Hierarchical Scheduling and Utility

Disturbance Management in the

Process Industry

Anna Lindholm ! Charlotta Johnsson !

Nils-Hassan Quttineh !! Helene Lidestam !!!

Mathias Henningsson !!! Joakim Wikner !!! Ou Tang !!!

Nils-Petter Nytzen !!!! Krister Forsman !!!!

! Department of Automatic Control, Lund University, Sweden(e-mail: anna.lindholm@control.lth.se)

!! Department of Mathematics, Linkoping University, Sweden!!! Department of Management and Engineering,

Linkoping University, Sweden!!!! Perstorp AB, SE-284 80 Perstorp, Sweden

Abstract: The integration of scheduling and control in the process industry is a topic thathas been frequently discussed during the recent years, but many challenges remain in orderto achieve integrated solutions that can be implemented for large-scale industrial sites. In thispaper we consider production control under disturbances in the supply of utilities at integratedsites together with the integration towards production scheduling. Utilities, such as steam andcooling water, are often shared between the production areas of a site, which enables formulationof an optimization problem for determining the optimal supply of utilities to each area atthe occurrence of a disturbance. Optimization in two timescales is suggested to handle thescheduling and disturbance management problems in a hierarchical fashion. The suggestedstructure has been discussed with companies within the chemical process industry. A simpleexample is provided to show how the structure may be used.

Keywords: Production control, hierarchical control, disturbance rejection, chemical industry,process control, optimization problems

1. INTRODUCTION

The chemical industry has during the past decades becomea global marketplace with strong competition betweenmanufacturers (Tousain (2002)), and this requires a moreagile plant operation to increase flexibility and decreaseproduction costs (Backx et al. (1998)). Planning, schedul-ing, and control are some key features that have largeeconomic impact on process industry operations (Shobrysand White (2002)). Planning and scheduling in the processindustry are two areas that are not easily distinguishable,and the border lines for these areas are di!use (Kallrath(2002)). Most authors, e.g. Kallrath (2002), Huang (2010),Engell and Harjunkoski (2012), and Rawlings and Amrit(2009), define planning as the activity to make production,distribution, and inventory plans, and scheduling to decidethe timing of actions to execute the plan and make useof the available resources. A more general definition ofplanning is given by APICS (2013) as ”the process ofsetting goals for the organization and choosing variousways to use the organization’s resources to achieve thegoals”. The stated timescales for the two activities varies,but usually, planning is said to work on a time periodof one or more months, and scheduling on a horizon ofweeks. Some work has been done on integrating planningand scheduling, either by combining them and solving the

planning and scheduling problems simultaneously or byvarious decomposition techniques. An extensive review isprovided in Grossmann and Furman (2009). The topic ofintegration of planning and scheduling with control, onthe other hand, is a topic that still has not received muchattention in the literature (Grossmann (2012); Craig et al.(2011)). This topic is also viewed di!erently by di!erentauthors, mainly because of di!erent interpretations of thearea of control, which can be said to work in timescalesof both milliseconds, minutes and hours. Shobrys andWhite (2002) and Engell and Harjunkoski (2012) providea good view of the activities that have to be integratedand describe the current practice and challenges for inte-grating the planning, scheduling and control functions inthe process industry. A lot of case-specific contributionsregarding integration of scheduling and control have alsobeen made, of which Harjunkoski et al. (2009) providean excellent overview. In Tousain (2002), an hierarchicalapproach for integrating scheduling with control is pre-sented, but here only a single plant/area is studied, andthe focus is on multi-grade plants. In the current study,a hierarchical approach to integrate scheduling with pro-duction control (on a timescale of hours) is suggested. Theapproach focuses on disturbances in the supply of utilitiesat one site with several connected production areas withcontinuous production. Utilities, such as steam and cooling

water, are often shared between the production areas at asite and management of these disturbances thus becomesan interesting topic, especially at integrated sites whereproduction areas are connected by the flow of products.The work presented in this paper is produced in collab-oration with process industrial companies, in particularwith Perstorp, that is a world leader within several sectorsof the specialty chemicals market (Perstorp (2013)).

2. HIERARCHY MODELS

To clarify at which levels of the physical and functionalhierarchy of an enterprise the current study is focused, therole-based equipment hierarchy, functional hierarchy andscheduling hierarchy are defined in this section.

