Optimal Event Point Determination for Short-Term Scheduling of Multipurpose Batch Plants via Unit-Specific Event-Based Continuous-Time Approaches

Scheduling of Batch Operation for a Wastewater Treatment Plant under Time-of-Use Electricity Pricing

High operating cost caused by electric energy consumption is a common problem challenging many municipal wastewater treatment plants (WWTPs). Due to the characteristics of intermittent inflow and aeration, WWTPs using sequencing batch reactor technology and its variants can be managed to relieve operating cost through taking advantage of time-of-use electricity pricing. However, little attention has been paid to the scheduling of treatment processes in the context of WWTPs. In this paper, a novel mixed-integer linear programming model is established for scheduling the batch operation of a WWTP under time-of-use electricity pricing, which considers constraints arising from task allocation, processing sequence, and processing duration. The modeling method is developed from the event-based continuous-time approach. The start time and end time of each treatment task are optimized to shift electricity consumption from peak hours to off-peak hours to the greatest extent, thus minimizing electricity cost. A case study demonstrates that the proposed model can quickly generate precise operational plans for the investigated WWTP. By implementing the optimum schedules, the WWTP can save on its electricity bill without changing the treatment capacity or the treatment process. The widening of peak and off-peak electricity pricing gap is favorable for the proposed model to display a more significant effect in reducing electricity cost.

Data-Driven Optimization of Mixed-integer Bi-level Multi-follower Integrated Planning and Scheduling Problems Under Demand Uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. In this paper, we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

The increasing demand of goods, the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units. Optimal scheduling of their processes can lead facilities towards this direction. Although a great number of mathematical models have been developed for such scheduling, they may still lead to large model sizes and computational time. In this work, we develop two novel mathematical models using the unit-specific event-based modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points. The computational results demonstrate that both proposed mathematical models reduce the number of event points required. The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.

Scheduling of Energy-Integrated Batch Process Systems Using a Pattern-Based Framework

In this paper, a novel pattern-based method is developed for the generation of optimal schedules for energy-integrated batch process systems. The proposed methodology is based on the analysis of available schedules for the identification of repetitive patterns. It is shown that optimal schedules of energy-integrated batch processes are composed of several repeating sections (or building blocks), and their sizes and relative positions are dependent on the scheduling horizon and constraints. Based on such a decomposition, the proposed pattern-based algorithm generates an optimal schedule by computing the number and sequence of these blocks. The framework is then integrated with rigorous optimization-based approach wherein it is shown that the learning from the pattern-based solution significantly improves the performance of rigorous optimization. The main advantage of the pattern-based method is the significant reduction in computational time required to solve large scheduling problems, thus enabling the possibility of on-line rescheduling. Three literature examples were considered to demonstrate the presence of repeating patterns in optimal schedules of energy-integrated batch systems. The effectiveness of the proposed methodology was illustrated using an integrated reactor-separator system.