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Decision Architecture for Scheduling Virtual Cellular Manufacturing Systems
© IFAC Decision,,1 Structures in Automated \falluLiCluring-. Ceno\"a. ltal~· . I ~'H~I
Copn'i~ht
DECISION ARCHITECTURE FOR SCHEDULING VIRTUAL CELLULAR MANUFACTURING SYSTEMS
J.
R. Drolet*, B. Montreuil** and C. Moodie***
*Industrial Engineering Dept. , Universite du Queber. Trois-Ril ·ihes. QlIlilw(, Canaria **OperatiollS & Decision Systems Dept., L'n/I'Pr.lite Lm 'a l. QU fber, Ca naria ***School of Industrial Engineering, Purdue Un/l 'n.lit.". Vlrest LajilYl'lIl' , IS . [ 'SA
Abstract. In this paper we present an architecture for scheduling a new type of manufacturing system termed "virtual cellular manufacturing systems", which we consider a viable alternative for next generation manufacturing systems. We first present and justify such systems. Second, we explore the dynamics of such systems. Third, we provide a scheduling architecture capable of taking advantage of the virtual cellular concept. Finally, we illustrate its application to a prototype system. Keywords. Architecture; scheduling; virtual cell; manufacturing system.
1. ENVISIONED ENVIRONMENT
We focus on a type of next generation factory which we envision as follows. The factory has at most 20 highly productive workstations composed of automated machinery and an automated material handling system. The factory operates in just-in-time mode under computer control. A typical workstation can be examplified by a milling workstation containing 3 milling machines, a robot and an input/output conveyor. In these workstations, many activities are executed in parallel: loading, unloading, processing, communicating, and cleaning, are a few examples. These systems, alghough much smaller than current factories, are much more productive and run around the clock. Cutting speeds, for example, are expected to be 5 times faster than now around the year 2000. The machines are generally more versatile than those currently available. Machining centers that perform milling, drilling and boring are already present in today's factories. In a metal working industry for example, no more than 5 workstation types are envisioned. One end result of machine versatility is that products do not visit as many workstations as currently. Products are envisioned to have more natural and simpler designs as a result of the design for manufacturing movement which emphasize reducing the component count, standardizing the components, and sustaining efforts toward the simplification and ingenuity of process automation. As a consequence of increased process speed, processing time is much shorter as compared with material handling time. Furthermore, the reduction in lot sizing down to single-unit production dramatically increases the demand on material handling even though the parts generally visit fewer stations. This implies that cooperative workstations must be as near as possible to each other. Because of this sophistication in computer control, it is possible for example to refrain from generating a numerical control code until the specific routing for a certain is known with quasi-certainty. This permits a scheduling flexibility in
selecting among workstations.
workstations
and
machines
within
A typical order requires at most lOO units, and generally less, down to single unit orders . These orders are produced in the exact quantity required, just-in-time for shipping it in the required time period. This insures minimal work-in-progress inventory and puts pressure on always reducing lead times. 2. VIRTUAL CELLULAR MANUFACTURING SYSTEM (VC MS) The concept of virtual cellular manufacturing systems extrapolates from the original concept of virtual cell presented by McLean (~982) from the american National Bureau of Standards (NES). A virtual cell is a grouping of workstations, recognized within data files, and processes in the computerized controller, but which does not translate into physical adjacency of the workstations as in classical group technology based cellular layouts. When a decision is taken to form a virtual cell, a virtual cell controller takes over the control of these workstations and sets up communication between them. When the need for a specific virtual cell ends, then the virtual cell controller is terminated and the workstations return to local control.
D
~O o
Fig. 1. A Generic Virtual Cellular Manufacturing System A virtual cellular manufacturing system organizes and runs production through the dynamic generation and control of
lOO
J.
R. Drolet, B. Montreuil and C. Moodie
temporary virtual cells. Figure I illustrates a system which has 15 workstations from a combination of 5 workstation types. At a specific point in time the system has 3 virtual cells. Two of these share a given workstation.
SERVICE DtSCIPUNE
In a virtual cellular manufacturing system for the envisioned next generation environment, a virtual cell is created to process each job order. At any given time, the manufacturing system is likely to contain several virtual cells, some of them overlapping over shared workstations. Graphically, at each point in time, this results in a network of more or less interlaced routes. It is clear that intelligent control of the system is required in order to avoid degenerating into anarchy.