2.1 Role-based Equipment Hierarchy

According to the standard ISA-95.00.01 (2009), there arefive levels of the role-based equipment hierarchy of anenterprise; the enterprise, site, area, production unit, andunit level. Traditionally, the area of process control isfocused on control of production units, e.g. reactors ordistillation columns, or of the connection of productionunits. This would correspond to the production unit levelor area level of the equipment hierarchy. In this study, thefocus is on the area and site levels of the hierarchy; oncontrol of the production in the di!erent areas of a site.The areas at a process industrial site are often connected,such that one area produces raw materials for other areas.This is in Wassick (2009) denoted an integrated site, andin process flow scheduling (PFS) a process train. Changingthe production rate in one area, e.g. due to a disturbance,may thus a!ect the production in several other areas at thesite. An example of an integrated site with six productionareas and three bu!er tanks is given in Fig. 1.

Area 1! Area 2! Area 5!

Area 3!

Product 1! Product 2!

Area 4!

Product 3!

SITE!

V1! V2!

V3! Area 6!

Product 1! Product 2!

Product 3!

Product 4!

Product 5!

Product 6!

Fig. 1. Example of an integrated site.

2.2 Functional Hierarchy and Scheduling Hierarchy

The functions that are used for operating an enterpriseare often viewed in a hierarchical structure. In papersthat discuss the integration of di!erent functions, such asproduction planning, scheduling and control, ’integrationpyramids’ like the one in Fig. 2 (left) are commonly used.These pyramids might look quite di!erent, which is no sur-prise since the people working in the field of process controlcome from many di!erent areas (Tousain (2002)). In thispaper, we stick to the definition in the standard ISA-95.00.01 (2009), as presented in Fig. 2 (right).

Fig. 2. Functional hierarchy of an enterprise.

The levels represent activities at various timescales, wherelevel 1-2 include activities with the shortest timescalessuch as sensing and reading (milliseconds, seconds, min-utes), level 3 includes activities with a longer timescalesuch as scheduling (minutes, hours, weeks) and level 4includes activities with an even longer timescale such asplanning (days, weeks, months).

There is also a scheduling hierarchy presented in theappendix of standard ISA-95.00.03 (2005), see Fig. 3. Thishierarchy is derived from common terms used in APICSdictionary (Blackstone and Cox (2004)) and ISA-95.00.03(2005)). The figure could be extended with a control layerat the very bottom, visualizing the fact that control andscheduling are tightly coupled.

Business Plan (APICS Terminology) (Per product line, per time – Very long time horizon)

Demand Plan (APICS Terminology) (Per product, per time – Very long time horizon)

Production Plan (APICS Terminology) (Per product, per time – Long time horizon)

Production Schedule – (or Master Production Schedule in APICS) (Per site/area, per product, per time – Medium time horizon)

Detailed Production Schedule – (Operations Schedule in APICS) (Per area/line/cell/unit, per product/intermediate, per time – Short time horizon)

Production scheduling activity (ISA-95.00.01)

Detailed production scheduling activity (ISA-95.00.03)

Production forecasting activity (ISA-95.00.01 )

Production Dispatch List (Per work center, per production unit, per produced item, per time – Very short time horizon)

Production dispatching activity (ISA-95.00.03)

Fig. 3. Scheduling hierarchy of an enterprise.

In this paper, we have adopted a hierarchical schedulingapproach in which the short-term scheduling (referred toas ’detailed production scheduling’) takes care of the fifthlevel in the scheduling hierarchy, whereas the long-termscheduling (referred to as ’production scheduling’) takescare of the fourth level.

3. UTILITY DISTURBANCE MANAGEMENT

Utilities, such as steam and cooling water, are often sharedbetween several production areas at a site. Disturbancesin the supply of utilities might therefore a!ect productionat large parts of the site. Examples of utility disturbancesare too high temperature of the cooling water, too lowor too high pressure in the steam net, or an electricityfailure. Utilities may be interpreted as volumes, or power,which all areas have to share (Lindholm and Giselsson(2013)), which means that if one area uses less of a utility,there is more of the utility available for other areas. Thisenables formulation of an optimization problem that aimsat dividing the utility resources among the areas at a siteat a utility disturbance. A reasonable goal is to try todivide the resources such that the total loss of revenue isminimized. Formulation of such an optimization problemis discussed in Lindholm and Giselsson (2013). The opti-mization problem becomes particularly interesting for in-tegrated sites, where both the plantwide nature of utilitiesand the area interconnections contribute to the complexityof the problem. In this paper, the optimization problemis part of the detailed production scheduling activity, asdescribed in section 4.

