Proactive scheduling of batch processes by a combined robust optimization and multiparametric programming approach

Abstract

We address short-term batch process scheduling problems contaminated with uncertainty in the data. The mixed integer linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, Ind Eng Chem Res. 1998; 37(11):4341-4359, contains parameter dependencies at multiple locations, yielding a general multiparametric (mp) MILP problem. A proactive scheduling policy is obtained by solving the partially robust counterpart formulation. The counterpart model may remain a multiparametric problem, yet it is immunized against uncertainty in the entries of the constraint matrix and against all parameters whose values are not available at the time of decision making. We extend our previous work on the approximate solution of mp-MILP problems by embedding different uncertainty sets (box, ellipsoidal and budget parameter regulated uncertainty), and by incorporating information about the availability of uncertain data in the construction of the partially robust scheduling model. For any parameter realization, the corresponding schedule is then obtained through function evaluation. V C 2013 American Institute of Chemical Engineers AIChE J, 59: 2013 Keywords: process scheduling, mixed integer programming, multiparametric programming, robust optimization IntroductionThe area of scheduling of chemical and pharmaceutical processes has received significant attention in industry and academia with a number of excellent reviews summarizing the key contributions in this field. [1][2][3][4][5][6][7][8] Scheduling is likely to be subject to uncertainty attributed to endogenous factors such as varying processing times or production rates, as well as to exogenous factors arising from variations in the market demand, product prices, or time horizon, etc. A classification of sources of uncertainty in process operations is found in the work by Pistikopoulos. 9 The optimal scheduling policy for a chemical process based on nominal data may not be optimal or even feasible any more once a deviation from the nominal values has occurred. Proactive scheduling is motivated by the need to address uncertainty upfront in order to restrict disruptions and avoid rescheduling in response to disturbances. Provided knowledge about the probability distribution of the uncertain data is available, stochastic programming methods are widely used in proactive scheduling. In this category fall the works of Bonfill et al., 10 Vin and Ierapetritou, 11 and Balasubramanian and Grossmann 12 addressing demand uncertainty, as well as Bonfill et al., 13 Bonfill et al., 14 and Balasubramanian and Grossmann 15 addressing operational level related uncertainty such as processing time variability. Scenario based formulations suffer from an increased problem size with respect to a growing number of uncertain parameters involved. In the open literature, another approach to account for the presence of uncertainty in the model is to employ its robust counterpart formulation. The objective of robust optimization is to identify scheduling policies tha...

Theoretical and computational comparison of continuous‐time process scheduling models for adjustable robust optimization

“…The second category relies upon a proactive scheme, where uncertainty is anticipated and accounted for in the optimization stage. One of the representatives of this category is parametric programing, where the parameter space is mapped in order to specify the optimal deterministic solution given any specific realization of uncertainty. Using this approach, one may identify a solution that exhibits satisfactory performance across a sufficiently wide range of parameter realizations.…”

Unraveling Optimal Biomass Processing Routes from Bioconversion Product and Process Networks under Uncertainty: An Adaptive Robust Optimization Approach

“…While parameters are treated as deterministic in most existing models, in practice uncertainty can arise due to unpredictable variations in compositions of feed streams, product demands, and material prices . An optimal pathway that ignores risks and considers only the nominal parameter values may lead to suboptimal or even infeasible solutions when uncertainties are inevitably realized. , Therefore, it is both practical and crucial to address uncertainty in the bioconversion processing network optimization model in order to obtain robust optimal pathways. , As uncertainty data for internal factors, such as process yields and technology conversion coefficients, are not available for many bioconversion technologies, we focus on well-documented, external sources of uncertainty. We consider the case where biomass supplies in our network are relatively abundant while their prices are volatile in the market.…”

“…10 An optimal pathway that ignores risks and considers only the nominal parameter values may lead to suboptimal or even infeasible solutions when uncertainties are inevitably realized. 11,12 Therefore, it is both practical and crucial to address uncertainty in the bioconversion processing network optimization model in order to obtain robust optimal pathways. 13,14 As uncertainty data for internal factors, such as process yields and technology conversion coefficients, are not available for many bioconversion technologies, we focus on well-documented, external sources of uncertainty.…”

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

“…The solution of multi-parametric scheduling problems has been previously discussed in [299] and [360]. In [183] the procedure for deriving and solving scheduling problems via multiparametric programming, using a state-space model representation [336] and a mp-MILP reformulation is presented.…”

“…While several publications have tackled the problem of robust hybrid MPC (see [56,235] and references therein), the topic of robust hybrid mp-MPC has so far received limited attention, as only robust multi-parametric proactive scheduling has been discussed [360]. The main reasons for this are (i) the conceptual di culty in approaching robust hybrid control, (ii) the increased computational burden when solving the control problem in a multi-parametric fashion and (iii) the occurrence of parameter dependence in the constraint matrix, a widely undescribed topic within multi-parametric programming.…”