Modeling

Generally, chemical production environments can be broadly classified into three categories, namely network, sequential, and the combination of the two, i.e. hybrid. Different material handling restrictions are present in each production environment, leading to different modeling approaches used for scheduling in these environments.

1) Sequential environment: Due to strict material handling restrictions (no-mixing/splitting of batches) mainly batch-based modeling approach is adopted. Unlike the majority of the models developed, we study MIP models for both multistage and multipurpose plants that can simultaneously account for batching and scheduling decisions, thereby leading to better solutions (Sundaramoorthy et al., 2009). The discrete-time representation that we adopt in the models offer many advantages such as linear modeling of inventory and resource utilization profiles, straightforward modeling of time-varying resource availability and cost, etc (Merchan et al., 2016).

2) Network environment: Batches of material can be freely mixed and split, thereby material-based modeling approach is adopted in this environment. We study new continuous-time representations that do not require tasks to start or end at a time point, reducing the number of time points needed for a solution. In addition, we introduce inventory variables for processing units, which allows us to model non-simultaneous and partial material transfers (Gimenez et al., 2009).

3) Hybrid environment: In hybrid environment, each material have different material handling restriction. Thus, both aspects of network and sequential environments are present in the system. While previous studies have solely focused on either sequential or network environment, we develop an approach that can handle hybrid processes by introducing different type of material balance and handling constraints (Sundaramoorthy and Maravelias, 2011; Velez and Maravelias, 2013). An example of a problem that can now be addressed using the new formulation is given in Figure 1.

Complex chemical facility consisting of different subsystems

Figure 1. Complex chemical facility consisting of different subsystems

Reference:

Gimenez, D. M., Henning, G. P. and Maravelias, C. T. (2009) A novel network-based continuous-time representation for process scheduling: Part I. Main concepts and mathematical formulation. Computers & Chemical Engineering. 33, 1511-1528.

Merchan, A. F., Lee, H. and Maravelias, C. T. (2016) Discrete-Time Mixed-Integer Programming Models and Solution Methods for Production Scheduling in Multistage Facilities. Computers and Chemical Engineering.

Sundaramoorthy, A. and Maravelias, C. T. (2011) A General Framework for Process Scheduling. Aiche Journal. 57, 695-710.

Sundaramoorthy, A., Maravelias, C. T. and Prasad, P. (2009) Scheduling of Multistage Batch Processes under Utility Constraints. Industrial & Engineering Chemistry Research. 48, 6050-6058.

Velez, S. and Maravelias, C. T. (2013) Mixed-Integer Programming Model and Tightening Methods for Scheduling in General Chemical Production Environments. Industrial & Engineering Chemistry Research. 52, 3407-3423.