4. STRUCTURE FOR SCHEDULING AND UTILITYDISTURBANCE MANAGEMENT

We suggest the structure for integrated scheduling anddisturbance management that is visualized in Fig. 4. Inthe production scheduling layer, a production schedule isset that serves as a reference for the detailed productionscheduling. The suggestion is that the production schedul-ing activity produces a production schedule one monthahead and updates the plan every day. This time step andhorizon has been suggested after discussions with Perstorp.The detailed production scheduling layer determines how

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Fig. 4. Suggested structure for scheduling and utilitydisturbance management.

the production should be controlled to handle utility dis-turbances in an economically optimal way. The suggestionis that this activity operates on horizon of one day and up-dates the schedule every hour. The resulting accumulateddaily production is reported to the production schedulinglayer every day. The detailed production scheduling alsohas an interface to the actual site, where the schedule is ex-ecuted. This could be done e.g. by the operators at the siteor using model-predictive control (MPC). Measurementsfrom the site report to the detailed production schedulinglayer how the production was actually conducted. Thislayer also gets a prediction of the disturbance trajectoriesover the horizon for the detailed production scheduling.

Our suggestion is to run both the production schedulingand detailed production scheduling in receding horizon,and produce a new schedule in every time step, but analternative would be to only redo the schedule only whenneeded, as in Kadam and Marquardt (2007). The sugges-tion to perform the production scheduling and detailedproduction scheduling separately is to make the solutionstransparent and understandable for the process operators.If the solutions are not accepted by the operators, theywill not be used in the long term (Engell and Harjunkoski(2012)). Also, the current apprehension among most au-thors in the field, among others Engell and Harjunkoski(2012), Kadam and Marquardt (2007) and Tousain (2002),seems to be that a hierarchical approach is currently theonly realistic one to tackle industrial-size problems, sincethe fully integrated solution often leads to large, complexand nonconvex optimization problems. In the followingsubsections, the production scheduling and detailed pro-duction scheduling activities, as suggested in this paper,are described in more detail.

4.1 Production Scheduling

The upper level in the hierarchy, the business and produc-tion planning, gives information on a long term perspective(strategic) to the lower level, production scheduling. Theinformation (input) needed for making the productionschedule can for example be di!erent kinds of capac-ity, levels of storage for di!erent products, incoming or-ders, planned maintenance and transports. The productionscheduling also uses the actual production per day as aninput together with the input from the upper level to makea production schedule for a month ahead divided into dailytime periods. The objective of the production schedulingis to make a production schedule that serves as an inputto the lower level in the hierarchy, the detailed productionscheduling. The production schedule can be seen as a planon the tactical level. The production schedule is executedevery day to update the monthly plan. The outcome of theproduction schedule is decisions like how much to produceof each product at each area on a specific site. The purposewhen making the production schedule is to minimize thedi!erence between the planned production and the actualproduction with respect to related costs for overproductionand underproduction respectively, and the levels of thecontribution margins for each product are also taken intoaccount. The forthcoming decisions on the level below theproduction scheduling, the detailed production schedulinglevel, can in turn be seen as decisions on an operationallevel.

4.2 Detailed Production Scheduling

The objective of the detailed production scheduling is tohandle daily utility disturbances at the site in order tominimize the economical influence of these disturbances.Reference values for the sales of products are given bythe production schedule, and predicted utility disturbancetrajectories are also given as input for the detailed pro-duction scheduling. If the volume interpretation of utilitiessuggested in Lindholm and Giselsson (2013) is used, thisis equivalent to trajectories that describe how much of theutilities that are available at each time instant. This couldbe represented in percent of how much that is available atnormal operation of the site and its utilities. The outputfrom the activity is trajectories that suggest how much toproduce and sell at each hour during the day, and how thebu!er tanks at the site should be utilized. The detailedproduction scheduling layer also provides information tothe production scheduling layer about how much that wasactually produced in total of each product during the day(one time step in the production schedule). This informa-tion is used in the production scheduling layer to updatethe production schedule that gives the reference values forthe detailed production scheduling. The detailed produc-tion scheduling is performed in receding horizon fashion,such that the operators may update their prediction ofthe duration, severity and shape of the disturbance everyhour. The model of the site that is used for the detailedproduction scheduling has to contain information aboutthe area and bu!er tank interconnections, the maximumand minimum limitations on production rates and bu!ertank levels, and at which areas at the site each utility isused. To make the model realistic, start-up costs for areasshould also be considered, since start-ups are often veryexpensive at process industrial sites.

