Deterministic Method for Input Sequence Modification in NEH-Based Algorithms

Scheduling of production jobs falls into the area of planning, which, according to Henri Fayol’s conception, is one of the basic functions of management. The permutation flow-shop scheduling problem (PFSP) with makespan criterion is one of the most studied scheduling problems in the area of scheduling theory and applications. The most-known polynomial complexity method for solving this complex problem is the Nawaz-Enscore-Ham (NEH) deterministic constructive algorithm. The subject literature shows that the results of NEH strongly depend on the input sequence of jobs. In this paper, we propose a new method to build the input sequence of jobs for NEH-based heuristics. The proposed Turn-off-Machine (ToM) method and its generalized version ToM+ (which has the feature to produce a set of input sequences that can be used in population-based optimization methods) compute the total processing time of jobs by virtually “turning off” one machine. The ToM+ method is one of a few deterministic methods for modifying the input sequence, and is the first one that modifies the input sequence based on individual machine processing times. Extensive numerical experiments on standard Taillard and VRF benchmarks show the good efficiency of the proposed method in solving PSFP with makespan criterion. The method improved the performance (measured using ARPD) of the NEH-based algorithms by up to nearly 35%. Moreover, by combining ToM+ method, SM
$\alpha $
P+, N-list, and
$vN$
-list technique, it was possible to improve the results of the original NEH algorithm by up to nearly 50% (the method outperformed most of the NEH-based methods). This confirms that creating an adequate input sequence is of great importance for the performance of NEH-based algorithms.