3. SCHEDULING ARCHITECTURE FOR VCMS The decision architecture allows the control of a VCMS by scheduling the creation, activation, and dissolution of virtual cells in a YCMS . The algorithm could be used automatically if coded in a computer, manually by a human scheduler, or in collaboration: the human scheduler supplying its expertise to the computer. The framework contains three phases. Briefly, the first phase aims at loading the jobs . It uses opportunistic scheduling rules to produce a list of prioritized jobs from the Material Requirement Planning (MRP) output and/or the current confirmed customer order list. The second phase is the creation of virtual cells. In this phase, one seeks to assign an optimal subset of workstations to each job. Here, available capacity and physical location of workstations are considered so as to minimize flow travel. The third phase consists of requesting, withholding and delivering related resources, such as tools and fixtures , to the selected workstations. Figure 2 illustrates the overall procedure. Each step will now be presented in more details. 3.1,Job Loading Scheduler The decision architecture begins with the job loading phase. The aim of job loading is to create a list of prioritized jobs using sequencing rules that are known to perform well in the situation prevailing at that instant. No scheduling rules are known to perform equally well in every situation, thus the job scheduler is provided with a library of scheduling rules. This phase can be extremely complex, incorporating an expert system coupled with constraints directed search optimizing techniques capable of dealing with hundreds of indices characterizing various situations. We do assume the presence of various sensors which sense in real-time the status, loading and processing advance characterizing the system. The expert system has the capability for "looking" at both the manufacturing system through its many sensors and the list of jobs yet to be launched into the system. The expert system analyses the sensory information, extracts its substance, and choose the appropriate sequencing rule. Then, the sequencing rule is used to compose a prioritized list of jobs. The number of jobs to be considered by the controller can be fixed by means of time window sizing, this way the search space is consi?erably reduced. However, potentially profItable alternattves may be lost, hence reducing system efficiency. After selecting the most prioritized job in the window, the cell creation phase is attempted. Then, a series of exchanges IS likely to occur with the module responsible for the virtual cell creation.
Fig. 2. Opportunistic scheduler for jobs loading. 3.2 Virtual Cell Creation This phase is responsible for three main tasks. First, it determines the set of workstations which will process the job l.e. the VIrtual cell. More specifically, one seeks to minimize flow travel by an optimal allocation of workstations into a temporary approximate production line (the virtual cell) for each incoming job order. Second, it finds the bottleneck workstation and determines the rate of introduction of the parts. Third, it creates an instance of a generic virtual cell controller. The general ideas enclosing this phase are portrayed in Fig. 3. In this figure, one can observe an example of the cell creation process. We do assume that JOB_X has been selected for introduction into the system. The top left frame illustrates a facility including 17 workstations. Each is expressed in terms of the following convention: the character represents the type of works tat ion (e.g. milling, turning, inspection, etc.), the numeral identifies each replication of a given workstation type. For example, node A4 represents replicate "4" of workstation type "A". The frame symbolizes the outside walls of the facility. The system of axes located nearby reminds that the frame contains a scaled layout and, thus , exact positions of workstations are known. From such a layout, one can calculate the inter-workstation distances which, along with the utilization profile of resources, are useful during the virtual cell creation. The second frame contains a set of workstations which can potentially be visited by the job, and achievable flow of parts between workstations. Only the arcs connecting successive workstations as restrained by the job precedence constraints are shown. Furthermore, arcs are included only if the phased
Virtual Cellular Manufacturing Systems utilization profile of the successive workstations guarantee sufficient capacity available at estimated production time. This way, the set of candidate workstations has been reduced from 17 to 6.
I () I
controller. The negotiation scheme which we propose here is similar to the task negotiation approach for coordinating the planning activities of manufacturing cells proposed by Shaw (1987). Our negotiation scheme differs at two levels. First, it
Sel of aulonomous workslations al lheir spec ific localions.
Sel of workslalions lhal can polentially be visiled by JOB_X along wilh lheir arcs.
t : ?nole
Every olher arcs do nol sa lisfy lhe precedence conslrainl for lhal job.
