Integrating Production Control and Scheduling in Multisite Enterprises

Article pubs.acs.org/IECR

Integrating Production Control and Scheduling in Multisite Enterprises on the Basis of Real-Time Detection of Divergence Preeti Rathi,† Shanmukha Manoj Bhumireddy,† Naresh N. Nandola,‡ Iiro Harjunkoski,§ and Rajagopalan Srinivasan*,† †

Indian Institute of Technology Gandhinagar, VGEC Complex, Chandkheda, Ahmedabad 382424, India ABB Global Industries and Services Limited, Whitefield, Block-1, Bhoruka Tech Park, Bangalore 560048, India § ABB Corporate Research, Wallstadter Strasse 59, D-68526 Ladenburg, Germany ‡

ABSTRACT: Scheduling and process control have been long recognized as the two critical building blocks in many manufacturing execution systems. Operating at the interface between the supply chain and the process, the scheduler generates a detailed schedule that has to be executed by the process so as to meet the demands originating from the supply chain. Given the tight interactions between the two, there has been wide interest in integrating scheduling and process control. Our key insight is that abnormalities which occur after generation of the original schedule trigger a divergence between the operational targets defined by the schedule and its execution. If left uncorrected, then the abnormalities will propagate between the process and the supply chain. A timely response could eliminate or minimize such effects. However, this is a challenge particularly in large multisite enterprises where the scheduling and production responsibilities are typically separated across departments and even across geographical locations. Recognizing this, we propose a novel, scalable framework for integrating scheduling and process control that detects in real time when a divergence occurs between the original schedule and its execution in the process. It then identifies the root-cause(s) of the divergence, i.e., the abnormality, and triggers a suitable response from the scheduler and the process so as to nullify or minimize its effect. In this paper, we will describe the proposed approach and illustrate it using two industrially motivated case studies.

1. INTRODUCTION A typical supply chain encompasses raw material procurement, storage of raw materials, processing, storage of products, and its dispatch to customers.1 During operations, customer orders are collected, demand for various products are calculated, and on the basis of these a production schedule is generated. The schedule is implemented on the process with the help of regulatory and advanced controllers that ensure that any disturbances are rejected and transitions are optimally executed. The performance of the supply chain can be measured through various key performance indicators such as number of orders fulfilled, number of partial orders, number of canceled orders, plant utilization, and volume of orders fulfilled over a horizon. On the basis of these key performance indicators, organizations determine the success of their operations in achieving their goals. Unhindered and timely flow of material, information, and finance between the entities in the supply chain is crucial in this context. Toward that end, companies have implemented various systems for planning, scheduling, and advanced control, but these technologies operate at different spatial and temporal scales in the decision-making hierarchy. Blockage in any of the supply chain entities would lead to undesirable events such as process shutdown, financial loss, undersupply, or oversupply.2 Integrated real-time decision making is therefore essential to smooth operation of the supply chain. This paper seeks to © 2016 American Chemical Society

study the role of integrated scheduling and process control in industrial-scale manufacturing supply chains. Scheduling involves deciding on the amount of products to be produced, the allocation of resources to each product, the sequence in which the different products are to be made, and the times these products are to be processed. The schedule also provides set points of the controlled variables.3 The scheduling problem is often formulated as an optimization problem that seeks to minimize the production timespan, lateness, earliness, or some other performance function.4 The time horizon for scheduling typically ranges from days to months and is a function of the typical run length of the operation or the lead time for critical raw materials. Schedules are sent to the production unit where process controllers control the transformation of raw materials into products as per the schedule. Control involves real-time manipulation of selected production variables to reject short-term process disturbances and to hold key product qualities and production rates near their desired target values while ensuring that equipment operating limits are not violated.5 Two types of control decisions can be Received: Revised: Accepted: Published: 5681

December 3, 2015 March 18, 2016 April 22, 2016 April 22, 2016 DOI: 10.1021/acs.iecr.5b04626 Ind. Eng. Chem. Res. 2016, 55, 5681−5695

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Industrial & Engineering Chemistry Research

Figure 1. Summary of information sharing for the offline approaches toward integrating scheduling and control.

decision that has to be jointly implemented by two distinct departments is often impractical. Finally, these require that companies adopt a completely new approach to scheduling and control that would rarely find industrial acceptance. A practical approach to integration would allow companies to retain their existing control and scheduling technologies, operate as per their decision-making roles, and yet enable their integration and the concomitant benefits. In this paper, we propose a novel framework, called attaché, which addresses this need. The structure of the rest of the paper is as follows. Section 2 summarizes the literature on integration of scheduling and process control. The proposed framework for integrated production control and scheduling is described in section 3. In section 4, the framework is illustrated on two industrially motivated case studies: a thermomechanical pulping (TMP) continuous process and a penicillin fermentation batch process. Different process abnormalities are considered to illustrate the benefits of integration. A robustness analysis is then performed in section 5 to show that the performance improvement gained is relatively insensitive to various parameters.

distinguished: multivariable supervisory (or model-based) control and regulatory control. The former receives targets in the form of set points from the scheduler, whereas the latter gets the set points of controlled variables from the former and acts directly on the process.3 The control horizon depends on the time constants of the process and ranges from seconds to minutes. The products thus produced by the process are dispatched to customers. Traditionally, scheduling and process control problems have been addressed separately. From a scheduling point of view, the focus is on determining optimal production sequence, production times for each product, and quantities that lead to maximum profit or minimum completion time. Commonly, during scheduling, the dynamic behavior of the underlying process is not taken into account. The transition times between the different product combinations are assumed to be known as fixed values; hence, the dynamic profile of the chosen manipulated and controlled variables is not taken into account.6 More recently, models that incorporate the process’ dynamic behavior have been embedded into the scheduling optimization formulation. Similarly, control problems focus on optimizing the periods of transition between products through selection of the transition trajectory.7 It is normally assumed that the production sequence is fixed. Hence at this level, scheduling decisions are taken as given and immutable.6 However, this leads to suboptimal outcomes especially during abnormal situations. Any abnormality that occurs during the execution of a schedule results in a deviation from production targets. If scheduling and control decisions could be suitably integrated or if information can at least be shared between scheduling and process control without delay, then it would facilitate more economical process operations because controllers will have enough information about the goals of the supply chain to plan sequences that avoid costly setups and change-overs, and the scheduler would consider the process capabilities and thus avoid schedules that lead to operational problems.8 In the literature so far, several new scheduling formulations have been proposed to achieve such integration. The integrated problem in most cases is formulated as a monolithic, complex, large-scale optimization problem whose solution determines both the control and scheduling decisions. This integrated problem is computationally challenging and not suitable for real-time use. Also, especially in large-scale multisite enterprises, different departments have responsibilities for decisions related to production control and scheduling. A complete conjoined

