ORIGINAL ARTICLE A new neuro-dominance rule for single-machine tardiness problem with double due date Tarik Cakar • Ras ¸it Ko ¨ker • Ozkan Canay Received: 2 April 2014 / Accepted: 8 December 2014 Ó The Natural Computing Applications Forum 2015 Abstract In this study, the single-machine total weighted tardiness scheduling problem with double due date has been addressed. The neuro-dominance rule (NDR-D) is proposed to decrease the total weighted tardiness (TWT) for the double due date. To obtain NDR-D, a back-propa- gation artificial neural network was trained using 12,000 data items and tested using another 15,000 items. The adjusted pairwise interchange method was used to prepare training and test data of the neural network. It was proved that if there is any sequence violating the proposed NDR-D then, according to the TWT criterion, these violating jobs are switched. The proposed NDR was compared with a number of generated heuristics. However, all of the used heuristics were generated for double due date based on using the original heuristic (ATC, COVERT, SPT, LPT, EDD, WDD, WSPT and WPD). These generated compet- ing heuristics were called ATC1, ATC2, ATC3, COV1, COV2, COV3, COV4, EDD1, EDD2, EDD3, WDD1, WDD2, WDD3, WSPT1, WSPT2, WSPT3, WPD1, WPD2, WPD3 and WPD4. The arrangements among the heuristics were made according to the double due date. The proposed NDR-D was applied to the generated heuristics and metaheuristics, simulated annealing and genetic algorithms, for a set of randomly generated problems. Problem sizes were chosen as 50, 70 and 100. In this study, 202,500 problems were randomly generated and used to demonstrate the performance of NDR-D. From the com- putational results, it can be clearly seen that the NDR-D dominates the generated heuristics and metaheuristics in all runs. Additionally, it is possible to see which heuristics are the best for the double due date single-machine TWT problems. Keywords Single-machine scheduling  Total weighted tardiness  Neuro-dominance rule  Double due date 1 Introduction Companies need to place much emphasis on coordinating priorities through functional fields in order to survive in a strongly competitive commercial environment. The new neuro-dominance rule (NDR-D) provides sufficient condi- tions for local optimality for a single-machine total weighted tardiness (TWT) problem. The single-machine TWT problem is presented as 1|| P w i T i . The literature survey for this paper has primarily concentrated on single- machine TWT and the same problem with due date. Sub- sequently, the same problem solved using artificial intel- ligence methods was reviewed and reported in this paper. Hsu et al. [1] focused on the analysis of single-machine scheduling and due date assignment problems based on position-dependent processing time. In their paper, two frequent due date assignment methods and two generally positional deterioration models are presented. The target functions include the cost of changing the due dates, the total cost of positional weight earliness and the total cost of discarded jobs which cannot be completed by their due T. Cakar (&) Engineering Faculty, Department of Industrial Engineering, Sakarya University, 54187 Adapazarı, Turkey e-mail: tcakar@sakarya.edu.tr R. Ko ¨ker Technology Faculty, Department of Electrical and Electronics Engineering, Sakarya University, 54187 Adapazarı, Turkey O. Canay Engineering Faculty, Department of Computer Engineering, Sakarya University, 54187 Adapazarı, Turkey 123 Neural Comput & Applic DOI 10.1007/s00521-014-1789-4