Journal of Mechanical Working Technology, 20 (1989) 183-194 Elsevier Science Publishers B.V., Amsterdam -Printed inThe Netherlands 183

S C H E D U L I N G F A C T O R I E S O F T H E F U T U R E

Jocelyn Drolet 1, Colin L. Moodie 2 and Benoit Montreuil 3

1Department d'ingenierie, Universit~ du Qu6bec k Trois-Rivi~res, C.P. 500, Trois- Rivi~res, Quebec, Canada GgA 5H7

2School of Industrial Engineering, Grissom Hall, Purdue University, West Lafayette, Indiana 47907, U.S.A.

3Department of Operations & Systems Decisions, University of Laval, FSA, Bureau 303A, Cit6 Universitare, Quebec, Canada G1K 7P4

S U M M A R Y

The trend toward factories of the future, indicates that world class manufacturing systems will have no more than 20 highly productive machines with an automated material handling system. These factories will operate in Just-In-Time mode under computer control. The machines, in general, will be more versatile. It is also expected that by the year 2000, cutting speed will be up to 10 times faster than today's standards.

Reduced lot sizes will dramatically increase the demand on material handling; cooperative workstations will have to be close to each other.

The numerical control code will not be generated until the specific routing for a certain order is known. A typical factory order will require only a few units up to less than a hundred. Every order will be produced in exact quantity Just-In-Time for shipping, hence with no inventory.

We strongly believe that the virtual cell concept, extensively documented by McLean, etc., and others, will meet the requirement for the factory of the future. This concept has the potential for making flexible manufacturing systems (FMS) even more efficient, because of its inherent capability for sharing resources. Contrary to the group technology cell configuration, a virtual cell is not identifiable as a fixed physical grouping of workstations, but as data files and processes in a controller. Upon selection of a job order, a virtual cell controller is created. The controller takes over the control of a set of workstations capable of processing the job for which they have been selected. This temporary grouping of workstations is called a virtual cell. Once all resources have been requested and awarded, processing can begin. Parts are moved from workstation to workstation similar to a flow line sequence.

We have extended the virtual cell concept proposed by McLean and we have developed a scheduling algorithm that permits the creation of virtual cells and schedule them under workstations and tools availability constraints. Equally important, the algorithm is characterized by its polynomial time complexity. The size of the model grows quickly, but linearly, and remains reasonable for a typical size factory. It is efficient enough to be executed in real time for scheduling any virtual cell based system within hundred of seconds with current computer technology.

The scheduling model has many advantages that makes it suitable for scheduling factories of the future. Firstly, it permits consideration of critical tools. Secondly, it provides a quick reaction to unexpected events. Finally, it enables a coherent planning of resource utilization, potentially reducing possibilities of delays and deadlock, which are very common in fast pace manufacturing systems.

0378-3804/89/$03.50 © 1989 Elsevier Science Publishers B.V.

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A VISION OF F U T U R E M A N U F A C T U R I N G S Y S T E M S

Factories of the future, are world class manufacturing systems, having no more than 20 highly productive machines with automated material handling system. These factories will operate in Just-In-Time mode under computer control [1].

Typically, two or three similar machines and a handling device, will be put together to form a workstation [2]. Figure 1 illustrates a workstation that contains three milling machines, a robot a n d a n input /output conveyor. In these workstations, many activities

will be going on in parallel; loading, unloading, processing, communicating, cleaning, are a few examples. Systems having up to 10 workstations working around the clock will not be uncommon [3]. These systems although much smaller than current factories will be much more productive.

i / / ' ¸ .... i ~ J ~ ....... ,,

/

Fig. 1. A typical workstation.

The machines will be generally more versatile. Machining centers that perform milling, drilling and boring operations are already present in todays factories. In a metal working industry, no more than 5 workstation types will be, on the average, present: turning center, milling center, stamping machine, welding station and grinding machine. The end result of machine versatility is that the products will not visit as many workstations as in today's factory [3]. Many more operations will be performed at every machine. Also, products will have more natural, simpler design as the result of components standardization and sustaining effort throughout the simplification and ingenuity of process automation. It is also expected that by the year 2000, cutting speed will be up to 10 times faster than today's standards, hence reducing the total processing time by so much.

