64 • IEEE ROBOTICS & AUTOMATION MAGAZINE • JUNE 2015 1070-9932/15©2015IEEE

T o effectively operate a refinery and make it com-petitive, efficient short-term scheduling tech-niques that utilize commercial software tools for practical applications need to be developed. However, cumbersome details make it difficult to solve the short-term scheduling problem (STSP) of crude-oil operations, and mathematical programming models fail to meet the industrial needs. This article proposes an inno-vative control-theoretic and formal model-based method to

tackle this long-standing issue. This method first models the STSP as a hybrid Petri net (PN) and then derives criti-cally important schedulability conditions. The conditions are used to decompose a complex problem into several tractable subproblems. In each subproblem, there are either continuous variables or discrete variables. For subproblems with continuous variables, this work proposes a linear pro-gramming-based method to solve them; while, for sub-problems with discrete variables, this work adopts efficient heuristics. Consequently, the STSP is efficiently resolved, and the application of the proposed method is well illustrat-ed via industrial case studies.

Short-Term Scheduling of Crude-Oil OperationsBy NaiQi Wu, MengChu Zhou, and ZhiWu Li

Enhancement of Crude-Oil Operations Scheduling Using a Petri Net-Based Control-Theoretic Approach

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Digital Object Identifier 10.1109/MRA.2015.2415047Date of publication: 15 May 2015

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Oil Refinery and Short-Term Scheduling

The Refinery ProcessAn oil refinery is composed of various production units such as tanks for material storage, a complex pipeline system, utili-ty system, and so on. The overview of a refinery in China is shown in Figure 1.

Roughly speaking, the operational process of an oil re-finery has three stages: 1) crude-oil operations, 2) produc-tion, and 3) final product distribution. At the first stage, crude oil is carried to the port near the refinery plant by crude-oil tankers and unloaded into storage tanks. The crude oil in the storage tanks is then moved into charging tanks in the plant using a pipeline. Finally, the charging tanks feed oil into distillers for processing, which ends the first stage. At the second stage, the middle products after distillation are further processed by various production units until a variety of components are obtained. These components are then mixed to form the final products. The final products are distributed to markets by different means at the third stage.

With intensive market competition and sustainable de-velopment requirements, extensive modifications have to be made to the operations of the process industry. Profits can be increased significantly by using advanced informa-tion technology to improve the operations of a process plant [16]. In recent years, great attention has been paid to process engineering tools to enable factory automation. A plant is operated in a hierarchical way with three levels: 1) production planning at the upper level, 2) production scheduling at the middle level, and 3) process control at the lower level. Presently, at the upper level, commercial soft-ware that is developed based on linear programming tech-niques is widely applied to generate production plans for a whole refinery. At the lower level, advanced control systems have been installed for unit control in most oil refineries to optimize various production objectives to maximize pro-ductivity gains.

In this process, the area that needs to be improved is the method and software tool at the middle level, or the so-called short-term production scheduling [16], [24]. This process is still being done manually by planners in today’s practice. Therefore, there is an urgent need to develop effective meth-odologies for the middle level so that full automation can be implemented in all three levels to achieve sharp productivity increases for the whole plant.

It is known that the STSP of crude-oil operations is one of the most difficult scheduling problems in a refinery, and this article attempts to solve this problem.

The Short-Term Scheduling ProblemTo address this issue, one has to realize various constraints and requirements. Before giving the constraints for the sys-tem, we first present a brief introduction to the process of an oil refinery.

To be profitable and to meet global market demands, a refinery should process a variety of crude-oil types. A dis-tiller is designed to process some types of oil, but not all types of oil can be processed by every distiller. This in turn means that a storage tank or charging tank can only hold one type of oil at a time. Thus, when a tank is charged, it should be empty or the oil type that is charged into it must be same as that in the tank. Before crude oil can be pro-cessed, the brine should be separated from it, which re-quires that the oil must sit in the tank after the tank is filled and before it can be discharged. This time delay is called oil residency time constraints. Furthermore, a tank cannot be charged and discharged at the same time, i.e., an overlap for charging and discharging a tank is not allowed.

A pipeline is used to transport crude oil from storage tanks to charging tanks, and there is always crude oil in the pipeline that cannot be emptied. Since a pipeline is tens of kilometers long and various crude-oil types are processed, there may be multiple oil segments in the pipeline with a different type of oil in each segment.

In distiller feeding, a charging tank is required to feed a distiller at any time and, therefore, poses the following con-straint. Assume that a charging tank is feeding a distiller and expected to be emptied at time .x To make the distillation process stable, the successor tank must start to feed the distill-er at time ,

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We also face the following process constraints: ● the uninterrupted operation requirement for distillers ● the occupation requirement of a charging tank in distiller

feeding ● the nonoverlap requirement in tank charging and

discharging ● oil residency time constraint ● charging-tank-switch-overlap constraint.

To schedule the system at the middle level, it needs to de-fine and arrange activities for all the devices and production units in every detail so that the constraints are satisfied and the given objectives are optimized.

State of the ArtWith the nondeterministic polynomial-time (NP)-hard com-plexity for solving a general scheduling problem, usually heuristics and metaheuristics are applied for discrete manu-facturing systems and batch processes [5], [10], [13], [14], [21]. Since heuristics and metaheuristics cannot ensure an optimal solution, the STSP of batch processes is formulated as mathematical programming models to obtain an optimal solution [3], [9].

As previously discussed, there are discrete decisions in oper-ating a refinery, just as there are in operating a general process industry. Hence, an STSP of refinery operations is essentially combinatorial and belongs to a set of NP-complete problems [2]. A good way to efficiently solve a complex scheduling prob-lem is to adopt heuristics and metaheuristics for suitable solu-tions but not exact optimal ones. This method is also used for scheduling discrete manufacturing systems and batch process-es. It is known that, to make these techniques applicable for a problem, the jobs to be performed should be well-defined and known before the scheduling process begins, and solution feasi-bility should not be a major issue. In scheduling a refinery, one needs to define and sequence the tasks simultaneously, i.e., the tasks to be scheduled are not known at the beginning. Furthermore, there are a large number of constraints to be dealt with. Therefore, it is challenging to find a feasible solution. Hence, heuristics and metaheuristics are difficult to apply.

Exact solution methods previously developed for batch processes are applied to the STSP of a refinery using mixed in-teger linear programming (MILP) and mixed integer nonlin-ear programming (MINLP) models. With both discrete-event and continuous variables, the key issue is how to model time. The existing studies offer two types of models, discrete-time representation and a continuous-time model [17]. In the dis-crete-time representation, the horizon is divided into a num-ber of uniform time slots. By this time representation, MILPs can be obtained as they are in [4], [6], [11], [15], [19], [20], [22], [23], and [38]. However, this method results in a huge number of binary variables leading to a problem that is almost impossible to solve [2], [33].

It seems that, if the number of binary variables can be re-duced, the problem becomes easier. Using continuous-time models and assuming that one knows the discrete events to be performed during the scheduling horizon, the number of

binary variables can be significantly reduced. Such models are adopted in [6]–[8], [12], and [25] to solve the problem. Nevertheless, nonlinear constraints are introduced in [19], which drastically complicates the solution process. Knowing the number of events that will occur in advance is unrealistic [2], because they are not known before a schedule is obtained. Moreover, to make the problem solvable, the models of both types make special assumptions so that some constraints are ig-nored, leading to an inefficient or unrealistic solution for real world cases [15]. Thus, it is necessary to search for a new tech-nique so that a software tool for practical use can be developed.

