In a JSSP problem, a set of machines M = {Mj | j = 1, 2, . . ., m} and a set of jobs J = {Ji | i = 1, 2, . . ., n} are considered. Each job has a sequence of operations O = {Ok|k = 1, 2, . . ., l}, and these n jobs (i.e., all the operations of these n jobs) have to be processed on m machines. Job splitting is not allowed, and the operations are non-pre-emptible, which means temporary interruption of an operation is not allowed after it has started. Each machine only performs one operation at a time, and each operation is performed only once on one machine.
JSSP aims to find a feasible assignment (schedule) of all the operations on the given machines with optimized objectives. Depending on the goals of the decision makers, different objectives are used. In the single objective JSSP problem, only one criterion (objective) is considered, while multi-objectives are considered in the MOJSS problem. In this paper, makespan is the objective considered for SOJSSP. Unlike SOJSSP, more than one objective is explored simultaneously in the MOJSSP as merely considering one objective is not sufficient for some situations. The optimization goal for MOJSSP is to find a set of best compromising solutions in the form of alternative trade-offs instead of generating a single optimum. Simultaneous consideration of several objectives in MOJSSP is more challenging.
The optimization goals for SOJSSP and MOJSSP considered in this research are as follows: