An embedding formulation for the optimal scheduling and design of multipurpose batch plants

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.

Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation

During the last two decades, the problem of short-term scheduling of multiproduct and multipurpose batch plants has gained increasing attention in the academic, research, and manufacturing communities, predominantly because of the challenges and the high economic incentives. In the last 10 years, numerous formulations have been proposed in the literature based on continuous representations of time. The continuous-time formulations have proliferated because of their established advantages over discrete-time representations and in the quest to reduce the integrality gap and the resulting computational complexities. The various continuous-time models can be broadly classified into three distinct categories: slot-based, global event-based, and unit-specific event-based formulations. In this paper, we compare and evaluate the performance of six such models, based on our implementations using several benchmark example problems from the literature. Two different objective functions, maximization of profit and minimization of makespan, are considered, and the models are assessed with respect to different metrics such as the problem size (in terms of the number of binary variables, continuous variables, and constraints), computational times (on the same computer), and number of nodes needed to reach zero integrality gap. Two additional computational studies with resource constraints such as utility requirements are also considered.

Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants

A novel mathematical formulation for short-term scheduling of multipurpose batch plants in chemical manufacturing

In this chapter, the concept of the state sequence network (SSN) representation, which is the cornerstone of the material entailed in this textbook, is presented. This representation is based on states only, eliminating the use of tasks and units. Using this new representation as a basis, a novel continuous time MILP formulation for short-term scheduling of multipurpose batch plants is developed (Majozi and Zhu, 2001, Ind. Eng. Chem. Res., 40(25): 5935–5949). The presented formulation can readily be extended to intermediate due date scenarios. Time points are used to denote the use or production of a particular state. This formulation leads to a small number of binary variables and much better results when compared to other continuous time formulations published in literature. The reduced number of binary variables is a result of considering states only, thereby eliminating binary variables corresponding to tasks and units. This method has been applied to literature examples and industrial problems which show significant improvement in reducing the number of binary variables, hence CPU times. The last section of this chapter introduces the concept of units aggregation in reducing the binary dimension of large-scale problems. This makes it possible for the method to solve large-scale industrial problems. In the forthcoming chapters of this textbook it will be demonstrated how this formulation is applied in the context of batch process integration with the ultimate aim of freshwater and energy optimization.

This paper discusses important hybrid aspects of chemical processing plants. It is outlined that discrete phenomena occur both on the physical level and in the control of these plants. As the dynamics of the transformations of energy and material are predominantly continuous, large and complex hybrid systems arise. We focus on three different aspects of dealing with such systems: (1) Modeling and simulation of hybrid systems for the design and optimization of plants, controllers and operating strategies. We present powerful simulation environments that have been developed in recent years. (2) Validation of plant instrumentation and discrete controllers. These systems are largely responsible for the safe and economic operation of chemical plants and the protection of the workforce, and the environment. Techniques for the verification of discrete controllers for continuous processes are discussed, which are based on a discrete approximation of the continuous dynamics. (3) Scheduling of batch plants. For plants that are operated in a discontinuous fashion, the timing and sequencing of the operations are very important for the efficient use of the equipment. This leads to large mixed-integer optimization problems. For a typical example, we show how the process and the constraints can be modeled and describe an efficient solution algorithm.

Integrated batch plant design: A polymer plant case study

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.

While the part 1 focuses on the application of the proposed formulation to scheduling, this paper focuses mainly on the integration of planning and scheduling in multipurpose batch plants. In dealing with this problem, the method presented in part 2 exploits the mathematical structure of the overall plant model. It is discovered that the overall model exhibits a block angular structure that is decomposed by raw material allocation. If raw materials can be allocated optimally to individual plants, solving individual models for each plant can produce the same results as solving an overall model for the site. This discovery leads to a decomposition strategy that consists of two levels. In the first level, only planning decisions are made, and the objective function is the maximization of the overall profit. The results from solving the planning model give optimal raw material allocation to different plants. In the second level, the raw material targets from the first (planning) level are incorporated into the scheduling submodels for each plant, which are solved independently without compromising global optimality. The objective function for each scheduling submodel is the maximization of product throughput. The scheduling level uses the concept of the state sequence network presented in part 1. Solving scheduling submodels for individual plants rather than the overall site model leads to problems with much a smaller number of binary variables and, hence, shorter CPU times. If conflicts arise, i.e., the planning targets are too optimistic to be realized at the scheduling level, the planning model is revisited with more realistic targets. This eventually becomes an iterative procedure that terminates once the planning and scheduling solutions converge within a specified tolerance. In this way, the planning model acts as coordination for scheduling models for individual plants. An industrial case study with three chemical processes is presented to demonstrate the effectiveness of this approach.

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

A Continuous-time MILP Model for Direct Heat Integration in Batch Plants

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

A new methodology for the optimal design of batch fermentation plants

Incorporating scheduling in the optimal design of multiproduct batch plants