Solving the STSPA refinery process is a continuous one, and so the short-term schedule obtained should be compatible with its initial state. With the dynamic nature of a plant and the insufficiency of sen-sors, one cannot exactly predict the state of the system in real time. Therefore, although the scheduling horizon for a refinery often lasts between a week and ten days (sometimes longer de-pending on the initial state), in practice, a short-term schedule should be generated within a few hours. This means that a sched-uling tool must work quickly. To make automation possible for this problem, similar to how it is done for scheduling discrete manufacturing systems and batch processes, it is important to have an approximate method for an excellent and feasible solu-tion but not an optimal one, which would take too long to ac-quire. However, heuristics and metaheuristics that are used in discrete manufacturing systems and batch processes are not ap-plicable to the problem addressed here.

By examining the STSP of a refinery, one can find that the feasibility issue and the characteristics of its hybrid nature make the problem difficult. With a large number of con-straints, the feasible space must be small, making it extremely difficult to find an exact optimal solution since the feasible space needs to search the whole space. In the control-theoretic domain, by building a proper model one can control the sys-tem so that the undesired states cannot be reached, or one can determine a feasible solution space. This leads to the problem addressed here in a control-theoretic perspective instead of the MILP or MINLP models used in the existing work.

Based on this idea, a hybrid PN is developed to model the process in this article. Using the PN models, the dynamic be-havior is analyzed using the control theory, and schedulability conditions are successfully derived, which can be checked in a simple way. Using these conditions, the problem is hierarchical-ly divided into two subproblems: 1) the refining scheduling problem at the upper level and 2) the detailed scheduling prob-lem at the lower level. By treating these conditions as con-straints, this work finds a realizable refining schedule by further decomposing it into subproblems so that each subproblem con-tains either discrete or continuous variables. By doing so, one can separate the discrete variables from the continuous ones such that the problem can be efficiently solved. In addition, with the schedulability conditions and the hybrid PN model, one can find a feasible detailed schedule in a simple way. Therefore, a computationally efficient methodology is provided

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that can be developed into a software tool for practical use. It is possible to extend the proposed approach to the STSPs of other process industries, which represents a breakthrough in the re-search field. This article briefly introduces the proposed novel approach without going into too much technical detail so that the readers can easily understand how it works.

Mathematical Programming Methods and ComplexityWhen operating a refinery, we face discrete events such as the start and end of charging and discharging a tank as well as con-tinuous processes, such as oil flow and distillation, resulting in a hybrid system. Unlike widely studied discrete production-scheduling problems, where jobs to be performed are well-de-fined and the machine capacities are known in advance, when scheduling the process of crude-oil operations, we only have the system state information, e.g., crude-oil inventory in the system and the status of all devices, including the tanks, pipeline, and distillers. We must first define the jobs and then schedule them. Intelligent optimization methods such as genetic algorithms, particle swarm optimization, mussel wandering optimization, and evolutionary algorithms completely fail to do so since they cannot even find their initial population (feasible solutions).

By recognizing the difficulty of the problem, researchers have tried mathematical programming methods. The key issue be-comes whether to describe the time as discrete or continuous. With the former, a scheduling horizon is divided into a number of slots so that it can happen at the boundary of a slot in any event. Then, one finds an optimal schedule using an exact solu-tion method [19], [22], [23], [38], which suffers from computa-tional complexity, as shown through the following example.

Assume that T is the number of time slots for a plant with K distillers, H is the number of oil types, and G is the number of tanks. Let fij be the production rate of distiller i during time slot

,j and let g j be the flow rate of the pipeline during time slot .j To further define ,h 1j = there is a crude-oil type switch in per-forming oil transportation through the pipeline at the beginning of slot ,j otherwise it is zero. Let CP be the cost coefficient for such a switch. We define d 1ij = if there is a charging tank switch in feeding distiller i at the beginning of time slot ,j other-wise it is zero. Let CDS be the cost coefficient for such a switch. The main objective is to maximize the production rate, mini-mize crude-oil inventory cost, and minimize changeover cost. An MILP is given as follows:

Maximize

.

J f C h

C dDS

ijjT

iK

P jjT

ijjT

iK

11 1

11

= -

-

== =

==

// ///

This is subject to the following:1) g j should be within the permissive flow rate range of the

pipeline, { , , , } .Nj T1 2T6 f! = 2) fij should be within the permissive feeding rate range of

the distiller ,i i NK6 ! and .j NT6 !3) Material balance for tankers during slot , .j j NT6 !4) Material balance for tank l during slot ,j l NG6 ! and

.j NT6 !

5) Material balance for crude-oil type k during slot ,j k NH6 ! and .j NT6 !

6) Oil residency time constraints for tank l during slot , Nj l G6 ! and .j NT6 !

7) Charging-tank-switch-overlap constraint, Ni K6 ! and .j NT6 !

Using this model for each time slot and each distiller, one needs to determine which oil type the distiller should be charged to or which tank the oil should be discharged from. A binary variable should be used to describe the occurrence of such an event. Thus, outside of the binary variables denoting the occurrence of events for constraints 6 and 7, there are at least T G H K# # # binary variables. A typical application scenario has 20 tanks (11 storage and nine charging tanks), six oil types to be processed, and three distillers with a ten-day scheduling horizon. To obtain a solution with acceptable ac-curacy, the application requires a time slot that is less than 15 min when one uses an MILP model with discrete-time repre-sentation [19]. Thus, for a ten-day scheduling horizon, there are 960 time slots and at least 960 # 20 # 6 # 3 = 345,600 bi-nary variables for this scenario. It is extremely difficult, if not impossible, for an existing commercial software package to solve such a large problem. Furthermore, a produced solution may not be applicable or feasible because of the requirement that an event should be scheduled to happen at the boundary of a slot. Any reduction of slot length will drastically increase the number of binary decision variables; e.g., reducing a time slot from 15 to 10 min will increase the binary variables to 518,400. This implies that such models are not applicable to real-life industrial practice.

The studies in [1], [6], [18], and [37] have offered continuous time models. These models drastically reduce the number of bi-nary variables but introduce nonlinear constraints [19], yielding a nonlinear programming model. Furthermore, the number of discrete events that are defined by a to-be-found schedule dur-ing the horizon needs to be known in advance [2]. Can we use continuous-time representation to formulate the problem? Unfortunately, this method is not used in practice; thus, the con-tinuous models are currently theoretically valuable. The last re-sort for solving this problem is to make special assumptions and neglect most of the constraints. Using this method, the resulting models (discrete or continuous) can be successfully solved. This solution gives decision makers some hints regarding ideal re-sults, which concludes in unrealistic and infeasible solutions. In conclusion, mathematical programming models cannot be ap-plied to large real-world problems. Therefore, we must seek a new breakthrough solution to the STSP.

Control-Theoretic and Hybrid PN-Based Approach

Problem Formulation in the Perspective of Hybrid System Control TheoryThe process of crude-oil operations is formed by a series of op-erations, including unloading oil from tankers, transporting oil from storage tanks to charging tanks, and feeding oil from charging tanks to distillers. The start and end of an operation

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form the discrete events. In addition, the process constraints are also related to a discrete-event process. A natural idea is to de-scribe this process with a dynamic hybrid model so that a sched-uling problem can be formulated from the perspective of the hybrid system control theory. When scheduling such a process, we should decide when an operation should take place, what should be done, and how it should be done. Therefore we pro-pose an important concept called an operation decision (OD).

Definition 3.1Define OD = (COT, , , , , ),S D a bg where COT represents crude-oil type; g represents the amount of oil to be delivered by the OD; S is the source from which the oil comes; D repre-sents the destination where the oil is delivered; and a and b are the starting and ending time of the OD. For a single opera-tion, the flow rate is generally a constant and described as

/ ( ) .b ag - In the definition, COT, ,S and D are discrete vari-ables, while g and flow rate / ( )b ag - are continuous vari-ables. When an OD is executed, the state of the system is transformed to another. Hence, using a hybrid control theory, an OD can be seen as a control command.

There are oil unloading ODs (ODU), oil transportation ODs (ODT), and oil feeding ODs (ODF). We use [ , ],a b [ , ],m n and [ , ]~ r to represent their time interval, respectively. For ODU, S is a tanker and D is a storage tank. Similarly, we can identify variables S and D for ODT and ODF. It should be pointed out that an ODT must be executed by a pipeline. Let ODFki be the i- th OD for feeding distiller ;k let

/ ( ), / ( ),g fg b a g n m= - = - and / ( )h g r ~= - be flow rates for ODU, ODT, and ODF, respectively; let [ , ]s ex xC= be the scheduling horizon (typically a week or ten days); and let K be the number of distillers. Initially we only know the oil in-ventory, the status of all the devices, and the tanker arrival in-formation. Then, given the initial state information at ,sx in the view of hybrid control theory, to schedule the system is to find a series of ODs with multiple objectives being optimized. This is described as

SCHD:A series of ODs:ODU , ,ODU ,ODT , ,

ODT ,ODF , ,ODF .w

x K

1 1

1

f f

f

(1)

It is subject to all the constraints given in the “Oil Refinery and Short-Term Scheduling” section, where w is the number of ODUs, x is the number of ODTs, both of which are un-known; ODFk = {ODF , ,ODF , ,ODF }, k N1 2 knk k Kkf f ! consists of all the ODFs for the feeding of distiller k during

[ , ] .s ex xC= The objectives to be optimized include productivity maxi-

mization, minimization of inventory, minimization of the number of crude-oil type switches for transporting oil through a pipeline, and minimization of the number of charging tank switches in distiller feeding.

Solution ArchitectureFeasibility is especially important when solving the STSP of crude-oil operations. The problem with this formulation is

that a large number of constraints exist and any violation of them results in an infeasible solution. With a large number of constraints, on the one hand, the feasible solution space is small, which makes it challenging to obtain a feasible solution by an exact enumeration-solution method using mathematical programming models. On the other hand, finding a feasible solution becomes easier if the search is done in a small, feasible space. In regards to the scheduling horizon, in addition to the feasibility issue, a schedule must present all actions in detail, which makes the problem large and too difficult to solve.

A control-theoretic solution architecture with a two-level hi-erarchy is proposed as a breakthrough solution. To guarantee solution feasibility with this architecture, we can take advantage of the control theory. We first describe the processes of crude-oil operations with a hybrid dynamical model called a hybrid PN. Then, we simply model the constraints via its structure, transition enabling and firing rules, and its properties, e.g., live-ness. Based on the hybrid control theory, we convert the live-ness conditions into schedulability conditions and feasible solution space. Consequently, we need to find a solution in the feasible space, which will drastically simplify the problem.

This proposed architecture offers us a novel strategy to hi-erarchically decompose a large problem into two small sub-problems. Using this architecture, one needs to find a refining schedule at the upper level, which is then realized by a detailed schedule at the lower level. The key here is that the obtained refining schedule must be realizable by a detailed schedule. This is possible since the schedulability conditions can be for-mulated as constraints into the model to find a refining sched-ule. Furthermore, one can further decompose the refining schedule problem into subproblems with each subproblem containing either continuous variables or discrete variables in the same formulation. In other words, we innovatively decou-ple the interaction of discrete and continuous variables such that one can efficiently obtain a realizable refining schedule.

In finding a detailed schedule to realize a refining schedule by using the schedulability conditions as constraints, the solu-tion feasibility can be guaranteed by making the system trans-form from one allowed state to another. An allowed state implies that it can evolve to a feasible schedule if the system is properly scheduled as shown in [29], [30], [33], and [35]. Thus, a feasible schedule to realize a given refining schedule can be found sequentially in a one-OD-by-one-OD way. Heuristics and metaheuristics can be applied to optimize these objectives. By optimizing these objectives one can effi-ciently find a short-term schedule for crude-oil operations.

Hybrid PN and Modeling of OperationsWe first present a hybrid PN and use it to model the process. The concept of a basic PN can be found in [34], [39], and [40]. The PN used in this work is extended from a resource-oriented PN devel-oped in [34] and [40]. It is defined as PN , , , , , ,P T I O M K=^ h where P is a finite set of places; T is a finite set of transitions,

, ; : { , , , }; :NP T P T I P T O P T0 1 2", + # #f! z z= = ; :N NM P" " is a marking with M0 being the initial marking;

and : \ { }NK P 0" with ( )K p being the largest number of

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tokens that place p can hold at a time. With colors being intro-duced, a colored PN is formed. One can find the transition en-abling and firing rules in [26] and [34].

We use a hybrid colored-timed PN (CTPN) to model the system, which is defined as CTPN ( , ,P P T T TD C D T C, , ,=, , , ),I O M0U where PD and PC denote finite sets of discrete

and continuous places, respectively; , ,T TD T and TC denote fi-nite sets of discrete, timed, and continuous transitions, respec-tively; I and O denote input and output relations, respectively;

( )pU and ( )tU represent the color sets in P and ,T respec-tively; and M0 is the initial marking. Figure 2 shows the icons used in our model.

A token in p PD! has the same meaning as a basic PN. A token p PC! indicates that there is oil in the tank modeled by p and its volume is given in a real number (called token vol-ume for short). A t TD! or t TT! acts like the one in a basic PN. When a t TC! fires, oil is moved from one place to an-other, and its flow rate is decided by an OD. The firing dura-tion of transition t TC! determines if the token is completely removed from its input place. Next, we present the PN mod-ules for tanks and a pipeline.

Modeling the DevicesDue to a charging-tank-switch-overlap constraint, the behavior of a storage tank is different from that of a charging tank; there-fore, they have different models. The model for the former is shown in Figure 3(a), in which we have ( ) ,K p 1=

.p P PD C,6 ! Two places p Ps C! and p Pc C! are used to model a tank’s state. When ( )M p 1s = or ( ) ,M p 1c = it means that the tank has oil in it. ( )M p 1s = indicates that the oil in the tank is not ready to be discharged. Only when both ( )M p 1c = and ( )M p 0s = is the oil in a tank ready to be discharged. Transitions t Tf C! and t TC! are used to model the charging and discharging of a tank, respectively. Transition t Td T! mod-els the oil residency time constraint. By ,t Td T! it guarantees that the oil must stay in ps for a time associated with td after charging the tank ends. After firing td ends, the token in ps goes into ,pc leading to the enabling of ,t which means that the oil in the tank can be discharged. Since ( ) , ,M p p P1 D0 3 3 != at any time, at most one of transitions , ,t tf d and t can fire, which guar-antees that charging and discharging a tank at the same time cannot occur. The inhibitor arc ( , )p ts and self-loop between p3 and td further ensures that the oil residency time constraint is satisfied. The token volume associated with the token in p PC1 ! is used to model the available capacity of the tank at a marking .M With this model, the dynamic behavior of a storage tank is well modeled.

Now let us augment the model in Figure 3(a) to obtain the PN model for a charging tank by adding a charging-tank-switch-overlap constraint. Assume that a distiller is being fed by charging tank (CTK) CTK1, and it is followed by CTK2. Using the charging-tank-switch-overlap constraint during period ,ovrx the distiller should be fed by both CTK1 and CTK2 simultane-ously with oil amount 1c and ,2c respectively. Assume that the oil residency time is .W Let / ( ),1 1 2c c cD = +

/ ( ),2 1 2c c cK = + and .X W D= + To model this constraint,

the process is treated not just as a constraint, but the process is scheduled so that the oil in CTK2 that is fed into the distiller is ready for discharging at least D time units earlier than ,W and, after being emptied, CTK1 is recharged at least K time units later. Therefore, this constraint can be met when an appropriate schedule is implemented. To model this mechanism, ,p PC2 !

,t Th T! inhibitor arc ( , ),p t f1 and a self-loop between p3 and th are added to Figure 3(a) to form the PN model shown in Fig-ure 3(b). At the same time, X and D time units are associated with td and ,th respectively.

