Multiobjective Batch Plant Design - American Chemical Society

Ind. Eng. Chem. Res. 2002, 41, 5727-5742

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Multiobjective Batch Plant Design: A Two-Stage Methodology. 1. Development of a Design-Oriented Discrete-Event Simulation Model Leonardo Bernal-Haro, Catherine Azzaro-Pantel,* Luc Pibouleau, and Serge Domenech Laboratoire de Ge´ nie Chimique, UMR CNRS 5503, ENSIACET INPT, 118, Route de Narbonne, 31077 Toulouse Cedex 04, France

This work reports development of a two-stage methodology for multiobjective batch plant design, which may be viewed as an alternative to traditional approaches based on mathematical programming techniques: (1) At the upper level, a genetic algorithm (GA) has been developed for solving the problem of design and proposing several plant structures. This kind of algorithm has proven previously its efficiency for the treatment of combinatorial problems. (2) At the inner level, a discrete-event simulation model (DES) tests the technical feasibility of the generated configurations. Part 1 of this series of papers is devoted to the implementation of the DES model whereas part 2 will tackle the development of the GA. The basic principles of the development of the design-oriented DES model are first recalled, and then the various potential uses of the simulator are presented. A detailed account of model assumptions for design purpose is also given. The formalism is illustrated by a typical example serving as a test bench in part 2. 1. Introduction Fine chemistry has contributed to reinforcing interest in batch processes for several years. Actually, most chemical products are manufactured using a batchprocessing mode. It is particularly appropriate for the low-volume synthesis of high value-added products (intermediate products, pharmaceutical active principles, agrochemicals, etc.), requiring close control of their operating conditions with a limited life cycle. Their production involves complex manufacturing processes and rigorous constraints due to purity and security to assess the traceability of the products. As reported by Bernal-Haro,1 many investigations have been devoted to designing an operation of a batch processing plant for the past 20 years. Despite the efforts, the development of efficient methods for optimal design of batch plants is generally restricted to smallscale problems, far from industrial-scale ones. This is all the more obvious as this development is compared with the available methods for the treatment of continuous plants. The general objective of this work is to propose a methodology for solving the design problem of industrialsize plants. A major difficulty concerns the underlying uncertainties, especially due to demand variations. Consequently, it may be illusory to use the term “optimal” design, although this adjective is overused in the established literature. Generally, a batch plant can manufacture several products sharing standard equipment units in a series of campaigns and has the ability to adapt itself to variations in the nature of raw materials and quality and to rapid market fluctuations. Consequently, a major asset of a batch plant is its flexibility, which can be considered in several ways: (1) Product flexibility, which characterizes the plant response to market needs: products (i.e., often a hundred * To whom correspondence should be addressed. E-mail: [email protected].

of references) can be declined in a wide range of references. (2) Processing flexibility: a product-specialized production system can be easily adapted to another production sequence. (3) Large-sense flexibility: the production system can simultaneously be used for the manufacture of various products. This work is devoted to the third case. Let us recall that it is quite common to classify batch processes into two categories: (1) multiproduct or flowshop plants, corresponding to a single set of processing units used in the successive production of a variety of different chemicals. (2) multiobjective or jobshop plants in which several product families are manufactured simultaneously, sharing the processing units according to specific synthesis. Due to the highest level of flexibility inherent in a multiobjective plant, this configuration has been adopted in this work. Note that the frontier existing between multiproduct or multiobjective batch plants is not always very rigid as the examples treated in the literature are often assigned to one or another category, according to recipe similarity and equipment sharing for the same production campaign. Figure 1 represents the different problems treated in the literature as functions of their complexity and flexibility. Note that most examples belong to categories 2 and 3. Due to the industrial importance of batch processes design operation and retrofit, multiobjective batch plant design problem has a strategic stake. The economic context makes redhibitory the semiempirical attitude, which has been prevailing until recently to design such plants, which often leads to too much equipment. The aim of this work is to determine the number and size of the necessary equipment items for every unit operation involved in the processing sequence of the different products to reach a given production level, while satisfying a technico-economical objective function. Three functions are classically distinguished, that is, long-term/medium-term planning and scheduling. They

10.1021/ie010646f CCC: $22.00 © 2002 American Chemical Society Published on Web 10/12/2002

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Figure 1. Complexity and flexibility of design problems.

all refer to temporal resource assignment for product manufacturing, but have different objectives: (1) The planning function is at the highest hierarchic level and pilots the physical production system within a long-term horizon. (2) Medium-term planning aims at implementing the preliminary operational planning for production capacity adjustment, supply definition, production, and annexed function synchronization (control, maintenance, delivery). (3) The next function consists of production scheduling that aims at the best use of material and human resources, with respect to manufacturing demands defined at the preceding level. It must be emphasized that despite their importance, the aspects relative to production planning are often simplified in the design problem resolution. Yet the specific features of fine chemistry imply taking into account intermediate products whose production must in turn be managed. Moreover, products may generate spatial constraints (storage in the active step of the equipment unit or in several external storage vessels in limited amounts) as well as temporal ones (stability conditions such as zero-wait, limited, or unlimited). More precisely, the design problem can be formulated as follows: Given (1) a set of N given products, production specifications, and a time horizon, (2) a set of equipment items classified according to their function in families, (3) manufacturing recipes for each product including precedence relations between unit operations and the corresponding operating times, (4) the set of possible equipment for each product, (5) the stable or unstable state of intermediate products and transfer rules between products, (6) use of levels for resources and transfer times between equipment, (7) storage availability, and (8) a technico-economical objective function, determine a workshop configuration that allows a given production level (i.e., capacity and number of both equipment units and storage vessels) to be reached to optimize the chosen performance criterion. A comprehensive review of the common approaches used in solving batch plant design is proposed in

