Minimize Total Completion Time, Total Number of Tardy Jobs, and the Range of Lateness for Single Machine Scheduling problems

الملخص

Machine scheduling challenges are growing more intricate and dynamic. The scale and complexity of these problems demand the creation of approaches and solutions that can deliver satisfactory outcomes within an acceptable timeframe. In response, this paper introduces a novel mathematical framework tailored to multi-objective functions, focusing on single-machine scheduling issues by minimizing the discounted total completion time (), the total number of tardy jobs (), and the range of lateness time () denoted or CUR-TC. Also, minimizing the sum of total completion time (), the total number of tardy jobs (), and the range of lateness time () denoted or CUR-TO. In this paper, we prove the existence of an efficient sequence for problem 1//, where jobs are sorted in ascending order based on their processing times. Certain specific cases are highlighted to provide efficient and, in some instances, optimal solutions to the problem under consideration. The dominance rule can be used to solve problems to improve them and find efficient solutions. Accordingly, we proposed two heuristic methods for solving search problems. These are two fast methods for finding (near-optimal) solutions to optimization problems with the least possible number of tables, in comparison to the complete enumeration method and the branch and bound method. The first method is based on dominance rules, while the second method is based on MST and SPT rules.