This paper gives a new application of DEA to evaluate the scheduling solutions of parallel processing. It evaluates the scheduling solutions of parallel processing using the non-convex DEA model, FDH model. By introducing each solution of parallel processing scheduling as a DMU with some relevant inputs and outputs this paper shows that how the most efficient schedule(s) can be identified.

The concept of trade-o reviews the rate of marginal substitution of inputs and outputs onto the e cient frontier; moreover, marginal rates of substitution (MRS) are important quantities for analysts and managers. In the current study, by changing Asmilds (2004) method, an algorithm has been found that can be used to calculate the marginal rate of the free disposal hull (FDH) model. An empirical study on 20 Iranian bank branches has been presented to illustrate the proposed approach.

In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) directional distance function through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH directional distance function. We prove that the proposed measures are translation invariant and unit invariant. In addition, we present effective enumeration algorithms to compute them. Our proposed measures have several practical advantages such as: (a) providing closest Pareto-efficient observed targets (b) incorporating the decision maker’s preference information into efficiency analysis and (c) being flexible in computer programming. We illustrate the newly developed approach with a real world data set.

In this paper, two methods named distance and triangle methods are extended to evaluate the quality of approximation of the Pareto set from solving bi-objective problems. In order to use evaluation methods, a bi-objective problem is needed to define. It is considered the problem of scheduling jobs in a hybrid flow shop environment with sequence-dependent setup times and the objectives of minimizing both the makespan and the total tardiness. The bi-objective genetic algorithm in literature is applied to solve this problem belongs to NP-hard class. In the structure of algorithm, 3 and 4 alternatives for dispatching rules and neighborhood search structure have been introduced respectively. Therefore, twelve algorithms are derived from a combination of dispatching rules and neighborhood search structures. After the execution of algorithms, efficient sets are compared through several evaluation methods. Computational results show that the FIFO rule is the best alternative for the dispatching rule in order to find the job sequence for the second to end stages.