We present two new mixed integer programming formulations for the order acceptance and scheduling problem in two machine flow shops. Solving this optimization problem is challenging because two types of decisions must be made simultaneously: which orders to be accepted for processing and how to schedule them. To speed up the solution procedure, we present several techniques such as preprocessing and valid inequalities. An extensive computational study, using different instances, demonstrates the efficacy of the new formulations in comparison to some previous ones found in the relevant literature. 
Order acceptance and scheduling problems in two-machine flow shops: New mixed integer programming formulations