Scheduling concerns the allocation of limited resources to tasks over time. In manufacturing systems, scheduling is nothing but assigning the jobs to the available processors over a period of time. Our research focuses on scheduling in systems of parallel processors which is challenging both from the theoretical and practical perspectives. The system of parallel processors is a common occurrence in different types of modern manufacturing systems such as job shop, batch shop and mass production. A variety of important and challenging problems with realistic settings in a system of parallel processors are considered. We consider two types of processors comprising discrete and batch processors. The processor which produces one job at a time is called a discrete processor. Batch processor is a processor that can produce several jobs simultaneously by keeping jobs in a batch form which is commonly seen in semiconductor manufacturing, heat treatment operations and also in chemical processing industries. Our aim is to develop efficient solution methodologies (heuristics/metaheuristics) for three different problems in the thesis. The first two problems consider the objective of minimizing total weighted tardiness in cases of discrete and batch processors where customer delivery time performance is critical. The third problem deals with the objective of minimizing the total weighted completion time in the case of batch processors to reduce work-in-process inventory. Specifically, the first problem deals with the scheduling of parallel identical discrete processors to minimize total weighted tardiness. We develop a metaheuristic based on Ant Colony Optimization(ACO) approach to solve the problem and compare it with the available best heuristics in the literature such as apparent tardiness cost and modified due date rules. An extensive experimentation is conducted to evaluate the performance of the ACO approach on different problem sizes with varied tardiness factors. Our experimentation shows that the proposed ant conony optimization algorithm yields promising results as compared to the best of the available heuristics. The second problem concerns with the scheduling of jobs to parallel identical batch processors for minimizing the total weighted tardiness. It is assumed that the jobs are incompatible in respect of job families indicating that jobs from different families cannot be processed together. We decompose the problem into two stages including batch formation and batch scheduling as in the literature. Ant colony optimization based heuristics are developed in which ACO is used to solve the batch scheduling problem. Our computational experimentation shows that the proposed five ACO based heuristics perform better than the available best traditional dispatching rule called ATC-BATC rule. The third scheduling problem is to minimize the total weighted completion time in a system of parallel identical batch processors. In the real world manufacturing system, jobs to be scheduled come in lots with different job volumes(i.e number of jobs) and priorities. The real settings of lots and high batch capacity are considered in this problem. This scheduling problem is formulated as a mixed integer non-linear program. We develop a solution framework based on the decomposition approach for this problem. Two heuristics are proposed based on the proposed decomposition approach and the performance of these heuristics is evaluated in the cases of two and three batch processors by comparing with the solution of LINGO solver.