Order acceptance and scheduling on unrelated parallel machines

This paper considers an order acceptance and scheduling problem on unrelated parallel machines. The objective is to select and schedule a subset of accepted orders that maximizes the total profit, which is defined as the sum of revenues of all the accepted orders minus their weighted tardiness penalties. We formulate the problem as a mixed-integer linear programming model. To solve this strongly NP-hard problem, we also propose a heuristic algorithm based on the Lagrangian relaxation technique and some greedy search operations.