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Fig. 3. Virtual cell creation. The third view which is a restructuration of the second frame pennits one to easily distinguish the sequence of operations depicted by the precedence constraint of JOB_X. The parts included in that job must go from a workstation of type "A", to a workstation type "E" and then to a workstation of type "C". The objective is to find the least expensive path from any workstation of type "A" to any workstation of type "E", via any workstation of type "C" . A variation of the shortest path algorithm of Dijstra is used for that purpose. CiJ represents the traveling time to go from workstation i to workstation j. The timely remaining capacity of each workstation is considered as a function of time. For example, workstation Cl will not be needed until the first part of JOB_X gets done at one of the workstation "E" plus the estimated time it takes to travel from this work station to workstation Cl. The result for JOB_X is shown in the last frame. The encircled set of workstations displayed in this frame is the virtual cell just created for JOB_X. Along with it, a virtual cell controller is created. A virtual cell controller lasts only for the duration of the job for which it has been created. If the cell creation phase fails, the shop controller repeats the process with the second highest priority job, and so 00. If no job in the allowed window succeeds cell creation, then cell creation is delayed until the punctual capacity of any critical resource increases significantly. 3.3 Resource Allocation The objective with this phase is to obtain related resources before cell activation. Upon a successful attempt at cell creation, the cell controller will request all related resources needed to perfonn the job and ensure that these resources will be available (at the requested rate) during the whole process duration. This is achieved through negotiation with the shop
concerns the allocation of resources, not the tasks. Second, the negotiation is done vertically, not horizontally. 4. ILLUSTRATIVE EXAMPLE In this section we illustrate the opportunistic scheduling strategy with an example. The system which will be used for the example is shown in Fig. 4, and its defining parameters are in table I. We will begin the procedure with an empty system. Table 2 shows the job orders available for processing, sorted using Shortest Processing Time (SPT) rule. A window size of 4 is to be used. The realization of an expert system for job loading is a laborious achievement which is non-essential to comprehend the overall scheduling strategy. Thus, for sake of simplicity, the job loading phase will be restricted to the use of the SPT rule. The first phase shall be executed upon the arrival of a new job and when significant changes occur on the shop floor. Let us now proceed with the example. The shop controller sees the first 4 prioritized jobs as shown in table 2. The virtual cell creation, which is the second phase, is attempted with job 6585 . There is no committed processing time yet on any workstation, thus, this job can be introduced instantly. The shortest path algorithm is executed. The objective is to find the best route from any workstation of type C to any workstation of type A. Possible routes are 6->1, 6-2, 7->1, and 7->2. In light of Fig. 4, we find that grouping workstations 6 and 2 creates a virtual cell which minimizes the shortest path for this job. The introduction rate is defined as the number of parts which can be introduced by period; this is fixed by the bottleneck workstation. In this example, a period has a 15 minute duration. Two workstations will be visited, workstation 6 and
J.
l()~
R. Drolet. B. MOlltreuil and C. Moodie
then workstation 2. Potential processing rate are respectively 6.0 parts/period at workstation 6, and 7.5 parts/period at workstation 2.
The fourth phase regards the dispatching of parts in that virtual cell. The dispatcher controls the rate at which the parts are being released to the virtual cell. The parts of job 6585 will be released at a rate of 6 parts/period beginning at time t = 0 for 2.166 periods, or until 13 parts have been introduced. The dispatcher controls also the flow of parts within the cell i.e. between work station 6 and 2. Finally, the dispatcher monitors the queue length at these workstations and ensures that work-in-process is under control. After initial loading, workstation 6 and 2 will be used at 100% and 80% respectively.
r
As illustrated in table 3, job 6585 has been removed from the window thus, the second job becomes the first, the third becomes the second and so on. Job 3847 can now be seen by the shop controller.
Fig. 4. A virtual cellular manufacturing system facility
TABLE 1 System summary. WORKSTATION TYPE
WORKSTATION NUM. OF MACH.! NUMBER WORKSTATION 1,2 3,4,5 6,7 8,9
A B
C D
The scheduling algorithm is repeated with job 8744 which has the highest priority. The virtual cell creation phase is attempted. The objective is to find the shortest path from a workstation of type A to a workstation of type C via a workstation of type B. There are 12 (2*3*2) possible routes. However, routes that use workstation 6 or 2 shall be removed since they are already being used almost at capacity. The shortest path algorithm uses the four eligible routes and finds that a grouping or workstations I, 4 and 7 minimizes flow travel for that job. The bottleneck among workstations 1, 4, and 7 is found and the introduction rate is fixed at 4.28 parts/period.
2
.The third phase can be by-passed since related resources were not considered in this example. Virtual cell (l,4,7) is activated instantly. A virtual cell controller takes over the control of work stations 1,4, and 7. Processing can begin.
3 2
I
In a serial process, the accumulation of work-in-process can be avoided only if the bottleneck workstation governs the introduction rate. Thus, the imposed rate in this virtual cell is 6 parts/period. The third phase consists of requesting, withholding and delivering all related resources before cell activation. In this example, always for sake of simplification, we did not consider any related resources. Thus, virtual cell (6,2) is activated instantly. The virtual cell controller takes in charge workstations 6 and 2, and processing can begin.
