(648b) A General Model for Periodic Chemical Production Scheduling

While short-term scheduling is used for processes producing products with relatively high demand variability, periodic scheduling is typically employed in facilities producing products with regular demand. The obtained schedules can be executed repeatedly to achieve the objectives and simplify the operation of the facility. Active research on periodic scheduling over the past three decades had led to significant advances in the development of scheduling models [1–4] and solution methods[5,6]. Despite these advances, however, there still exist some limitations because existing approaches are based on various assumptions and approximations. For example, the available approaches typically assume aggregated demand either in the form of constant demand rate or constraints on the production rate. However, in reality, products are usually shipped at specified times. Thus, the current approaches may lead to infeasible or low-quality schedules when actually deployed. Moreover, inventory cost is usually approximated due to the adoption of continuous time representation (e.g., to avoid bilinear terms of [inventory level]*[length of the time]).

In this work, we present a general model for periodic chemical production scheduling that can be applied to address problems in all production environments considering various features. We first define the concept of “periodic scheduling”, which is a generalization of “cyclic scheduling”, in that it considers a broader set of solutions (interestingly, the generalization is analogous to the way a cycle in a graph is a special case of a closed trail). Second, we propose a model that does not rely on five commonly made assumptions in previous works: (1) each product can be produced in only one unit; (2) unlimited storage policy; (3) no task crossover between the execution of the periodic solutions; and (4) final products are shipped at constant rates. The relaxation of these assumptions allows us to find solutions that are very different, and better, than the solutions obtained by the previous approaches. We also discuss alternative types of constraints for sequence-independent setups and sequence-dependent changeovers to study the tradeoffs between switchover costs and inventory costs, one of the fundamental trade-offs in periodic scheduling. Further, we propose a method to systematically convert shipment information to parameters that can be used in the inventory balance constraints, where detailed product demand profiles are considered. Finally, the model is extended to handle continuous processes.

We provide illustrative examples to demonstrate how the relaxation of the previously made assumptions can lead to better solutions and/or solutions that remain feasible when, for example, detailed (periodic) demand profiles are taken into account. We close with a number of large-scale instances to illustrate the computational efficiency of the proposed models.

[1] N. V. Sahinidis, I.E. Grossmann, MINLP model for cyclic multiproduct scheduling on continuous parallel lines, Comput. Chem. Eng. 15 (1991) 85–103. doi:10.1016/0098-1354(91)87008-W.

[2] J.M. Pinto, I.E. Grossmann, Optimal Cyclic Scheduling of Multistage Multiproduct Plants, Comput. Chem. Eng. 18 (1994) 797–816. https://doi.org/10.1016/0098-1354(93)E0021-Z.

[3] N. Shah, C.C. Pantelides, R.W.H. Sargent, Optimal periodic scheduling of multipurpose batch plants, Ann. Oper. Res. 42 (1993) 193–228. doi:10.1007/BF02023176.

[4] P.M. Castro, A.Q. Novais, Optimal periodic scheduling of multistage continuous plants with single and multiple time grid formulations, Ind. Eng. Chem. Res. 46 (2007) 3669–3683. doi:10.1021/ie0613570.

[5] Y. Pochet, F. Warichet, A tighter continuous time formulation for the cyclic scheduling of a mixed plant, Comput. Chem. Eng. 32 (2008) 2723–2744. doi:10.1016/j.compchemeng.2007.09.001.

[6] F. You, P.M. Castro, I.E. Grossmann, Dinkelbach’s algorithm as an efficient method to solve a class of MINLP models for large-scale cyclic scheduling problems, Comput. Chem. Eng. 33 (2009) 1879–1889. doi:10.1016/j.compchemeng.2009.05.014.