2. LITERATURE REVIEW Integration of scheduling and control has received some attention in the literature.9 Engell and Harjunkoski8 provide a detailed review of the nature of the integration; because there is some variability in the scope of scheduling and control as practiced in different contexts, as pointed out by Lindholm and Nytzen,10 the role of integration is not uniquely specified. Much of the published literature has looked at case-specific issues such as cyclic scheduling in batch plants or short-term schedules. There is also a dichotomy in the literature between continuous and batch processes which originates from the fact that the nature of the scheduling problem as well as of the control problem are significantly different between the two modes of operation. Previous work can also be broadly classified as offline and online approaches. In the former, the predominant approach has been to incorporate detailed knowledge of the process dynamics into the scheduling formulation and solve the scheduling and control formulations simultaneously. In contrast, the latter seeks to account for process abnormalities as they arise and generate new schedules. Below we summarize some of the key themes in the literature; the interested reader is referred to Baldea and Harjunkoski3 for a detailed review. 5682

DOI: 10.1021/acs.iecr.5b04626 Ind. Eng. Chem. Res. 2016, 55, 5681−5695

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Figure 2. Typical information exchange between scheduling and control layers.

the schedule, accounting for them offline is not always possible and rescheduling may become necessary.15,16 As real-time integration requires close coordination between the scheduling and process control decision layers, Munoz et al.4 proposed an ontology for effective communication between the two levels so as to improve the decision-making process. The online approach to integration of scheduling and control relies on a feedback mechanism to deal with disturbances whose effects propagate to the supply chain. Zhuge and Ierapetritou7 proposed a closed-loop approach to counteract process disturbances. As in previous work, scheduling and process dynamics were modeled simultaneously by incorporating the latter as constraints in the scheduling problem. First the integrated problem was solved off-line to obtain the scheduling solutions and controller inputs and then the solutions implemented in the process. Then in real time, state variables that reflect the process were tracked vis-à-vis precalculated reference values. If a significant difference between the state and reference values was detected, then a feedback was activated wherein the integrated problem was solved again for the remaining part of the production cycle. Consequently, both the scheduling solutions and control inputs were updated. An online strategy has also been reported by Chu and You17 who focused on the computational complexity of the integrated problem and pointed out that the computationally expensive nature of solving MIDO problems restricts their use to the offline case. They therefore proposed a computational strategy based on the decomposition of the control problem from the integrated one and uses the PI controller parameters as the decision variables. To deal with uncertainties and abnormalities, the integrated problem was resolved to update the processcontrol parameters rather than process-control variables. Chu and You18 extended their prior approach17 by formulating it as two different feedback loops working in different time scales: a top-level rescheduling feedback loop and a bottom-level process-control feedback loop. The top-level rescheduling feedback loop was event-driven and did not need to be solved in the same high frequency as the controller loop. As evident from the above review, previous approaches to integration require totally new scheduling technologies whose robustness and resilience in real-life industrial settings have not yet been widely demonstrated. More importantly, industrial-

A summary of the offline approaches to integrated scheduling and control is presented in Figure 1. Traditionally, scheduling and control shared limited information such as transition times, transition cost, task lengths, quantities produced, and production schedule. This leads to various shortcomings. The scheduler is ignorant of the process because it does not consider the dynamic behavior of the process while making decisions. The controller also does not consider the (economic) objective of the scheduler. This motivated sharing of more detailed process information while generating schedules. Among the earliest works, Bhatia and Biegler11,12 integrated process dynamics consideration in batch scheduling and demonstrated a significant improvement in profitability. Flores-Tlacuahuac and Grossmann6 proposed a simultaneous scheduling and process control formulation by explicitly incorporating process dynamics in the form of differential/ algebraic constraints into the scheduling model. The simultaneous problem was cast as a mixed-integer dynamic optimization (MIDO) problem. Because the direct solution of the MIDO problem for systems with the complex dynamics is not computationally feasible, it was transformed into a mixedinteger nonlinear programming (MINLP) problem based on orthogonal collocation on finite elements. The formulation was able to handle nonlinearities arising from input and output multiplicities in the process. More recently, Capon-Garcia et al.13 proposed an approach for the short-term scheduling of batch plants that explicitly accounts for complete process dynamics with the focus on optimization of dynamic control variables as well as scheduling ones. As another variant, Park et al.,14 proposed using low-order models describing the closedloop input−output behavior of the process, called internal coupling models, with the scheduling formulation. It is well-known that both supply chain and processes are prone to abnormalities from various sources. Examples of the former include order changes/cancellations, transport delay, unplanned resource unavailability (e.g., power, water supply, and gas), and even absence of operators and skilled personnel. Similarly, the process can also suffer from abnormalities such as quality problems in raw materials and/or products, equipment and instrumentation failures, and changes in the process performance (e.g., processing times and yield). Because these disturbances may happen or be known only after generation of 5683


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Figure 3. Illustration of attaché concepts. Real-time value of indicator variables are compared against their target values at various landmarks established based on the schedule. Landmarks (a) at start of period Pk, and (b) after an abnormality at time lk3.

scale enterprises are organized into various departments1,19−23 each with its own distinct role and responsibilities. In a typical enterprise, scheduling and production control are distributed across different departments that may often be in geographically different locations.1 The monolithic integration approach widely proposed in literature results in a complete conjoined decision that has to be jointly implemented by two distinct departments, which may not be always practical. A complementary strategy is to seek architectures that would engender the benefits of integration while retaining the scheduling and control technologies currently in use by the different departments. Here we seek to develop such an approach and evaluate its benefits on the supply chain.

execution system (MES). This system is responsible for monitoring all process operations and tracking all manufacturing information in real time. In Figure 2, each slot indicates a period. The squiggle above each slot shows process fluctuations; the large zigzag highlights a period of process abnormality. At the beginning of period Pk, the scheduler gives a schedule for that period to the process containing a set of tasks with their start and end times, product ID, controller set points, quantity, throughput, and so on. This schedule is executed by the process during period Pk. At the end of the period, the process sends a production report comprising quantities produced, transition times, costs, quality parameters, and so on back to the scheduler. In the case illustrated in Figure 2, there is no process abnormality during period Pk, and the schedule is executed as intended. When the next period Pk+1 begins, the scheduler again generates a new schedule for this period and sends it to the process for execution. In this period, a process abnormality occurs which is not rectified by the process control layer. Because the abnormality occurs after generation of the original schedule, a divergence would occur between the targets specified in the schedule and their actual realization by the process. If the abnormality leads to a reduction in the process throughput, then the resulting production shortfall will be evident to the supply chain layer at the end of period Pk+1. Hence, the effect of the abnormality will propagate from the process to the supply chain and manifest in the form of delayed or missed deliveries. In this situation, the ability of the process to ameliorate the effects of the abnormality has not been utilized fully.