The dispatcher will control the rate at which the parts of job 8744 will be released to the Virtual cell. The parts of job 8744 are introduced at an approximate rate of 4.28 parts/period, beginning at time t = 0 for 8/4.28 = 1.9 periods or until 8 parts have been introduced. After initial loading, workstations I, 4, and 7 will be used at 100%, 85.6% and 28.57% respectively.
TABLE 2 A list of job orders. PRIORITY #
JOB - ID
SEQUENCE & PROC. TIME(Min)
PARTS QTY
TOTALPROC. TIME(Min)
10 9 8 7 6 5
8887 6586 2957 8476 5594 3847
(B,6)(C,8) } (A,14)(D,5)} (A ,8)(B,14)(D,IO) } (D,6)(B,7)} (C,4)(B,9) } (B,5)}
48 32 15 35 32 78
672 608 480 455 416 390
---------------------------------------------------------------
4 3 2 1
5585 7674 8744 6585
(B,9)(C,4)(D,4) } (A,5)(B, 1O)(C,7)} (A,7)(B,9)(C,2) } (C,5)(A,4) }
21 17 8 13
357 374 144 117
TABLE 3 Window view 2. PRIORITY #
JOB ID
SEQUENCE & PROC. TIME(Min)
PARTS QTY
TOTALPROC. TIME(Min)
5 4 3 2
3847 5585 7674 8744
(B,5)} (B,9)(C,4)(D,4) } (A,5)(B, 1O)(C,7)} (A,7)(B,9)(C,2) }
78
21 17 8
390 357 374 144
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Fig. 5. Virtual cell formation activated or being activated over time The procedure is continued until all jobs considered are introduced. Figure 5 illustrates the virtual cell formation activated or being activated over time. The solution proposed is not unique but it satisfies the guidelines of the decision architecture algorithm. The need for considering other resources such as critical tool s would normally make scheduling more elaborate. As illustrated in the previous example, the decision regarding the introduction of a job was solely based on current capacity of the workstations concerned. Thus, the decision architecture was applied in a myopic mode . However, the algori thm is not limited in this respect. As we remember, the utilization profile graphs contain not only the current capacity but the planned utilization over a certain horizon. With this information, it is possible to plan the creation of virtual cells a way ahead instead of doing it on the spot, increasing considerably the efficiency of the system.
5. CONCLUSION A decision architecture for scheduling VCMS has been presented. The decision architecture consists of three phases: the loading, the virtual cell creation , and the resource allocation. An expert system is proposed for the first phase, a network based algorithm for the second phase and a negotiation protocole for the third phase. The scheduling framework presented in this paper is a first cut at addressing the real·time planning and control of virtual .cellular manufacturing systems. We understand that sequential scheduling may not be the most efficient approach since a decision taken at time t may have a negative impact on the future. We are therefore currently investigating more comprehensive scheduling strategies and models.
REFERENCES McLean, C. R., Bloom, H. M., and Hopp, T. H., "The Virtual Manufacturing Cell". Proceedings of Fourth IFAC/IFIP Conference on Information Control Problems in Manufacturing Technology, Gaithersburg, MD, October 1982. McLean, C. R. and Brown, Charles F., "The Automated Manufacturing Research Facility At The National Bureau Of Standards". Proceedings of the IFIP W.G. 5.7 Working Conference on New Technologies for Production Management Systems, Tokyo, Japan , October 1986. O'Grady, Peter J. and Menon, Unny, "A Concise Review Of Flexible Manufacturing Systems And FMS Literature". Computers in Industry, Vol. 7, No. 2, April 1986, pp. 155·167. O 'Grady, Peter and Lee, Kwan H., "An Intelligent Cell Control System For Automated Manufacturing". Int. Journal Prod. Research, Vol. 26, No. 5, 1988, pp. 845·861. Schonberger, R. J., "World Class Manufacturing: The Lessons Of Simplicity Applied". The Free Press New York, NY, 1986. Shaw, Michael J. and Whinston, Andrew B., "Task Bidding And Distributed Planning In Flexible Manufacturing", 1985. Shaw, Michael l., "A Distributed Scheduling Method For Computer Integrated Manufacturing: The Use Of Local Area Networks In Cellular Systems". Int. Journal Prod. Research, Vol. 25, No. 9, 1987, pp. 1285·1303. Warnecke, HJ. and Steinkilper, R., "Flexible Manufacturing Systems". IFS(Publications) Ltd, 1985, pp. 235·311.
