Abstract
In this paper, we investigate some methods to solve one of the multi-criteria machine scheduling problems. The discussed problem is the total completion time and the total earliness jobs To solve this problem, some heuristic methods are proposed which provided good results. The Branch and Bound (BAB) method is applied with new suggested upper and lower bounds to solve the discussed problem, which produced exact results for in a reasonable time.
Highlights
There are many definitions for machine scheduling; scheduling problem is the allocation of resources over time to perform a collection of tasks
5.3 Comparison of the Results of P1-problem In Table-9, we show a comparison between the optimal results of Complete Enumeration Method (CEM)(F1) and the results of the heuristics Shortest Processing Time (SPT)-Minimum Slack Time (MST)-SCSE(F1), Dominance rule (DR)-SCSE(F1) and TREE(F1) n=4:10 for P1-problem
We noticed that MST for sum of earliness (MST-SE) is better than DR of Sum Earliness (DR-SE) for in accuracy and CPU-time
Summary
There are many definitions for machine scheduling; scheduling problem is the allocation of resources over time to perform a collection of tasks. Resources and tasks are called machine and jobs respectively and both of than can take many forms [1]. A schedule is called feasible schedule if it satisfies the two main constraints, and if it satisfies many requirements relating to the discussed problem type. The type of the problem is related to the machine environment, the job characteristics, and the criterion of optimality. There are many known exact and approximation solution methods to solve the Machine Scheduling Problem (MSP). The exact solutions are obtained using the Complete Enumeration Method (CEM), Branch and Bound (BAB) method, and Dynamic Programming (DP) method [3]
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