Maximizing the profit in customer's order acceptance and scheduling problem with weighted tardiness penalty

In recent decades, many studies have been done on scheduling problems and one of its issues is “order acceptance and scheduling” that deals with simultaneous decision on the rejection or acceptance of orders, and sequencing them. This causes more coordination between production and sales department. In many cases, customers tend to take all their orders to one company. They are not willing to take some of their orders to an organization and the others to another one. In this study, the customer is discussed. This means that, all orders of a customer must be considered in decision process. In other words, the entire customer's order is accepted or all of his orders are rejected. It can be noted as customer acceptance or rejection. We consider an order acceptance and scheduling problem, in which a pool of customers with number of orders exists. Total weighted tardiness is considered as penalty function. The goal is to choose a subset of customers and schedule their orders that results in the highest total profit. The problem has been shown to be strongly NP-hard. We develop a branch and bound procedure with capability of solving instances up to 10 customers with 50 jobs within 1-hour limit time.