Copn'i~ht
DECISION ARCHITECTURE FOR SCHEDULING VIRTUAL CELLULAR MANUFACTURING SYSTEMS
J.
R. Drolet*, B. Montreuil** and C. Moodie***
*Industrial Engineering Dept. , Universite du Queber. Trois-Ril ·ihes. QlIlilw(, Canaria **OperatiollS & Decision Systems Dept., L'n/I'Pr.lite Lm 'a l. QU fber, Ca naria ***School of Industrial Engineering, Purdue Un/l 'n.lit.". Vlrest LajilYl'lIl' , IS . [ 'SA
Abstract. In this paper we present an architecture for scheduling a new type of manufacturing system termed "virtual cellular manufacturing systems", which we consider a viable alternative for next generation manufacturing systems. We first present and justify such systems. Second, we explore the dynamics of such systems. Third, we provide a scheduling architecture capable of taking advantage of the virtual cellular concept. Finally, we illustrate its application to a prototype system. Keywords. Architecture; scheduling; virtual cell; manufacturing system.
1. ENVISIONED ENVIRONMENT
We focus on a type of next generation factory which we envision as follows. The factory has at most 20 highly productive workstations composed of automated machinery and an automated material handling system. The factory operates in just-in-time mode under computer control. A typical workstation can be examplified by a milling workstation containing 3 milling machines, a robot and an input/output conveyor. In these workstations, many activities are executed in parallel: loading, unloading, processing, communicating, and cleaning, are a few examples. These systems, alghough much smaller than current factories, are much more productive and run around the clock. Cutting speeds, for example, are expected to be 5 times faster than now around the year 2000. The machines are generally more versatile than those currently available. Machining centers that perform milling, drilling and boring are already present in today's factories. In a metal working industry for example, no more than 5 workstation types are envisioned. One end result of machine versatility is that products do not visit as many workstations as currently. Products are envisioned to have more natural and simpler designs as a result of the design for manufacturing movement which emphasize reducing the component count, standardizing the components, and sustaining efforts toward the simplification and ingenuity of process automation. As a consequence of increased process speed, processing time is much shorter as compared with material handling time. Furthermore, the reduction in lot sizing down to single-unit production dramatically increases the demand on material handling even though the parts generally visit fewer stations. This implies that cooperative workstations must be as near as possible to each other. Because of this sophistication in computer control, it is possible for example to refrain from generating a numerical control code until the specific routing for a certain is known with quasi-certainty. This permits a scheduling flexibility in
selecting among workstations.
workstations
and
machines
within
A typical order requires at most lOO units, and generally less, down to single unit orders . These orders are produced in the exact quantity required, just-in-time for shipping it in the required time period. This insures minimal work-in-progress inventory and puts pressure on always reducing lead times. 2. VIRTUAL CELLULAR MANUFACTURING SYSTEM (VC MS) The concept of virtual cellular manufacturing systems extrapolates from the original concept of virtual cell presented by McLean (~982) from the american National Bureau of Standards (NES). A virtual cell is a grouping of workstations, recognized within data files, and processes in the computerized controller, but which does not translate into physical adjacency of the workstations as in classical group technology based cellular layouts. When a decision is taken to form a virtual cell, a virtual cell controller takes over the control of these workstations and sets up communication between them. When the need for a specific virtual cell ends, then the virtual cell controller is terminated and the workstations return to local control.
D
~O o
Fig. 1. A Generic Virtual Cellular Manufacturing System A virtual cellular manufacturing system organizes and runs production through the dynamic generation and control of
lOO
J.
R. Drolet, B. Montreuil and C. Moodie
temporary virtual cells. Figure I illustrates a system which has 15 workstations from a combination of 5 workstation types. At a specific point in time the system has 3 virtual cells. Two of these share a given workstation.
SERVICE DtSCIPUNE
In a virtual cellular manufacturing system for the envisioned next generation environment, a virtual cell is created to process each job order. At any given time, the manufacturing system is likely to contain several virtual cells, some of them overlapping over shared workstations. Graphically, at each point in time, this results in a network of more or less interlaced routes. It is clear that intelligent control of the system is required in order to avoid degenerating into anarchy.