3. PROPOSED METHODOLOGY Our key insight is that the primary motivation for integration between the control and scheduling layers arises primarily when (i) the process control system is unable to meet the goals set by the scheduler because of various abnormalities originating at the process level, or (ii) the scheduler layer demands the process to operate differently at short-notice due to some unforeseen events in the supply chain. Traditionally, as shown in Figure 2, the scheduling and process control layers exchange information periodically (e.g., daily, weekly, fortnightly, or monthly), with the scheduling layer transmitting the needs from the supply chain in the form of a schedule and the control layer reporting on the actual performance of the process through a production report at the end of the period. This information exchange is done through the manufacturing 5684


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Figure 4. Information exchange between scheduling and control layers with attaché framework.

so on. (4) Intraperiod schedule: This is a (new) schedule generated by the scheduler for the reminder of the period starting from the landmark where the abnormality has been detected until the end of the current period. It takes into account the prevailing state of the plant. Attaché is an intermediary between the scheduler and process layers that monitors the execution of the process. It functions as follows: At the beginning of each period, indicator variable(s) are decided and landmarks specified on the basis of the schedule. Target values of the indicator variable at these landmarks are calculated. These are the values of the indicator variable calculated as per the original schedule. A number of approaches can be used to specify the target values including simple linear interpolation for inventory variables, constant values for residence/cleaning times, and so on. After this assignment of target values, attaché performs its role during the execution of the process. At every landmark, attaché obtains the real-time value of the indicator variable from the control layer and calculates the extent of deviation, if any. The detection of deviation can be performed in many ways including simple threshold violation or multivariate statistical process control techniques.24 In one simple approach, deviation can be calculated as the ratio between the target and the real-time values. This deviation is compared with a prespecified threshold (parameter) that is the amount of acceptable deviation of the real-time value of the indicator variable from the target value of indicator variable. If the deviation is beyond this threshold, then a significant abnormality in the execution of the schedule has been detected. It is now necessary to evaluate if there is a potential to overcome the effects of the abnormality (lost production) using the amelioration potential. This threshold denotes that the potential is significant enough to initiate measures to compensate for the effects of the abnormality. If there is a significant potential, then attaché would trigger an episodic status report from the control layer to the scheduler layer as shown in Figure 4 and trigger rescheduling. This status report would include the information available in the periodic production report and additionally the production time remaining in the period, the quantities yet to be produced, and state of the plant equipment, and so on. Using this information, the scheduler can generate a new intraperiod schedule that is cognizant of the abnormality and its effects on the process. Rescheduling can be performed by any algorithm; it could also be the same one used to produce the original schedule. This new intraperiod schedule is then executed by the process. On the basis of the new schedule, attaché sets new landmarks and calculates the target values at these landmarks, and the entire process is repeated for the rest of the period.

Furthermore, the nominal information exchange between the scheduling and process control layers introduces delays in initiating rectification actions and further accentuates the effects of the abnormality. One approach to reduce these delays would be to uniformly increase the frequency of information exchange; however, this may be difficult to achieve in practice and also lead to other undesired effects (suboptimal scheduling due to shorter horizons, frequent transitions, etc.). In summary, nominal periodic information exchange between the scheduling and process operations departments is adequate only during normal operations. Here, we propose a novel controlscheduling integration framework, called attaché, that seeks to achieve more timely information exchange in a practicable fashion. The framework is also capable of effectively responding to abnormal situations. The primary purpose of integration is to ensure that any information available to one layer is made available to the other layer in a timely fashion for overall benefit. Attaché achieves this by supplementing the nominal (periodic) information exchange with episodic exchanges when abnormalities occur. Attaché achieves this by nonintrusively monitoring the process execution vis-à-vis the original schedule. Attaché is built upon the following concepts: (1) Indicator variables: These are process variables that can be observed in real time to track the execution of the schedule. These variables are the ones which are capable of reflecting the presence of an abnormality. On the basis of the nature of the expected abnormalities, the corresponding variable(s) that can be measured in real time and reflect process deviations should be selected as indicator variable(s). Examples are equipment conditions such as availability, residence time and cleaning times in batch processes, and throughput and inventory levels in continuous processes (2) Landmarks: The real-time values of the indicator variables are compared with their targets (established using the schedule) at certain time points within each period. These time points are called landmarks. Landmarks can be evenly or unevenly distributed throughout the period. The number and position of landmarks can be same or may vary with the chosen indicator variable. Figure 3a shows examples of six landmarks, l1−l6. (3) Amelioration potential: This is a measure of the “slack” available within a period to overcome the effects of an abnormality. The slack could arise from flexibilities in the process or supply chain. The amelioration potential could enable the scheduler and control layers to have a better knowledge of each other’s constraints and operating limits. Examples include the remaining time in the period available to make up for the effects of the abnormality, availability of spare capacities/equipment, possibility of increasing throughput, and 5685


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Figure 5. Thermomechanical pulping process.