Since cutting speed will drastically increase, processing time will be much shorter compared with material handling. Furthermore, the reduction of lot sizing up to the unit will dramatically increase the demand on material handling even though the parts will generally visit fewer machines. Given this, it is clear that cooperative workstations will have to be close to each other when dealing with factories of the future.

185

The numerical control code will not be generated until the specific routing for a

certain order is known. This will permit the option of using many different machines.

A typical factory order will require only a few units up to less than a hundred. The desire of keeping the inventory as low as possible and the pressure for quick response time, backed up by no significant set-up times, will account for this. The underlying philosophy will be to produce every order in exact quantity Just-In-Time for shipping, hence with no inventory [1].

Throughout this paper, we will focus on manufacture of medium size, metal products. However, the virtual cell concept can be applied to any category of factory. The only requirement is that they must produce discrete products. Chemical industries and other continuous processes are in a different category and thus are not considered here.

V I R T U A L CELL SYSTEMS

The virtual cell concept was proposed by McLean in the early 1980's [4]. A virtual cell is not identifiable as a fixed physical grouping of workstations, but as data files and processes in a controller. When a job order needs a set of workstations to be "put together", a virtual cell controller takes over the control of these workstations and makes communication between them possible. Figure 2 illustrates a system of 15 workstations comprising 5 workstation types. Currently, the system has 3 active virtual cells and one shared workstation.

J

Fig. 2. A typical virtual cell system.

Figure 3 illustrates an analogy between the life of a virtual cell and a biological cell. Once a job has been selected for processing, one needs to create a virtual cell controller and thus a cell. Among the set of workstations available in the shop, the controller assigns a subset of workstations that satisfies the technological and capacity requirements for that job. This is virtual cell creation. Then, once the cell has been created, the controller seeks other resources such as tools and fixtures needed at the workstation site. Once all resources have been requested and awarded, they are sent to the workstations. The workstation that will be visited first will be the first to receive the needed resources, then

186

the second and so on. When the first workstation is ready to process the job, the

controller may decide to dispatch it. Once the first part 1 is done on the first workstation,

the part is moved to the second one and so on, similar to a flow line sequence. This phase

is called cell growing. When all workstations are assigned to the job, one says that the

cell is mature. Then the reverse process will inevitably occur. The cell shrinks, and

finally dies, which means that, the virtual cell controller will no longer exist.

JS-O~ ( ~ O j - ~ VIRTUAL CELL CREATION

~' , - ~ @ or~o~No CELL

<

~ " SHRINKING CELl,

r.?

0 O DY1NG CI':I,L O 0

CELL . . . . . . . . . . ~ J0P O WORKSTATION

i i . . . . . . . . . . . . .

Fig. 3. Virtual cell life.

At any given time, the manufacturing system is likely to contain several virtual cells,

some of them overlapping over shared workstations. Figure 4 illustrates overlapping cells

and some others complexities that may arise when dealing with these systems.

A N O P P O R T U N I S T I C S C H E D U L I N G S T R A T E G Y

In this section, we propose a framework for scheduling and controlling a virtual cell

based system. The proposed framework contains four phases.

1. Job loading: prioritization and selection.

2. Virtual cell creation.

3. Resource allocation.

4. Dispatching of part units.

1 C a n also be a f ix tu re m o u n t e d pa l le t ho ld ing a f ew p a r t s .

187

OVERLAPPING cEILS

COMPETING CELI~

\ ! RESOURCES

HANDICAPPED CELL

MULTI-FLOW CELL

IMMATURE CELL

SYNCHRONIZED CELLS

©

MUTATING CELL

REC UI~IVE- FLOW CELL

Fig. 4. Cell dynamics terminology.

Figure 5 illustrates the overall procedure. Each step will now be presented in more detail.

Job loading consists of the prioritization and selection of jobs to be introduced into the system. It uses opportunistic scheduling rules to produce a list of prioritized jobs. No scheduling rules are known to perform equally well in every situation, thus the job scheduler is provided with different scheduling rules for different situations. Following prioritization, the number of jobs to be considered for selection is reduced by means of window sizing. After selecting the most prioritized job in the window, the cell creation phase is attempted. If this phase fails, the controller repeats the process with the second most prioritized job in the window, then the third and so on. This sequence is repeated when the capacity of any critical resource increases.