3. SCHEDULING ARCHITECTURE FOR VCMS The decision architecture allows the control of a VCMS by scheduling the creation, activation, and dissolution of virtual cells in a YCMS . The algorithm could be used automatically if coded in a computer, manually by a human scheduler, or in collaboration: the human scheduler supplying its expertise to the computer. The framework contains three phases. Briefly, the first phase aims at loading the jobs . It uses opportunistic scheduling rules to produce a list of prioritized jobs from the Material Requirement Planning (MRP) output and/or the current confirmed customer order list. The second phase is the creation of virtual cells. In this phase, one seeks to assign an optimal subset of workstations to each job. Here, available capacity and physical location of workstations are considered so as to minimize flow travel. The third phase consists of requesting, withholding and delivering related resources, such as tools and fixtures , to the selected workstations. Figure 2 illustrates the overall procedure. Each step will now be presented in more details. 3.1,Job Loading Scheduler The decision architecture begins with the job loading phase. The aim of job loading is to create a list of prioritized jobs using sequencing rules that are known to perform well in the situation prevailing at that instant. No scheduling rules are known to perform equally well in every situation, thus the job scheduler is provided with a library of scheduling rules. This phase can be extremely complex, incorporating an expert system coupled with constraints directed search optimizing techniques capable of dealing with hundreds of indices characterizing various situations. We do assume the presence of various sensors which sense in real-time the status, loading and processing advance characterizing the system. The expert system has the capability for "looking" at both the manufacturing system through its many sensors and the list of jobs yet to be launched into the system. The expert system analyses the sensory information, extracts its substance, and choose the appropriate sequencing rule. Then, the sequencing rule is used to compose a prioritized list of jobs. The number of jobs to be considered by the controller can be fixed by means of time window sizing, this way the search space is consi?erably reduced. However, potentially profItable alternattves may be lost, hence reducing system efficiency. After selecting the most prioritized job in the window, the cell creation phase is attempted. Then, a series of exchanges IS likely to occur with the module responsible for the virtual cell creation.
Fig. 2. Opportunistic scheduler for jobs loading. 3.2 Virtual Cell Creation This phase is responsible for three main tasks. First, it determines the set of workstations which will process the job l.e. the VIrtual cell. More specifically, one seeks to minimize flow travel by an optimal allocation of workstations into a temporary approximate production line (the virtual cell) for each incoming job order. Second, it finds the bottleneck workstation and determines the rate of introduction of the parts. Third, it creates an instance of a generic virtual cell controller. The general ideas enclosing this phase are portrayed in Fig. 3. In this figure, one can observe an example of the cell creation process. We do assume that JOB_X has been selected for introduction into the system. The top left frame illustrates a facility including 17 workstations. Each is expressed in terms of the following convention: the character represents the type of works tat ion (e.g. milling, turning, inspection, etc.), the numeral identifies each replication of a given workstation type. For example, node A4 represents replicate "4" of workstation type "A". The frame symbolizes the outside walls of the facility. The system of axes located nearby reminds that the frame contains a scaled layout and, thus , exact positions of workstations are known. From such a layout, one can calculate the inter-workstation distances which, along with the utilization profile of resources, are useful during the virtual cell creation. The second frame contains a set of workstations which can potentially be visited by the job, and achievable flow of parts between workstations. Only the arcs connecting successive workstations as restrained by the job precedence constraints are shown. Furthermore, arcs are included only if the phased
Virtual Cellular Manufacturing Systems utilization profile of the successive workstations guarantee sufficient capacity available at estimated production time. This way, the set of candidate workstations has been reduced from 17 to 6.
I () I
controller. The negotiation scheme which we propose here is similar to the task negotiation approach for coordinating the planning activities of manufacturing cells proposed by Shaw (1987). Our negotiation scheme differs at two levels. First, it
Sel of aulonomous workslations al lheir spec ific localions.
Sel of workslalions lhal can polentially be visiled by JOB_X along wilh lheir arcs.
t : ?nole
Every olher arcs do nol sa lisfy lhe precedence conslrainl for lhal job.
Leasl e xpens ive palh in a direcled graph wiln nonnegalive arc weights.
® @ @ VIRTUAL
CELL CREATION
cl
@
@ @
@~ @ @) @
~
Cl
ALGORITHM
@)
@ @
Sequence for JOB_X: IA.E.C! Workslation nearly al capac ily: IA3.A5 .E3!
