The Prize-collecting Scheduling Problem with Deadlines

We study a prize-collecting single machine scheduling problem with hard deadlines, where the objective is to minimise the difference between the total tardiness and the total prize of selected jobs. This problem is motivated by industrial applications, both as a standalone model and as a pricing problem for column generation approaches to parallel machine scheduling problems. It is handled through the use of exact approaches, in the form of a Branch and Bound (B&B) algorithm and an Integer Linear Programming (ILP) formulation. The B&B and ILP formulation are compared in their efficiency on randomly generated benchmark instances.