结构，有些可能更有效，有些可能从业务角度来看更有意义。我个人喜欢处理事物集合，尤其是元组集合。了解数据结构类型以及如何在 OPL 中组合它们，因为拥有正确的数据结构总是有助于您的建模。

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