Batch process, scheduling

BonfiU, A., Espuna, A., Puigjaner, L. (2005). Addressing robustness in scheduling batch processes with uncertain operation times. Industrial and Engineering Chemistry Research, 44,1524-1534. 

Stefanis, S.K., Livingston, A.G., Pistikopoulos, E.N. (1997) Environmental Impact Considerations in the Optimal Design and Scheduling of Batch Processes. Computers in Chemical Engineering, 21(10), 1073-1094. 

However, the designer should not loose sight of the fact that, whilst schedule planning and optimization provides the basis for the design of batch processes, production schedules are often disrupted once production has commenced. For example, what happens if a key item of equipment breaks down and needs to be repaired What happens if... 

Production schedules for batch processes can be sequential, overlapping, parallel, use intermediate storage, or use a combination of these. Such schedules can be analyzed using Gantt charts. Batch processes often produce multiple products in the same equipment and can be distinguished as flowshop or multiproduct plants. Equipment cleaning and material transfer policy have a significant effect on the production schedule. 

In this chapter, state sequence network (SSN) representation has been presented. Based on this representation, a continuous-time formulation for scheduling of multipurpose batch processes is developed. This representation involves states only, which are characteristic of the units and tasks present in the process. Due to the elimination of tasks and units which are encountered in formulations based on the state task network (STN), the SSN based formulation leads to a much smaller number of binary variables and fewer constraints. This eventually leads to much shorter CPU times as substantiated by both the examples presented in this chapter. This advantage becomes more apparent as the problem size increases. In the second literature example, which involved a multipurpose plant producing two products, this formulation required 40 binary variables and gave a performance index of 1513.35, whilst other continuous-time formulations required between 48 (Ierapetritou and Floudas, 1998) and 147 binary variables (Zhang, 1995). 

Ierapetritou, M.G., Floudas, C.A., 1998. Effective continuous-time formulation for short-term scheduling. 1. Multipurpose batch processes. Ind. Eng. Chem. Res., 37 4341-4359. 

A mathematical formulation based on uneven discretization of the time horizon for the reduction of freshwater utilization and wastewater production in batch processes has been developed. The formulation, which is founded on the exploitation of water reuse and recycle opportunities within one or more processes with a common single contaminant, is applicable to both multipurpose and multiproduct batch facilities. The main advantages of the formulation are its ability to capture the essence of time with relative exactness, adaptability to various performance indices (objective functions) and its structure that renders it solvable within a reasonable CPU time. Capturing the essence of time sets this formulation apart from most published methods in the field of batch process integration. The latter are based on the assumption that scheduling of the entire process is known a priori, thereby specifying the start and/or end times for the operations of interest. This assumption is not necessary in the model presented in this chapter, since water reuse/recycle opportunities can be explored within a broader scheduling framework. In this instance, only duration rather start/end time is necessary. Moreover, the removal of this assumption allows problem analysis to be performed over an unlimited time horizon. The specification of start and end times invariably sets limitations on the time horizon over which water reuse/recycle opportunities can be explored. In the four scenarios explored in... 

Two illustrative examples are presented. The first deals with the scheduling of a small batch process operating in zero effluent mode and the second deals with the synthesis of a small batch operation. 

Two formulations were derived. The first deals with minimising the amount of effluent produced from an operation where wastewater can be reused in product formulation and the plant structure is known. The minimisation is achieved by scheduling the operation in such a manner as to maximise the opportunity for wastewater reuse. The second deals with the synthesis of a batch process operating in zero effluent mode. The formulation determines the number and size of processing and storage vessels as to minimise the cost of the equipment and the amount of effluent produced from the resulting operation, while achieving the required production. 

Constraints (10.1), (10.2), (10.8)-(10.14), in conjunction with the overall plant scheduling constraints, constitute a complete MILP formulation for direct heat integration in batch processes in a situation where the batch size is allowed to vary at different instances along the time horizon of interest. 

Majozi, T., Zhu, X.X., 2001. A novel continuous time MILP formulation for multipurpose batch plants. 1. Short-term scheduling. Ind. Eng. Chem. Res., 40(25) 5935-5949 Obeng, E.D.A., Ashton, G.J., 1988. On pinch technology based procedures for the design of batch processes. Chem. Eng. Res. Des., 6 255-259... 

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