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Analytical approach of determining job division in manual assembly systems
international journal of
production kconomics
ELSEVIER
Int. .I. Production
Economics
51 (1997) 123-134
Analytical approach of determining job division in manual assembly systems Gert Zdch, {fab ~ Institute
Wolfgang
J. Braun, Emmerich
of Human and Industrial Engineering (Institut fir Arbeitswissenschaft KaiserstraJe
12. D-76128 Karlsruhe,
F. Schiller*
und Betriebsorganisation). Germany
University of Karlsruhe.
Abstract Requirements upon modern production systems have changed considerably. One of the main results of these changes is that organizational improvements have become more and more important. In contradiction to this, the available approaches to support adjusted design of production systems in an early planning stage - especially regarding manual assembly systems - are deficit. Particularly, the consideration of process organizational effects by determination of the job division fails because the planning knowledge is limited to rather vague hints than based on precise planning rules. An analytical approach for the determination of job division in assembly systems under different goals has been developed to overcome this weakness. Basis is a parametric description of the important factors of the planning problem. Set up on this, a simulation-based investigation has been carried out to detect dependencies between the goal system and the assembly tasks. The result is an analytical approach based on regression models to determine a suitable form of job division for a clear-cut assembly task. Keywords:
Analytical
1. Tendencies
approach;
Job division; CAP; Center of gravity of a graph; Simulation study
in production systems
Decreasing lifecycles of industrial products, appropriate consideration of customers wishes, increasing complexity of products and the number of variants coming along with high-quality standards are forcing the industry to accept short developing times for their products as well as for the corresponding production systems. Taking this and the fact of low-manufacturing penetration into account, the central point of all planning efforts
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should be in the field of assembly, in which almost 50% of all manufacturing costs accrue meanwhile (VDI, 1989, p. 19). For all this, requirements concerning planning accuracy and planning reliability are extremely high and pressed for time. Therefore, it is obvious that traditional, usually manual planning approaches do not achieve those goals. For that reason many analytical approaches and computer-aided planning tools in the field of assembly planning were developed in the last years. Examples are precedence diagram derivation (Ammer, 1984, p. 42), standard time fixing (Kohler, 1989, p. 81), line balancing programs (a comprehensive survey of line balancing approaches is given in Brybars, 1986), process order determination
1997 Elsevier Science B.V. All rights
reserved
124
G. Ziilch et al. ilnt. J. Pxxluction
(Thaler, 1993, p. 39) or computer-aided workplace design (Braun et al., 1996). The attention is set on supporting the planning engineer mainly in his routine work with a focus on single detail tasks in order to give him more scope for the creative aspects of the planning process. Typical problems within this creative planning process are, for example, the selection of a suitable flow principle, the rating of the degree of automation, the planning of the assembly system structure or the determination of the job division. Analytical approaches supporting this process are not known, so that the results of these planning steps are mainly depending on the knowledge, experience and intuition of the planning engineer.
2. Procedures for the design of assembly systems Besides the technical and ergonomical aspects, organizational questions in connection with the design of production systems are becoming more and more important. In contradiction to this, the developing of adjusted planning approaches and methods has not kept up sufficiently with these changes. Especially, the consideration of process organizational aspects within the early planning process in the form of an arithmetical approach turns out extremely difficult. The available planning knowledge in literature (e.g. Eversheim et al., 1981, p. 25; Bullinger, 1986, p. 139; REFA, 1990, p, 160) describes some hints rather than precise planning rules (Ziilch and Braun, 1995, p. 41). In addition to this, those hints mostly cover the extremes of a design parameter. In this context there are also only vague hints available for the two extremes of job division, namely job division by operations and by quantity. Information about the large number of intermediary forms cannot be found in literature. For example, more than 700 forms of mixed job divisions can be shaped within an assembly system built up of only 10 workplaces and one can suppose that they differ in meeting the planning goals, depending on the products or its variants that have to be assembled. The general job division problem now is to find the best suitable mixed form of job division.
Economics
51 (1997) 123-134
-
..,
<‘ij)- -(5&+2~-/
asse&bly operation -------assembly
Fig. 1. Precedence
diagram
,
task-
of an assembly
task.