During virtual cell creation, one seeks to minimize the flow distance by affecting an optimal set of workstations in a temporary production line (the virtual cell) for the selected job order. The outcome is the list of workstations that minimizes the material flow for that job order while being consistent with the requirement regarding the precedence and capacity constraints. Even though certain elements have been omitted, the general ideas enclosing this phase are portrayed in figure 6. Before proceeding, it is necessary to define the main elements represented in this figure.

88

~CDOW SlZE (~)=

3 2 1

PRIORITY INDEX J

12 J BI, .~"~,~...~..~ 11 JOB 6 5 8 6

i|.0 JOB 8 5 8 5 9 JOB 5 5 8 5 8 JO~B 5 5 9 4

,,7 JO~l 8744 ...... 6 J O ~ 3 0 4 7 5 JOB ~1.476

JOB, 2 9 5 7 JOB 8 8 8 7 I JOB 4 7 5 9 JOB 7 6 8 7 _j

I A .p, CELL CREATION .~succ~ ~L

2ELLSoOUATRC0~ I ~

• ~SUCCEED

DISPATCH JOB I ERASE JOB FROM LIST mrn~z~ COUNTER "C"

LIZATION PROFILE I FOR ALL I

RESOURCES I

Fig. 5. Opportunistic scheduling.

SERVICE DISCIPLINE RULE I RULE 2 4"

R~LE N

I

!I ]3

~j

The top left frame illustrates a facility including 17 nodes; each one representing a workstation. Each node is expressed in terms of the following convention: the numeral represents the type of workstation e.g. milling, turning, inspection, etc., the character identifies each replication of a given workstation type. For example, node "ld" denotes replication "d" of workstation type "1". The frame itself symbolizes the outside walls of the facility. The axis system, located nearby, reminds us that the frame contains a scaled layout and thus, exact position of input /output workstations are known. From such a layout, one can calculate the inter-workstation distances (rectilinear or euclidean); these measures, along with the utilization profile of resources, are useful during the virtual cell

creation.

The second frame comprises the set of nodes, which can potentially be visited by the job, with their arcs. Each arc represents an achievable flow of parts between two nodes. Only the arcs connecting successive nodes as restrained by the precedence constraint are

shown.

After restructuring the second frame into the third view, one can easily distinguish the sequence of operations depicted by the precedence constraint of the job. The parts included in that job must go from a workstation of type 1 to a workstation of type 5 and then to a workstation of type 3. The objective is to find the least expensive path from any workstation of type 1 to any workstation of type 3 via any workstation of type 5 while satisfying other constraints to be mentioned later. The output contains the tlst of

189

Set of autonomous workstations at Set of workstations that can potentially their specific locations, be visited by JOB_X along with their

arcs.

@® @@ @@ @

I @ @@@@

@@ ®@ I note: Every other arcs do not satisly the

precedence constraint for that lob.

Least expensive p~th in a directed graph with nonnegative arc weights. (~

¢ oo, o Sequence for JOB_~: 11.5,31 Workstations nearly at capacity: llc,le,5cl

Fig. 6. Virtual cell creation.

workstations that minimizes the material flow for that job while being confined with the requirement regarding the precedence and capacity constraints. The result of our

example is shown in the last frame. The set of workstations displayed in this frame represent the virtual cell just created for JOB-X. Along with it, a virtual cell controller will be created.

The third phase consists of assigning resources such as tools and fixtures to the newly created cell. The resources are delivered just before the activation of the virtual cell and stay there as long as the job is not finished.

The final phase aims at dispatching the parts within, and occasionally between, each virtual cell. In this phase, the flow of parts and communication between cooperative workstations (members of the same virtual cell) is particularly important. The virtual cell controller has the logic and the know how to control the advance of processes within these workstations.

AN O P T I M I Z A T I O N BASED S C H E D U L I N G M O D E L

In this section, we propose an efficient linear programming model for creating and scheduling virtual cells. The solution satisfies the capacity constraints on all considered resources: tools, workstations and fixtures.

We now define the decisional variable VCkl p which is used in the first set of

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We now define the decisional variable VCk] p which is used in the first set of

constraints. Variables VCkl p represent a virtual cell created for job k starting at period p

using the workstations on routing i. A variable such as VC3,146,1 can also be represented with the help of a gantt chart as follow:

2 Z 0 2 3

4 < 5

r_D : 36

7 0

9

I

. , . - . . - . ' . . . . . . . .

