Maximizing Total Profit in Two-agent Problem of Order Acceptance and Scheduling

In competitive markets, attracting potential customers and keeping current customers is a survival condition for each company. So, paying attention to the requests of customers is important and vital. In this paper, the problem of order acceptance and scheduling has been studied, in which two types of customers or agents compete in a single machine environment. The objective is maximizing sum of the total profit of first agent's accepted orders and the total revenue of second agent. Therefore, only the first agent has penalty and its penalty function is lateness and the second agent's orders have a common due date and this agent does not accept any tardy order. To solve the problem, a mathematical programming, a heuristic algorithm and a pseudo-polynomial dynamic programming algorithm are proposed. Computational results confirm the ability of solving all problem instances up to 70 orders size optimally and also 93.12% of problem instances up to 150 orders size by dynamic programming.