CPLEX / OPL模型-具有子集索引的約束

Question

我當前正在使用IBM ILOG CPLEX Optimization Studio編程CPLEX / OPL模型。 我在使用包含子集並依賴於另一個參數/變量的總和或索引時遇到問題，例如，檢查以下約束：注意2,3,4,8）。

誰能幫助我適當地納入這些限制？

請找到隨附的源代碼：

  //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

目前尚不清楚您的問題是什么，但我想您的問題是與在約束2中對諸如product（j）之類的事物建模有關。嘗試對它們使用集-因此在每個產品系列中創建一組產品集。 在安裝過程中提供的OPL示例中有此示例。 例如，在examples \\ opl \\ models \\ AssemblySequencing \\ Sequence模型中

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

所以你可以做類似的事情，例如

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

編輯：使用新結構...嘗試類似的方法：

 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));

還有許多其他方法可以執行這種數據結構，某些方法可能更有效，某些方法從業務角度來看可能更有意義。 我個人喜歡處理一組事物，尤其是處理元組。 了解數據結構類型以及如何在OPL中組合它們，因為擁有正確的數據結構總是可以幫助您建模。