Rippin.2 Most decisions in such a problem relate to structure choices as well as to unit sizes, which are discrete variables. The focus of design research was initially on the development of programming techniques. Various assumptions were introduced to simplify the formulation of batch plant design and to reduce the problem size. A summary of the various contributions in the treatment of this kind of problem is presented in Table 1. Because of the combinatorial explosion associated with the design problem, unbearably long computational time is generally involved with the use of mathematical programming. Moreover, some assumptions are generally introduced to effectively solve the problem, but they limit the generality of the approach. The objective of this paper is to present an alternative methodology based on a two-stage approach: (1) At the upper level, a genetic algorithm has been developed for solving the design problem and proposing several plant structures; this kind of algorithm has proven its efficiency for solving combinatorial problems (see a survey of optimization algorithms used in chemical engineering applications in Pibouleau et al.28 (2) At the inner level, a discrete-event simulation model (DES) is implemented for testing the technical feasibility of the generated configurations. This paper deals with the implementation of the DES model and is organized as follows. Section 2 develops the basic principles of the development of a discreteevent simulation model. Section 3 presents the various potential uses of the simulator. Section 4 gives a detailed account of model development and adaptations for design purposes. To demonstrate the effectiveness of the methodology, section 5 presents the features of the example serving as a test bench and being further used in part 2 of this series of papers devoted to the development of the GA. 2. Basic Principles of the Development of a Discrete-Event Simulation Model: From Scheduling to Design This section presents the principles of the discreteevent simulator AD-HOC previously developed in our

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5729 Table 1. Various Contributions on Batch Plant Design reference

resolution method/criterion

3

MILP-“branch and bound” cost minimization,profit maximization

4

MILP-NLP cycle time minimization

5

MINLP cost minimization

6

NLP cost minimization

7

MILP-NLP cost minimization

8


9

MINLP-simplex cost minimization

10

evolutive method (scheduling and design) cost minimization

11

NLP-MILP cost minimization

12

heuristic-NLP cost minimization

13

MINLP-heuristic cost minimization simulated annealing cost minimization

14

15

heuristic

16

MINLP cost minimization

17

MILP-“branch and bound”

18

heuristics “branch and bound”

19

MILP-“branch and bound” profit maximization

20

MILP-“branch and bound”

21

evolutive method interactive decisions cost minimization

22

genetic algorithms cycle time minimization (design and retrofit)

assumptions multiobjective connections between equipment, unstable products, storage vessels nondiscrete equipment size campaign mode production multiproduct cyclic campaigns one equipment unit/step storage policies: unlimited and zero wait multiproduct (linear recipes) parallel equipment (up to four) storage policies: unlimited and zero wait multiobjective one or two equipment units/step long campaigns of compatible products zero wait policy multiproducts one equipment unit/step identical batch size cyclic campaigns and zero-wait policy multiproducts monoproduct campaigns identical size for parallel equipment zero wait policy multiobjective long campaigns of “compatible products” one equipment unit/step zero wait policy multiobjective (nonlinear recipes) cyclic campaigns several equipment units per step, different sizes and zero wait policy multiobjective mono- and multiproduct campaigns (compatible products) no storage multiobjective out-of-phase parallel equipment storage policy: not mentioned multiproduct limited time storage policy multiproduct in-phase parallel equipment one storage vessel multiproduct one monoproduct campaign multiproduct one storage vessel nonidentical parallel equipment multiobjective storage policies: zero wait (between equipment) and unlimited (between operating steps) long campaigns in-phase parallel equipment multiproduct campaigns are not defined parallel equipment, discrete sizes multiproduct parallel equipment, discrete sizes limited storage policy uncertainty on products multiobjective parallel equipment multiproduct in-phase identical parallel equipment discrete sizes mono- and multiproduct campaigns one storage vessel multiproduct identical parallel equipment no storage

examples two products, four operating steps

example 1: two products, three operating steps example 2: six products, four operating steps example 1: three products, four operating steps example 2: six products, six operating steps seven products, ten operating steps

three products, four operating steps

three products, eight operating steps (semicontinuous and batch) example 1: 7 products, 10 operating steps example 2: 12 products, 10 operating steps four products, four operating steps (three equipment types) seven products, ten operating steps.

no example

two products, three batch and five semibatch operating steps several examples: up to 15 products, 3 batch and 7 semibatch operating steps three products, five batch and semibatch operating steps 15 products, 3 batch and 7 semi-batch operating steps three products, six operating steps (four equipment types)

three products, four operating steps two products, four operating steps

3 products, 3 operating noncyclic campaign steps, 13 tasks example 1: 15 products, 3 batch operating steps, 7 semi-batch operating steps example 2: 5 products, 10 batch operating steps and 15 semibatch operating steps four products, five operating steps

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Table 1 (Continued) reference

resolution method/criterion

assumptions

23

MILP cost minimization

multiproduct and multiobjective storage policies: zero wait and unlimited identical parallel equipment or one equipment unit/step with discrete sizes

24

MILP cost minimization, cycle time minimization, profit maximization MINLP genetic algorithms cost minimization

multiobjective zero wait and unlimited storage cyclic campaigns

25

26


27

SA/LP

multiproduct monoproduct campaigns parallel equipment with nondiscrete sizes storage policies: zero wait and unlimited monoproduct parallel equipment with nondiscrete sizes storage policies: zero wait and unlimited multiproduct and multipurpose batch plants

examples example 1 (multiproduct): five products, six operating steps example 2 (multiobjective): four products, three operating steps examples: up to five products, five operating steps (seven equipment units) examples: up to 15 products, 3 batch operating steps, 7 semibatch operating steps one product, five operating steps 5 products, 14 production routes

