exact algorithm

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.

The heterogeneous fixed fleet open vehicle routing problem (HFFOVRP) is one of the most significant extension problems of the open vehicle routing problem (OVRP). The HFFOVRP is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. In this problem, the vehicle doesn’t return to the depot after serving the last customer. Because of its numerous applications in industrial and service problems, a new model of the HFFOVRP based on mixed integer programming is proposed in this paper. Furthermore, due to its NP-hard nature, an ant colony system (ACS) algorithm was proposed. Since there were no existing benchmarks, this study generated some test problems. From the comparison with the results of exact algorithm, the proposed algorithm showed that it can provide better solutions within a comparatively shorter period of time.