A new multi-objective scheduling problem on batch parallel machines with maximum allowable incompatibility for jobs

Science development and industry progress motivate researchers to solve the problems of the real world. This paper presents a new multi-objective mathematical model on identical batch processors arranged in parallel in order to minimize three objective functions including time, cost and jobs incompatibility simultaneously. The concept of jobs incompatibility used to classify the previous studies can be considered in many different ways. Since the jobs have been divided into compatible or incompatible ones, we should consider a certain parameter (i.e., maximum allowable incompatibility of each job), then jobs are assigned into batches by observing the relative constraints. Because of its impact on other functions, we express it as a new objective. The presented model is solved for a small-sized problem by the ε-constraint approach coded in GAMS software. By using the data envelope analysis (DEA) method, the most efficient optimal-Pareto solution is determined among all Pareto solutions.