In justify; TEXT-INDENT: 14.2pt; MARGIN: 0in 0in 0pt; unicode-bidi: embed; DIRECTION: ltr" But in many situations, different jobs may have different customers, that the difference in their needs applies various objectives to the system. Therefore, in many cases, applying an objective function for all the jobs is not logical and evaluating them is not the same. In multi-agent scheduling, there are a number of different customers, each with several jobs, for the given number of sources. In literature, these customers are called agents. In such problems, there are several agents which have received special attention. Each agent consists of a cost function that only depends on the sequence of its jobs. Thus, having only one general objective function is not considered and each answer should be taken into account according to the function of each agent. In this thesis, two-agent single machine scheduling problem is studied with the objective of minimizing total weighed tardiness for jobs belonging to agent 1, so that the maximum tardiness of second agent is not more than a certain amount. To solve the problem above, two mathematical models and a backward branch and bound procedure with four theorems, lower bound, upper bound, and five dominance rules is presented. Computational results for 2250 generated instances show that the proposed procedure is able to solve 96.66% of instances. Moreover, it is able to solve up to 65 jobs for instances with 2 to 1 ratio of agent 1 and 2, up to 45 instances with equal ratio of agent 1 and 2, and up to 35 instances with 1 to 2 ratio of agent 1 and 2 in 3600 seconds limit of time.