To describe this problem formally, it is necessary to give a description of all necessary parameters of an assembly task. In connection with the job division problem, these parameters are the product with its respective variants, the production program and the technical assembly system itself. Industrial products are usually made up of several parts and sub-assemblies. Variants of these products are created by changing, adding or omitting single parts. The essential question in the case of assembly is the quality of the products rather than the (joining) relations among them, e.g. the sequence in which they have to be assembled or the kind of assembly operation. A common way to depict these relations is the use of the precedence diagram (see Fig. 1). The precedence diagram, developed by Prenting and Battaglin (1964) is a directed graph where the nodes represent the assembly operations, specified by the parts which have to be assembled and the kind of assembly operation (according to DIN 8593); the arches characterize the logical and technological constraints between them. Using the precedence diagram as a basis for the job division problem, it has to be built up for each product including its variants, which form together a product family. Traditional planning approaches confine to build up a precedence diagram for only one representative product of each product family, putting up the disadvantage that all the other variants cannot be taken into account in the planning process. A complex graph has been developed, to overcome this weakness. This graph is an extension of the precedence graph, representing all variants of a product family in a single graph which are similar enough. Similar in this context means that their precedence graphs contain similar assembly that means similar sub-structures sequences,
G. Ziilch et al. lint. J. Production
Economics
(sub-graph automorphisms) within the graphs (see Fig 2). As an extension of the approach introduced by Thomopoulos (1970) this similarity is described by parameters, allowing a comparison with the help of cluster analysis. Differences between the frequency of the assembly operations are considered by using an accumulated standard time, calculated out of
precedence variant A
diagram
automorphism
diagram
Fig. 2. Derivation
of a complex
by operations
graph
q
q quantity per period time per unit
t
+ short learning time
clrr + -
mixed _.. (i.e.)
by quantities
q
q
; L
Fig. 3. Capacity
fields of different
forms of job division
125
the standard time of each operation multiplied with the frequency of its appearance in the expected production program. The frequency of the appearance of each assembly operation depends, on the one hand, on the number of variants it has to be carried out in and, on the other hand, on how often these variants have to be assembled in total. Herewith, the frequency is determined by the production program of each product family, which states how many products of type, variant or version have to be produced. Describing the assembly system, one can concentrate on describing the essential parameters. In the case of the job division problem, these parameters are the capacity of the assembly system and the distribution of this capacity onto assembly operations. To describe this, the capacity field has been developed (Dittmayer, 1981, p. 37). This two-dimensional representation of the capacity requirements is characterized by time per unit necessary for the complete assembly task and the number of products to be assembled within a period, e.g. a shift. It follows from this that each rectangle
complex graph
precedence variant B
51 (1997) 123-134
flow principle low self responsability idle time lack of flexibility
+ full product responsability + good flexibility + individual performance - high educational requirements
t inclusive
corresponding
advantages
and disadvantages.
126
G. Zilch et al. 11~. J. Production
represents a workplace which has to fulfill a defined work content (see Fig. 3). Based on these considerations, it is desirable to find a parametric description of the job division problem in order to develop an analytical approach to solve it. A feasible approach for this is described in the following section.