The PN model for the pipeline with three different oil seg-ments is shown in Figure 4. Places ,p PC1 ! ,p PC2 ! and p PC3 ! model the three segments, and t TD1 ! and t TD2 ! are used to connect these places in a serial way. Transitions t TI C1 ! to t TIk C! and t TO C1 ! to t TOk C! are used to model oil flowing into and out of the pipeline. Let

{ , , }T t tI I Ik1 f= and { , , }T t tO O Ok1 f= be the sets of input and output transitions of the pipeline. The firing of

, { , , , },t i k1 2Oi f! continuously consumes the token volume in ,p1 until ( ) .M p 01 = According to the transition enabling and firing rules, then t1 fires immediately, resulting in the token in p2 and its whole volume being moved into .p1 This way the transition t TOi O! can continuously fire. When a transition , { , , , }t i k1 2Ii f! fires, a token goes into p3 imme-diately. The continuous firing of tIi results in the continuous

Figure 2. The icons used in the PN model.

Discrete Place

Continuous Place

Continuous Transition

Timed Transition

Discrete Transition

Figure 3. The PN modules for tanks.

tftf

td

ps

pcpc

td th

tt

psp3

(a) (b)

p1

p3

p1

p2

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increase of the token volume in .p3 To make the model be-have correctly, we allow only one transition in TI to fire at a time, and, if one transition in TI is firing, only one transition in TO should fire. The number of continuous places in the model shown in Figure 4 represents the number of oil segments. We can set this number as the largest one that may occur. Since the rate for flowing into and from the pipeline must be same, the pipeline can be abstracted by a macro transition .y By doing so, p1 in y can be denoted as ( ) .p y1 In this model, when y fires, one fires a transition in TI and another in TO with the same rate at the same time. Based on the PN models for the devices, we construct the PN model for the entire system.

Modeling a Whole SystemWhen we model the whole system we focus on its model structure using prior-developed modules. Thus, for the sake of easy visualization, we omit some unimportant elements, e.g., p3 and its associated arcs, and ( , )p ts in a tank PN module. We use a simple system to illustrate the modeling process (shown in Figure 5). The system is configured with a tanker, one dock, two storage tanks, two charging tanks, and two distillers for crude-oil operations. In this model, p0 models a tanker with H tokens, meaning that the tanker carries H oil types. Place p1 represents the dock and a token in it implies that there is an oil type in the tanker that is ready to be unloaded. By this model, a token can only be moved into p1 by firing t1 if

( ) ,M p 01 = which models the requirement that only one oil type can be unloaded at a time. Since the pipeline modeled by y discharges a storage tank and charges a charging tank, y is the discharging and charging transition for storage tanks and charging tanks, respectively. Thus, in the model, { , , , , , }t t y p p pf d s c1 1 1 1 11 and { , , , , , }t t y p p pf d s c2 2 2 2 21 are for the two storage tanks, while { , , , , , , , }y t t t p p p pd h s c3 3 3 3 3 31 32 and { , , , , , , , }y t t t p p p pd h s c4 4 4 4 4 41 42 are for the two charging tanks,

respectively. We use p3 and p4 to model the two distillers. A token in p3 or p4 means that the corresponding distiller is working. By defining the colors in the model, only a suitable token can go into p3 or p4 by firing t3 or .t4

With the PN model shown in Figure 5, the structure of the process is well described. However, the detailed dynam-ics of oil flow is not modeled. To do so, let ( )M p be the number of tokens in p regardless of the token color, { the color of a token for an oil type, ( ( ))V M p the amount of oil in ,p and ( ( , ))V M p i{ the amount of oil type i with color

.i{ Then, the dynamical behavior can be exactly described by defining the transition enabling and firing rules seen in [26], [31]–[33], and [35].

In summary, the operational requirements and constraints are guaranteed by the model structure, transition enabling and firing rules. However, the constraint that any distiller should op-erate uninterruptedly has not been modeled yet. Thus, the live-ness definition of a model is needed to ensure that the last constraint is met. Let Pdsl be the set of places modeling the dis-tillers in the model and assume that .P hdsl =

Definition 3.2A PN model for a process of crude-oil operations is said to be live if, at any time, there is at least a ,t p p Pdsli i i6! !: that is firing or enabled and { } { } { } ,t t th1 2+ + + Qf = where pi: is the set of the input transitions of .pi

A hybrid PN is made live if it can be properly controlled by ODs that form a complete short-term schedule. With this nota-tion, we are now ready to derive the schedulability conditions.

Schedulability ConditionsFor crude-oil operations, a short-term schedule is formed by an unknown number of ODs. The execution of an OD, implying that its corresponding operation is executed or the transition is fired in the model, transforms the state of the system to another. Although there may be several ODs that are being executed si-multaneously in the system, the PN model shows that, with each OD being deterministic, the state of the system can be easily cal-culated when its execution ends. Thus, when the system is con-trolled by a schedule, it evolves in a way that the ODs are executed one by one and the system evolves from one state to another. At the initial state ,S0 after OD1 is executed, the system reaches .S1 Then OD2 is executed and S2 is reached. Finally, n ODs are executed, yielding .Sn

Definition 3.3A state is said to be infeasible if the system violates at least one of the constraints. This state corresponds to a marking in the PN model of a system that either violates the transi-tion enabling and firing rules or is a nonlive state according to Definition 3.2. For example, the model may reach a state at which an OD is performed to discharge a nonready tank, or no appropriate OD can be performed for feeding a dis-tiller. It follows from the PN model that a state of the pro-cess is either feasible or infeasible. Then, an unsafe state is defined as follows.Figure 5. The PN model for a simple system.

H

t1

t1f t1d

t2dt2f

p0 p1

p11

p1cp2c

p21

p42 p41

t3h t3 t5p3

t4 t6p4

t4d

t4h

p4st3dp3s

p4cp3c

p32 p31

p1sp2s

y

H

t1

t1f t1d

t2t dt2t f

p0 p1

p11

p1cp2c

p21

t3h t3 t5p3

t4t t6p4

t4dt

t4t h

p4st3dp3s

p4cp3cp1s

p2s

y

Figure 4. The PN module for a pipeline.

tIk

t2 t1

tI1 tO1

p3p2 p1

tOk

y

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Definition 3.4Assume that by starting from initial state ,S0 after OD1, OD2, …, and ODi are executed, at time ,x a system reaches state Si that is feasible. Then, Si is unsafe if, with Si being an initial sate, an infeasible state is finally reached no matter what ODs are performed.

By Definition 3.4, the states of the system are divided into two mutually exclusive categories: safe and unsafe states. Thus, if the execution of any OD in a schedule transforms the pro-cess from one safe state to another, the schedule must be feasi-ble. In addition, if the state of the process is safe at any time, there must be a feasible short-term schedule. Thus, to schedule the crude-oil operations, we need to identify the set of safe states using the developed hybrid PN model.

Since the operation of any distiller cannot be terminated, a feasible schedule SCHD {OD ,OD , ,OD }n1 1 2 f= that is found for a time duration ,a06 @ does not mean that one can find a feasible schedule SCHD {OD ,OD , ,OD ,n2 1 2 f= OD , ,OD }kn n1 f+ + with SCHD SCHD1 21 for time dura-tion ,b06 @ with .b a2 For a process with initial state ,S0 if a feasible short-term schedule can be found for a time duration

[ , ],0 3C = then this process is schedulable.

