Design of a chemical batch plant with parallel production lines: Plant configuration and cost effectiveness

Highlights

• MILP model for the design of a multiproduct chemical batch plant with parallel production lines as a strategic design option.

• Incorporation of, besides capital costs, startup, contamination and operating costs in the objective function.

• Illustration of advantages of multiple lines design model for the different cost components.

Abstract

We present a model for the design of multiproduct sequential batch plants extended with parallel production lines. This model is meant to support strategic capacity decisions and is formulated as a MILP model. First, we introduce the concept of parallel production lines as a new design option into existing plant design models. Then, we optimise the number of production lines, their design and the product assignment to the installed lines by minimising capital costs of the equipment. Furthermore, we extend the objective function with startup and contamination costs and study the influence of these costs on the chosen plant design options. We find the presence of parallel production lines beneficial as not all products have to share all equipment anymore. Moreover, we show that the incorporation of operating costs affects volume-wise asset utilisation per batch. An example to illustrate the applicability of our model is presented.

Introduction

Increasing pressure on supply chain performance forces production companies nowadays to take appropriate strategic decisions on plant design. We focus on such decisions for chemical batch plants in a flow shop environment in particular. Batch plants are typically equipped with tanks and reactors, in which all the input material is treated for a certain period of time and then passed on to the next operation (and equipment) (Rippin, 1983).

The design of such plants at a strategic decision level considers plant configuration (i.e. number, size and connectivity of equipment), the related batch sizes of the different manufactured products and the related production policy (e.g. campaign length, product-equipment dedication). This design depends on several strategic choices on production environment, mode of operation, design options and the business objective.

The plant design problem has been studied extensively in the past. Loonkar and Robinson (1970) calculated the optimal equipment sizes for a single product batch plant with one production line. The objective of their nonlinear program was to minimise capital investment via iteratively solved algebraic equations. By extending this model to batch plants producing different products, two major production environments are considered in literature: multiproduct plants, also denoted as flow shops, and multipurpose plants or job shops. Among the pioneering work on multiproduct plants, Sparrow et al. (1975) solved the design problem extended with parallel equipment per processing stage, assuming single product campaign mode of operation, by both a branch-and-bound method and a heuristic approach. Grossmann and Sargent (1979) formulated this problem as a mixed-integer nonlinear programming problem (MINLP), which was later reformulated as a linear problem (MILP) by Voudouris and Grossmann (1992). Other multiproduct design models were extended for semicontinuous- and intermediate storage equipment, but still consider a single production line (Knopf et al., 1982, Takamatsu et al., 1982, Modi and Karimi, 1989). A review on the design of multiproduct and multipurpose plants is presented by Barbosa-Póvoa (2007). The aim of all the aforementioned design problems is to minimise capital costs, however other costs have been included as well: e.g. the minimisation of energy costs (Knopf et al., 1982) and of environmental impact (Dietz et al., 2006). Some articles consider profit maximisation and include, besides capital costs, also e.g. raw material and disposal (e.g. Corsano et al., 2007, Moreno and Montagna, 2007) and maintenance costs (Pistikopoulos et al., 1996, Goel et al., 2003).

Moreover, in order to better incorporate the operational use of a plant, the plant design models incorporated scheduling techniques. In these design and scheduling papers, the problems are classified into two categories according to process topology: sequential and network processes. In sequential processes, each batch is processed following a sequence of stages and the identity of the batch is preserved. In more complex network processes, batch mixing, splitting as well as material recycling occurs and material balances are needed to describe all the flows. Furthermore, two modes of operation can be distinguished: cyclic and non-cyclic. Cyclic models assume a campaign mode of operation, whereas in non-cyclic models production may occur at arbitrary points in time and in arbitrary sequences. For network processes, the design problem is solved incorporating both (non-cyclic) discrete-time and continuous-time formulations. Barbosa-Póvoa and Macchietto (1994) presented a discrete-time maximal State Task Network (STN) representation, based on the original STN formulation of Kondili et al. (1993). Barbosa-Póvoa and Pantelides (1997) and Pinto et al. (2005) developed a discrete-time model relying on the Resource Task Network (RTN) framework. Continuous-time models are reported by Xia and Macchietto (1997), Lin and Floudas (2001) and Seid and Majozi (2013) based on the STN formulation and by Castro et al. (2005) based on the RTN representation. All these models optimise multipurpose plants with complex processes that are well suited for a network representation. We refer to recent review papers on short-term batch scheduling for a more complete overview (Floudas and Lin, 2004, Méndez et al., 2006, Harjunkoski et al., 2014). Alternatively, literature on plant design models for sequential processes consider mostly a cyclic mode of operation. Birewar and Grossmann, 1989, Birewar and Grossmann, 1990 introduced multiple product campaigns as opposed to the single product campaigns. More recently, the combination of designing and cyclic scheduling via multiple product campaigns has been studied e.g. by Corsano et al. (2007) using a heuristic solution method and by Fumero et al. (2013) solving a MILP model extended for parallel machines in each stage of the production process.

