In nowadays growing competitive markets, surpassing the competitors by attracting, keeping and satisfying customers, is one of the most important issues of managers in manufacturing and service systems. Meeting due dates is one of the fundamental objectives in scheduling problems from customers viewpoint. Emerging methodologies like Just-in-time manufacturing has increased the importance of scheduling problems with these kind of due date-related performance measures. Most of early/tardy studies share the common feature that they consider min-sum criteria decreasing the average costs. However, there may exist large values of earliness or tardiness for some jobs that cause difficulties in production systems. In many cases, priority is given to balancing job costs by minimizing the maximum cost of the schedule of each job (min-max criteria). One of the criteria that can fulfill this objective is minimizing the sum of maximum earliness and tardiness. In classical scheduling problems, all jobs have to be evaluated by a specific performance measure, but in some cases, different customers with different requirements may oblige the system to make distinction between the jobs of each customer. Multi-agent scheduling problems has received growing attention in recent years, in which, each agent, owning a set of jobs, competes to perform its respective jobs on shared processing resources and wants to minimize a certain cost function. In this thesis, “Scheduling problems considering the weighted sum of maximum earliness and maximum tardiness penalties”, including single and two agent scheduling problems with unrestricted common due date and minimizing the weighted sum of maximum earliness and maximum tardiness penalties in a single machine, two machine flow shop and two identical parallel machines environments are studied, which in the two agent case, the objective is to minimize weighted sum of maximum earliness and maximum tardiness penalties of the first agent with the constraint that no tardy job is allowed for the second one. In this thesis, it was attempted to propose polynomial optimal algorithms for special cases of the problems by focusing on optimal properties, and for the remaining cases, it was attempted to investigate complexity and prove that they can be reduced to common problems in the literature. Also, for the two agent flow shop scheduling problem a heuristic algorithm and a branch and bound algorithm was proposed. In order to evaluate the performance of the proposed algorithm, some instances were randomly generated and solved. Numerical experiments showed the capability of proposed algorithm in solving 93.54% of generated instances up to 2000 jobs for the case than tardiness penalty is more important that earliness penalty and 96.11% of generated instances up to 700 jobs for the case that earliness penalty is more important than tardiness penalty