(76c) Online Scheduling Design Principles
The goal of this work is to develop the principles and a methodology that would allow us to address the following fundamental question: Given a production environment (i.e., resource availability and recipes) and the distributions of the disturbances, what are the best rescheduling frequency and prediction horizon?
We first study how demand uncertainty affects the quality of the implemented schedule. For example, does the time at which uncertainty is observed affect solution quality? How does demand variability affect solution quality? Do different demand patterns, characterized by, for example, the frequency of orders, pose any particular challenges? In addition, how do network characteristics (e.g. shared intermediate materials, availability of buffer production capacity), aggravate or diminish the above effect?
Thereafter, we identify the key factors that affect the selection of online scheduling parameters, namely, production load, demand uncertainty, and process network characteristics. Second, for each factor, we define an âauxiliary parameterâ to quantify it. In some cases, defining this auxiliary parameter is straightforward (e.g., use standard deviation to describe demand variability) but in some cases it is far from trivial. For example, quantifying the load of a facility, subject to a demand pattern, depends on a series of factors and there is no explicit expression to calculate it. We present procedures to calculate all these auxiliary parameters. Third, we present methods to determine the online scheduling parameters (e.g., horizon of optimization problem and re-optimization frequency) from the instance-specific auxiliary parameters. Finally, to test our framework, we present results for various networks.
Interestingly, the work presented herein can be viewed as the counter part of controller design for dynamic systems. Given a production system (rather than a dynamic process) described in terms of the aforementioned auxiliary variables (rather than time constants(s)), we decide the parameters of the online scheduler (rather than controller). To our knowledge, the proposed framework is the first systematic attempt to design the online scheduling algorithm, and thus takes us one-step forward, towards synthesizing a general strategy to obtain high-quality closed-loop schedules.
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Gupta, D.; Maravelias, C.T.; Wassick, J.M. From rescheduling to online scheduling. Chemical Engineering Research and Design, 116 (2016), 83-97.