Consider the example shown in Figure 3. A schedule having two tasks is implemented for period Pk. Attaché monitors the execution of the process by monitoring the values of an indicator variable. The real-time values of the indicator variable will be compared to target values at landmarks l1−l6. The upper and lower bound on the target values denote the threshold limits beyond which rescheduling is considered necessary. No significant deviation is detected at landmarks l1 and l2; however, at landmark l3, the indicator variable value is below the lower threshold and signifies an abnormality. Attaché then collects information on the abnormality, production status, and the state of the plant and escalates the problem to the scheduler. The scheduler then considers possible arbitrage to compensate for the lost production and meet its objectives in the face of the new situation and generates a new intraperiod schedule which is transmitted to the process. Hence, from landmark l3, the process stops implementing the original schedule and executes the new intraperiod schedule. Attaché recalibrates the target values based on the new schedule, and the entire process starting from monitoring is repeated again. Thus, the deviation is identified at landmark l3 by attaché, which otherwise would have been detected only at the end of the period, and no action to compensate for the lost production could have been taken by the scheduler during period Pk. The proposed attaché framework offers a number of benefits: (1) It is not an additional layer in the plant automation hierarchy. The existing scheduling and control technologies are retained as is, and the attaché intermediary is configured to nonintrusively acquire real-time process data from the process control layer. It is hence a low-risk approach to integration. (2) It increases the frequency of interaction between scheduling and process control layers only when necessary, such as when abnormalities occur. When the process and the supply chain are unaffected by disturbances, attaché does not induce any changes in their functioning, and there are no overheads of integration. (3) It is applicable to all processes independent of their type, continuous or batch processes, their extent of automation, or the specific formulations for control and scheduling. (4) It is capable of compensating for the small abnormalities or noises that do not have a significant effect on

the production targets individually but are significant when considered in a cumulative fashion. (5) It does not necessitate any significant computational cost or need sophisticated technologies for deployment. We illustrate these benefits of attaché in the following section using two case studies, a continuous thermomechanical pulping process (TMP) and a batch penicillin fermentation process.

4. CASE STUDIES 4.1. Case Study 1: Thermomechanical Pulping Process. The thermomechanical pulping (TMP) process is considered for the case study. This process is used for making mechanical pulp for producing newsprint. Figure 5 shows the typical process arrangement for a two-stage TMP operation. The unit has two pressured refiners, primary and secondary, operating in series. The primary refiner produces a coarse pulp from a feed of wood chips and water. The secondary refiner further develops the pulp bonding properties to render it suitable for papermaking. The refiners consist of two disks (either contrarotating or one static and the other rotating) with overlaid grooved surfaces. These surfaces impact on the threephase flow of wood fibers, steam, and water that passes from the center of the refiner disks to their periphery. The impact of the disk surfaces on the wood fibers breaks the rigid chemical and physical bonds and microscopically roughens the surface of individual fibers, enabling them to mesh together on the paper sheet. The quality of the pulp is defined by its consistency, which is the proportion of solid content in the pulp. For the case study, three grades of pulp, G1, G2, and G3 are considered. Each product has a different consistency and is produced at different (but fixed) feed rpm’s, as shown in Table 1. Table 1. Products Considered in TMP Case Study

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product ID

feed rpm

set point of secondary consistency

minimum quality bound

maximum quality bound

G1 G2 G3

31 30 29

0.30 0.34 0.38

0.26 0.31 0.34

0.32 0.36 0.39


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Figure 6. Schedules for period P17: (a) original and (b) implemented from 117 TU.

with their due dates within a period are collected, and the demand of each grade for period Pk is calculated. Because of the stochastic nature, different grades have different cumulative demands at each period. The scheduler therefore generates a schedule that usually contains a set of three tasks corresponding to the three grades. Each task has a start and end time; the duration of the task is determined by the demand for that product grade. The schedule is then given to the process for execution. Transitions between the grades are executed by the MPC controller. At each landmark, the inventory and quality of products are assessed. Quality is determined as bounds on secondary consistency. Products that are within quality specifications are sent to distribution to fulfill the customer orders. Orders that cannot be fulfilled in a period are canceled. The scheduler then generates the schedule for the next period Pk+1 that is then executed by the process. The performance of the entire system is measured using the following key performance indicators: percentage of order volume fulfilled, average inventory and shortfall, and number of partial orders. The process and its supply chain are all simulated in MATLAB. The time unit considered in the case study is represented as “TU”, and each period is considered to consist of 7 TUs. The simulation horizon considered is that of 52 periods. Schedules are generated at the beginning of each period using the TORSCHE scheduling toolbox.26 For simplicity, list scheduling is used for schedule generation. It is a heuristic algorithm in which a prespecified list of tasks are ordered on the basis of a heuristic strategy. Each task is defined

From a control perspective, sufficient energy has to be applied to derive pulp with good physical properties and without fiber damage. The objective is to reduce the energy costs. The TMP process is difficult to control using classical multiloop methods; hence, it is controlled using a MPC controller as proposed by Bemporad et al.25 The controlled variables are primary and secondary refiner consistencies, primary and secondary refiner motor loads, and vibration monitor measurements on the two refiners. The manipulated variables are the feed rate of chips (screw feeder rpm), the dilution water flow to each of the refiners, and the set points to two regulatory controllers that control the gap between the rotating disks in each set of refiners. Various abnormalities in the normal operation of the process that are beyond the realm of the controller lead to loss of production. We have abstracted the effect of the abnormality through their effect on the feed rpm. As feed rpm changes, the pulp consistency changes. Because consistency is a controlled variable, the control loop (MPC) tries to bring it back to its set point by manipulating the other variables. Three different states of process operation are considered: (1) plant operating at desired feed rpm, i.e., no abnormality, (2) operating at a reduced throughput, i.e., feed rpm reduces to a lower value, and (3) complete shutdown, i.e., the feed rpm is 0. The process operates to meet the needs of the supply chain which functions as follows. At the beginning of each period Pk, orders that reflect stochastic demand are collected. Each order is defined by product quantity, grade, and due date. All orders 5687