Definition 3.5If a process with S being the initial state is schedulable, then S is safe for the process. By Definition 3.5, safeness is equivalent to schedulability. Therefore, based on the hybrid PN model, one can analyze its schedulability. Let DS i denote distiller i with an oil feeding rate of ,fdsi let CTK j denote charging tank j with ca-pacity jp and initial volume jg of oil in it, let F ( )MAXp be the maximal oil flow rate of the pipeline, and ,fdsii #a X= where X and K are as given above. It should be pointed out that, when a refinery is scheduled, the maximal productivity is ideal. To maximize productivity, we should have enough oil in the storage tanks or in the coming tankers. Thus, the key to finding a feasible schedule is to properly decide the ODTs for oil trans-portation and ODFs for distiller feeding. Then, based on the hy-brid PN model developed for the system, we derive the following schedulability conditions [33].

For a process of crude-oil operations composed of K distill-ers DS K1- with ,f f fds ds dsK1 2 f! ! ! the system is schedula-ble if the following conditions are met:

● There are K3 charging tanks CTK K1 3- with their capacity b e i n g , , , , ,2 2 2 2i i1 1 2 1 3 1 3 1 1f$ $ $ $p a p a p a p a+ +

,2 ( )i i i3 2 1 3 1$ $p a p+ + + , .i K1 1i 1 # #a -+ ● .F f f( ) ds dsKMAXp 1 f= + + ● At the initial state, the amount of oil type 1 in CTK1 and

CTK2 is 1 1g a= and , ,22 1 fg a= the amount of oil in CTK i3 1+ and CTK i3 2+ is i i3 1g a=+ and ,2i i3 2g a=+

, ,i K1 1 0< i3 3 3# g g- = =+ i K1 1< # - the oil in CTK ,CTK ,i1 3 1+ ,i K1 1< # - can be discharged for feed-ing distillers, and CTK3 is ready for charging.

● ( ) .f f 2ds dskkK

1 11

$ K X K-=

-` j/These conditions require that f fds ds1 2 f! ! ,fdsK!

but this does not pose a restriction on the system. In fact, a process is much easier to schedule if we have fds1 = .f fds dsK2 f= = Condition 2 indicates that the

maximum production rate is .F ( )MAXp The initial condi-tion i ig a= means that, when one charges a charging tank volume, i ig a= should be charged into it, which is the boundary for schedulabilty. In reality, a tank’s capaci-ty is much larger than .i ig a= Thus, to reduce the num-ber of oil-type switches in performing the ODTs and the number of charging tank switches in performing the ODFs, when we charge a charging tank it should charge as much oil as possible. Using this method, we can easily satisfy constraints.

For the case of ( ),f f 2ds dskkK

1 11

$ K X K-=

-` j/ assume that ,2X K= and there are four distillers, i.e., .K 4= Then, it requires ( ) .f f f f 3ds ds ds ds1 2 3 4$ + + It always holds, as one can take the largest one as .fds1 Furthermore, if it requires that a charging tank that is assigned for feeding distiller DS1 is charged to ,5 1a we have ( ) ,f f f f 9ds ds ds ds1 2 3 4$ + + which must hold. In fact, a charging tank’s capacity is more than that. Using these schedulability conditions, we discuss how to find a short-term schedule by presenting computationally efficient techniques. For different situations, the schedulability condi-tions can be found in [29]–[32] and [35].

1

2

3

Oil Number 3 (27,000) Oil Number 1 (63,000)

Oil Number 2 (55,200)

Oil Number 4 (27,000) Oil Number 5 (55,000) Oil Number 6 (38,000)

020 40 60 80 100 120 140 160 180 200 220 240

Time (h)

Dis

tille

r

Figure 6. An example of a refining schedule.

72 • IEEE ROBOTICS & AUTOMATION MAGAZINE • JUNE 2015

Refining SchedulingBy examining the schedulability conditions, Condition 4 is easy to satisfy. For Conditions 1 and 3, we need to check the initial state to verify that they are satisfied, which can be easily done. Then, only Condition 2 needs to be embedded into the model for the refining scheduling problem. How can this be done? To answer it, we first introduce a concept called a feed-ing parcel (FP) of oil.

Definition 3.6Define FP (COT, , , )g a b= as an FP of a crude-oil type, where COT is the type of oil to be fed to a distiller; g is the amount of oil to be fed; and a and b are the time points at which the feeding of this oil parcel starts and ends, respectively.

For an FP, the feeding rate is / ( )-g b a and it is a constant. Assume that during the scheduling horizon there are Q FPs for feeding distiller .i For DS i a refining schedule can be de-noted as RS FP ,FP , ,FP .iQi i i1 2 f= " , Let / ( )fij ij ij ijg b a= - denote the feeding rate for FP .ij Then, the refining scheduling problem for a system with K distillers is to find RS {RS ,1=RS , ,RS }K2 f that is an ordered set of FPs. A refining sched-ule example for a three-distiller system is shown in Figure 6.

In solving the refining scheduling problem, the objectives to be optimized are summarized as follows. The first objective is to maximize the production rate. Notice that by maximizing

it we minimize crude-oil inventory cost. In crude-oil opera-tions, different types of crude oil are processed by different dis-tillers, and sometimes an oil type can be processed by some of the distillers but not all. The processing of an oil type by differ-ent distillers results in different processing effectiveness. Thus, the second objective is to minimize the cost results from pro-cessing crude-oil types by different distillers.

Although the refining scheduling problem is a subproblem of the STSP of crude-oil operations, it is a combinatorial one and is characterized by the interaction of discrete-event and continuous processes. To solve this problem, a three-stage method is proposed as shown in Figure 7. At Stage 1, a linear programming model that only contains continuous variables is used to determine the feeding rate for each distiller by max-imizing the production rate. Based on the result obtained at Stage 1, a transportation problem model is built to assign crude oil to distillers at Stage 2 so that the oil-processing effec-tiveness is maximized. By doing so, a number of crude-oil parcels are formed for each distiller. Stage 3 sequences the parcels for each distiller obtained at Stage 2 to minimize the number of oil-type switches in performing the ODTs and charging tank switches in performing the ODFs. Notice that the problem at Stage 2 is also a purely continuous one. It is well known that it is more computationally efficient to solve a transportation problem than to solve a linear programming

problem, which can be solved effi-ciently using commercial software tools. The problem at Stage 3 is pure-ly discrete and can be efficiently solved by heuristic rules.

Since tankers arrive at different times, crude oil is available at differ-ent times. Thus, in refining schedul-ing we divide the scheduling horizon to form a number of buckets. Let Q be the number of buckets and BUK { , , , },Q f0 1 ijf= be the feed-ing rate of DS i during bucket ,j let F ( )MINi and F ( )MAXi be the minimum and maximum feeding rates for DS i respectively, and F ( )MAXp be the max-imum flow rate for the pipeline. Then, the problem for Stage 1 can be formulated as follows. The readers can refer to [27] and [28] for details.

Stage 2 Stage 3Stage 1

ObjectiveMaximization ofProduction Rate

Linear ProgrammingModel

Technique

ObjectiveMaximization of Oil

Processing Effectiveness

Transportation ProblemModel

Technique

ObjectiveMinimization of the

Number of OperationalSwitches

Heuristic RulesTechnique

Stage 2 Stage 3Stage 1

ObjectiveMaximization ofProduction Rate

Linear ProgrammingModel

Technique

ObjectiveMaximization of Oil

Processing Effectiveness

Transportation ProblemModel

Technique

ObjectiveMinimization of the

Number of OperationalSwitches

Heuristic RulesTechnique

Figure 7. The three stages for refining scheduling.

Table 1. A transportation problem model for assigning crude oil to distillers at Stage 2.