. . . . . . . ] , " . . I

1 2

i _ _

m _ _

D

3 PERIOD

Fig. 7. A Gantt Chart representing VC3,14s, 1

In this gantt chart, the route is 1-.4---6, the virtual cell begins at period 1 and the

job is 7674 (3). Considering the capacity available at each workstation, no more than

4.28 parts/period can be produced without accumulation of work in process. Thus, in

this case, the rate of introduction is 4.28 parts/period. Even a slight increase would

accumulate work in process at workstation 6 during periods 2, 3, and 4. If variable

VCsj48,1 comes out equal to 1 then a virtual cell having workstations 1, 4 and 6 will be

created and the job will begin at period 1 at a rate of 4.28 parts/period until the job is

done. If for example, the variable comes out equal to .5 then, the rate of introduction will

be 2.14 parts/period. As one can see, although the bottleneck fixes the boundaries for the introduction rate, the rate is really fixed within these boundaries by the scheduling model.

The first set of constraints makes sure that each job will be produced in its totality.

This means that for each job, one or more virtual cells will be created at some period in time. In addition, all the parts of each job will be produced in that / these virtual cells.

The first set of constraints is now presented.

E VCklp=l ~-/(k) (1) l , p

For each job k, we sum all the virtual cells starting at period p using routing I.

The second set of constraints makes sure that the demand on each virtual cell will

not exceed the capacity available on any workstation for any period during the planning horizon. At this point, two new variables must be introduced. PTklp represents the

191

processing time required at period p for job k according with routing 1. Cpr represents the

available capacity of resource r (processing time) at period p. The set of constraints is now presented.

PTkl p * < Cpr k-/(r,p) (2) k,l

For each resource, one has a set of constraints (one for each period).

The constraints have been fully defined, thus one shall proceed with the objective function. The objective function uses the following notations which have not yet been defined.

CKkP

Nk Dl T

Fk

Ckp

---- Penalty cost if job k starts at period p. ~- Number of parts in job k.

= Traveling distance associated with routing 1. ---- Total planning Horizon. ---- Flow time for job k.

c * ( p - ( T - F k ) i f p > T - F k

0 if p < = T - Fk

where c is any large cost

Each virtual cell has a routing associated with it, for example, if virtual cell VCs,14%l is adopted for job 3, then its parts will visit workstations 1, 4, and 6. These workstations are physically located somewhere in the facility. Assuming a distance matrix such as the one presented at figure 8, the traveling distance associated with this virtual cell is 67.

W S ~ 1 2 3 4 5 6 7 8 1 0 77 77 25 53 60 75 60 2 0 30 42 95 30 42 22 3 0 42 95 50 20 17 4 0 53 42 20 25 5 0 95 73 78 6 DISTANCES 0 62 43 85 7 OR 0 20 47 8 TIME 0 55 9

Fig. 8. Distance matrix.

Depending upon the types of material handling available and

9 32 70 70 43 22

their physical

configuration, the traveling distance from one workstation to another can sometimes differ in the reverse order. This can be handled by using a complete matrix instead of a half one.

The objective function is now presented.

Min ~ VCkl p ~" (N k Dl + Ckp ) (3) k,l,p

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This objec t ive func t ion creates a n d schedules v i r tua l cells in a way t h a t minimizes

the to ta l d is tance flow for all considered jobs. Also, when the p roduc t ion of a j ob is

beh ind schedule, the model accept a small increase in d i s tance flow if this allows a

compression of the schedule.

I L L U S T R A T I V E E X A M P L E

Table 1 shows a set of job orders which are avai lable for processing; the LP

schedul ing a lgo r i thm will be appl ied on them.

TABLE 1

Job Sequence & Proc. Tota l Proc. # _ID T ime (Min) Q T Y Time (Min)

10 8887 9 6586 8 2957 7 8476 6 5594 5 3847 4 5585 3 7674 2 8744 1 6585 I

2 , 6 ) ( 3 , 8 ) } 48 872 2,14)(4,5~)} 32 608 1,8)(2,14)(4,10)} 15 480 4 , 8 ) ( 2 , 7 ) } 35 455 3,4){2,9)~ 32 416 2,5)~ 78 390 2,9)(3,4)(4,4)} 21 357 1,5)(2,10)(3,~)} 17 374 1,7)(2,9)(3,2)} 8 144 3,5)(1,4)~ 13 117

Note: {(2,6)(3,8)} means tha t JOB 887 must visit a workstation of type 2 with processing time of 6 MIn. and then a workstation of type 3 with processing time of 8 Min.

