Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of pro...

In this paper, we propose a novel method using multiple-objective programming problems to answer the following question: if among a group of decision making units (DMUs), a subset of DMUs are required to merge and form a new DMU with specific input/output levels and a predefined efficiency target, how much should be the outputs/inputs of the merged DMU? This question answered according to the c...

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the sam...

We derive conditions on the functions ', , v and w such that the 0–1 fractional programming problem max x2f0I1gn 'ıv.x/ ıw.x/ can be solved in polynomial time by enumerating the breakpoints of the piecewise linear functionˆ. / D max x2f0I1gn v.x/ w.x/ on Œ0IC1/. In particular we show that when ' is convex and increasing, is concave, increasing and strictly positive, v and w are supermodular and...

In this paper we consider a global optimization approach for solving fuzzy fractional posynomial geometric programming problems. The problem of concern involves positive trapezoidal fuzzy numbers in the objective function. For obtaining an optimal solution, Dinkelbach’s algorithm which achieves the optimal solution of the optimization problem by means of solving a sequence of subproblems ...