Fig. 3. Virtual cell creation. The third view which is a restructuration of the second frame pennits one to easily distinguish the sequence of operations depicted by the precedence constraint of JOB_X. The parts included in that job must go from a workstation of type "A", to a workstation type "E" and then to a workstation of type "C". The objective is to find the least expensive path from any workstation of type "A" to any workstation of type "E", via any workstation of type "C" . A variation of the shortest path algorithm of Dijstra is used for that purpose. CiJ represents the traveling time to go from workstation i to workstation j. The timely remaining capacity of each workstation is considered as a function of time. For example, workstation Cl will not be needed until the first part of JOB_X gets done at one of the workstation "E" plus the estimated time it takes to travel from this work station to workstation Cl. The result for JOB_X is shown in the last frame. The encircled set of workstations displayed in this frame is the virtual cell just created for JOB_X. Along with it, a virtual cell controller is created. A virtual cell controller lasts only for the duration of the job for which it has been created. If the cell creation phase fails, the shop controller repeats the process with the second highest priority job, and so 00. If no job in the allowed window succeeds cell creation, then cell creation is delayed until the punctual capacity of any critical resource increases significantly. 3.3 Resource Allocation The objective with this phase is to obtain related resources before cell activation. Upon a successful attempt at cell creation, the cell controller will request all related resources needed to perfonn the job and ensure that these resources will be available (at the requested rate) during the whole process duration. This is achieved through negotiation with the shop
concerns the allocation of resources, not the tasks. Second, the negotiation is done vertically, not horizontally. 4. ILLUSTRATIVE EXAMPLE In this section we illustrate the opportunistic scheduling strategy with an example. The system which will be used for the example is shown in Fig. 4, and its defining parameters are in table I. We will begin the procedure with an empty system. Table 2 shows the job orders available for processing, sorted using Shortest Processing Time (SPT) rule. A window size of 4 is to be used. The realization of an expert system for job loading is a laborious achievement which is non-essential to comprehend the overall scheduling strategy. Thus, for sake of simplicity, the job loading phase will be restricted to the use of the SPT rule. The first phase shall be executed upon the arrival of a new job and when significant changes occur on the shop floor. Let us now proceed with the example. The shop controller sees the first 4 prioritized jobs as shown in table 2. The virtual cell creation, which is the second phase, is attempted with job 6585 . There is no committed processing time yet on any workstation, thus, this job can be introduced instantly. The shortest path algorithm is executed. The objective is to find the best route from any workstation of type C to any workstation of type A. Possible routes are 6->1, 6-2, 7->1, and 7->2. In light of Fig. 4, we find that grouping workstations 6 and 2 creates a virtual cell which minimizes the shortest path for this job. The introduction rate is defined as the number of parts which can be introduced by period; this is fixed by the bottleneck workstation. In this example, a period has a 15 minute duration. Two workstations will be visited, workstation 6 and
J.
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R. Drolet. B. MOlltreuil and C. Moodie
then workstation 2. Potential processing rate are respectively 6.0 parts/period at workstation 6, and 7.5 parts/period at workstation 2.
The fourth phase regards the dispatching of parts in that virtual cell. The dispatcher controls the rate at which the parts are being released to the virtual cell. The parts of job 6585 will be released at a rate of 6 parts/period beginning at time t = 0 for 2.166 periods, or until 13 parts have been introduced. The dispatcher controls also the flow of parts within the cell i.e. between work station 6 and 2. Finally, the dispatcher monitors the queue length at these workstations and ensures that work-in-process is under control. After initial loading, workstation 6 and 2 will be used at 100% and 80% respectively.
r
As illustrated in table 3, job 6585 has been removed from the window thus, the second job becomes the first, the third becomes the second and so on. Job 3847 can now be seen by the shop controller.
Fig. 4. A virtual cellular manufacturing system facility
TABLE 1 System summary. WORKSTATION TYPE
WORKSTATION NUM. OF MACH.! NUMBER WORKSTATION 1,2 3,4,5 6,7 8,9
A B
C D
The scheduling algorithm is repeated with job 8744 which has the highest priority. The virtual cell creation phase is attempted. The objective is to find the shortest path from a workstation of type A to a workstation of type C via a workstation of type B. There are 12 (2*3*2) possible routes. However, routes that use workstation 6 or 2 shall be removed since they are already being used almost at capacity. The shortest path algorithm uses the four eligible routes and finds that a grouping or workstations I, 4 and 7 minimizes flow travel for that job. The bottleneck among workstations 1, 4, and 7 is found and the introduction rate is fixed at 4.28 parts/period.
2
.The third phase can be by-passed since related resources were not considered in this example. Virtual cell (l,4,7) is activated instantly. A virtual cell controller takes over the control of work stations 1,4, and 7. Processing can begin.
3 2
I
In a serial process, the accumulation of work-in-process can be avoided only if the bottleneck workstation governs the introduction rate. Thus, the imposed rate in this virtual cell is 6 parts/period. The third phase consists of requesting, withholding and delivering all related resources before cell activation. In this example, always for sake of simplification, we did not consider any related resources. Thus, virtual cell (6,2) is activated instantly. The virtual cell controller takes in charge workstations 6 and 2, and processing can begin.