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despite the MPC controller. The quality deviations resulting from the abnormality are also shown in the figure. Attaché detects the abnormality at the 117 TU landmark because the target value of inventory of G3 is 2900 units, and its real-time value is 1405 units, i.e., a 51.5% deviation. Attaché then checks the amelioration potential. The last task in the original schedule ends at 117.8 TU, and the period ends at 119 TU. The task is also originally scheduled on the basis of the nominal flow rate of 29 rpm, which can be increased to 30 rpm if necessary. Hence, there is adequate amelioration potential, and attaché triggers rescheduling by sending a status report to the scheduler. The scheduler employs both these flexibilities while rescheduling and thus (1) extends the task for the remaining duration of the period from 117 to 119 TU as illustrated in Figure 6b and (2) sets a secondary consistency set point of 0.36, which results in a feed flow rate of 30 rpm. This is expected to produce 3912 units of G3 as shown in Table 4. When the process executes this new schedule, attaché again decides new landmarks (at t = 118.1 and 118.4 TU) and monitors the inventory of products as shown in Table 5. In this run, no further abnormalities occur, and the schedule is executed completely. The final schedule as executed by the process is shown in Table 6. At the end of the period, after quality assessment is done, the total produced quantities of inspecification products are as follows: G1, 5758 units, G2, 5728 units, and G3, 5505 units. When fulfilling the market orders, a total shortfall of 119 units of G2 occurs in this period. An inventory of 30 units of G1 and 188 units of G3 is left. Without the timely intervention of attaché, 1723 units of G3 would have been lost, i.e., attaché completely offsets the effect of the abnormality in this case. 4.1.2. Illustration 2: Multiple Abnormalities in a Period. In this illustration, two abnormalities occur within a period. Consider period P11 that begins at 70 TU and ends at 77 TU. At the beginning of the period, demand for G1 is 5720 units, G2 5796 units, and G3 5498 units. Considering the previous period’s inventory, the target quantity for G1 is 5720 units, for G2 is 5796 units and for G3 is 5391 units. On the basis of the target quantities, the schedule shown in Figure 8a is generated. During the period, the abnormality “reduced throughput” occurs from 72.1 to 72.8 TU, and a shutdown occurs from 73.5 to 74.2 TU. Attaché monitors the execution of the process by tracking the inventories. At the 73.1 TU landmark, attaché detects a deviation of 66.5% between the target value of 3100 units of G1 and the real-time value of 1037 units. The amelioration potential is 1.2 TU; hence, rescheduling is triggered. The new schedule shown in Figure 8b is generated. At the 74.2 TU landmark, attaché again detects a deviation of 59.6% and estimates an amelioration potential of 0.6 TU. Again, rescheduling is done, and the new schedule, shown in Figure 8c, is generated. After this new schedule, the amelioration potential becomes zero; hence, attaché does not intervene in the process. At the end of the period, the total quantities of in-specification products are G1, 5607 units, G2, 5728 units, and G3, 5018 units. There is a total shortfall of 113 units of G1, 68 units of G2, and 373 units of G3 vis-à-vis the target quantity in the period. Without attaché, the shortfall would be 3741 units of G1, 68 units of G2, and 790 units of G3. Therefore, with attaché, 96.9% of G1 and 52.7% of G3 have been compensated. The above illustrations bring forth the benefits of attaché within a period. For a period when no abnormalities occur, attaché did not intervene in the process, and no rescheduling

by a task number, start time, duration, and end time. In our case, each schedule consists of at most three tasks corresponding to the three product grades. We use the longest processing time heuristic for generating the schedule wherein the task that requires the longest time is scheduled first; however, any other strategy can be used as well. This schedule is then executed by the process, which is simulated by a Simulink model of the thermomechanical pulping process with a MPC controller. A switching time of 0.1 TU is considered between different grades (in addition to the transition time). The process abnormalities discussed above affect the system’s performance. The probability of each state is prespecified: normal operation 80%, reduced throughput 15%, and shutdown state 5%, with each instance of the abnormal states lasting 0.7 TUs. Better integration between the process control and scheduling layers is desired to improve the overall performance and is achieved using the attaché framework. To deploy attaché, the inventories of each product grade are selected as indicator variables. Inventory is chosen because it is directly affected by the considered abnormalities and is hence capable of effectively reflecting their presence. The nominal values of attaché parameters landmark interval and deviation threshold are chosen to be 1 TU and 10%, respectively. When an abnormality occurs, its effect can be ameliorated in two ways: (a) by extending the duration of the task in the period or (b) by increasing the feed rpm, which results in higher throughput by decreasing the set point of the secondary consistency to its lower limit. Hence, amelioration potential is measured by the time remaining at the end of the period after the last task in the schedule has been executed, i.e., the difference between the completion time of the period and the end time of the last task in the schedule. It is also indicated by the potential to increase the feed rpm. The amelioration potential threshold, i.e., the minimum amelioration potential of slack in the period for attaché to trigger the scheduler, is chosen to be 0.1 TU or 1 rpm. Next, we illustrate the functioning of attaché framework when abnormalities occur. 4.1.1. Illustration 1: Single Abnormality in a Period. Consider one run of the process and one specific period P17 that begins at 112 TU and ends at 119 TU. In this period, the demand for G1 is 5771 units, G2 5847 units, and G3 5445 units. Considering the previous period’s inventory, the target quantity for G1 is 5728 units, for G2 is 5847 units, and for G3 is 5317 units. On the basis of the target quantities, a schedule is generated, as shown in Figure 6a, with the production data listed in Table 2. Attaché monitors the execution of the process Table 2. Original Achedule for Period P17 (112−119 TU) start time

stop time

product ID

target quantity

112.1 114.1 116.0

114.0 115.9 117.8

2 1 3

5847 5728 5317

based on the schedule by tracking the inventory of products at each landmark, as shown in Table 3. As per the production sequence, the target value of inventory for G2 is calculated for the first two landmarks; for the next two landmarks, the target value is based on the inventory of G1 and so on. An abnormality, reduced throughput, occurs stochastically in this period and lasts from 116.2 to 116.9 TU as shown in Figure 7. Because of this, without attaché, only 3722 units of G3 meeting the quality specifications would be produced by the process 5688


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Industrial & Engineering Chemistry Research Table 3. Attaché Illustration for Period P17 target value landmark 113.1 114.0 115.1 115.9 117 117.8

product G1

product G2

product G3

upper threshold

lower threshold

real-time value

deviation (%)

2900 5220

3300 6270 3410 6138 3190 5742

2700 5130 2790 5022 2610 4698

3022 5728 3206 5758 1405

−0.007 −0.005 −0.034 −0.032 0.515

3000 5700 3100 5580

Figure 7. Product feed rpm during period P17 (a) without attaché and (b) with attaché.

Table 4. New Schedule for Period P17 Implemented from 117.1 TU start time

stop time

product ID

target quantity

117.1

118.4

3

3912

was necessary. This illustrates that the attaché framework incurs the overheads of integration only when necessitated. Next, we summarize the cumulative result of attaché over a 52 period simulation run. In one run, there were a total of 81 895 orders

Table 5. Attaché Illustration for Period P17 from 117.1 TU target values landmarks 118.1 118.4

product G1

product G2

product G3

upper threshold

lower threshold

real-time values

deviation (%)

