Design and Synthesis of Multipurpose Batch Plants Using a Robust Scheduling Platform

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.

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

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

Summary of the Basic StepsThe basic steps in the suggested procedure for the optimal design of multi-purposebatch plants can be summarized as follows:1. List the candidate product groups.2. Obtain the super-structure that contains the candidate groups.3. Derive the horizon constraints..4. Examine the horizon constraints. If at least one horizon constraintimplicitly contains all the time periods, complete the merged formulationand solve the MINLP given in Equations (38) to (44) with the correspondinghorizon constraints. Otherwise, go to step 5.5. Select a product(s) that breaks the loop(s) in the super-structure. Treat thechosen product(s) as two or more artificial products.6. Revise the super-structure to include the additional products. Verify thatthe loop is broken. If this condition is met, go to step 7. Otherwise,return to step 5 and modify the products chosen for splitting.7. Derive the multi-period form of the constraints for the product(s) that aresplit into its (their) values for the time periods in which it (they) appear.Formulate the merged representation of the model for the rest of theproducts, including the horizon constraints. At least one horizonconstraint will contain implicitly all the time periods.Example 2The seven product, ten stage example problem of Suhami and Mah (1982) has beensolved to illustrate the design of a large multi-purpose batch plant. From the super-structure of this problem (Figure 4), the horizon constraints shown in Table II arederived.Using these constraints, the example has been solved with the merged formulation.Data for this problem appears in Table III. In addition, the following specificationshave been used: H = 6200 hr, a = 250 SFr, fi = 0.6, 1 < N <, 3, and 250 < V£ 10,000. As seen in Table IV, the MINLP formulation involves 48 variables and 67constraints. MINOS/Augmented (Murtagh and Saunders, 1980) required 16.09 secondsof CPU-time on a DEC-20 computer to solve the relaxed nonlinear program.

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.

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.

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

Effective scheduling of a large-scale paint production system

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.

Integrated batch plant design: A polymer plant case study

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

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

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

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