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(749a) A Generalized State-Space Model for Online Scheduling

Gupta, D., University of Wisconsin-Madison
Maravelias, C. T., University of Wisconsin-Madison
Due to disruptions or arrival of new information, an incumbent schedule can become suboptimal or even infeasible, thus motivating the need for online (re)scheduling (Gupta et al., 2016). Subramanian et al. (2012) proposed the first scheduling state-space model, providing a systematic way to account for different uncertainties as disturbances, viz., demand fluctuation, task delays, unit breakdowns, and material handling losses. Many common applications, however, require a richer set of disturbances and counter-decisions. For example, in bio-manufacturing, the use of live systems such as bacteria, mammalian, or insect cells, introduces several operational challenges, including batch-to-batch variability, parallel growth of desired products and unwanted toxic byproducts, and possible random shocks that can lead to complete failure of a batch (Martagan et al. 2018). There is currently no scheduling formulation for modeling these operational features, and more importantly, no model that can be used for the online scheduling of such processes.

We have developed a general state-space model, particularly motivated by an online scheduling perspective, that allows modeling (1) task-delays and unit breakdowns with a new, more intuitive convention over that of Subramanian et al., 2012, (2) fractional delays and unit downtimes, when using discrete-time grid, (3) variable batch-sizes, (4) robust scheduling through the use of conservative yield estimates and processing times, (5) feedback on task-yield estimates before the task finishes, (6) task termination during its execution, (7) post-production storage of material in unit, and (8) unit capacity degradation and maintenance. Further, we propose new methods for updating the state of the process, as well as methods to enforce additional constraints, based on feedback information, on future decisions. We demonstrate the effectiveness of this model on a case study from the field of bio-manufacturing.

Through this new state-space model, we have enabled a natural way to handle routinely encountered processing features and disturbance information in online scheduling, in general. The proposed model, therefore, greatly extends and enables the possible application of mathematical programming based online scheduling solutions to diverse application settings. Finally, it is important to note, that although our model uses state task network based representation, these generalizations can also be adapted to resource task network based representation (Pantelides, 1994).


Gupta, D.; Maravelias, C.T.; Wassick, J.M. From rescheduling to online scheduling. Chemical Engineering Research and Design, 116 (2016), 83-97.

Subramanian, K.; Rawlings J.B.; Maravelias, C.T. A state-space model for chemical production scheduling. Computers & Chemical Engineering, 47 (2012), 97-110.

Martagan, T.; Krishnamurthy, A.; Leland, P.; Maravelias, C.T. Performance Guarantees and Optimal Purification Decisions for Engineered Proteins. Operations Research, 6 (1), (2018), 18-41.

Pantelides, C. C. (1994). Unified frameworks for optimal process planning and scheduling. In Proceedings of the second conference on foundations of computer aided operations (pp. 253--274). New York: Publications, Cache.