On the state-task network: Time representations

To model and solve complex Supply Chain problems we study the relationship between the discrete- and continuous-time State-Task Network (STN) representations. We show that the first is a special case of the second. We also propose a new mixed-time representation where the time grid is fixed but processing times are allowed to be variable and span an unknown number of time periods. The proposed scheme accounts linearly for holding and backlog costs, can be extended to handle continuous processes, accounts for due dates at no additional computational cost, and handles variable processing times; i.e. it combines the modelling advantages of both discrete- and continuous-time STN models. Finally, we present strong cutting planes that are used to enhance the solution of the proposed MIP model.