A Hybrid Approach of DEA and Support Vector Machine for Decision Making in Optimistic and Pessimistic Environment

Abstract

Data envelopment analysis (DEA) developed by Charnes, Cooper and Rhodes in 1978, is a powerful non- parametric technique used to measure the relative performance of similar organizations. This technique is used to compare the relative performance of several homogeneous units called decision making units (DMUs). DEA is based on linear programming approach.The presence of multiple inputs and outputs is the great advantage of DEA over other techniques which measure the performance of organizations.This is because, generally, multiple inputs and outputs are not comparable, but it also makes the technique a little bit difficult. The CCR model (Charnes et al., 1978) and the BCC model (Banker et al., 1984) are some standard DEA models which are based upon the assumption of input minimization and output maximization. However,DEA technique requires accurate input and output data for its successful implementation. But data of real- life problems is not always accurate or crisp. For instance,data in manufacturing sector, banking sector and health care sector is usually complex or imprecise due to lack of some information or some other reasons. So, to solve these types of problems, input and output data is represented by fuzzy numbers or interval numbers. Machine learning is an application of artificial intelligence (AI) that provides systems the ability to automatically learn and improve from experience without being explicitly programmed. Machine learning is of three types: Supervised Machine Learning, Semi-Supervised Machine Learning and Unsupervised Machine Learning. SVM is a supervised machine learning algorithm that is used for the classification, regression or other purposes like outlier detection. It is a fast and dependable classification algorithm that performs very well with a limited amount of data. The goal of the SVM is to train a model that assigns new unseen objects into a particular category. Over the last thirty years, the organization failure prediction is an important issue that has attracted the intention of wide academic studies. Organization failure refers to situation when bill is overdrawn, the company is not able to pay the wages etc. So, the objective of our present study is to use the optimistic and pessimistic efficiencies of several DMUs calculated by using proposed DEA models and SVM technique to predict the accuracy of organization failure. In the proposed study (IDEA-SVM), DEA technique use the interval data to calculate the optimistic and pessimistic efficiencies. Further, using SVM approach, prediction of efficiencies of organization is estimated. The summary of thesis is given below. Chapter 1 is introductory type. This chapter gives the brief introduction of data envelopment analysis and its various approaches. It also represents the introduction of machine learning along with its different categories.It gives the brief review of Support vector Machine which is a widely used algorithm of supervised machine learning. Chapter 2 includes the basic definitions and important theorems related to convex optimization problem. It also determines the dual of convex optimization problem and presents the brief review of CCR model developed by Charnes, Cooper and Rhodes in 1978. It presents the Charnes-Cooper transformation which transform the Fractional Programming Problem (LFP) into Linear Programming Problem (LPP). Chapter 3 includes the working of SVM and basic definitions related to it. It represents the properties of maximal margin method and various metrics to compare the hyperplanes. Finally, it derives the SVM optimization problem and presents the relationship between primal and dual of SVM optimization problem. In Chapter 4, DEA models from optimistic as well as pessimistic point of view are presented. In these models, interval data is used. Then on these models SVM technique is applied and finally present IDEA-SVM approach in optimistic environment and IDEA-SVM approach in pessimistic environment.