In recent decades, many studies have been done on scheduling problems. In these problems, there is a set of accepted orders and the goal is to find a sequence of orders to optimize the desired criteria. But it should be noted that prior to the issue of scheduling, order selection has a great importance. Since simultaneous decision on scheduling and acceptance of orders causes more coordination between production and sales department, "order acceptance and scheduling" problem were discussed that considers the two scheduling and order acceptance processes simultaneously. In many cases, customers tend to take a set of their orders to one company. They are not willing to take some of these orders to an organization and the others to another one. This assumption is added to the "order acceptance and scheduling" and new issue in scheduling was introduced that is called "customer’s order acceptance and scheduling". The new problem consider customer acceptance and order scheduling simultaneously. In this study, the customer is discussed. This means the entire customer's order is accepted or all of his orders are rejected. The goal is to choose a set of customers and schedule their orders that results in the highest total profit. We consider a customer’s order acceptance and scheduling problem and total weighted tardiness as a penalty function. We develop a heuristic algorithm and two branch and bound procedure with dominance rules, upper bound and lower bound. 2650 problems for first branch and bound and 3080 problems for second branch and bound are solved. Computational results show if the number of customer orders is in the intervals [1, 1], [5, 1] and [9, 1] first branch and bound procedure solves up to 26, 14 and 10 customers and second branch and bound solves up to 22, 16 and 13 customers.