Managing Multiple Product Variants in Assembly Control with a Fuzzy Petrinet Approach

typeof I numberof relations

fmaterial f focussed flow process

chain f syncro-

nized pre- assembly

Prof. Dr.-lng. Dr. h. c. Walter Eversheim ( l ) , Dip1.-lng. Thomas Hack, Werkzeugmaschinenlabor der RVVTH Aachen, Aachen, Germany

Received on January 9,1996

typeof I numberof elements

f assembly f product resource

z operation f due date f criteria for

lot-sizing

Bbstract

Companies with maka-to-order busineases are facing increasingly dynamic movements within their sales

markets. This leads to a growing variaty of products and a demand for higher flexibility in order processing.

Different logistical goals, process flexibiiii and fuzzy-expressed dimensions aa well as short-term changes

due to rush-orders or disturbances, have to be considered within this multiple product variant environment.

This paper describes how these controversial requirements can be appropriately represented within a

scheduling model, by applying a fuzzy Petri-net approach. All in all, control personnel can be efficiently sup-

ported. The described model and methods are verified within an industrial application.

Kewvords: Scheduling, Fuzzy Constraints, Flexibility

1. Hlghw and mom .pacific demand. on product8 n d aervkw

Many series batch producers are confronted with increas- ingly dynamic markets. Customers are expressing more specific demands on the desired products and expected services, which have to be satisfied in order to keep up with competition. The main cause is market saturation, so that companies have to concentrate on smaller market segments, as well as country-specific adaptations conse- quent to generally increasing globalization. Based on this background, the variety of variants has increased rapidly since the eighties [l] and it appears, that innovative com- petitiin will become even tougher in the nineties. Only those companies, which can realize the demands of short lead-times and low tardiness for multiple product variants will remain competitive in the future.

This requires more flexibility m all departments and for all resources, taking part in customer-specific order process- ing. Due to this situation, the assembly at the end of the order processing chain becomes more and more impor- tant as lead-times in this phase represent up to 40% of the total customer order lead-time. This means, the suc- cess of a company is strongly influenced by the efficiency of its order management at the point of assembly.

2. Increasing wheduling complexity by product

Series batch producers used to be able to build lot-sizes of several hundred identical products to satisfy the market demand. Even pre-productions on stock were available. Due to the above mentioned change, they are becoming more and more single to small batch manufacturers. Every product variant is supposed to be delivered on time. In order to achieve this, every product variant has to be individually controlled, which is a very complex task growing with every variant. Complexity can be measured by connectivity and variety [4]. Connectivity is characterized by the type and number

variant.

of relations, whereas variety is influenced by the type and number of elements. demonstrates, that scheduling complexity increases with every new product variant. As pertains to the scheduling problem, this involves on one hand the new process plan with its material flow and operations, as well as more due dates for a higher num- ber of small orders. On the other hand, with adaptation of the assembly structure, you might focus on a longer as- sembly process chain with more pre-assemblies a9 well as more assembly resources and consequently more criteria for lot-sizing.

-.-- -_-__ ; .< “3 ;- globalkhtlon 3;

comptetlve factor: tlh?:c+. focus oh emallor market oognpnts

.’ Y .

E L s more product vanants need for a flexible assembly structure

I conseauences for schedulina? 1

Eiez; Higher scheduling complexity as a consequence of

Due to these effects, organizational measures should be applied, such as assembly-oriented product structur- ing, customer-neutral product variant reduction, installa- tion of teamwork or a more flexibb assembly structure. This can make a valuable contribution to reducing its- sembly control complexity even to the point of self-

adaptations to market changes

Annals of the ClRP Vol. 45/1/7996 45

organized assembly order processing. But in cases with a high number of assembly steps and a large variety of different assembly resources needed, of which some might be even very expensive, scheduling remains a complex problem.

Aside from the complexity, scheduling the multiple prod- uct variant assembly is a very dynamic problem. Among other frequently occurring organizational disturbances,

rush orders, missing parts, missing assembly resources, delayed operations a. s. o.,

have a big influence on assembly order processing. In- vestigations at companies with single to small batch as- sembly of complex products point out, that 25% of all operations are always disturbed and 22% of all operations are finished too late [2]. Even though this investigated type of assembly is only an extreme type of the overall focused assernbty structures, if points out, that assembly is not predictable.

