(492b) Optimization for Sustainable Scheduling of Batch Manufacturing Processes Under Economic and Environmental Concerns

Batch processing plays an important role in producing low-volume high-value-added products due to its flexibility, thus the subject of batch production scheduling has been extensively studied in the past decades, and still remains an active research area nowadays both in industry and academia [1, 2]. While most works tend to improve the economic performances of batch scheduling, the associated environmental impact has long been disregarded, which becomes the focus of this work. Due to the increasingly stringent environmental regulations imposed on chemical process industries and the call for green manufacturing from the public, it has become a goal in process manufacturing to incorporate the environmental consideration in addition to the economic objective in the decision-making process [3].

In this work, we propose a novel bi-criterion optimization framework which simultaneously takes into account the economic and environmental concerns in batch scheduling problems [4]. Two fractional-term objective functions are considered that allows further improvement compared to the conventional linear economic and environmental objectives. The economic performance is measured by productivity, defined as the net profit divided by the corresponding makespan. This objective would take into account both the absolute profitability of given batch processes as well as the temporal responsiveness perspective. The environmental performance is measured by the environmental impact embedded in per functional unit of the products, evaluated through a “cradle-to-gate” Life Cycle Assessment (LCA) procedure [5, 6]. We explicitly optimize based on the functional unit in this work. Moreover, the interpretation phase of classical LCA is coupled with the multi-objective optimization, thus leading to the concept of Life Cycle Optimization (LCO).  All decisions (e.g., batch sequencing, task assignment, processing timings, batch sizing, etc.) are simultaneously optimized under both the economic and environmental objectives. Furthermore, it worth highlighting that the selections among multiple changeover and cleaning options with different economic and environmental properties are considered as variables in this work, which is rarely considered in conventional batch scheduling problems.

The bi-criterion optimization model is solved using the ε-constraint method, in which the Pareto-optimal solutions are derived by solving a sequence of subproblems with different ε-parameter values. Due to the presence of fractional economic and environmental objective functions, the subproblems are formulated as mixed-integer linear fractional programming (MILFP) problems. MILFP is a special class of mixed-integer nonlinear programming (MINLP) problems which can become computationally intractable due to its combinatorial nature and pseudo-convex objective functions. Therefore, to globally optimize the MILFP subproblems, we employ two tailored solution methods, namely the parametric algorithm and the reformulation-linearization method, which are proved to be much more efficient than general-purpose MINLP methods [7, 8]. The resulting Pareto curve reveals how the inherent tradeoffs between the economic and environmental objectives would influence the production schedule and resource allocation in batch manufacturing, which provides insights to the sustainable scheduling problem. To illustrate the application of the proposed modeling framework and solution methods, we consider two short-term sustainable scheduling problems as our case studies, which involve a multi-product acrylic fibers batch production process and a multi-purpose batch plant with a reaction-separation network structure, respectively.

References

[1]        C. A. Mendez, J. Cerda, I. E. Grossmann, I. Harjunkoski, and M. Fahl, "State-of-the-art review of optimization methods for short-term scheduling of batch processes," Computers & Chemical Engineering, vol. 30, pp. 913-946, May 2006.

[2]        C. A. Floudas and X. X. Lin, "Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review," Computers & Chemical Engineering, vol. 28, pp. 2109-2129, Oct 2004.

[3]        E. Capón-García, A. D. Bojarski, A. Espuña, and L. Puigjaner, "Multiobjective Optimization of Multiproduct Batch Plants Scheduling Under Environmental and Economic Concerns," AIChE Journal, vol. 57, pp. 2766-2782, Oct 2011.

[4]        D. Yue and F. You, "Sustainable scheduling of batch processes under economic and environmental criteria with MINLP models and algorithms," Computers & Chemical Engineering, vol. 54, pp. 44-59, 7/11/ 2013.

[5]        A. Azapagic, "Life cycle assessment and its application to process selection, design and optimisation," Chemical Engineering Journal, vol. 73, pp. 1-21, Apr 1999.

[6]        A. Azapagic and R. Clift, "The application of life cycle assessment to process optimisation," Computers & Chemical Engineering, vol. 23, pp. 1509-1526, Dec 1999.

[7]        F. Q. You, P. M. Castro, and I. E. Grossmann, "Dinkelbach's Algorithm as An Efficient Method to Solve A Class of MINLP Models for Large-Scale Cyclic Scheduling Problems," Computers & Chemical Engineering, vol. 33, pp. 1879-1889, Nov 2009.

[8]        D. Yue, G. Guillén-Gosálbez, and F. You, "Global Optimization of Large-Scale Mixed-Integer Linear Fractional Programming Problems: A Reformulation-Linearization Method and Process Scheduling Applications," AIChE Journal, submitted, 2013.