Network formulations for the design and scheduling of multiproduct batch plants with parallel lines

Design of a chemical batch plant: a study of dedicated parallel lines with intermediate storage and the plant performance

Optimal design of batch plants under economic and ecological considerations: Application to a biochemical batch plant

PurposeThe purpose of this paper is to set up a two‐stage stochastic integer‐programming model (TSM) for the multiperiod scheduling of multiproduct batch plants under demand uncertainty involving the constraints of material balances and inventory constraints, as well as the penalty for production shortfalls and excess.Design/methodology/approachScheduling model is formulated as a discrete‐time State Task Network. Given a scheduling horizon consisting of several time‐periods in which product demands are placed, the objective is to select a schedule that maximizes the expected profit for a single and multiple product with a given probability level. The stochastic elements of the model are expressed with equivalent deterministic optimization models.FindingsThe TSM model not only allows for uncertain product demand correlations, but also gives different processing modes by a range of batch sizes and a task‐dependent processing time. The experimental results show that the TSM model is more appropriate than another model for multiperiod scheduling of multiproduct batch plants under correlated uncertain demand.Research limitations/implicationsThe choice of penalty parameter of demand uncertainty is the main limitation.Practical implicationsThe paper provides very useful advice for multiperiod scheduling of multiproduct batch plants under demand uncertainty.Originality/valueA stochastic model for the multiperiod scheduling of multiproduct batch plants under demand uncertainty was set up. A test problem involving 12 correlated uncertain product demands and two alternative models verified the availability of the TSM.

In this paper, we address the short-term scheduling of multiproduct batch plants with parallel identical/nonidentical reactors, a challenging problem that has been motivated by a real-world application at the Dow Chemical Company. The main challenges include handling sequence-dependent changeovers with high variance as well as two-stage production with shared intermediate storage and batch splitting. In order to deal with these issues, we propose a new continuous-time mixed-integer linear programming (MILP) model based on the concept of asynchronized time slots. The proposed model has the unique feature that it incorporates slot-based mass balances and accounts for sequence-dependent changeovers. While effective for small problems, the proposed model becomes computationally expensive to solve for larger problems, mainly because of the fact that the necessary number of slots is not known a priori and the model requires postulating an upper bound on the slots. Therefore, we propose a bilevel decomposition algorithm in which the original problem is decomposed into an upper-level sequencing and a lower-level scheduling and sequencing problem. The upper-level model is a recent planning model where mass balances are aggregated over time periods and detailed timing constraints are dropped. However, the effects of changeovers are accounted for by incorporating scheduling constraints. Thus, the upper-level model yields very accurate predictions and a tight upper bound. In the lower level, the original problem is solved for the number of slots and subsets of products as predicted by the upper level, yielding a lower bound. These subproblems are solved iteratively until the bounds converge. In order to reduce the number of total iterations, we propose a new class of symmetry breaking constraints. The application of the proposed approach is illustrated with several examples.

Integrating environmental impact minimization into batch plant design: Application to protein production

Alternatives in the optimal allocation of intermediate storage tank in multiproduct batch plants

Batch manufacturing plants require the frequent adaptation of production facilities to incorporate internal and external uncertainties. The introduction of flexibility in the design of general-purpose plants represents a cornerstone for the design and retrofit of batch processes along the plant’s lifecycle. Moreover, the integration of batch process development decisions during the plant design also contributes to handle uncertainty. This paper presents a novel optimization-based approach for the flexible design of batch plants by integrating process synthesis and plant allocation decisions, such as feed-forward control trajectories of processing conditions or the selection of operating modes and equipment items. To do so, a modeling strategy based on Mixed-Logic Dynamic Optimization and two-stage stochastic formulation is used to maximize the expected profit taking into account several uncertain scenarios. Moreover, a heuristic algorithm is proposed to solve the resulting problem that is characterized by a great complexity, consisting of an iterative procedure with embedded deterministic solutions of the integrated problem. The proposed approach is illustrated through the design of a single-product batch plant to carry out a competitive reaction process.

Incorporating scheduling in the optimal design of multiproduct batch plants

Integrated batch plant design: A polymer plant case study

Optimal scheduling of batch plants satisfying multiple product orders with different due-dates

Many multiproduct batch plants in the chemical industry employ multiple stages of nonidentical parallel units and operate on the basis of customer orders with different delivery dates. In this work, we present a new continuous-time mixed integer linear programming formulation without using time slots for the short-term scheduling of such plants. Our formulation allows both sequence-dependent and unit-dependent setup times and common operational considerations such as initial plant state and order/unit release times. We develop several novel constraints for the assignment of consecutive orders on a single unit and evaluate them thoroughly to identify the best constraints. Finally, we solve several examples to demonstrate the superiority of our proposed formulations. In comparison to existing works, our formulation requires roughly 30% fewer constraints, yields superior schedules, and reduces the computational times by 65%. We highlight the impact of M in big-M constraints on solution times and propose an i...

The increasing interest in multipurpose batch plants is evident, because of their inherent flexibility to cope with an ever changing market environment. These plants are easily reconfigured for product modifications, to cover a wide range of operating conditions. They are also suitable for producing different products within the same facility. In spite of this advantage, the design, synthesis, and scheduling of multipurpose batch plants can be a challenging task. This paper addresses design, synthesis, and scheduling simultaneously. It is known that the scheduling platform employed has a significant impact on the computational performance of the overall model in the design and synthesis of batch plants. The recent scheduling model that results in better computational efficiencies is extended to incorporate design and synthesis. Computational studies are presented to illustrate the effectiveness of the proposed model. A comparison with earlier formulations showed that better computational times and objective functions were obtained by this work.

The paper addresses the problem of including aspects of uncertainty in process parameters and product demands at the design stage of multiproduct/multipurpose batch plants. A conceptual two-stage stochastic programming formulation is proposed with an objective function comprising investment costs, expected revenues from product sales, and a penalty term accounting for expected losses due to unfilled orders. It is shown that (i) the proposed formulation captures the various decision-making policies toward demand satisfaction in a unified way, (ii) the employed feasibility criterion for the incorporation of the uncertainty enables the exact reformulation of the two-stage model as a single large-scale optimization model, (iii) for the case of discrete equipment sizes and despite the use of general continuous probability distribution functions to describe the uncertainty, linearity of the model is preserved, allowing detailed scheduling models to be included directly in the optimization model, and (iv) for th...

Design and retrofit of periodic batch plants: A RTN based approach

This is paper proposes a new particle swarm optimization (NPSO) algorithm to short-term scheduling of single-stage batch plants with parallel units using the continuous-time domain representation. The model is formulated as a mixed-integer linear programming (MILP) problem. The key to the improvement of the algorithm is the introduction of mutation operators, crossover operators and some heuristic rules which can get better initialization population and no effect on the optimality of the scheduling problem. Computational examples show that NPSO are clearly more appropriate than GA and PSO algorithm in resolution for batch plants to minimize earliness for scheduling problems with due date constraints, and NPSO becomes more effective after involving heuristic rules