Sequencing and scheduling are the forms of decision-making approach that play a vital role in the automation and services industries. Efficient scheduling can help the industries to achieve the full potential of their supply chains. Conversely, inefficient scheduling causes additional idle time for machines and reduces productivity, which may escalate the product price. This study aims to find the most effective algorithm for solving sequencing and scheduling problems in a non-preemptive flow shop environment where the objective functions are to reduce the total elapsed time and idle time. In this research, four prominent exact algorithms are considered and examined their efficiency by calculating the ‘total completion time’ and their goodness. In order to demonstrate the comparative analysis, numerical examples are illustrated. A Gantt chart is additionally conducted to exhibit the efficiency of these algorithms graphically. Eventually, a feasible outcome for each condition has been obtained by analyzing these four algorithms, which leads to getting a competent, time and cost-efficient algorithm.