Pablo A. Marchetti

A general resource-constrained scheduling framework for multistage batch facilities with sequence-dependent changeovers

This work introduces a new MILP sequential approach to the short-term scheduling of multistage batch plants that accounts for sequence-dependent changeover times, intermediate due dates and limited availability of renewable resources. It relies on a continuous-time formulation based on the general precedence notion that uses different sets of binary variables to handle allocation and sequencing decisions. To avoid resource overloading, additional constraints in terms of sequencing variables and a new set of 0-1 overlapping variables are presented. They allow tracking the set of tasks requiring the same resource and running in parallel at the start of another process operation. In this way, the proposed formulation involves a reasonable number of binary variables and constraints and features a very good computational behavior, even in the presence of hard bottleneck resources. Four illustrative examples, one of them including multiple bottleneck resources shared by several processing stages, have been efficiently solved.

Efficient Precedence-Based Multistage Batch Scheduling Formulation with Nontrivial Tightening Constraints

Abstract An efficient continuous-time precedence-based formulation is proposed to address scheduling problems in multistage multiproduct batch plants. The approach is based on the concept of unit-dependent general precedence, which requires sequencing binary variables to be defined for each pair of distinct batches and potentially shared unit. Despite big-M constraints are still needed, this sequencing scheme allows to introduce several nontrivial tightening constraints to make the feasible region more compact. The new constraints can be interpreted either as valid relations between allocation and sequencing decisions or as valid estimations of process variables, such as the starting times, the completion times, and the makespan. As other precedence-based methodologies, sequence-dependent changeovers are handled. The proposed model is based on the underlying idea that the relaxed value of binary variables, even if somewhere between 0 and 1, can be regarded as a decision partially made. The information available on the allocation and sequencing variables is used to generate better lower and upper bounds that tighten the feasible space in order to accelerate the solution process. The proposed approach is applied to three large multistage examples with a remarkable computational efficiency.

Optimal planning and feedstock-mix selection for multiproduct polymer production

Abstract In this paper, we describe a nonlinear programming model to determine the optimal balance of feedstocks to manufacture multiple polymer grades in a polypropylene production facility. The main units of the process are a distillation column and a polymerization reactor, for which accurate short-cut process models were developed. Both a single and multiple product formulations are presented. The proposed models seek to maximize the plant throughput while minimizing the production costs. The possibility of adding extra production is also considered. The formulations are applied to several case studies, both to analyze the performance of the model and to illustrate its potential economic impact. The trade-off between feedstocks costs and production rates is analyzed by solving the multiple-product model with different time horizons. An annualized-slate long term case study is presented. The proposed formulation with a user-friendly interface has been deployed to assist with commercial and operation decisions at the plant.

IMPROVED TIGHTENED MILP FORMULATIONS FOR SINGLE-STAGE BATCH SCHEDULING PROBLEMS

Abstract This work presents a set of improved MILP mathematical formulations for the scheduling of single-stage batch plants with parallel production lines. Minimization of the average weighted earliness and the makespan, i.e. the time needed to complete all processing tasks, are considered as alternative problem goals. For each objective function an enhanced model that incorporates specific tightening constraints is presented. These constraints improve each models efficiency by increasing the corresponding objective function lower bound, thus accelerating the branch and bound node pruning process. Several problem instances with different number of batches demonstrate that the proposed approach reduces the computational effort by orders of magnitude. Sequence dependent setup times can also be effectively accommodated.

An approximate framework for large multistage batch scheduling problems focusing on bottleneck resources

Abstract A rigorous representation of the batch scheduling problem is often useless to even provide a good feasible schedule for many real-world manufacturing facilities. In order to derive simpler scheduling methodologies, some usual features of multistage processing structures should be exploited. A common observation in industry is the fact that most plants have very few bottleneck operations and the bottleneck resource controls the plant throughput. Consequently, the quality of the plant schedule heavily depends on the proper resource assigment and sequencing of bottleneck operations. Every other part of the processing sequence should be properly aligned so that the right amount of material required by the bottleneck timely arrives. This work introduces a bottleneck-based MILP scheduling model for multiproduct batch facilities that can also account for bottleneck resources other than equipment units and critical operations performed at different processing stages. Three large-scale examples have been solved at very low CPU time, despite near-optimal schedules are still encountered.