further study on an extended shortest path problem a data envelopment analysis approach

Amirteimoori proposed an approach based on data envelopment analysis (dea) for  multiobjective path problems on networks whose arcs contain multiple positive and negative attributes [a. amirteimoori, an extended shortest path problem: a data envelopment analysis approach, applied mathematics letters 25 (2012) 18391843]. the approach is to define a relative efficiency for each arcs using dea models, and then to solve a longest path problem for obtaining a path with maximum efficiency. in this note, we focus on two drawbacks of the approach and illustrate them using examples. then, we propose remedies to eliminate them.