4405 5305

4845.5 5835.5

3964.5 4774.5

4619 5505

−0.048 −0.037

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Industrial & Engineering Chemistry Research Table 6. Complete Schedule As Implemented for Period P17 start time

stop time

product ID

target quantity

112.1 114.1 116.0 117.1

114.0 115.9 117 118.4

2 1 3 3

5847 5728 2900 3912

685 768 units of product. In terms of orders, out of the 81 895 orders, 65 317 orders would be completely fulfilled and 16 578 orders would be partially fulfilled, i.e., only 79.81% of the order volumes will be fulfilled. With attaché, the performance of the supply chain is improved significantly as summarized in Table 7. For the same market demands and abnormalities, the total volume of orders completely fulfilled increases to 75 716 units, i.e., 92.48%. Thus, with attaché, the order volume fulfilled increased by 12.67%. Given the stochastic nature of the market demand for the products as well as the number, timings, and types of abnormalities, the KPIs for each run would be different even with the same parameter settings. Therefore, KPI comparison cannot be made using single runs; following the convergence index of Jung et al.,27 we determined that 500 runs are required to adequately approximate the true values of the KPIs for a given parameter setting. On the basis of the

for all the three grades together; the cumulative demand volume from these orders was 859 260 units for an average order size of 10.49 units. As mentioned earlier, the plant has a 20% probability of being in an abnormal state, either reduced throughput or shutdown. In this run, there were a total of 75 occurrences of reduced throughout as can be seen in Figure 9 (for a total of 52.5 TU) and 18 occurrences of shutdowns (12.6 TU). Without attaché, this would result in total production of

Figure 8. Schedules for period P11: (a) original, (b) implemented from 73.1 TU, and (c) implemented from 74.2 TU. 5690


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Figure 9. Product feed rpm variation over a horizon of 52 periods with attaché.

Table 7. Summary of Key Performance Indicators with Longest Processing Time Heuristic key performance indicators total order volume total demand volume total demand volume fulfilled % of order volume fulfilled number of partially fulfilled orders average inventory total shortfall

without attaché

with attaché

improvement (%)

81895 859260 685768 79.81 16578

81895 859260 794681 92.48 6179

13.7 12.67 62.7

14.72 173491

24.23 64578

62.8

Figure 10. Robustness analysis. Performance improvement by attaché at different threshold values (landmark interval of 1.5 TU).

performance of 500 runs, the KPI values with attaché improved in all cases. The average increase in the total volume of order fulfilled was 11.73%. Next, we study the effect of tuning of attaché to the case study. Attaché uses two parameters, landmark interval and threshold, to decide when to intervene in the process. If the landmarks are widely spaced, then attaché would intervene after long durations, and the effects of the abnormality may not be adequately ameliorated. In contrast, if intervention is too frequent, then frequent rescheduling might occur, which is also undesirable. Similarly, if the threshold value is set too high, then the abnormality would be detected at a later stage and reduce the ability to exploit the available amelioration potential. However, if the threshold is set too low, then even small fluctuations will trigger rescheduling. The proper selection of these parameters determines the effectiveness of attaché. We have evaluated the robustness of attaché’s performance with respect to the landmark interval and threshold. The benefits of attaché with various threshold values ranging from 5 to 30% was studied while keeping the landmark interval constant at 1.5 TU. The results are summarized in Figure 10, which shows the first and third quartiles in orange and gray, respectively. The plot shows that for a wide range of threshold values from 10 to 25% the performance improvement in terms of order volume fulfilled by attaché is nearly constant at 11.4%. This signifies that the performance improvement gained from attaché is relatively insensitive to the threshold. Various values of landmark intervals from 0.5 to 3 TU were evaluated while keeping the threshold fixed at 10%. The results shown in Figure 11 (first and third quartiles in orange and blue, respectively)

Figure 11. Robustness analysis. Performance improvement by attaché at different landmark intervals (threshold value of 10%).

indicate that the performance improvement from attaché is also relatively insensitive to the value of the landmark interval. 4.2. Case Study 2: Fed-Batch Fermentation Process. In this case study, penicillin production by fed-batch fermentation is considered. Penicillin is a secondary metabolite of Penicillium. Glucose is used as a feed to the batch fermenter. The microorganisms are first grown in the batch culture because the formation of the antibiotic is not associated with cell growth. After a threshold concentration of glucose is reached, fed-batch operation begins to promote the synthesis of penicillin. The process model reported by Birol et al.28 was implemented in Simulink. Each batch takes 400 h of operation to complete, out of which 395 h is the processing time and 5 h is the cleaning 5691


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Figure 12. Schedules for periods P23 and P24: (a) original, (b) implemented from 17 850 h, and (c) implemented from 18 300 h.

its due date. The demand for each period varies stochastically (typically between two and four batches) reflecting the varying demand. At the beginning of each period, the demand is sent to the scheduler, which schedules the batches on the three fermenters. The schedule specifies the start time for each batch on each fermenter. This schedule is then sent to the operations department, which oversees the operation of the fermenter as per the schedule. At the end of the period, any backlogs that cannot be fulfilled are incorporated into the demand for the following period. The performance of the supply chain is

time. Various abnormalities can occur in the operation of the fermenter as discussed by Birol et al.28 The abnormality considered in this case study is a 30% decrease in glucose feed rate to the fermenter. The process operates to meet the needs of the supply chain, which functions as follows. At the beginning of each period Pk, orders with due dates in that period are collected. Three fermenters are available for production. Each period consists of 800 h, i.e., a maximum of six batches can be made in any period. Each order is defined by the number of batches to be made and 5692


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line indicates the point when rescheduling occurs. Blue color in a task indicates that it has been executed, and the red color indicates that a batch had an abnormality and was stopped. With rescheduling, the task scheduled on the third fermenter from 18 000 h is shifted to the second fermenter. When the process executes this new schedule, attaché again decides new landmarks and monitors the indicator variables. Another abnormality occurs stochastically starting at 18 100 h in fermenter 2. Attaché́ detects the abnormality at 18 300 h and checks the amelioration potential. At 18 300 h, two fermenters are idle, and attaché triggers rescheduling by sending a status report containing the target quantity for the remaining period to the scheduler. Because the remaining time in this period is not adequate to complete the batch, the rescheduled batch will run into the next period. The new schedule to be executed is illustrated in Figure 12c. The vertical green line indicates the end of period P23 and the beginning of period P24. At the end of period P23, out of four batches to be made, three were completed successfully, and the demand is fulfilled. The task continuing from the previous period is delivered at 18 700 h instead of 18 400 h, incurring a penalty of 30 units. Without the timely intervention of attaché, two unfulfilled tasks of this period would be considered as a backlog and would incur a penalty of 80 units with delivery at 18 800 h. As period P24 begins, the demand for this period is calculated, and the schedule shown in Figure 12c generated. The above illustration brings forth the benefits of attaché. Next, we summarize the cumulative result of attaché over a 26 period simulation run. In one run, there were a total of 77 orders. The percent volume fulfilled for both with and without attaché case was 100%. The number of late orders without attaché was 10 orders, whereas with attaché, only 3 orders were delayed. The total penalty incurred without attaché was 880 units, whereas with attaché, only 220 units of penalty were incurred. Hence, the total profit without attaché is 7898 units, whereas with attaché, it increased by 7.71% to 8558 units. Given the stochastic nature of the market demand as well as the number and timings of the abnormality, the KPIs for each run would be different even with the same parameter settings. We have conducted large-scale studies to establish statistically the benefits of attaché in this case study as well. The details are similar to those of case study 1 above; hence, in the interest of space, they are not repeated here. Only a summary is reported. On the basis of the performance over 400 runs, the KPI values with attaché́ improved in all cases. The average increase in the total profit was 4.05%. This case study further illustrates that the attaché framework is general and can be deployed in any enterprise with continuous and/or batch processes and with any scheduling and control technologies that they already have.