The above literature overview illustrates the several strategic choices that affect the design: on production environment (the production of single or multiple products, in multiproduct or multipurpose plants, etc.), on mode of operation (cyclic or non-cyclic), on the business objective (cost minimisation and profit maximisation) and on the design options allowed. It is on this last strategic choice that we will focus in this paper.

In the aforementioned literature on chemical batch plant design, there are several design options reported: the introduction of parallel equipment per stage and/or intermediate storage between stages. These options aim at eliminating or reducing capacity issues which slow down the entire process. Indeed, these design options lead to shorter cycle times, hence more batches in smaller and thus cheaper equipment. In practice however, we observe another design option that is frequently used in chemical plants, namely the installation of parallel production lines. These parallel lines are installed on one production site and operate independently but simultaneously with each other. The lines have the same processing steps and hence products may be produced on multiple lines. As total production volume is now divided over these lines, products can be dedicated to lines, which may reduce the required size and/or number of the capital intensive stages.

We found the presence of comparable parallel lines in batch plants in several types of short-term scheduling articles. However, all these articles assume a given design. On the one hand, parallel lines are referred to in scheduling on single-stage batch plants with nonidentical equipment that work independently. A MILP model was presented for the scheduling of single-stage parallel-line multiproduct batch plants based on batch precedence (Cerdá et al., 1997), and time-slots (Chen et al., 2002), which was extended with resource constraints and raw material supplies by Lamba and Karimi (2002). This type of problems are also referred to as parallel flowshop models (Gooding et al., 1994). On the other hand, in literature on short-term scheduling in multistage, sequential batch plants some semi-parallel lines occur. In these articles, there is limited connectivity between some equipment, but the lines are not entirely separated nor do they work independently. Pinto and Grossmann (1995) developed a MILP model with time-slots for the scheduling of multistage batch plants with parallel equipment. The model is based on parallel time coordinates for units and tasks. Méndez et al. (2001) proposed a mathematical model for the resource-constrained short-term scheduling problem. They considered a sequential batch plant with multiple stages and several units working in parallel, where assignment and sequencing decisions are handled independently. Recently, however, Hill et al. (2016) proposed a scheduling heuristic for realistic production planning in a multiproduct, multistage blending plant with parallel production lines as defined previously.

In this paper, a MILP model is proposed for determining the design of sequential multiproduct batch plants, operating in cyclic mode. However, in addition to existing design models, the strategic decision of installing parallel lines and, if so, how many is explicitly taken into account.

Next, we not only solve this design problem for the minimisation of capital costs of the batch equipment, but we include additional cost components such as setup costs and product batch-related operating costs. We assume in this paper that the business objective is to optimise cost effectiveness.

Regarding the setup costs, we distinguish two components: a startup and contamination cost. The fixed startup cost is incurred for every equipment unit, every time a series of batches of the same product starts, and represents the cost of setting the equipment parameters to the required level (such as temperature and pressure), preparing the inflow of ingredients, performing quality tests, etc. When parallel production lines are installed, a decrease in the total startup cost can be expected if there is a reduction in number of equipment used per product. The contamination cost, on the other hand, depends on the combination of products produced on the same equipment units. In practice, products with similar characteristics are often grouped into product families. As products from different families often generate contamination among each other, it is preferred not to produce them on the same line. Consequently, if production lines are installed and dedicated to certain products/product families, high contamination costs can be avoided.

Finally, we consider an operating cost that accounts for labour, use of utilities, etc. per batch of every product. Because of the variable character of this cost component, i.e. dependent on the number of batches, production of the demand in the least number of batches is favoured. If this operating cost does not impact the design choices, a consequence of minimising this operating cost is an increase in volume-wise asset utilisation per batch. Time-wise asset utilisation, on the other hand, will be lower, and thus idle time will occur. However, this phenomenon can provide a welcome buffer for small unforeseen events.