5. AN EXAMPLE

To demonstrate the suggested hierarchy for schedulingand disturbance management, a very simple example isgiven in this section. This simple setup is chosen to clearlyshow the integration of the two scheduling levels. Moreindustrially relevant examples are handled in ongoingresearch. Here, a site with two areas that share onecommon utility is considered, as shown in Fig. 5. The areasproduce one product each, product 1 and product 2, withcontribution marginmi, maximum hourly production qmax

i

and minimum hourly production qmini for product i = 1, 2.

The two areas are not connected by the flow of products,which means that the only way they interact is that theyshare the same utility. Table 1 summarizes the productiondata for the two products in the example. The productionschedule for the two products is denoted qPS

1 and qPS2 ,

and has a horizon NPS of one month (30 days) with timesteps of one day. The detailed production schedule forthe two products is denoted qDPS

1 and qDPS2 , and has

a horizon NDPS of one day (24 hours) with time steps

Area 1! Area 2!

Utility!

Product 1!

Product 2 !

Fig. 5. Two areas that share the same utility.

Table 1. Production data.

qmin qmax m

Product 1 0.1 1 0.5

Product 2 0.1 1 1

one hour. The actual production of the two products thatwas performed at the production scheduling and detailedproduction scheduling level are denoted qPS

i and qDPSi

respectively, for i = 1, 2. The hierarchy of the schedulingis shown in Fig. 6.

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q1PS,q2

PS !q1PS, !q2

PS

q1DPS,q2

DPS !q1DPS, !q2

DPS

U

Fig. 6. Scheduling hierarchy in the example.

5.1 Production Scheduling

The production scheduling determines the productionschedule, which is updated each day after getting infor-mation from the detailed production scheduling on theactual production during the last day. It is also possiblethat demands di(!) change from one day to the next dueto new incoming orders. The objective of the productionscheduling is to minimize the cost for backlog, and theinput is daily demands of each product di(!). Due to pos-sible mismatch in the actual daily production, the initialbacklog is set to Bi(0) = di(0) ! qPS

i (0). Notice that ifthe actual production during the previous day was greaterthan the demand, the initial backlog could be negative. Aslong as there are some demand each day, this does not poseany real problem. Variables for this problem are qi(!), theamount to produce of each product i during time step ! ,and Bi(!), the accumulated backlogged amount of producti at time step ! . The optimization problem may be posedas the linear program (LP)

minimizeNPS!

!=1

[B1(!) +B2(!)]

s.t. Bi(!) = Bi(! ! 1) + di(!) ! qi(!) " i, !

NDPS · qmini # qi(!) # NDPS · qmax

i " i, !

Bi(!) $ 0 " i, !

Since the two production areas are coupled only by utilityusage, the optimal production scheduling strategy is toadjust the production in the next time step in order toaccount for the production error, i.e. backlog, accordingto the plan for the previous time step. If the backlog cannot be adjusted at once due to minimum or maximumlimitations on the possible accumulated production in atime step, it is instead adjusted in the succeeding step.The production schedule is updated in every time stepover the horizon NPS = 30 days.

5.2 Detailed Production Scheduling

At a disturbance in the utility, the production in thetwo areas is limited by the amount of the utility that isavailable at time t, U(t), according to

u1(t) + u2(t) # U(t) (1)

where ui(t) is the assignment of the utility to area i attime t. It is assumed that the utility is of continuoustype, which means that greater assignment of the utilityto an area makes it possible to increase production in thatarea (Lindholm and Giselsson (2013)). It is also assumedthat the relationship between assignment of the utility toan area and production in that area is linear, and that zeroassignment of the utility gives zero production, i.e.

qi(t) = ciui(t) (2)

where qi(t) is the production in area i at time t and ci is aconstant that is specific for the utility and area i. If U = 1(100 %) corresponds to normal operation of the utility, andthe utility is shared equally between the production areasat maximum production, we get ci = 2qmax

i for i = 1, 2,where qmax

i corresponds to the maximum production rateof area i. This means that the constraint the utility poseson the production in the two areas may be expressed as

1

2qmax1

q1(t) +1

2qmax2

q2(t) # U(t) (3)

There are also production rate constraints given by capac-ity limitations:

qmini # qi(t) # qmax

i , i = 1, 2 (4)

The detailed production scheduling aims to maximizethe total contribution, or minimize the loss, at a utilitydisturbance. Since the areas are not connected and thereare no bu!er tanks at the site, the optimization onlyconcerns choosing the optimal production rates for thetwo areas, given a predicted utility disturbance trajectory,U . The production scheduling gives the reference forthe accumulated daily production (qPS