In this situation, on one hand, the assembly order assign- ment to resources has to be adapted continuously. On the other hand, man's ability to overview the complete assembly process contributes much to the optimization of order processing. The assembly controller uses flexibility reserves such as

assigning two assembly workers to an order instead

. splitting an order, overlapping operations of orders a. s. o.,

in order to still meet the middle-term assembly goals. But these scheduling adaptations are very time consum- ing and lack clearness. For example in the case of apply- ing special measures to accelerate a rush order, the con- sequences for all other orders are not known. This lack of coordination leads to high work-in-process, high average order tardiness and long waiting times between opera- tions. The met production goals derive from the desired. This demonstrates that the economy of assembly can be distinctly increased through systematic IT-support, which generates goal-oriented assembly schedules as well as offers short-term re-scheduling possibilities using flexibil- ity reserves to adjust the schedule to the current job shop situation. Nowadays, available MRPII-systems or shop floor control systems are not able to accomplish these complex scheduling tasks. Algorithms and methods of Operations Research can not be applied. Therefore, a knowledge-based approach is preferable. 3. Integration of a knowledge-baaed scheduler

Such a scheduling system can be linked by an inleriace to an existing IT-system which represents the assembly control information [fiez). In practice, this can be a MRPllaystem (on a more rough level) as well as an as- sembly control system. In the scheduling system, a model of assembly structures with all constraints and the in- tended scheduling strategy has to be represented as a knowledge-base.

This data has static character, whereas information about actual orders, the type of order, actual progress, priorii, due date and overall resource availability, are dynamic data, which have to be transferred in periodic intervals. In return, a schedule is generated showing the optimal short-term resource assignment and indicating possible

of only one,

lnplementation of simulation-based scheduling

middle-term bottlenecks.

4. Modeling with fuzzy Petri-nets

To represent simulation knowledge for scheduling, the fuzzy Petri-net approach developed by LlPP [3] has been selected. Petri-nets are event-driven and can represent concurrent process structures. Therefore, they have al- ready been successfully implemented for discrete control tasks. Aside from this, fuzzy Petri-nets can represent knowledge about desired states or changes. This is de- scribed by the Fuzzy-Set-Theory developed by L. A. ZADEH [5]. A membership function with continuous val- ues from '1' (ideal) to '0' (unwanted) expresses the de- gree of fulfillment depending on the actual Petri-net situa- tion (fin3).

Switching of a fuzzy Petri-net depending on fuzzy evaluated number of tokens in places

With this fuzzy Petri-net approach, the number of tokens in a place, the stepwise change of the number of tokens in a

the intensity of a transition's switching, the stepwise change of a transition's switching intensity

and the activity of edges to switch,

can be evaluated using a fuzzy set. This range of para- meterization offers a lot of modeling possibilities.

place,

46

The evaluations determine the switching of specific tran- sitions since the token-flow of the fuzzy Petri-net is driven by those states evaluated as worst. The fuzzy evaluation can be applied to evaluate logistical goals based on their fulfillment. With the drive based on the worst state, each scheduling step (equal to one simulation step) can be oriented towards the fulfillmnt of goals. Depending on the shape of the membership-functions, the represented goals influence each other so that even contrary goals can be modeled. The effort to meet a specific goal is dependent on the overall situation.

In the example shown in fig. 3, parts are represented by tokens, buffers by places, one operation by a transition and the material flow by edges of a Petri-net. The M- sumption is to model an assembly line where the buffer levels should be optimized. This is expressed by the places' membership-functions: buffer 1 should preferably contain no or only 1 part, for buffer 2, the optimal level is reached with 2 parts. In order to coordinate these two goals as well as possible based on the actual situation, 2 more parts have to be processed.

Due to the above mentioned complexity of the scheduling problem, the appropriate representation of a simulation model deserves special attention. For an easy handling of the model and to reach useful simulation times, the model should be only as precise as necessary, but still represent all information necessary for efficient assembly control.

represents different modeling techniques, which can be applied to create a more rough scheduling model.

types. The number of orders belonging to each type and their actual progress, is transferred periodically with the dynamic data (compare with fig. 2).

Furthermore, a two-level hierarchical model structure can be installed. That way, the cooperation of local and global goals can be simplified. With the possibility to describe the fulfillment of goals depending on states by fuzzy-sets and their cooperation by the represented structure, an overall scheduling strategy for every possible combination of states can be represented. W h ail these different measures, a simpliied model can k built up. But since the fuzzy Petri-net modeling method b very complicated with its many adjustable parameters to reach specific effects (one membership-function is determined by, on average, 8 parameters), predefined common model structures could be a valuable contribu- tion in order to build up case-specific simulation models which are structured rapidly and with more ease. Therefore, based on an analysis of the most commn assembly objects, logistical goals and flexibility reserves, a catalogue of complex model components has been created Mia.. These predefined fuzzy Petri-net- components can be combined and integrated, respec- tively, step by step to build up the complete model. Moreover, the adjustable parameters of each model corn ponent are displayed.