Figure 2. Finite state automaton for equipment.

laboratory for scheduling purposes.29 In the methodology adopted in this work, the simulator aims at determining the scheduling of the different operations and at using efficiently the necessary resources to reach the production level. In the following, the initial development phase of AD-HOC and the discrete-event simulation principles are briefly recalled. Since the queuing network model problem cannot be solved analytically, the chosen technique to represent the workshop behavior is based on a discrete-event simulation (DES) approach.30,31 The model allows the determination of the exact chronology of discrete events occurring in the facility. In this formulation, time evolution occurs by “event jump”, that is, from one event to the following one. To be concise, only the key points of the approach are presented in the following sections. Discrete-Event Simulation Objects. The following objects have been taken into account and modeled using the classical formalism of finite state automata: raw materials, utilities, maximal admissible effluent threshold, and products (final products, subproducts that can be either in situ recycled or not, and renewable resources (equipment, operators, and storage vessels for intermediate products)). Each state finite automaton is represented by a set of possible states and transitions between them, either conditional or predetermined, as well as by fixed or variable attributes. For the sake of illustration, the finite state automaton for “equipment” is presented in Figure 2.

Notion of Production Recipe. The model objects are linked by a production recipe for final products and recycling recipe for subproducts to be recycled in situ. Each recipe is thus constituted by successive operations representing the sequence synthesis: admissible equipment, reactive products, operators, utilities, operating conditions, operating times (input, treatment, output, and cleaning times). Typical Events. All the events have been characterized by their occurrence conditions and by their consequences, especially logical changes on finite state automata and generation of scheduled events. The typical events considered in the simulation core are of three types, conditional, predetermined, or reserved: (1) Conditional events (for instance, product load in an equipment item) are characterized by occurrence conditions, the associated state change logic, and the generation of the induced predetermined events. Seven conditional events have been considered: operator pause, storage vessel/equipment maintenance, storage vessel/equipment cleaning, and product load/unload. (2) Predetermined events occur at fixed dates (for instance, raw material supply). A predetermined event concerns only a system object and also involves an associated state change logic. (3) Reserved events (for instance, storage vessel reservation for a storage vessel), necessary for intermediate product treatment before the latest dates, complicate strongly the system behavior dynamics by

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imposing predetermined events which are much more difficult to manage than the previous ones. A reserved event can be viewed both as predetermined (since it occurs with no condition at a scheduled date) and conditional (with a state change logic concerning several system objects and involving one or several predetermined events). With all these elements in mind, the model dynamics is relatively complex. Some assumptions are classical, that is, fixed operating times, nonpreemptive tasks. Others are specific to Chemical Process Industries. The assumption set is presented in great detail in Baudet et al.29 For the sake of illustration, let us examine the reservation case, which is of major importance in the model. A product load is allowed under strict conditions concerning both necessary resource needs (equipment, operators, utilities, raw materials, etc.) and the future of the generated products, which have to be stored at an operation end as intermediate products if not directly consumed by the following operation. Since unstable or limited time stable products have to be managed, necessary resources for their treatment have to be reserved to prevent degradation. Every reserved resource may be used if its availability for a given reservation is guaranteed. For example, an equipment item reserved for the treatment of an unstable intermediate product may be indifferently used for maintenance, cleaning, or operation treatment under the condition that it will be available for the reserved event. The list of scheduled events is kept by increasing the occurrence date on the simulation module so that when no more events are possible at a time, the simulator engine looks for the next one in the scheduled list. Then the model progresses stepwise from one event to another, and the time progression jumps from an occurrence date to the following one until the end of the simulation. Finally, a decision rule library has been implemented for conflict management (competition of two products waiting for the same equipment item for instance) since several conditional events may occur simultaneously. It has been previously shown4 that their execution order has a major influence on production system performance. 3. Simulator Use The data, which are necessary for simulation runs, are as follows: (1) workshop architecture (equipment and storage vessels for intermediate products); (2) labor; (3) number, amount, and supply calendar of raw materials (RM); (4) number and nature of shared intermediate products (SIP); (5) final products (FP); (6) recycled products (RP); (7) nonrecycled products (NRP); (8) production or recycling product recipes; (9) production data: simulation horizon, batch treatment priority, batch release order (imposed or fixed by heuristic rules), and heuristic rules for conflict management. The simulator provides an important set of results. Only the most significant are presented here. At the end of a simulation run, the batch sequence, the beginning/ end of treatment times for each operation, and the cycle time are computed for every product. Other information concerning equipment (use and operation number) is useful for detecting bottlenecks. More precisely, the detailed activity of each equipment unit is available (treatment, load/unload, maintenance, cleaning, and the