The dispatcher will control the rate at which the parts of job 8744 will be released to the Virtual cell. The parts of job 8744 are introduced at an approximate rate of 4.28 parts/period, beginning at time t = 0 for 8/4.28 = 1.9 periods or until 8 parts have been introduced. After initial loading, workstations I, 4, and 7 will be used at 100%, 85.6% and 28.57% respectively.
TABLE 2 A list of job orders. PRIORITY #
JOB - ID
SEQUENCE & PROC. TIME(Min)
PARTS QTY
TOTALPROC. TIME(Min)
10 9 8 7 6 5
8887 6586 2957 8476 5594 3847
(B,6)(C,8) } (A,14)(D,5)} (A ,8)(B,14)(D,IO) } (D,6)(B,7)} (C,4)(B,9) } (B,5)}
48 32 15 35 32 78
672 608 480 455 416 390
---------------------------------------------------------------
4 3 2 1
5585 7674 8744 6585
(B,9)(C,4)(D,4) } (A,5)(B, 1O)(C,7)} (A,7)(B,9)(C,2) } (C,5)(A,4) }
21 17 8 13
357 374 144 117
TABLE 3 Window view 2. PRIORITY #
JOB ID
SEQUENCE & PROC. TIME(Min)
PARTS QTY
TOTALPROC. TIME(Min)
5 4 3 2
3847 5585 7674 8744
(B,5)} (B,9)(C,4)(D,4) } (A,5)(B, 1O)(C,7)} (A,7)(B,9)(C,2) }
78
21 17 8
390 357 374 144
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Fig. 5. Virtual cell formation activated or being activated over time The procedure is continued until all jobs considered are introduced. Figure 5 illustrates the virtual cell formation activated or being activated over time. The solution proposed is not unique but it satisfies the guidelines of the decision architecture algorithm. The need for considering other resources such as critical tool s would normally make scheduling more elaborate. As illustrated in the previous example, the decision regarding the introduction of a job was solely based on current capacity of the workstations concerned. Thus, the decision architecture was applied in a myopic mode . However, the algori thm is not limited in this respect. As we remember, the utilization profile graphs contain not only the current capacity but the planned utilization over a certain horizon. With this information, it is possible to plan the creation of virtual cells a way ahead instead of doing it on the spot, increasing considerably the efficiency of the system.
5. CONCLUSION A decision architecture for scheduling VCMS has been presented. The decision architecture consists of three phases: the loading, the virtual cell creation , and the resource allocation. An expert system is proposed for the first phase, a network based algorithm for the second phase and a negotiation protocole for the third phase. The scheduling framework presented in this paper is a first cut at addressing the real·time planning and control of virtual .cellular manufacturing systems. We understand that sequential scheduling may not be the most efficient approach since a decision taken at time t may have a negative impact on the future. We are therefore currently investigating more comprehensive scheduling strategies and models.
REFERENCES McLean, C. R., Bloom, H. M., and Hopp, T. H., "The Virtual Manufacturing Cell". Proceedings of Fourth IFAC/IFIP Conference on Information Control Problems in Manufacturing Technology, Gaithersburg, MD, October 1982. McLean, C. R. and Brown, Charles F., "The Automated Manufacturing Research Facility At The National Bureau Of Standards". Proceedings of the IFIP W.G. 5.7 Working Conference on New Technologies for Production Management Systems, Tokyo, Japan , October 1986. O'Grady, Peter J. and Menon, Unny, "A Concise Review Of Flexible Manufacturing Systems And FMS Literature". Computers in Industry, Vol. 7, No. 2, April 1986, pp. 155·167. O 'Grady, Peter and Lee, Kwan H., "An Intelligent Cell Control System For Automated Manufacturing". Int. Journal Prod. Research, Vol. 26, No. 5, 1988, pp. 845·861. Schonberger, R. J., "World Class Manufacturing: The Lessons Of Simplicity Applied". The Free Press New York, NY, 1986. Shaw, Michael J. and Whinston, Andrew B., "Task Bidding And Distributed Planning In Flexible Manufacturing", 1985. Shaw, Michael l., "A Distributed Scheduling Method For Computer Integrated Manufacturing: The Use Of Local Area Networks In Cellular Systems". Int. Journal Prod. Research, Vol. 25, No. 9, 1987, pp. 1285·1303. Warnecke, HJ. and Steinkilper, R., "Flexible Manufacturing Systems". IFS(Publications) Ltd, 1985, pp. 235·311.