Nowadays, because of intensive competition between the manufacturers, attracting costomers, satisfying and keeping them are vital for manufacturers participating in the competitive markets.Therefore, a problem with the name of “Order Acceptance and Scheduling” has been defined in the literature of operations research. But, it seems that in the all related studies, only one type of penalty function was considered for all the customers. However, in practice customers have different requests because of their different necessities. For example one customer may not accept tardy orders and another one may accept them by getting some money as penalty. In addition, it is possible that the earliness of orders is not important for one customer but another one may reward it. To simultaneously consider these cases, in this thesis the order acceptance and scheduling problem is integrated with another problem with the name of “Multi-Agent Scheduling” and the new integrated problem was solved. The multi-agent scheduling problem is defined as scheduling of some sets of jobs such that each set has its specific objective function. In this thesis the integration of the two mentioned problems was studied in the case of two-agent one,named as “two-agent order acceptance and scheduling”. For the first agent the total weighted lateness and for the second one the weighted number of tardy orders is considered as penalty function. To better understand the properties of the new problem, first, three special cases of it were investigated and it was attempted to propose some exact algorithms to solve them. The common assumptions of the first two cases are disallowing of the second agent orders and unity of the weight value of all orders. Besides, in the first case it was assumed that processing times of all agent one orders are equal and in the second case a common due date was considerd for the second agent. In the third case the only assumption is common due date of the second agent orders. Numerical experiments show the capability of proposed algorithms in solving the problem instances, such that the dynamic programming, which was developed for the first case,was capable of optimally solving the instances up to 60 orders in size and the proposed branch and price for the second case optimally solved all instances up to 110 orders in size. Besides, the proposed branch and price for the third case, solved all small processing time instances up to 150 orders in size and all large processing time instances up to 60 orders in size. After studing these there special cases, the problem was investigated in the general form and three integer programming modelswere developed to optimally solve it. One of thesemodels solved all instances up to 60 orders in size. But, because of high complexity of the problem in the general form, it is not expected to solve large size instances. So, in continue of the thesis, a meta-huristic algorithm was developed which is a hybrid of linear programming and genetic algorithm. The average deviation of this algorithm from optimal solution is lower than 0.21% up to 60 orders in size and its deviation from an upper bound is lower than 0.40% up to 150 orders in size.