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Job-shop scheduling is the allocation of machines over time to perform a collection of jobs to minimize/maximize a specific performance measure while satisfying the operation precedence constraints, machine capacity constraints, processing time and ready time requirements, and the resources are machines and jobs. Job-shop scheduling belongs to the class of NP-complete problems. In this Book, for solving NP-complete problem Artificial neural network models have been applied. The main objective is to minimize the total weighted completion time of the jobs in the system that is the minimization of the makespan (Time needed to complete all jobs) time by using the heuristic method, which gives a high quality approximate solution in reasonable time.