Publication

Abstract : This study addresses a research problem on scheduling of a diffusion furnace (a Batch Processing Machine) in the wafer fabrication area of semiconductor manufacturing industry with incompatible job-families, dynamic job-arrivals, and non-agreeable release times and due-dates to optimize each one of the due-date based scheduling objectives: Total Weighted Tardiness (TWT), Number of Tardy Jobs (NT), On Time Delivery (OTD) rate, Total Earliness/Lateness (TE/L) and Maximum Lateness (Lmax). For the research problem considered in this study and for each one of the due-date based scheduling objectives, (0-1) Mixed Integer Linear Programming (MILP) model is developed. Appropriate ‘LINGO’ set code is developed to generate each of the proposed five MILP models for any given data. Using LINGO set code, a numerical example is solved for each one of the due-date based scheduling objectives to validate the respective proposed models. Then a set of numerical examples are solved for each one of the due-date based scheduling objectives and the computational time required to get the optimal solution for each of the numerical examples is observed. From the analysis of the computational time required to optimize each of the scheduling objectives, it is observed that when the size (number of job) of the problem increases the computational time follows non-deterministic and non-polynomial, which indicates that the research problem considered in this study to optimize each one of the due-date based scheduling objectives: TWT, TE-L, NT, Lmax and OTD rate is NP hard. In addition to that, the inter-relationship on the performance between the due-date based scheduling objectives: TWT, NT, OTD rate, TE/L and Lmax has been analyzed empirically. One of the utility of the proposed mathematical model is that the learning in analyzing the optimal solutions for various small scale problems can provide a lot of insights and these could be used while developing an alternate method such as heuristic algorithm. Another utility is that these proposed mathematical models could be used as bench mark solution procedure for any alternate methods at least for small scale problems.