associated operators). Similar results concerning operators are also provided (number of interventions, global activity rate, etc.). Several uses of the simulator AD-HOC are possible: (1) predictive decision-aid tool for predicting batch completion times with different operating conditions, detecting bottlenecks, and lack of raw materials; (2) direct production aid and determination of production system operating conditions; (3) reaction to breakdowns and evaluation of different policies; (4) design aid tool for analyzing different workshop structures. This work aims at using AD-HOC for design purposes by automatically generating workshop configurations, satisfying the required production level with respect to a technico-economical criterion. The following sections present the assumptions and adaptations of AD-HOC implemented for its coupling with a genetic algorithm (GA). The previously existing program AD-HOC has thus been extended and modified to take into account a design purpose. Of course, the initial version of AD-HOC was implemented with a reutilization purpose in mind. Since the objectives are quite different from short-term scheduling, it is necessary to present the main guidelines of the design approach. 4. A Discrete-Event Simulation Model for Design Purposes In our previous works, AD-HOC has been developed for short-term scheduling. When considering the preliminary design of batch plants, a long-term horizon has to be taken into account and a very precise plant simulation is not necessary. Campaign Mode Operation. First note that a general consensus for campaign definition does not exist. Several authors13 use indifferently the notions of campaign and long-term production horizon. They consider that the total production is achieved in only one time and neglect short-term production problems. Others8 consider successive long-term monoproduct campaigns providing the production level of several products. Another approach commonly used in the literature concerns the simultaneous manufacturing of several products under the condition that they do not share equipment, the so-called multiproduct campaigns.24 In this work, since a long-term production level is considered, the planning horizon has been partitioned into a number of time periods (campaigns), each dedicated to the production of a subset of products; campaigns are assumed to be identical (same length and same set of products for each campaign). According to Papageorgiou and Pantelides,32 the complexity of management and control of the plant operation is further reduced by operating in a more regular fashion, such as in a cyclic mode within each campaign, with the same pattern of operations being repeated as a constant frequency. This approach has the advantage of facilitating equipment polyvalence. The configuration feasibility is determined by its ability to reach a steady state, meaning that the number of work-in-process (WIP) products for each family is constant from one campaign to the following one so that the required production level is satisfied. Let us recall that WIP refers to the number of products which have not completed their production sequence at a given campaign. In each campaign, several batches are to be manufactured. The campaign length and batch size are assumed to be fixed. Each campaign is associated with

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Figure 3. Product release dates in a campaign.

a start date corresponding to raw materials availability. Note that the batch residence time is computed from this date to the product completion time in the last unit operation. The effective start of treatment is determined in fact by the equipment availability of the first recipe step. It is also possible to put back some product release dates in a campaign. An illustration is presented in Figure 3 where four batches have to be produced per campaign; the first two begin their production sequence at the start of the campaign and the other two start at D1 and D2 time units. Note that the simulation model logic requires knowledge of all batch data from the beginning of simulation. Model parameters thus include the number and batch volume as well as batch release date for the first campaign. Parallel Equipment Treatment. Each task represents a fine chemistry unit operation. All parallel equipment is assumed to be available for carrying out a unit operation (i.e., polyvalent equipment) for all recipes using this unit operation. For the design of a batch process, the decision on the mode of operation of the parallel units (i.e., in-phase or out-of-phase) is one of the key influential factors to the behavior of the process. Let us recall that the in-phase mode corresponds to the synchronous activity of two or more parallel units (start and completion times of tasks are the same for all concerned units); in turn, an out-of phase mode corresponds to asynchronous behavior. Such constraints are generally included in the majority of published works for purely mathematical reasons since they reduce the complexity and size of system equations. In our approach, the coupling DES/GA allows both cases to be modeled easily. Practically, it means that the operation mode of a set of parallel units for a particular stage is decided automatically by the simulator and selected from equipment availability criterion. In the original version of the model, addition or suppression of an equipment unit implies changes for recipes using this unit. Since our approach implies the scanning of different configurations, an extension has been proposed to easily change the workshop configuration without modifying the product recipes. Discrete Sizes of Equipment. Discrete sizes of equipment items are assumed and a set of sizes is available for each operation (see Figure 4 for a plant involving three equipment items and three sizes per

Figure 4. Example of discrete sizes for equipment items.

equipment item). This hypothesis is valid since, on one hand, the majority of available equipment for fine chemistry applications has a standard size and, on the other hand, the batches considered in this study have discrete sizes. It must be emphasized that there exists an interdependency between equipment and batch sizes. This aspect will be detailed in the example treatment. Note that batch merging is possible for batches arriving at the same manufacturing step (limited to two batches). Batch splitting is also considered (with no limitation concerning its number); it is yet obvious that this tendency must not be favored systematically since it can contribute to workshop performance degradation and particularly deteriorate product residence times. In the approach, the number of possible sizes for an equipment item has been limited to three, that is, “big”, “average”, and “small”, which also further simplifies configuration encoding in the GA implementation phase. Practically, the more adequate equipment volume corresponds to the manufacturing of one batch by using the unit at 100% of the allowed maximal capacity. In the case of very different recipes requiring the same type of equipment, it seems interesting to favor equipment sizes, allowing the treatment of one batch per equipment unit, and to limit splitting. Steady-State Regime. The objective is to satisfy the demand in the studied time horizon. For this purpose, the workshop simulation is performed from an empty


