C Rajendran

88In this chapter, we consider the development of mixed integer linear programming (MILP)-based classifier and linear programming (LP)-based classifiers for solving a classification problem. The conventional MILP-based/LP-based classifiers generally provide good results in terms of accuracy when the data set is linearly separable. However the challenge is to develop computationally efficient classifiers that can handle data that are not linearly separable. In this chapter, we propose a novel LP-based classifier that can address the classification of such data sets with multiple objectives. The salient contributions of the proposed LP-based two-phase classifier are in terms of treating the decision variables as unrestricted in sign; accounting for the contribution of attributes from their interaction effects and the contribution of attributes from their higher order polynomial degrees; treating the classification threshold/cut-off as a decision variable; converting the bandwidth of boundary of threshold to a crisp boundary with the consideration of multiple objectives; and finally the ability to find a nondominated set of solutions with respect to multiple objectives. Consequently, the proposed LP-based classifier is able to handle data that are not inherently linearly separable, unlike the conventional MILP-based and LP-based classifiers. To evaluate the performance of the proposed classifiers, we consider two data sets that are already available in the literature. We also compare the accuracy of all the proposed LP-based classifiers with the artificial neural networks, and the results indicate that one of the proposed LP-based classifiers (LP-based two-phase classifier) is able to give good results even when the data set is not linearly separable.

In this paper, we study the problem of transforming a job-shop layout into a flow-shop layout by introducing additional machines, so that all job-related operations can be processed in a flow-shop layout. The objective is to find the shortest sequence of machines, so that the overhead of introducing additional machines can be reduced. This transformation of job-shop layout into flow-shop layout has the advantage of automating the flow-line, which is an important step in digital manufacturing. The study first focuses on a special case (which is studied generally in the literature) where all the jobs would have the same and equal number of operations to be performed in a job-shop, but each job has a different machine routing when compared to other jobs. We propose a Mixed Integer Liner Programming (MILP) model for solving this special case. Further, in order to evaluate the performance of the proposed MILP model, we compare the same with an existing model in literature. From the results, we confirm that the proposed model is superior in terms of the CPU time, in solving the problem instances considered for the study. The study also extends this special case, and considers the generalized case where jobs could have different number of operations, and the study proposes a comprehensive MILP model for solving the generalized case.