Efficient, Non-Dominated, or Pareto Optimal Solution

A solution x°eS to MCMP is said to be efficient if/t(x) /i(x ) for some, xeS implies that (x) fj(x9) for at least one other index/. More simply stated, an efficient solution has the property that an improvement in any one objective is possible only at the expense of at least one other objective. A dominated 

NOTE Even though the solution of MCMP reduces to finding the efficient set, it is not practical because there could be an infinite number of efficient solutions. 

Multiple Criteria Decision Making in Supply Chain Management 

An ideal solution is the vector of individual optima obtained by optimizing each objective function separately, ignoring all other objectives. In Example 2.4, the maximum value of Zj, ignoring Zj, is 26 and occurs at point D. Similarly, maximum Zj of 15 is obtained at point C. 

NOTE One of the popular approaches to solving MCMP problems is to find an efficient solution that comes as close as possible to the ideal solution. It is similar to the Lj, metric method discussed earlier. We will discuss this approach later in Section 2.12. 

---