measured using the profit, demand volume fulfilled, total shortfall, and the total number of late orders as the key performance indicators. The process and its supply chain are all simulated in MATLAB. The simulation horizon consists of 26 periods. Schedules are generated at the beginning of each period. Scheduling is considered as a profit maximization problem29 with constraints relating to allocation and sequencing, capacity limitations, and material balance. A discrete time representation is used here. The objective function is to maximize the profit. In the interest of space, the reader is referred to the formulation of Kondili et al.29 that is followed in this work. The resulting mixed integer linear programming problem (MILP) is solved using the internal ILP solver “glpk” of TORSCHE scheduling toolbox.26 The schedule thus generated is executed by the Simulink model of the fermenter. The process abnormality discussed above has 3% probability of occurrence on each fermenter and can occur at any time during the fermenter. An ICA-based monitoring algorithm is used to detect the abnormality. The interested reader is referred to Albazzaz and Wang30 for details of the monitoring algorithm. Because of the slow effect of the fault, the fault is observable only after nearly 165 h of its introduction.30 The abnormality affects the system’s performance, and unacceptable quality product will be produced at the end of the batch. To achieve better overall performance, attaché framework is deployed. To implement attaché, the independent components are chosen as the indicator variables. Any violation of the lower and upper control limits of any indicator variable implies that the batch is abnormal. The indicator variables are evaluated at every 100 h from the start of a batch (any other interval can be used as well). The amelioration potential is considered to be the availability of idle fermenter and the remaining time of the period. When an abnormality is detected, the batch is stopped (rework is not considered here because of the nature of the product), and the fermenter is cleaned (time duration of 50 h) and then made available for another batch. When an abnormality is detected, the remaining target quantity for the period is calculated and is sent to the scheduler described above for rescheduling. The functioning of attaché during an abnormality is described in detail in the following illustration. 4.2.1. Illustration. Consider one run of the process and a specific period P23, which begins at 17 600 h and ends at 18 400 h. In this period, the demand is for four batches. No backlog is carried forward into this period. On the basis of this demand, the schedule shown in Figure 12a is originally generated. The orange color of a task indicates that it is yet to be executed. Attaché monitors the execution of the process by tracking the indicator variables at each landmark. An abnormality, reduced glucose feed rate, occurs stochastically in fermenter 3 starting at 17600 h. Attaché detects the abnormality at the second landmark at 17 800 h. It then checks the amelioration potential. Because all three fermenters are running at this time, rescheduling does not occur immediately. The batch on fermenter 3 is stopped by operations, cleaned, and after 50 h is available for use for the next batch. When fermenter 3 becomes available, attaché detects the amelioration potential of this idle fermenter and triggers rescheduling by sending a status report containing the target quantity for the remaining period to the scheduler. The target quantity is calculated as the demand for the period minus the number of successful batches. The scheduler then generates a new schedule for the remaining time in the period as illustrated in Figure 12b. The vertical red

5. CONCLUSIONS AND FUTURE WORK In this paper, we proposed a novel framework to deal with abnormalities along with the integration of scheduling and process control layer in industrial-scale manufacturing supply chain networks. Although this problem has received some attention in literature, the existing techniques predominantly focus on integrating the optimization formulations of control (considering detailed process dynamics) with that of scheduling. This leads to complex MIDO problems that can rarely be solved in real time or practicably implemented given the distributed characteristics of large-scale enterprises. Here, we adopt a different perspective and note that the benefits of integration primarily arise during abnormal situations where 5693


