Unification of STN and RTN based models for short-term scheduling of batch plants with shared resources

• A novel resource balance is presented that treats utility resources similar to material states.
• Proposed unit-specific alignment of utility related tasks resulting in reduction of events.
• Unification of all resources done for the first time for unit-specific event based approaches.
• The framework offers unification of STN and RTN based models with similar equations.
• Proposed better ways to handle shared storage tanks, multiple order problems.

State-task-network (STN) and resource-task-network (RTN) representations are popularly used for formulating mathematical models of scheduling problems. In contrast to STN representation, RTN representation offers unified treatment for different resources such as processing and storage units, material states and utilities. In global-event (or single-time grid) based models processing tasks occurring in different units are aligned globally, hence, they explicitly do not distinguish handling of resources such as utilities and material states. While, unit-specific event (or multi-time grid) based models offer better computational performance due to requirement of lesser number of events, but there is no unified treatment for handling of utility or discrete resources due to heterogeneous location of events. Usually, global alignment is enforced for different tasks that use the same utility, while for material states unit-specific alignment is used. Hence, for unit-specific event-based models it is desirable to have a unified framework for handling of material states and utility resources, which, not only offers a unification of STN and RTN formulations, but, potentially can result in further reduction in the number of events required to find optimal solutions. In this work, we propose a unified framework and develop two unit-specific event-based approaches for STN and RTN representations by incorporating a novel resource balance that offers these two unifications. The key features of the proposed approach are: (i) all resources are treated in unified way for the first time, (ii) simplified handling of multiple orders using the concept of active task, (iii) handling of shared storage problems in non-aggregated storage tanks by considering explicit storage tasks. The proposed features are demonstrated on few benchmark examples from literature.