Crude Oil

Distiller 1 Distiller 2 Distiller 3

B1 B2 B1 B2 B1 B2 Pipeline Dummy Supply

Volume of crude oil in the charging tanks

Type 1 C11 C11 C21 C21 C31 C31 M M VC1… … … … … … … M M …

Type H C1H C1H C2H C2H C3H C3H M M VCHVolume of crude oil in the pipeline

Type 1 C11 C11 C21 C21 C31 C31 M M VP1… … … … … … … M M …

Type H C1H C1H C2H C2H C3H C3H M M VPHVolume of crude oil in the storage tanks

Type 1 C11 C11 C21 C21 C31 C31 0 0 VS1… … … … … … … 0 0 …

Type H C1H C1H C2H C2H C3H C3H 0 0 VSHVolume of crude oil in the tanker

Type 1 C11 C11 C21 C21 C31 C31 0 0 VT1… … … … … … … 0 0 …

Type H C1H C1H C2H C2H C3H C3G 0 0 VTHDemand D11 D12 D21 D22 D31 D32 DP DD

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Problem P1:Maximize .J fDS ijijQ

0= != // (2)

Subject to

1) , DSF f F i( ) ( )MIN MAXi ij i 6# # ! and BUK.j ! 2) BUK.,f F jDS ( )MAXiji p 6# !!/3) During any bucket, the oil available for processing by

each distiller is enough.Notice that, by Constraint 2, the schedulability condition 2 is

guaranteed. By solving Problem P1, the amount of crude oil re-quired for processing by each distiller during the scheduling hori-zon is determined. With crude oil that is available during each bucket in the charging tanks, pipeline, storage tanks, and tankers known, the crude oil can be assigned to a distiller using a trans-portation problem model at Stage 2. To do so, the oil processing effectiveness of type j by distiller i can be described by a cost co-efficient .Cij If it is the most effective, Cij is set small; otherwise it is large. If distiller i is unable to process crude-oil type ,j a big M is set for it. For a system with three distillers, two buckets, H oil types, and one tanker, the problem for Stage 2 can be briefly de-scribed by a transportation problem model as shown in Table 1, where Dij and Vij denote a demand and supply, respectively. The readers can refer to [27] and [28] for further details.

Since a pipeline should be full of oil all the time, this re-quirement must be met when a schedule is completed at the end of the scheduling horizon. Thus, crude oil should be as-signed to the pipeline too. The oil assigned to the dummy rep-resents the remaining oil in the pipeline at the end of horizon.

Using the results obtained from the problem at Stage 2, the oil is divided into a number of parcels for each distiller. Notice that in modeling the problem at Stage 2 the crude oil comes from different sources and a source is treated as a supplier. However, for this problem, different sources do not represent different oil types. Hence, some parcels of crude oil from dif-ferent sources that are assigned to a same distiller may be the same type. Therefore, it is profitable to merge parcels with the same oil type if possible so that the cost resulting from oil-type switches in oil transportation and charging tank switches in distiller feeding is reduced. This can be done by checking the available time of each parcel. Because of the limited number of crude-oil types, one can do the parcel merging easily. Notice that by doing so we minimize the number of operational switches, though we cannot ensure an optimal solution.

Detailed SchedulingSince the schedulability conditions are modeled as constraints in the refining scheduling problem, the realizability of an obtained refining schedule is ensured. Then, given a refining schedule, one needs to find a detailed schedule to realize it. In a detailed schedule an FPij is realized by a number of ODs. In other words, an FPij in a refining schedule should be divided into m ODFs, i.e., ODF ,ODF , ,ij ij1 2 f and ODFijm , which should be included in a detailed schedule. By using this detailed schedule, the schedulability conditions are satisfied.

Since the set of safe states for a system can be identified by using the schedulability conditions given a refining schedule, a

detailed schedule can be found. Starting at the initial state, a charging tank, say CTK1, is released for the first time, one can as-sign it to feed a distiller, say DS .i It is known from the given refin-ing schedule that the oil type and amount for FPi1 are COTi1

SchedulabilityCondition

A ChargingTank CTK

Is Released

AssignCTK to

Distiller DSi

Createan ODT

Create anODF for

DSi

Safe StateSk

Safe State Sk+1

Figure 8. The creation of ODs in finding a detailed schedule.

Table 2. The costs for processing oil types by differ-ent distillers.

Distiller 1 Distiller 2 Distiller 3

Crude-oil number 1 1 M M

Crude-oil number 2 M 1 M

Crude-oil number 3 4 10 6

Crude-oil number 4 M 8 3

Crude-oil number 5 M 5 10

Crude-oil number 6 M 8 5

Table 3. Oil in charging tanks at the initial state.

TankCapacity (Ton)

Type of Oil in Tank

Amount (Ton)

Distiller in Feeding

Tank number 129

34,000 Crude-oil number 3

27,000 DS1

Tank number 128

34,000 Crude-oil number 2

30,000 DS2

Tank number 116

34,000 Crude-oil number 4

27,000 DS3

Tank number 117

34,000 Crude-oil number 5

30,000

Tank number 115

34,000 Crude-oil number 5

25,000

Tank number 127

34,000

Tank number 182

20,000

Tank number 180

20,000

Tank number 181

20,000

74 • IEEE ROBOTICS & AUTOMATION MAGAZINE • JUNE 2015

and ,i1g respectively. Assume that the available amount of oil with type COTi1 in the charging tanks is .0g Then, using the schedu-lability conditions, CTK1 is charged with volume i1 1 0#g g g- so that the resulting state is safe. ODTi1 is created by setting COT COT , ,D CTK ,i1 1 1g g= = = and b a- = / .f maxp1g Notice that a is the moment at which it starts to charge CTK1 so that a and b are decided. With ODTi1 being created, an ODFi1 for feeding DS i can be created by feeding volume 1g in CTK1 after feeding volume .0g This process can repeat and a detailed schedule can be obtained by creating the ODs one by one in a re-cursive way. Therefore, when each OD is performed the system is transformed from a safe state to another safe state. This is done using the derived schedulability conditions. The process for creat-ing ODs in finding a detailed schedule is shown in Figure 8.

One key question is how to assign a charging tank that is available to feed a distiller. To do so, let C j be the capacity of charging tank ,j KDi the set of charging tanks that are serving for distiller i at a time, and KDC CKDi jj i= !/ be the sum of capacity of the charging tanks serving for distiller .i Then, an ef-ficient heuristic is designed to do so. Using this heuristic, when a charging tank is released and becomes available, it is assigned to serve a distiller so that KDC /KDCi k . / ,f fdi dk where fdi and fdk are the feeding rate of distillers i and k [36], respectively.

Until now, we have presented the scheduling method. It should be pointed out that by using the proposed method the obtained solution may not be globally optimal. However, a good and feasible solution can be quickly found to meet prac-tical applications.

Industrial Case StudyNow consider a real-life refinery scheduling scenario from China. This is a three-distiller refinery, and every ten days it re-quires creating a short-term schedule for the next ten days. Considering the scheduling horizon, there are six crude-oil types to be processed. Among the oil types, crude-oil type num-ber 1 can be processed by only DS ,1 while crude-oil number 2 can be processed by only DS .2 Any of the distillers can process crude-oil number 3, but the best distiller is DS ,1 and then DS ;3 the worst is DS .2 Both DS2 and DS3 can process crude-oil number 4, number 5, and number 6 with different costs. These costs are quantified as shown in Table 2, where M for cost Cij means that distiller DS j cannot process crude-oil number .i

The refinery has nine charging tanks that are usable for this horizon. Initially, charging tanks number 129, number 128, num-ber 116, number 117, and number 115 hold a certain amount of oil while the others are empty. Furthermore, at this state, charging tanks number 129, number 128, and number 116 are used for feeding DS ,DS ,1 2 and DS ,3 respectively. The oil type and its vol-ume in each tank are shown in Table 3. The pipeline in this refin-ery has a capacity of 12,000 tons and is full of crude-oil number 2. The oil in the storage tanks includes 28,000 tons of oil number 3, 54,000 tons of oil number 2, and 64,000 tons of oil number 1. In addition, during the horizon, a tanker that carries 132,000 tons of oil number 6 will arrive. With ,h0sx = only after 96 h one can use the oil in the tanker for distillation. Therefore, we have two buckets [0, 96] and [96, 240] for this case problem.