Table 2 shows the results ob t a ined wi th the schedul ing model for th is s imple case.

TABLE 2

Job Pe r iod Lot R a t e / P e r i o d VCell

6585 1 4.9 2.3 6 2 6585 4 8.1 3.7 6 2 8744 1 8.0 4.0 1 4 7 7674 3 17 2.2 1 4 7 5585 1 7.7 1.1 3 7 8 5585 1 7.0 1.0 4 7 8 5585 4 6.3 0.9 4 7 8 3847 4 5.0 0.5 4 3847 1 73.0 7.7 5 5594 1 25.0 3.0 7 3 5594 3 7.0 0.4 7 4 8476 1 19.2 1.1 8 3 8476 1 15.8 0.9 9 5

Note: 1 period ~ 15 Min.

193

This table provides all necessary information for creating and scheduling the virtual

cells for the next hour The first column indicate the job number. The second column indicates in what period the virtual cell will be created. The third column indicates the number of parts to be processed in each job or they add up to it. In most cases, the rate of introduction will vary and sometime, more than one virtual cell will be created for a given job. When this happen, the lot represents the portion of the job tied to the virtual cell. The rate/period indicates how many parts will be launch per period within each virtual cell. The rate stays the same as long as the lot is not completely finished. For

example, 4 parts/perlod will be launched for job 8744. Parts will be introduced at period 1 for 2 periods or until all 8 parts have been launched. The virtual cell controller created for this job will make the communication possible between workstation 1, 4, 7 and will control the flow of parts between them.

Beside these results, it is interesting to draw a chart showing the loading on each resource within each period. This can be done easily since the output generated by every linear programming package includes the slack, if any, for each constraint. Figure 9 illustrates such graph for the case just presented over the first 4 periods. The reader should not interpret this as an attempt to maximize workstation utilization; this would be kind of conflicting with the Just-In-Time concept.

O3 z 0

<

5']

I

2

3

4

21.4

2 3 4 5 6 7 8 9

21.4

42.8

29.12

~20.8

1

f I i

i: .:?: ii 7%~::..; i.:iii-?i!i;:2:i:iii? ??:i..?i:ii "171:i,'i? :, i .[.[:i~i 30 30 30

3 4 5 1 2 6 PERIOD

Fig. 9. Resource loading.

M O D E L S O L V I N G

The model can be solve in a reasonable amount of time with current computer technology. The size of the model will grow quickly, but linearly, and remains reasonable for a typical size factory as described in the introduction. We conducted a series of tests on a workstation SUN 3/50. In its latest version, the model can solve any realistic problem within 2 minutes. Much less than what would take an experienced scheduler for diverting the flow of parts and solve the contentions of critical tools after the occurrence of a breakdown.

194

C O N C L U S I O N

We believe the virtual cell concept will be a common denominator for factories of the future. Metal cutting, forging, plastic or electronic industries, no matter their categories, they will most probably be based on the virtual cell concept.

The presented model has many advantages that makes it suitable for scheduling small batch manufacturing systems. Firstly, it permits consideration of critical tools. Secondly, it provides a quick reaction to unexpected events. Finally, it enables a coherent planning of resource utilization, potentially reducing possibilities of delays and deadlock, which are very common in fast pace manufacturing systems.

A more sophisticated near optimal model for scheduling virtual cell systems was also developed. This new version was shown to be more efficient; the size of the model growing at a much slower pace. This new model will be published later.

R E F E R E N C E S

[1] Schonberger, R.J., '~¢Vorld Class Manufacturing: The Lessons of Simplicity Applied". The Free Press, New York, NY, 1986.

[2} Dupont-Gatelmand, Catherine, "A Survey Of Flexible Manufacturing Systems". Journal of Manufacturing Systems, Vol. 1, No.l, lg82-83, pp. 1-15.

[3] Solberg, James J., Anderson, David C., Barash, Moshe M., and Paul, Richard P., '~Factories Of The Future: Defining The Target". A report of a research study conducted under National Science Foundation Grant MEA 8212074, Purdue University, West Lafayette, IN, January 1, 1985.

[4] 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, Galthersburg, MD, October, 1982.