Tham khảo tài liệu 'multiprocessor scheduling part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 230 Multiprocessor Scheduling Theory and Applications Formulations naturally include constraints and objectives. These differ according to the setting studied. Often all constraints are not formally considered. Some of these are addressed in an approximate manner at a lower level in the decision making. In the integrated scheduling problem addressed by a number of authors classical objectives are often used. We mean by classical objectives system objectives and due date objectives Graves et al. 1981 . Common Objective Functions Commonly used objectives in the production scheduling literature include Minimize the makespan Cmax Minimize the maximum tardiness Tmax Minimize the total tardiness STj Minimize the total weighted completion times Swj Cj Minimize total completion times Cj Minimize the total discounted weighted completion times wj 1-re-rcj dt Minimize total weighted tardiness EwjTj Minimize the number of tardy jobs EUj Minimize the weighted number of tardy jobs EwjUj Objectives used in material handling scheduling problems are also numerous. Examples follow Maximize throughput Minimize dead heads Maximize the utilization or the average utilization of material handling equipment Minimize the number of utilized equipment Minimize the average flow time for jobs Maximize the production volume or the average production volume average number of finished jobs Minimize the maximal length of queues Minimize the average waiting time Minimize the total traveled distance Minimize the transportation time Minimize the jobs completion time Minimize the total lateness Minimize the makespan Minimize the number of tardy jobs Minimize the work in process Most of the literature addresses mono-objective problems. Bagchi 1989 solves a multicriteria single machine problem. Other researchers also solved multi-criteria single machine problems. However material handling system constraints were not considered. This situation proposes that the problems addressed corresponded to a .