state and then goes on by updating the corresponding dates at each campaign, until one of the following conditions is reached: (1) the required production level is reached (steady-state or oscillatory regime); (2) the maximal product residence time for the first campaign is reached; (3) the maximal residence time for any product is reached; (4) the maximal campaign number is reached. Only the plant configurations, which lead to a steadystate or oscillatory regime, are allowed. Of course, this notion seems ideal since the production may be altered by unpredictable situations such as operator unavailability, storage limitations, flow bottlenecks, and equipment failures. This assumption may be found restrictive but has been adopted since it efficiently prevents plant bottlenecking. (See our previous works on semiconductor manufacturing where model predictions and experimental behaviors of wafer fabs were compared.33) The other stop conditions mean that the configuration proposed by the GA does not allow the required production in good conditions. They constitute threshold values introduced by the user in the list of data for simulation runs and prevent an excessive number of simulations when a given configuration does not satisfy the required production level in an acceptable time horizon. Typical values for these stop control variables are presented in the example. The parameters considered in the control procedure for steady state are the production level and the average and maximal residence times for all products of the same campaign. The steady-state regime is assumed to be reached when the values of these parameters are identical for three consecutive campaigns. This value has been determined from trial and error simulations and appears to be a good compromise to avoid an excessive number of calls to the simulator. This consideration allows short-term scheduling and long-term planning conciliation, with the aim of guaranteeing the long-term required production level. An illustration is proposed in Figure 5a,b. In this example, the required production level is 1000 L of product A, 1000 L of product B, and 500 L of product C per campaign. The production is organized in four batches (one of A, one of B, and two of C). Yet the production level is not a sufficient criterion for determining whether a steady-state regime is reached. From the example (see Figure 5a), it can be considered that this regime is reached from the second campaign since the production level is reached. Figure 5b shows that the average residence time increases from campaigns 2 to 3, thus inducing a WIP increase. If this trend goes on, it may lead to production level degradation and even to a workshop blocking (it is not the case in the proposed example). It is to be noted that the production level and the residence time of the products in campaign 1 are less than those of the other campaigns since the plant is underutilized at the beginning. The oscillatory case is illustrated in Figure 6a,b: the production levels per campaign and/or the average and maximal residence times are alternated between two nonconsecutive campaigns, under the condition that the average production level of the two last campaigns reaches the required production level for each product. Figure 6a shows that the production level of product A begins to oscillate between the fourth and sixth campaigns (the levels of products B and C are constant). This phenomenon is repeated in the following cam-

Table 2. Different Types of Products Considered in the Model and Corresponding Storage Capacity product type raw material (RM) intermediate product (IP) final product (FP) shared intermediate product (SIP). nonrecycled product (NRP). recycled product (RP)

storage capacity unlimited limited unauthorized storage for unstable products unlimited unlimited limited or unlimited limited

paigns. From Figure 6b, the average and maximal residence times oscillate too. Although the production levels for product B in the fourth and sixth campaigns are inferior to the required level, it can be observed that the level at the fifth campaign is greater and makes up for lack of product during the fourth campaign. Products, Raw Materials, and Intermediate Products. Table 2 presents the different types of products considered in the model and the corresponding storage capacity. Raw materials (RM) can be provided by external supplies or can be released as secondary products; they are stored in unlimited capacity vessels (i.e., raw material excess does not generate constraints). Yet the lack of one or several raw materials may penalize production. To prevent this, a mass balance, which will be presented later, has been integrated in the simulation model to compute the necessary amounts and to prevent supply management. Intermediate products (IP) are manufactured in the workshop and are classified according to their nature in either stable, unstable, or limited-time stable products. Stable intermediate products can be stored in limited capacity vessels; their management may thus involve some constraints linked to their reservations during the coupling between the GA and the simulation model. This aspect will be tackled later. Final product (FP) manufacturing sequences are described by recipes, which involve raw materials and intermediate product use (even secondary and/or shared intermediate products). Final products are stored in unlimited capacity vessels. In the context of this study, the control on final product periodical output is very important with respect to the steady-state regime test. Shared intermediate products (SIP) are manufactured in the workshop as main products according to a specific recipe (they may also be generated as secondary products in an operation output). They are then used in the production of several different products (final and/or other intermediate products). Since they can be considered as either raw materials for some products or final products for some recipes, the same storage policy has been adopted, that is, in unlimited capacity vessels. SIP overproduction does not generate constraints but their underproduction may limit final product manufacturing. Nonrecycled products (NRP) and effluents are secondary products and do not follow a specific manufacturing recipe. In the simulation model, different storage vessels for NRP can be considered, either limited in capacity or unlimited (for instance, when discarded directly to waste). In a short-term study, it is necessary to predict the regular outputs outside the workshop. Several simulations have shown that the vessels filling up may disturb the establishment of the steady-state regime. To prevent this phenomenon, important vessel sizes have been introduced. In the original version of the simulation model, products to be recycled in situ are taken into account

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Figure 5. (a) Production level for the steady-state regime. (b) Average residence time for the steady-state regime.

and share workshop resources for their production following specific recycling recipes. Yet, in the context of design, the recycling of these products becomes a secondary task since priority is given to the production of main products; the treatment of products to be recycled is achieved at the end of the campaign when all the main products are manufactured, which can disturb steady-state regime.

Flexible Storage Tanks for Intermediate Products. The maximal storage capacity for intermediate products is fixed (i.e., maximal number and volume of vessels). In the design version of the model, the effective storage need is then computed according to the vessel number and capacity effectively used by each configuration. Investment cost for storage vessels is taken into account for the total cost computation.


Figure 6. (a) Production level for the oscillatory regime. (b) Residence time for the oscillatory regime.