For the three distillers, it is known that the minimum pro-duction rates are 312.5, 205, and 458 tons/h; and the maximum production rates are 375, 230, and 500 tons/h, respectively. For the pipeline, the maximum flow rate is F ( )MAXp =

, tons/h.1 250 The oil residency time and charging-tank-switch-overlap time are the same (four hours), leading to 6X = and h,2K = respectively.

According to the schedulability conditions, we find that the initial state is safe. Hence, by the proposed method, one can find a feasible short-term schedule. Then, the method presented in

Table 4. The oil to be processed during each bucket.

BucketDistiller 1 (Ton)

Distiller 2 (Ton)

Distiller 3 (Ton)

(0, 96) 36,000 22,080 48,000

(96, 240) 54,000 33,120 72,000

Figure 9. The detailed schedule of distiller feeding for the case study.

1

2

3

Number 127 Number 129

Number 129 Number 182Oil Number 3 (27,000) Oil Number 2 (63,000)

Number 180Number 128 Number 181

Oil Number 2 (55,200)

Number 117 Number 116

Number 116 Number 115 Number 117Oil Number 4 (27,000) Oil Number 5 (55,000) Oil Number 6 (38,000)

020 40 60 80 100 120 140 160 180 200 220 240

Time (h)

Dis

tille

r

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the “Refining Scheduling” section is applied to obtain a refining schedule. We solve the formulated model for problem P1 and yield tons/h, tons/h,f f f f375 23010 11 20 21= = = = and f f30 31= tons/h.500= Notice that, by using this result, the

maximum production rate is reached. Then, with the produc-tion rate decided for each distiller during each bucket, the amount of crude oil to be processed by each distiller is calculated as shown in Table 4.

Based on the results obtained from Stage 1, the transporta-tion problem model at Stage 2 can be easily formed and solved, and a number of oil parcels are obtained for each distiller. The oil parcels that have the same oil type are then merged at Stage 3, yielding a refining schedule as shown in Figure 6.

With the obtained refining schedule and the schedulability conditions, we use the method presented in the “Detailed Scheduling” section and the heuristic given in [36] to find a detailed schedule. For this schedule, the ODFs for distiller feeding and the ODTs for charging tank filling are shown by Gant charts in Figures 9 and 10, respectively. By observing the obtained schedule, one can conclude that all the constraints, including crude-oil residency time and charging-tank-switch-overlap constraints, are satisfied. Notice that, for the refining scheduling problem, we aim at maximizing the productivity using a linear programming formulation presented in the “Refining Scheduling” section. Hence, for the obtained sched-ule, the production rate is maximal [27], [28]. In addition, from the obtained result, when a charging tank is charged according to an ODT, it is charged to capacity. By doing so, the number of oil-type switches in performing ODTs for oil trans-portation and the number of charging tank switches in per-forming ODFs for distiller feeding are minimized.

ConclusionsA refinery is a large-scale and complex system containing both discrete-event and continuous operations. Its scheduling prob-lem is essentially combinatorial and extremely challenging. Due to its continuous processes, the jobs to be scheduled are not de-fined and unknown at the beginning of the process. Therefore, they need to be defined and sequenced during a scheduling pro-cess. Such a feature disables heuristics and metaheuristics meth-ods that are widely used to schedule discrete manufacturing processes. Prior studies attempted mathematical programming methods to study its STSP. However, because of the huge com-putation requirement, they are not applicable to real-life applica-tions. To solve this challenging problem, instead of using

mathematical programming methods, this article proposes a control-theoretic approach to the STSP of crude-oil operations. Using the proposed method, a hybrid PN is developed to model the system. Based on this model, schedulability conditions are derived by analyzing the schedulabilty of the process in the view of control theory. After obtaining the schedulability conditions, we successfully decompose the problem into tractable subprob-lems and solve them in a hierarchical way. By doing so, the inter-action of discrete-event and continuous variables is decoupled with each subproblem having either continuous or discrete vari-ables but not both. For subproblems with continuous variables, linear programming-based techniques can be used; however, for those with discrete variables, heuristics can be applied. Thus, the problem can be efficiently solved and the proposed approach is applicable to solve real-life problems. This is the first time such an efficient method for this problem has existed to the best knowledge of the authors.

There are several promising future research directions: to extend the proposed approach to other scheduling problems in the process industry, e.g., steel production and food pro-cessing; to develop software tools like Process Industry Mod-eling System at the planning level for the commercialization of the proposed methodology; and to incorporate some recent developments from big data and sustainable produc-tion into the proposed method.

AcknowledgmentsThis work is supported in part by the FCDT of Macau under grants 065/2013/A2 and 066/2013/A2, and the NSF of China under grant 61273036.

References[1] X. Chen, I. Grossmann, and L. Zheng, “A comparative study of continuous-time models for scheduling of crude oil operations in inland refineries,” Comput. Chem. Eng., vol. 44, pp. 141–167, Sept. 2012.[2] C. A. Floudas and X. Lin, “Continuous-time versus discrete-time ap-proaches for scheduling of chemical processes: A review,” Comput. Chem. Eng., vol. 28, no. 11, pp. 2109–2129, 2004.[3] N. F. Giannelos and M. C. Georgiadis, “A simple new continuous-time for-mulation for short-term scheduling of multipurpose batch processes,” Ind. Eng. Chem. Res., vol. 41, no. 9, pp. 2178−2184, 2002.[4] K. Glismann and G. Gruhn, “Short-term scheduling and recipe optimization of blending processes,” Comput. Chem. Eng., vol. 25, pp. 627–634, May 2001.[5] Y. He and C.-W. Hui, “A binary coding genetic algorithm for multi-purpose pro-cess scheduling: A case study,” Chem. Eng. Sci., vol. 65, no. 16, pp. 4816−4828, 2010.

Figure 10. The detailed schedule of charging tank filling.

Number 2 Number 1 Number 1Number 180 Number 181 Number 127 Number 182

020 40 60 80 100 120 140 160 180 200

Number 2

Time (h)