tie4; Modeling techniques ro reduce scheduling com-

Uncritical resources, e. g. material supplied by Kanban or assembly space which is always linked to a worker al- ready considered within the modeling, which almost never become a bottleneck, can be neglected. If several serial

plexity

component Petri-net modeling

5. Industrial application processed operations have the same resource demand, they can be represented as one operation. Another reduction of model complexity can be reached by implementing order types instead of distinguishing every order. Orders belonging to one order type have the same material flow, the same resource demand, almost the same operation times (depending on the level of detail) as well as the same set-up-states per resource. Thus, the simulation model represents a limited number of order

catalogue to support fuzzy

The final assembly in the regarded company can be roughly divided into three different stages 0. First, smaller parts (like mounts) are tacked and welded to the basic product body. Two dinerent types of welding sta- tions are available for this operation. Since the next as- sembly stage is cycled, a fix order-sequence has to be determined. After priming, the assembly of the complete product is realized as one cycled assembly line synchro- nously supplied by pre-assembly units. This organization

47

was chosen, because all products are geometrically very similar and need to be processed the same way. After this, about 6O0/o of the products receive special, customer- specific components through additional, manual assembly boxes.

a 7 1 controlled product var la nt 8

cycled manual organl- assembly I assembly zatlonr StetionS line in boxes

A I -

processes

have to be considered to reduce set-up-times. At the manual assembly boxes, the set-up times can be ne- glected. But for a comprehensive solution, it is important that all of these boxes are well loaded at all times without an overflow of the supplying buffer. Therefore, too narrow a sequence of product types, which need additional as- sembly, has to be avoided. To represent an assembly model within a scheduling system, many simpliiications (such as the definition of order types) have to be made. A simple model is achieved, if all technical information which does not influ- ence the resulting schedule, is neglected. For example, two successive operations without a significant buffer and without different set-up criteria can be regarded as one operation with duration equal to the individual sum of the operation times. To represent a cycled assembly line as one process, is an example for such an allowable simplifi- cation. After the simplified, general concept was built up, a com- pany-specific model based on the complex model com- ponents within the model catalogue, was created. Order data transfer is guaranteed by an interface to the existing MRPl I-system. Based on this fuzzy Petri-net model, comprehensive con- sideration of customer-specific assembly is possible. Simulation runs show, that order lead-times of only one day can be achieved in spite of a high work load on the cycled assembly line. The work-in-process is drastically reduced. Even customer-specific order changes can be considered up to one day before delivery. All in all, logisti- cally lean assembly could be achieved.

6. Conclusion

Modeling with fuzzy Petri-nets to build up an objective- oriented simulation model for assembly scheduling, offers new possibilities to manage multiple product variant as- semblies. In the case of organizational disturbances, fast re-scheduling is possible using existing flexibility re- serves. All in all, the demand for more flexible assembly order processing as a response to more dynamic sales markets can be met, which is an important contribution allowing make-to-order companies to remain competitive.

References

(1) Eversheim, W., Kihper, R., 1993, Varianten- management durch ressourcenorientierte Produkt- bewertung. krp 4, 233-238 .

(2) Lehmann, F., 1992, t i n d a r Finzel- MKlelnserlenmontaae , Dissertation RWTH Aachen

(3) Lipp, H.P., Ginther, R., Sonntag, P., 1989, Unscharfe f.iiLcomDuter-

EntscheldunasDrozesseinkomDlexen Petrr-Netze:Ein-

m, Wissenschaftliche Schriftenreihe der TU Chemnitz 7

(4) Patzak, G., 1982, -nik - PI- -, Springer-Verlag, Berlin

(5) Zadeh, L.A., 1965, Fuzzy Sets, Information and con- trol 8, 338-353

48

f&& Parameters of scheduling conplexity in the

In this industrial case, the customer-specific products can be described using 15 features with about 700 possible values, such as 'length = 1900 mm". This allows several thousand possible combinations based on customer wishes. For assembly control, specific order types could be defined. Only features or ranges of possible values (such as length from 1500 mm up to 2000 mm) are impor- tant, which

In this industrial case, six features with a total of 20 pos- sible value ranges, were identified to define order types. This still leaves approximately 100 possible variant order types which have to be distinguished to control this as- sembly. But this rough thinking in order types represents the mental picture in the scheduler's mind. Through experi- ence he or she knows which criteria are relevant for lot- sizing. The relevant product features can often not easily be identified by the product part number or process plan. Because of this lack of clarity, a schedule is written manually on a daily basis. It takes up to almost half a day to write the production schedule for the next day.

One order including additional manual assembly needs at least three days lead-time for the three stages described above. The division of scheduling into three different phases is caused by the lack of clarity over all orders and their features relevant for scheduling. To solve this, com- panies keep more parts in the buffers. Order coordination is simpler this way, because there are always several basic product bodies of order types which can be grouped for the next day's operation. But the cost of additional tied-up capital is very high.

To run a dynamic production program with short lead- times, met due-dates and low work-in-process, compre- hensive consideration including all three stages is neces- sary. For the cycled assembly line, it is important to group all orders with the same strength. On the other hand. the bearing of the product has no significance for the welding stations, considering operation times or set-up-conditions. At this station, other criteria, such as the type of mounts,

regarded company

need different operation times at one station or need set-up before processing at a station.