1 and qPS2 ). This

production is divided evenly over the each hour of the dayto produce reference production rates for the two productsat each time step in the detailed production schedule,qref1 and qref2 . The optimization problem for the detailedproduction scheduling may be formulated as the quadraticprogram (QP)

minimizeNDPS!

t=1

"

"q21(t) +"q22(t)!m1q1(t)!m2q2(t)#

subject to (3)! (4)

with U(t) = U(t) and "qi(t) = qi(t) ! qrefi for i = 1, 2.The horizon for the detailed production scheduling in theexample is NDPS = 24 hours. The profit maximizing terms!m1q1(t) and !m2q2(t) are gray because they are onlyincluded in the cost function when the site is a!ected bydisturbances. For disturbance-free periods, pure referencetracking is performed to avoid overproduction.

5.3 Results

The initial production schedule for the example is shownin Fig. 7. This schedule is updated every day based on theactual daily production the previous day. In the example,utility disturbances only occur at day 2 and 17. All other

days of the month, the detailed production schedule couldbe executed without deviations from the reference givenby the production schedule. Fig. 8 and 9 show the detailedproduction schedule at days without and with the influenceof a utility disturbance. For simplicity, perfect prediction ofthe disturbance is assumed, i.e. U = U . In the figures, thecurrent time step in the receding horizon of the detailedproduction scheduling is hour 12, and both the actualand predicted trajectories are shown. Fig. 10 shows theactual production after the entire month together withthe initial production schedule. In the figure it can beseen that at the days where utility disturbances wherepresent, the production was not performed according tothe initial schedule. This was corrected by updating theplan and producing more or less of the two products one ormore days later. After the entire month, the accumulatedproduction of both products was the same as the plannedamount. Both the LP and QP problems were solved usingCPLEX.

5 10 15 20 25 300

5

10

15

20

25

q 1PS

5 10 15 20 25 300

5

10

15

20

25

q 2PS

Time

Fig. 7. Initial production schedule.

2 4 6 8 10 12 14 16 18 20 22 240

50

100

U (%

)

2 4 6 8 10 12 14 16 18 20 22 240

0.5

1

q 1DPS

ReferenceCapacity limitationsPredictionOperation

2 4 6 8 10 12 14 16 18 20 22 240

0.5

1

q 2DPS

Time (hours)

Fig. 8. Detailed production schedule at day 1, hour 12.

This example shows how the structure where a schedulerand a detailed production scheduler operate in recedinghorizon may be used. A very simple example was presentedto keep focus on the structure and avoid optimizationproblems where the solutions are too complex to under-stand intuitively.

6. CONCLUSIONS AND FUTURE WORK

A hierarchical approach to scheduling and utility distur-bance management for integrated process industrial siteswas presented, where the production scheduling and de-tailed production scheduling are both performed in re-ceding horizon at di!erent timescales. The production

2 4 6 8 10 12 14 16 18 20 22 240

50

100

U (%

)

2 4 6 8 10 12 14 16 18 20 22 240

0.5

1

q 1DPS

ReferenceCapacity limitationsPredictionOperation

2 4 6 8 10 12 14 16 18 20 22 240

0.5

1

q 2DPS

Time (hours)

Fig. 9. Detailed production schedule at day 2, hour 12.

5 10 15 20 25 300

5

10

15

20

q 1PS

Initial planCapacity limitationsExecuted plan

5 10 15 20 25 300

5

10

15

20

q 2PS

Time (days)

Fig. 10. Initial production schedule and actual production.

scheduling produces a production schedule for a monthwith time steps of one day, based on e.g. incoming orders,transports, and the results from the detailed productionscheduling. The detailed production scheduling handlesutility disturbances given estimated disturbance trajec-tories, and operates on a horizon of one day with timesteps of one hour. The reference for sales of products areprovided to the detailed production scheduling layer bythe production scheduling layer each day of the month.Current research is focused on developing a generic pro-duction scheduler that may be used in the hierarchicalstructure described in this paper. In the example givenin the paper, a very primitive production scheduler isused. This could be replaced by a more advanced version,that takes more aspects of the planning into account. Theobjective is also to improve the model used for the detailedproduction scheduling, and shape the objective functionof the posed optimization problem to really reflect theeconomic aspects of the production control. The aim isalso to try the structure on a real industrial case, andcompare the results with current planning methods.

ACKNOWLEDGEMENTS

The research is performed within the Process IndustryCentre (PIC) supported by the Swedish Foundation forStrategic Research (SSF). The first and second authors aremembers of the LCCC Linnaeus Center and the eLLIITExcellence Center at Lund University.

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