STNS, state-task networks

Another important aspect of batch plants relates to the representation of the recipe which is invariably the underlying feature of the resultant mathematical formulation. The most common representation of recipe in the published literature is the state task network (STN) that was proposed by Kondili et al. (1993), which comprises of 2 types of nodes, viz. state nodes and task nodes. The state nodes represent all the materials that are processed within the plant. These are broadly categorized into feeds, intermediates and final products. On the other hand, task nodes represent unit operations or tasks that are conducted in various equipment units within the process. 

In this chapter, state sequence network (SSN) representation has been presented. Based on this representation, a continuous-time formulation for scheduling of multipurpose batch processes is developed. This representation involves states only, which are characteristic of the units and tasks present in the process. Due to the elimination of tasks and units which are encountered in formulations based on the state task network (STN), the SSN based formulation leads to a much smaller number of binary variables and fewer constraints. This eventually leads to much shorter CPU times as substantiated by both the examples presented in this chapter. This advantage becomes more apparent as the problem size increases. In the second literature example, which involved a multipurpose plant producing two products, this formulation required 40 binary variables and gave a performance index of 1513.35, whilst other continuous-time formulations required between 48 (Ierapetritou and Floudas, 1998) and 147 binary variables (Zhang, 1995). 

The same problems occur using state task network (STN) formulations that use binary variables. There, possible events may occur for each instant expressed by a binary variable and the models become very large. No calculation was carried out for this formulation. 

The most relevant contribution for global discrete time models is the State Task Network representation proposed by Kondili et al. [7] and Shah et al. [8] (see also [9]). The model involves 0-1 variables for allocating tasks to processing units at the beginning of the postulated time intervals. Most important equations comprise mass balances over the states, constraints on batch sizes and resource constraints. The STN model covers all the features that are included at the column on discrete time in Table 8.1. 

The batch distillation operation can be schematically represented as a State Task Network (STN). A state (denoted by a circle) represents a specified material, and a task (rectangular box) represents the operational task (distillation) which transforms the input state(s) into the output state(s) (Kondili et al., 1988 Mujtaba and Macchietto, 1993). For example, Figure 3.1 shows a single distillation task producing a main-cut 1 (Di) and a bottom residue product (Bj) from an initial charge (B0). States are characterized by the amount and composition of the mixture residing in them. Tasks are characterized by operational attributes such as then-duration, the reflux ratio profile used during the task, etc. 

State Task Network (STN) representation of operating sequence for binary and multicomponent batch distillation... 

Symbolic-network representations of these separation systems, called state-task networks (STNs), are shown in Fig. 13-64. In this representation, the states (feeds, intermediate mixtures, and products) are represented by the nodes (ABC, AB, BC, A, B, C) in the network, and the tasks (separations) are depicted as lines (1, 2,. .., 6) connecting the nodes, where arrows denote the net flow of material. This STN representation was used by Sargent to represent distillation systems [Comp, ir Chem. Eng., 22, 31 (1998)] and has been widely used ever since. Originally STNs were introduced by Kondili, Pan-... 

In MultiVBD column, the products will be produced simultaneously while in the conventional column these will be produced sequentially as shown by State Task Network (STN) in Figure 3. Note, there is an extra middle vessel to produce an off-cut between D and Dj. 

Maravelias and Grossmann (2004) have recently developed a hybrid MILP/CP method for the continuous time state-task-network (STN) model in which different objectives such as profit maximization, cost minimization, and makespan minimization can be handled. The proposed method relies on an MILP model that represents an aggregate of the original MILP model. This method has been shown to produce order of magnitude reductions in CPU times compared to standalone MILP or CP models. 

In the following sections, we will introduce the reader to the basics of batch scheduling and the formulation of so-called state-task networks (STNs). In addition, we will provide a flavor of the mathematical formulation of scheduling problems, and with a simple example, we will familiarize the reader with the implementation... 

Due to the nature of the problem there is not a one to one match between separation tasks and columns that perform a given separation. Even more, a given feasible sequence of separation tasks can be performed by different sequences of thermodynamically equivalent columns. In this paper we present a task based superstructure with intermediate characteristics between the pure State Task Network (STN) (Yeomans and Grossmann, 1999) in which all the separation tasks are explicitly enumerated, and a superstructure in which equipment is previously determined. Figure 2 shows the superstructure for a mixture of 5 components. Although the picture by itself... 

The resulting maximal State Task Network (m-STN) is shown in Figure 2. Eleven nodes are obtained where storage, processing and transfers of material are handled explicitly, as well as the materials location. Thus, we have three dedicated storage (SlA l, S2/V2 and S3/V3), two iStates (iel, ie2) one oState (iol), three transfer tasks (pil/cl, pi2/c2 and pi3/c3) and two processing tasks (eTasks Tl/Rl and T2/R1). 

This example was first presented by Kondili et al. (1993). Two products are produced from three feeds according to the State-Task Network (STN) shown in Fig. 8.9. The STN utilizes five tasks which can be performed in four different units. The corresponding operational data for this example including units, tasks, and materials is given in Tables 8.3, 8.4 and 8.5, respectively. 

Very similar to the STN is the state sequence network (SSN) that was proposed by Majozi and Zhu (2001). The fundamental, and perhaps subtle, distinction between the SSN and the STN is that the tasks are not explicitly declared in the SSN, but indirectly inferred by the changes in states. A change from one state to another, which is simply represented by an arc, implies the existence of a task. Consequently, the mathematical formulation that is founded on this recipe representation involves only states and not tasks. The strength of the SSN lies in its ability to utilize information pertaining to tasks and even the capacity of the units in which the tasks are conducted by simply tracking the flow of states within the network. Since this representation and its concomitant mathematical formulation constitute the cornerstone of this textbook, it is presented in detail in the next chapter. 

In general, if the amount and composition of the feed state are known then fixing two degrees of freedom (as mentioned above) for each distillation task (STN module) determines the thermodynamic distillation map which should be followed and results in a distillation profile which is well defined. The technique presented is general and can be easily extended to other networks involving larger number of operation tasks and components. 

To deal with the ambiguities in recipe networks, Kondili et al. [5] introduced the concept of the STN representation. The main difference that the STN has with the recipe network is that it contains two types of nodes tasks and states. The state nodes represent the feeds, intermediate and final products, while the task nodes represent the processing operation that transforms materials from one form to another. The state nodes are represented by circles and the tasks by rectangles. 

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