Initially, the simulation model logic has implied that a storage vessel is reserved every time an operation is involved in an equipment item. (Storage inside the equipment unit which serves as the active step of the process is not allowed here.) This reservation policy may lead to a storage vessel over-equipment since a storage tank may not be used after being reserved. Another approach has been implemented for limiting their

number. The evolution of the intermediate product amount, which has been effectively stored, is followed and the storage vessel volume is computed. The new management rules are as follows: (1) Storage vessels are considered to be polyvalent (only one type is available). (2) When an intermediate product does not find any available equipment unit for the following step of its

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Figure 7. Elimination of nonused equipment.

manufacturing sequence, it is preferentially stored in a storage vessel that already contains this product or in an empty vessel. (3) Cleaning times are not taken into account: as soon as an intermediate product can go on its procedure synthesis, the storage vessel is considered free and clean, that is, available for storing another product. (4) The volume of any vessel finally taken into account in the criterion computation is equal to the maximal stored volume during a simulation run. It must be emphasized that the effective use of storage vessels depends markedly on product scheduling. Any change in campaign management parameters (fixed by the user) and the simulator logic may have a major impact on intermediate product storage. This aspect will be tackled in part 2 of this series of articles. Moreover, it is generally admitted that, except for specific cases, the investment cost of a storage vessel is far less important than that of the equipment: a slight storage vessel over-equipment generally contributes to the best workshop flexibility. In most of the studied cases here, a production release order has been imposed for all batches: all batches begin their production in a predefined order with the intermediate products first followed by the final product, the order of which has been fixed. This release order may be unfavorable in some contexts but it allows estimation of the order of magnitude in storage vessel needs. Results have yet shown that flexible enough configurations can be generated in most cases with respect to steady-state establishment. An optimization of this parameter can also be envisaged a second time during the scheduling phase, which takes place after the design phase. Elimination of Nonused Equipment. Let us recall that the aim of the GA is to propose possible workshop configurations. It is yet possible that, in some cases, one or several equipment units are not effectively used during the simulation of the proposed configuration. The nonused equipment items are then eliminated in the final structure, as previously done for storage vessels (see Figure 7). A difference yet exists: the effectively used volume is not taken into account for equipment: a partially used equipment item will be kept and its nominal capacity unchanged. This assumption confers a noticeable flexibility in the possible configuration propositions; overequipped superstructures will be corrected by the simulator according to the effective equipment needs. Other Assumptions. Despite their importance, resources such as operators and utilities are not taken into account at the workshop design phase. Preliminary

simulations have shown that the establishment of the steady-state regime may be very sensitive to these parameters. The unavailability of an operator may disturb production even with a workshop configuration, which is an excellent option with a sufficient number of operators. In this study, we had rather not take into account operators and utilities in recipe modeling, instead of considering them in excess as unlimited quantities. Moreover, the optimization of the operator number and of the utility amount is an entire problem, which seems more judicious to relegate to the short-term scheduling phase, as carried out in our previous works.4 The same assumption is valid for preventive maintenance scheduling, which has not been modeled for design purposes. Since operators and utilities are not taken into account and since storage vessels are considered to be polyvalent, the workshop is constituted of only one production zone (in the original version of the model, several zones can be modeled). Another simplification resulting from the hypothesis about operators concerns the input/output times of products in equipment. Load/unload are not conditioned by operators. As soon as an equipment item is free, the following operation can begin by waiting queue management. (Heuristic rules will be presented later.) The hypothesis is identical for unload: as soon as an operation ends, the generated product can go to the following step. Input and output times are actually globally considered in the operating time. The cleaning time can also be added to the operating time. Two predetermined events, which constitute data for the simulation model, have a great impact on simulation execution: (1) External supplies: a lack of raw materials may considerably delay the production of a given product. (2) Storage vessel emptying for in situ nonrecycled products: when a storage vessel used for an NRP reaches its maximal capacity, the operations generating the given NRP are delayed until partial or total vessel emptying. The occurrence of at least one of these events may delay the establishment of the steady-state regime unless they are scheduled at regular intervals. We consider once more that this calendar management belongs to the scheduling phase and that its interest is marginal for design. As previously mentioned, a mass balance procedure has been introduced in the model to determine the necessary raw materials quantities and the exact production level for NRP (for which the storage vessel volume is limited). The balance also verifies that enough shared intermediate products are produced over the


Figure 8. Data, results, and applications of the mass balance.

total time horizon constituted by the successive campaigns, to satisfy the required production level for the main products. Another use of the mass balance results concerns the batch organization for SIP. From the necessary SIP amounts to be produced per campaign, several scenarios are proposed by the model: (1) production of the concerned intermediate product in only one batch; (2) production of the concerned intermediate product in several batches (one batch for each main product using this SIP; (3) the SIP batch size can be chosen by the user: a coherence test verifies if the declared volume is sufficient or exceeds the necessary quantity. An example will illustrate this approach. The data, results, and applications of the mass balance are presented in Figure 8. Choice of Heuristic Rules. Due to the simplifications introduced in the design version of the model, an important number of conditional events are removed and the corresponding heuristic rules become unnecessary. In the following, conditional events, which have been effectively considered, and the selected heuristic rules are presented: (1) Operation load, choice of an equipment item among several units: priority is given to equipment for which the workload already carried out is maximal. This choice is based on the idea of maximizing equipment use rate, to find configurations with relatively low equipment number. Another heuristic rule consists of selecting the equipment item which is available since the least amount of time and similar results have been obtained. (2) Operation load, choice of an operation among several waiting operations: the rule consists of selecting the operation that arrived first in the waiting queue (the so-called “first in first out” (FIFO) rule); it has proven to be the most efficient in a campaign production policy since it aims at reducing product waiting time in front of equipment; otherwise, some products may wait during several campaigns, thus disturbing steady-state establishment. Concerning the order of conditional event execution, priority has been given to equipment unload to release them for the following tasks as soon as possible.