Number 6 Number 1 Number 2Number 116 Number 117 Number 129 Number 128

Number 3Number 127

Number 6

76 • IEEE ROBOTICS & AUTOMATION MAGAZINE • JUNE 2015

[6] Z. Jia, M. Ierapetritou, and J. D. Kelly, “Refinery short-term scheduling using continuous time formation: Crude oil operations,” Ind. Eng. Chem. Res., vol. 42, no. 13, pp. 3085–3097, 2003. [7] Z. Jia and M. Ierapetritou, “Efficient short-term scheduling of refinery op-erations based on a continuous time formulation,” Comput. Chem. Eng., vol. 28, pp. 1001–1019, June 2004.[8] R. Karuppiah, K. C. Furmanb, and I. E. Grossmann, “Global optimization for scheduling refinery crude oil operations,” Comput. Chem. Eng., vol. 32, no. 11, pp. 2745–2766, 2008. [9] E. Kondili, C. C. Pantelides, and R. W. H. Sargent, “A general algorithm for short-term scheduling for batch operations-I. MILP formulation,” Comput. Chem. Eng., vol. 17, no. 2, pp. 211–227, 1993.[10] G. A. Kudva, A. Elkamel, J. F. Pekny, and G. V. Reklaitis, “A heuristic algo-rithm for scheduling multiproduct plants with production deadlines, intermedi-ate storage limitations, and equipment changeover cost,” Comput. Chem. Eng., vol. 18, no. 9, pp. 859–875, 1994. [11] H. Lee, J. M. Pinto, I. E. Grossmann, and S. Park, “Mixed integer linear pro-gramming model for refinery short-term scheduling of crude oil unloading with inventory management,” Ind. Eng. Chem. Res., vol. 35, no. 5, pp. 1630–1641, 1996.[12] W. K. Li, W. H. Chi, and B. Hua, “Scheduling crude oil unloading, storage, and processing,” Ind. Eng. Chem. Res., vol. 41, no. 26, pp. 6723–6734, 2002.[13] B. Liu, L. Wang, Y. Liu, B. Qian, and Y.-H. Jin, “An effective hybrid parti-cle swarm optimization for batch scheduling of polypropylene processes,” Comput. Chem. Eng., vol. 34, nos. 4–5, pp. 518−528, 2010.[14] D. C. Mattfeld and C. Bierwirth, “An efficient genetic algorithm for job shop schedul-ing with tardiness objectives,” European J. Oper. Res., vol. 155, no. 2, pp. 616–630, 2004.[15] C. A. Mendez, I. E. Grossmann, I. Harjunkoski, and P. Kabore, “A simul-taneous optimization approach for off-line blending and scheduling of oil-re-finery operations,” Comput. Chem. Eng., vol. 30, no. 4, pp. 614–634, 2006.[16] L. F. L. Moro, “Process technology in the petroleum refining industry—Current situation and future trends,” Comput. Chem. Eng., vol. 27, nos. 8–9, pp. 1303–1305, 2003. [17] S. Mouret, I. E. Grossmann, and P. Pestiaux, “Time representations and mathematical models for process scheduling problems,” Comput. Chem. Eng., vol. 35, no. 6, pp. 1038–1063, 2010.[18] M. Pan, X. Li, and Y. Qian, “New approach for scheduling crude oil opera-tions,” Chem. Eng. Sci., vol. 64, no. 5, pp. 965–983, 2009.[19] J. M. Pinto, M. Joly, and L. F. L. Moro, “Planning and scheduling models for refinery operations,” Comput. Chem. Eng., vol. 24, no. 9, pp. 2259–2276, 2000.[20] R. Rejowski and J. M. Pinto, “Scheduling of a multiproduct pipeline sys-tem,” Comput. Chem. Eng., vol. 27, nos. 8–9, pp. 1229–1246, 2003.[21] I. Sabuncuoglu and M. Bayiz, “Job shop scheduling with beam search,” Eur. J. Oper. Res., vol. 118, no. 2, pp. 390–412, 1999.[22] G. K. D. Saharidisa, M. Minoux, and Y. Dallery, “Scheduling of loading and unloading of crude oil in a refinery using event-based discrete time for-mulation,” Comput. Chem. Eng., vol. 33, no. 8, pp. 1413–1426, 2009.[23] N. Shah, “Mathematical programming techniques for crude oil schedul-ing,” Comput. Chem. Eng., vol. 20, suppl. S1227–1232, 1996.[24] N. K. Shah, Z. Li, and M. G. Ierapetritou, “Petroleum refining operations: Key is-sues, advances, and opportunities,” Ind. Chem. Eng. Res., vol. 50, pp. 1161–1170, 2011.[25] N. Shah, G. K. D. Saharidis, Z. Jia, and M. G. Ierapetritou, “Centralized–decentralized optimization for refinery scheduling,” Comput. Chem. Eng., vol. 33, no. 12, pp. 2091–2105, 2009.[26] N. Q. Wu, L. P. Bai, and C. B. Chu, “Modeling and conflict detection of crude-oil operations for refinery process based on controlled-colored-timed Petri net,” IEEE Trans. Syst. Man, Cybern. C, vol. 37, no. 4, pp. 461–472, 2007.

[27] N. Q. Wu, L. P. Bai, M. C. Zhou, F. Chu, and S. Mammar, “A novel ap-proach to optimization of refining schedules for crude oil operations in re-finery,” IEEE Trans. Syst. Man, Cybern. C, vol. 42, no. 6, pp. 1042–1053, 2012.[28] N. Q. Wu, L. P. Bai, and M. C. Zhou, “An efficient scheduling method for crude oil operations in refinery with crude oil type mixing requirements,” IEEE Trans. Syst. Man, Cybern. Syst., 2015, to be published, DOI: 10.1109/TSMC.2014.2332138. [29] N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, “Short-term schedulability analysis of crude oil operations in refinery with oil residency time constraint using Petri net,” IEEE Trans. Syst. Man, Cybern. C, vol. 38, no. 6, pp. 765–778, 2008.[30] N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, “Short-term schedulability analysis of multiple distiller crude oil operations in refinery with oil residency time constraint,” IEEE Trans. Syst. Man, Cybern. C, vol. 39, no. 1, pp. 1–16, 2009.[31] N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, “Hybrid Petri net modeling and schedulability analysis of high fusion point oil transportation under tank grouping strategy for crude oil operations in refinery,” IEEE Trans. Syst. Man, Cybern. C, vol. 40, no. 2, pp. 159–175, 2010.[32] N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, “Tank cycling and schedul-ing analysis of high fusion point oil transportation for crude oil operations in refinery,” Comput. Chem. Eng., vol. 34, no. 4, pp. 529–543, 2010b.[33] N. Q. Wu, C. B. Chu, F. Chu, and M. C. Zhou, “Schedulability analysis of short-term scheduling for crude oil operations in refinery with oil residency time and charging-tank-switch-overlap constraints,” IEEE Trans. Automat. Sci. Eng., vol. 8, no. 1, pp. 190–204, 2011.[34] N. Q. Wu and M. C. Zhou, System Modeling and Control with Resource-Oriented Petri Nets. Boca Raton, FL: CRC Press and New York: Taylor & Francis Group, Oct. 2009.[35] N. Q. Wu, M. C. Zhou, L. P. Bai, and Z. W. Li, “Short-term scheduling of crude oil operations in refinery with high fusion point oil and two transportation pipel ines,” Enterprise Inform. Syst ., 2015, to be published, DOI: 10.1080/17517575.2014.948936. [36] N. Q. Wu, M. C. Zhou, and F. Chu, “A Petri net based heuristic algorithm for realizability of target refining schedule for oil refinery,” IEEE Trans. Automat. Sci. Eng., vol. 5, no. 4, pp. 661–676, 2008.[37] S. Yadav and M. A. Shaik, “Short-term scheduling of refinery crude oil op-erations,” Ind. Chem. Eng. Res., vol. 51, no. 27, pp. 9287–9299, 2012.[38] U. Yuzgee, A. Palazoglu, and J. A. Romagnoli, “Refinery scheduling of crude oil unloading, storage and processing using model predictive control strategy,” Comput. Chem. Eng., vol. 34, no. 10, pp. 1671–1686, 2010.[39] M. C. Zhou and K. Venkatesh, Modeling, Simulation and Control of Flexible Manufacturing Systems: A Petri Net Approach. Singapore: World Scientific, 1998.[40] N. Q. Wu, M. C. Zhou, and Z. W. Li, “Resource-oriented Petri net for deadlock avoidance in f lexible assembly systems,” IEEE Trans. Syst. Man, Cybern. A, vol. 38, no. 1, pp. 56–69, 2008.

NaiQi Wu, Macau University of Science and Technology, Macau, and Guangdong University of Technology, Guangzhou, China. E-mails: nqwu@must.edu.mo, nqwu@gdut.edu.cn.

MengChu Zhou, New Jersey Institute of Technology, Newark, New Jersey, and Tongji University, Shanghai, China. E-mail: zhou@njit.edu.

ZhiWu Li, Macau University of Science and Technology, Macau; King Abdulaziz University, Saudi Arabia; and Xidian Univeristy, Xi an, China. E-mails: zwli@must.edu.mo, zhwli@xidian.edu.cn.

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Short-Term Scheduling of Crude-Oil Operations: Enhancement of Crude-Oil Operations Scheduling Using a Petri Net-Based Control-Theoretic Approach学霸图书馆link:学霸图书馆