465458 A Theoretical and Computational Study of Continuous-Time Process Scheduling Models in the Context of Adjustable Robust Optimization
Uncertainty about process parameters at the time of decision-making is a fundamental reality when scheduling the operation of multi-purpose batch plants. This uncertainty might pertain to parameters such as processing durations, production yields, material prices and demands, as well as availability of raw materials and utilities. It is well-understood that optimizing the schedule deterministically, using nominal values for all these parameters, often leads to a schedule that is suboptimal or even infeasible in view of the actually realized scenario. One of the methods proposed to mitigate the effects of uncertainty is Robust Optimization (RO) [4-7], which guarantees the feasibility of the schedule for any realization of the uncertain parameters in a postulated uncertainty set. The traditional approach, however, treats all of the decisions as “here-and-now,” yielding conservative solutions in general. In addition, the “here-and-now” assumption renders RO inadequate to handle some frequent cases such as the case of uncertainty in process yields or the handling of zero-wait materials.
We have previously showed  that deferring a subset of the decisions for later (“wait-and-see”) can lead to more profitable, yet equally robust, schedules. Furthermore, it was shown that the possibility for time-dependent parameter realizations must be taken into account for a realistic treatment of the problem, leading to the need to consider more involved, decision-dependent uncertainty sets. The application of the ARO framework using affine decision rules in this scheduling context revealed solutions that improved up to 50% compared to the corresponding RO solution, while accounting for the same level of uncertainty in the processing times, and exhibiting the potential for even better solutions when utilizing more complex decision rules. The computational tractability of the approach however, is expected to vary with the selection of deterministic model that is used as the basis for the computations as well as the subset and combinations of the parameters that are considered uncertain.
In this study we discuss the strengths and limitations of various continuous-time deterministic models [8-15] in terms of their amenability to serve as the basis for both a traditional RO as well the ARO framework, and we discuss available strategies to mitigate some of those limitations. A comprehensive computational study using standard literature benchmarks was performed for various levels of uncertainty in the fixed and variable (related to batch size) processing times. Furthermore, the flexibility of the ARO framework allows us for the first time in the open literature to also present robust solutions of problems that involve uncertainty in the production yields, which is a common issue in the chemical industry.
 C. Floudas, and X. Lin, 2005. Mixed integer linear programming in process scheduling: Modeling, algorithms, and applications. Annals of Operations Research 139 (1), 131–162.
 I. Harjunkoski, C. Maravelias, P. Bongers, P. Castro, S. Engell, I. Grossmann, J. Hooker, C. Mendez, G. Sand, J. Wassick, 2014. Scope for industrial applications of production scheduling models and solution methods. Computers & Chemical Engineering 62, 161–193.
 N. Lappas, and C. Gounaris, 2016. Adjustable robust optimization for process scheduling under uncertainty. AICHE Journal 62, 1646–1667.
 X. Lin, S. Janak, C. Floudas, 2004. A new robust optimization approach for scheduling under uncertainty: I. bounded uncertainty. Computers & Chemical Engineering 28 (6), 1069–1085.
 S. Janak, X. Lin, C. Floudas, 2007. A new robust optimization approach for scheduling under uncertainty: II. uncertainty with known probability distribution. Computers & Chemical Engineering 31 (3), 171–195.
 Z. Li, M. Ierapetritou, 2008. Robust optimization for process scheduling under uncertainty. Industrial & Engineering Chemistry Research 47 (12), 4148–4157.
 Z. Li, R. Ding, C. Floudas, 2011. A comparative theoretical and computational study on robust counter optimization: I. robust linear optimization and robust mixed integer linear optimization. Industrial & Engineering Chemistry Research 50 (18), 10567–10603.
 C. Maravelias, and I. Grossmann, 2003. New general continuous-time state - Task network formulation for short-term scheduling of multipurpose batch plants. Industrial & Engineering Chemistry Research 42 (13), 3056–3074.
 P. Castro, A. Barbosa-Povoa, H. Matos, A. Novais, 2004. Simple Continuous-Time Formulation for Short-Term Scheduling of Batch and Continuous Processes. Industrial & Engineering Chemistry Research 43 (1), 105–118.
 S. Janak, X. Lin, C. Floudas, 2004. Enhanced Continuous-Time Unit-Specific Event-Based Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies. Industrial & Engineering Chemistry Research, 43(10), 2516–2533.
 A. Sundaramoorthy, and I. Karimi, 2005. A simpler better slot-based continuous-time formulation for short-term scheduling in multipurpose batch plants. Chemical Engineering Science 60 (10), 2679–2702.
 D. Giménez, G. Henning, C. Maravelias, 2009. A novel network-based continuous-time representation for process scheduling: Part I. Main concepts and mathematical formulation. Computers & Chemical Engineering, 33(9), 1511–1528.
 N. Susarla, J. Li, I. Karimi, 2009. A novel approach to scheduling multipurpose batch plants using unit-slots. AICHE Journal, 56(7), 1859–1879.
 R. Vooradi, and M. Shaik, 2012. Improved three-index unit-specific event-based model for short-term scheduling of batch plants. Computers & Chemical Engineering, 43(19), 148–172.
 R. Seid, T. Majozi, 2012. A robust mathematical formulation for multipurpose batch plants. Chemical Engineering Science, 68(1), 36–53.
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