5. General Presentation of the Treated Example The study presented here is performed using a didactic workshop presenting the common features of a fine chemistry workshop: presence of shared intermediate products, unstable intermediate products equipment, and storage share throughout the same campaign. Let us recall that this element confers a large flexibility to the workshop by favoring the inherent polyvalence to a multiobjective production policy. The data necessary for simulation runs are the same as those presented in the companion paper of this article for design purposes. For simulation runs for scheduling purposes, the data list is more important (see Baudet et al.4 for more details). Product Range. Five ranges of products have to be manufactured (A, B, C, D, and E). Products D and E are generated from a shared intermediate product SIP1. Beside these products, four in situ nonrecycled products have to taken into account in the simulation phase (NRP1 to NRP4). Equipment Type. The considered workshop has five different equipment items as presented in Table 3: two kinds of reactors, a settling tank, a distillation column, and a filter unit. Recipes. Recipes represent the detailed description of the necessary processes to transform raw materials into final products. Let us note that other useful formalisms are used in the literature for representing chemical processes (Table 4). The state task network (STN) of Kondili et al.34,35 was developed as a way of representing chemical processes. The STN shows only the process recipe and gives information about plant resources, units, and their connectivity. The resourcetask network (RTN) representation of chemical processes was proposed by Pantelides36 to describe processes by way of classifying their components resources and tasks. In contrast to the STN representation, the RTN makes no distinction between the different types of resources (e.g., equipment units, utilities, and manpower are all treated in the same manner). The formalism used in this study (see Figures 9-14) is presented and the example of the recipe of product A is detailed widely (Figure 9).

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Table 3. Different Equipment Items for the Example

Table 4. Symbols Used in the Recipes Presentation nomenclature RM PNR R% β% T.EQ T.OP SF U S

raw material nonrecycled product proportion of entrant reactive quantities as a function of the operating volume of the input operation proportions of generated products as a function of the operating volume of the output operation equipment type operating time size factor unstable product stable product

(1) Reaction: raw materials RM1 (10%) and RM2 (90%) are introduced in the double-jacketed reactor. After 100 min of reaction time, an unstable product is formed, F1A, and immediately transferred to the following step. (2) Reaction: product F1A and raw material RM3 are equally introduced in the simple reactor. After a 120-

Figure 9. Recipe of product A.

min reaction time, an unstable product, F2A, is generated. (3) Settling purification: product F2A is transferred to the settling unit. After 200 min, two phases are present: a liquid phase containing a stable intermediate product (F3A representing 95% in volume of the operation) and a crystalline phase containing an in situ nonrecycled product NRP1 (5%). (4) Filtration: product F3A (40 min) is then purified by filtration to obtain product A, by elimination of the crystals of NRP1, which are still remaining in the solution. The amount of crystals at filter output has the same volume proportion as in the previous step. This recipe is formulated using the following concepts: (1) relationship between operation unit of the recipe and equipment type; (2) operating time; (3) the “size factor” of the operation (SF), defined as the ratio between the total operation volume and reference volume ratio of 100 units of volume of final product; (4) entrant reactive quantities and their proportions as a function of the


Figure 10. Recipe of product B.

Figure 11. Recipe of product C.

Figure 12. Recipe of product D.

operating volume of the input operation; (5) generated products and their proportions as a function of the operating volume of the output operation; (6) stable or unstable nature of the outgoing intermediate products; (7) the future of the generated intermediate products, that is, the number of the operations in which they will be consumed. Production Data. Products to be manufactured and their respective amounts are assumed to be imposed by market demand. In this case, the campaign production policy is defined in the following terms: (1) number of batches for each campaign; (2) batch size; (3) campaign length. Of course, an identical production level can be obtained through different production planning strategies. In this way, the determination of campaign length and batch size constitutes true optimization problems,

which are not taken into account in this study. Let us note that this problem is strongly dependent on industrial practices and on equipment size, which conditions the most adequate batch size. The production level considered in the example is summarized in Table 5. Note that the final product volumes correspond to an operating volume of 100 L for the last operation of each recipe. The amount of intermediate product depends on the quantities consumed by final product manufacturing (500 L of SIP1 to produce a batch of 1000 L of D and 500 L for each of the two batches of product E, i.e., 1500 L). This amount is computed by the mass balance module, which proposes three scenarios: (1) production of SIP1 in only one batch (1500 L here); (2) production of a SIP1 batch for each final product batch (three

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Figure 13. Recipe of product E.

Figure 14. Recipe of SIP1. Table 5. Production Level Considered in the Example production per campaign of 600 min

total

final product A: two batches of 900 L final product B: one batch of 600 L final product C: one batch of 950 L final product D: one batch of 1000 L final product E: two batches of 1000 L shared intermediate product 1: three batches of 500 L

1800 L 600 L 950 L 1000 L 2000 L 1500 L

batches of SIP1 in this example); (3) number and batch size given by the user. The data concerning both the order and release dates of products (via a calendar which will be used in the following campaigns) are also defined in this module. The chosen scenario is the following one: the shared intermediate products are produced first followed by final products. Data on Equipment Sizes. Equipment sizes are considered as discrete values. For each unit operation, a maximum of 10 parallel equipment items is assumed and a range of three possible sizes is proposed. The model actually guides the user by proposing adequate values in accordance with the computation of the socalled size factor and with batch volumes using this kind of equipment. The procedure is illustrated for equipment of type 1 (double-jacketed reactor). The recipes using this unit are relative to final products A, B, C, and D and to shared intermediate product SIP1. Table 6 mentions the data concerning the size factors and batch volumes using this equipment type. From these data, the calculation of the adequate sizes proceeds by multiplying the batch volumes by the corresponding size factor and dividing it by 100. They simply represent the volumes, which fill the unit with at first no consideration of splitting or merging. The obtained values are as follows: 500, 1000, 950, 1000, and 500. The simulator will then propose {1000, 950, 500}. The same procedure is applied for other equipment types (see the results in Table 7). If these values strongly differ from the available market standard sizes, it is then advised to consider again batch sizes and campaign length to find a satisfy-

