MIP modeling of energy-conscious FJSP and its extended problems:From simplicity to complexity

Regarding four different energy-conscious scheduling problems, namely, flexible job shop scheduling problem (FJSP), FJSP with transportation time (FJSP-T), FJSP with sequence-dependent setup time (FJSP-SDST), and FJSP with both transportation time and sequence-dependent setup time (FJSP-SDST-T), thirteen mixed integer programming (MIP) models are developed to optimally solve the problems. These models include three nonlinear models and ten linear models, and they are designed from three different modeling ideas, namely, sequencebased modeling idea, adjacent sequence-based modeling idea and machine-position based modeling idea. For each modeling idea, the MIP models are formulated by following the principle: from the simplest FJSP to the most complex FJSP-SDST-T. Regarding nonlinear MIP models, different linearization techniques are used to obtain different linear models. Comparison experiments are conducted from both size and computational complexities to evaluate the models of different modeling ideas for the same problem, the models of the same modeling ideas for the same problem, the models of the same modeling idea for different problems and the models of different modeling ideas for different problems. Experimental results indicate the effectiveness and differences of the proposed MIP models. Specifically, in terms of the average percentage deviation of obtained solution (APE), for FJSP, the machine-position based model with APE being 0.30 outperforms the sequence and adjacent sequence-based models with APE being 0.34 and 3.0 respectively. For FJSP-T, the best sequence-based model with APE being 0.22 outperforms the best machine-position based model with APE being 0.79. For FJSPSDST, the machine-position based model with APE being 0.06 outperforms adjacent sequence-based model with APE being 1.35.