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(3) Baldea, M.; Harjunkoski, I. Integrated production scheduling and process control: A systematic review. Comput. Chem. Eng. 2014, 71, 377−390. (4) Munoz, E.; Capon-Garcia, E.; Moreno-Benito, M.; Espuna, A.; Puigjaner, L. Scheduling and process control decision-making under an integrated information environment. Comput. Chem. Eng. 2011, 35, 774−786. (5) Shobrys, D.; White, D. Planning, scheduling and process control system: why cannot they work together. Comput. Chem. Eng. 2000, 24, 163−173. (6) Flores-Tlacuahuac, A.; Grossmann, I. E. Simultaneous Cyclic Scheduling and process control of a Multiproduct CSTR. Ind. Eng. Chem. Res. 2006, 45, 6698−6712. (7) Zhuge, J.; Ierapetritou, M. G. Integration of Scheduling and process control with Closed Loop Implementation. Ind. Eng. Chem. Res. 2012, 51, 8550−8565. (8) Engell, S.; Harjunkoski, I. Optimal operation: Scheduling, advance control and their integration. Comput. Chem. Eng. 2012, 47, 121−133. (9) Grossmann, I. E. Advances in mathematical programming models for enterprise-wide optimization. Comput. Chem. Eng. 2012, 47, 2−18. (10) Lindholm, A.; Nytzen, N. P. Hierarchical scheduling and abnormality management in the process industry. Comput. Chem. Eng. 2014, 71, 489−500. (11) Bhatia, T.; Biegler, L. T. Dynamic optimization in the design and scheduling of multiproduct batch plants. Ind. Eng. Chem. Res. 1996, 35, 2234−2246. (12) Bhatia, T.; Biegler, L. T. Dynamic optimization for batch design and scheduling with process model uncertainty. Ind. Eng. Chem. Res. 1997, 36, 3708−3717. (13) Capon-Garcia, E.; Guillen-Gosalbez, G.; Espuna, A. Integrating process dynamics within batch process scheduling via mixed integer dynamic optimization. Chem. Eng. Sci. 2013, 102, 139−150. (14) Park, J.; Dua, J.; Harjunkoski, I.; Baldea, M. Integration of Scheduling and Process Control Using Internal Coupling Models. In Proceedings of the 24th European Symposium on Computer Aided Process Engineering, 24 June 15−18, 2014, Budapest, Hungary; Klemeš, J. J., Varbanov, P. S., Liew, P. Y., Eds.; Computer Aided Chemical Engineering Series; Elsevier: Amsterdam, The Netherlands, 2014; Vol. 33, pp 529−534. (15) Adhitya, A.; Srinivasan, R.; Karimi, I. A. A Model-based Rescheduling Framework for Managing Abnormal Supply Chain Events. Comput. Chem. Eng. 2007, 31 (5-6), 496−518. (16) Adhitya, A.; Srinivasan, R.; Karimi, I. A. Heuristic Rescheduling of Crude Oil Operations to Manage Abnormal Supply Chain Events. AIChE J. 2007, 53 (2), 397−422. (17) Chu, Y.; You, F. Integration of scheduling and process control with online closed-loop implementation: Fast Computational Strategy and large scale global optimization algorithm. Comput. Chem. Eng. 2012, 47, 248−268. (18) Chu, Y.; You, F. Moving Horizon Approach of Integrating Scheduling and process control for Sequential Batch Processes. AIChE J. 2014, 60, 1654−1671. (19) van Dam, K. H.; Adhitya, A.; Srinivasan, R.; Lukszo, Z. Critical evaluation of paradigms for modeling integrated supply chains. Comput. Chem. Eng. 2009, 33 (10), 1711−1726. (20) Julka, N.; Srinivasan, R.; Karimi, I. A. Agent-based Supply Chain Management − 1: Framework. Comput. Chem. Eng. 2002, 26, 1755− 1769. (21) Julka, N.; Karimi, I. A.; Srinivasan, R. Agent-based Supply Chain Management − 2: A Refinery Application. Comput. Chem. Eng. 2002, 26, 1771−1781. (22) Pitty, S. S.; Li, W.; Adhitya, A.; Srinivasan, R.; Karimi, I. A. Decision Support for Integrated Refinery Supply Chains. 1. Dynamic Simulation. Comput. Chem. Eng. 2008, 32, 2767−2786. (23) Koo, L. Y.; Adhitya, A.; Srinivasan, R.; Karimi, I. A. Decision Support for Integrated Refinery Supply Chains. 2. Design and Operation. Comput. Chem. Eng. 2008, 32, 2787−2800.

improved and timely awareness of events enables more holistic decision making. In this context, the proposed attaché framework seeks to utilize the existing control and scheduling schemes to achieve better performance through episodic exchange of information in addition to the periodic ones. Specifically, attaché serves as an intermediary between scheduling and process control departments of the enterprise and acts as a feedback provider for the scheduler. It observes the process nonintrusively, monitors the indicator variables at prespecified landmarks, and detects if there is any significant divergence in their target values. When a significant divergence is detected, it checks for amelioration potential(s) within the current period to annul the effects of the abnormality. It then triggers an episodic status report to the scheduler, which in turn generates a new intraperiod schedule that could utilize available controller flexibility, spare capacities, or time for amelioration. We have evaluated attaché using two distinctly different case studies and have demonstrated that it leads to significant improvement in the system performance in both cases. In each case study, attaché helps exploit the available degrees of freedom (duration in the TMP process and spare fermenter capacity in the fermentation process) to recover from abnormalities in a more efficient fashion compared to a situation where no information exchange occurs between the control and supply chain layers, i.e., without attaché. The nature of the scheduling algorithm, i.e., heuristic or mathematical programming based, is incidental to attaché, which is not restricted by this and simply reflects the technology currently in use in that enterprise. The benefits of attaché are contingent on the ability of the scheduler to take advantage of intraperiod opportunities. In case study 1, the longest processing time heuristic was used to generate the schedules; however, in case study 2, a MILP-based scheduling methodology was used for generating the original schedule as well as the intraperiod schedule. This clearly indicates that the significant potential for the attaché framework is not restricted to a specific scheduling algorithm. Our robustness analysis studies also demonstrate that the performance improvement is relatively insensitive to the selection of the parameters. Finally, the framework is computationally efficient and does not entail large-scale changes to the automation deployed in the plant. Our future work would seek to study the effects of abnormalities in the supply chain and evaluate case studies incorporating more complex control and scheduling algorithms.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +91 79-32210155. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support from ABB under the ABB research grant program 2013. REFERENCES

(1) Adhitya, A.; Srinivasan, R. Dynamic simulation and decision support for multisite specialty chemicals supply chain. Ind. Eng. Chem. Res. 2010, 49, 9917−9931. (2) Bansal, M.; Adhitya, A.; Srinivasan, R.; Karimi, I. A. An Online Decision Support Framework for Managing Abnormal Supply Chain Events. Comput.-Aided Chem. Eng. 2005, 20, 985−990. 5694


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Industrial & Engineering Chemistry Research (24) Douglas, C. M. Introduction to Statistical Quality Control, 7th ed.; Wiley: New York, 2012 (25) Bemporad, A.; Ricker, L. N.; Owen, G. J. Model Predictive Control − New tools for design and evaluation. In Proceedings of the 2004 American Control Conference; IEEE: New York, 2004; pp 5622− 5627. (26) Šůcha, P.; Kutil, M.; Sojka, M.; Hanzálek, Z. TORSCHE Scheduling Toolbox for Matlab. IEEE International Symposium on Computer-Aided Control Systems Design 2006, 1181. (27) Jung, J. Y.; Blau, G.; Pekny, J. F.; Reklaitis, G. V.; Eversdyk, D. A simulation based optimization approach to supply chain management under demand uncertainty. Comput. Chem. Eng. 2004, 28, 2087−2106. (28) Birol, G.; Undey, C.; Cinar, A. A modular simulation package for fed-batch fermentation: penicillin production. Comput. Chem. Eng. 2002, 26, 1553−1565. (29) Kondili, E.; Pantelides, C. C.; Sargent, R. W. H. A general algorithm for short-term scheduling of batch operations-I. MILP formulation. Comput. Chem. Eng. 1993, 17, 211−227. (30) Albazzaz, H.; Wang, X. Z. Statistical Process Control Charts for Batch Operations Based on Independent Component Analysis. Ind. Eng. Chem. Res. 2004, 43, 6731−6741.

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