Table 6. Batch Volumes and Size Factors for Equipment of Type 1 (Double-Jacketed Reactor) batch size [type of product]

size factor (operation(s) using equipment of type 1)

two batches of 900 [product A] one batch of 600 [product B] one batch of 950 [product C] one batch of 1000 [product D] three batches of 500 [PIP1]

55.56 (operation 1) 166.67; 166.67 (operations 1 and 4) 100 (operation 4) 100 (operation 3) 100 (operation 1)

Table 7. Equipment Sizes Proposed by the Simulator equipment type 1 double2 3 4 jacketed simple settling distillation 5 reactor reactor tank column filter proposed size(s)

1000 950 500

2000 1000

2000 1000

1000

1000 950 500

ing compromise. In the example, it can be observed that two very similar values are obtained for reactors as for filters (950 and 1000 L). In these conditions, it seems much more judicious to adopt the value of 1000 for favoring equipment polyvalence. Let us now assume that the available market standard equipment sizes are 500, 1000, 2000, and 4000 L for the five equipment types. We have then to choose among them the most adapted values to the production planning by considering the proposed volumes (see Table 7) but also batch merging and/or splitting. The size ranges, which will be finally taken into account in the example, are presented in Table 8. The abbreviations [M], [N], and [S] correspond respectively to the following possibilities: [M] ) merging, [N] ) normal path, and [S] ) splitting. Let us recall that, in most cases, it had rather favored merging instead of splitting. Thus, in the case of the

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5741 Table 8. Volume Range: [M] ) Merging, [N] ) Normal Path, and [S] ) Splitting equipment type volume range 1 2 3

1 double-jacketed reactor 2000 1000 500

[M] [N],[M] [N],[S]

2 simple reactor 4000 2000 1000

[M] [N],[M] [N],[S]

4 distillation column

3 settling tank 4000 2000 1000

[M] [N],[M] [N],[S]

2000 1000 500

5 filter

[M] [N] [S]

2000 1000 500

[M] [N],[M] [N],[S]

Table 9. Values of Coefficients A, B, and C Used in the Example cost coefficients

double-jacketed reactor

simple reactor

settling tank

distillation column

filter

storage vessels

A: B: C:

105 000 650 0.6

82 000 550 0.6

70 000 550 0.6

320 000 600 0.6

120 000 450 0.8

35 000 120 0.6

simple reactor, the proposed sizes are {4000, 2000, 1000} instead of {2000, 1000, 5000}. Moreover, workshop configurations with reactors of 500 L could not be accepted by the simulator due to the unstable nature of the first intermediate product of the final product A recipe. Data on Storage Vessels. The capacity and maximum number of storage vessels have to be defined in the data input module. All storage vessels are considered as polyvalent and several batches of the same product can be stored in the same unit. A storage vessel per stable intermediate product for the recipe set is first introduced. The simulator then computes the storage vessel number and volume, which have been effectively used. In the treated example, 14 stable intermediate products are involved: (F2A, F3A, F1B, F2B, F3B, F4B, F1C, F2C, F3C, F1D, F2D, F1E, F2E, F1SIP1). A maximum volume of 5000 L is considered for each storage vessel. Data on Cost Coefficients. The investment cost for equipment and storage vessels is deduced from classical relations of the type

cost ) A + B (volume)

C

Coefficients A, B, and C are defined for each equipment type and storage vessel. The values used in the example are presented in Table 9. (Note that they are arbitrary values.) Stop Control Variables of the Simulator. In the two-stage methodology, the simulator calls represent the main computation time. The maximum number of campaigns to be run has thus an important influence. This explains why it is particularly judicious to stop the simulator when the steady-state regime is reached or when the number of accumulating products is so high that this regime will not be reached for the actual configuration far below the maximum campaign number. Additional data are therefore necessary and concern the following: (1) The maximum residence time of products of the first campaign: in some cases, during the workshop start-up phase, it seems important to guarantee the product output below an admissible given time. If not, the proposed configuration will not reach the steadystate regime and will be rejected. (2) The maximal residence time of any product: the product sequence in the first campaign (i.e., when the workshop is empty and equipment available) is not the same as in the following ones. An additional constraint rejecting configurations for which any product exceeds a given residence time has thus been introduced since

the increase in product residence times is attributed to a lack of equipment for carrying out the necessary tasks from raw materials to final products. In the example, a maximum residence time of four campaigns (i.e., 2400 min) for the products of the first campaign has been adopted. Conclusion This paper has presented a simulation model for design purposes of batch plants that takes into account the specific features of a multiobjective plant. This prediction model can be useful for improving a design and can estimate the changes in plant performance by varying some parameters. This model will now be embedded in an outer optimization loop based on a GA to be systematically used for design purposes. The formalism presented through the detailed example will now be used in the companion paper of this article. Notation A, B, C ) coefficients for computing the investment cost for equipment and storage vessels DES ) discrete-event simulation FP ) final products GA ) genetic algorithm IP ) intermediate products N ) number of products NRP ) nonrecycled products RM ) raw materials RP ) recycled products SF ) size factor SIP ) shared intermediate products WIP ) work-in-process

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Received for review July 30, 2001 Revised manuscript received June 27, 2002 Accepted June 27, 2002 IE010646F

Multiobjective Batch Plant Design - American Chemical Society

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