3. Conception of a parametric description of products and production systems As set out in the last section, the tasks necessary to design production systems, above all the design of mainly manual assembly systems, can be classified by the two objects product and production. While the concentration of the tasks assigned to the object product is placed on the analysis of available input information, the emphasis of those assigned to the object production is placed mainly on the design. In order to describe these two objects exactly, a lot of data is required. As pointed out earlier, a usual kind of representation of a product is the precedence diagram. If there are only 40 production operations required to produce a product at least 79 data are necessary to describe this precedence diagram, 40 nodes and 39 precedence relations. In addition to characterize one single assembly operation, one date is not sufficient. At a minimum three data are required to describe the two parts or components that have to be connected and the kind of assembly task, like e.g. joining by splaying (see Braun, 1995, p. 53). On this assumption, the minimal number of data necessary to describe the precedence diagram increases to 159. Since a product usually exists of several variants, the number of required data increases again. In the case of 50 product variants, what certainly is not untypical for modern products, the number of required input data concerning the object product reaches a minimum of 7950. This example already clarifies, that because of the complexity of the description, the design of product systems cannot be done neither manually nor computer aided if each date and information should be taken into consideration. One possibility to solve this problem and to simplify the planning process is to compress these
Economics
51 (/997)
123-134
data by describing them with a limited number of parameters. In literature, several useful parameters for describing universal graphs are listed. Examples are the length (Ritzmann and Krajewski 1986, p. 51) or the breadth (Philipoom et al. Fry 1989, p. 215), the degree of interweaving (DIN 69900, Part 1, p. 4), the relative number of edges (Neumann 1975, p. 54), the complexity (Davis 1975, p. 136) as well as the degree of complexity (Griinwald et al., 1989, p. 288) the degree of parallelity and the degree of meshing (Grobel, 1994, p. 31). As a common feature, all these parameters are not suited to describe this special kind of a graph like the precedence diagram or the complex graph. This is due to the fact that all these parameters represent a kind of ratio of the number of nodes to the number of edges. Information concerning e.g. the position of nodes within a graph cannot be received. But exactly these informations are very important. For example, it can be supposed that in connection with a precedence diagram or a complex graph, where a lot of (parallel) nodes can be found, a high flexibility exists. This flexibility probably leads to a good solution for the line balancing problem. Appropriated algorithms to solve the line balancing problems have been developed e.g. by Jackson (1956), Arcus (1966) Dar-El (1973) or Tonge (1965). This demonstrates the fact that in each line balancing step more than one operation is available for assignment. On the contrary, there are often several possible operations with different operation times existing, which can be assigned to a certain station. In order to receive a more suitable description of the precedence diagram, a new parameter has been developed. It bases on the definition of the center of gravity of a plane surface, known from mechanics and is called center of gravity of a graph. In this context, it is supposed that the precedence diagram is a two-dimensional structure consisting of several plane surfaces in the form of nodes. Each plane surface is assigned the uniform area one, where the area of the edges is not considered. Due to the fact that the value of the center of gravity of a graph depends on the arrangement of the nodes, several rules for this arrangement have to be considered. For this, the nodes must be assigned to one field within a matrix. In this matrix, the lines represent
G. Zilch et al. lint. J. Production
levels and the columns represent ranks. Because of this, the matrix is called the level-rank-matrix. First of all, in the direction of the x-axis each node is assigned to the next higher rank of its direct predecessor with the highest rank. In y-direction each node is assigned to the lowest possible level within the corresponding rank. Therefore, in the case of 4 nodes within one rank, they have to be assigned to the levels 0, 1, 2, and 3. Taking these assumptions into account, the x-coordinate CPX and the y-coordinate CPY can be calculated with the help of the following formulas: Ca”“:-’ NON,a for LGR > 1, NON(LGR - 1) (I) 1 for LGR = 1,
!?
with a being the index for ranks, LGR the length of the graph and NON the number of nodes,
1gy-’
NON,b
CPY = ’ NON(BGR
- 1)
0
for
BGR > 1,
for
BGR = 1,
(2)
with b the index for levels, BGR the width of the graph. The range of value of CPX is the interval between 0 and 1. Graphs with CPX close to 0 are left inclined. This means that most of the nodes are on the left side of the graph. Correspondingly, graphs with CPX close to unity are right inclined. The
Economics
51 (1997) 123-134
range of value of CPY is the interval between 0 and 0.5. With this, an increasing breadth of the graph leads to increasing CPY. Using both coordinates, a sufficient description of the structure of the product is available, which allows an interpretation of a graph, on the one hand, and a classification, on the other. The classification can be carried out in the sense of the right or left inclination of the graph using the coordinate CPX and in the sense of a constant or non-constant breadth of the graph using the coordinate CPY. In Fig. 4, the center of gravity of a graph is visualized as an example. In addition to the description of the object prodtact represented in the form of a precedence diagram or in the case of product variants in the form of a complex graph, a description of the object production is also required. For a visualization of this object, the cupucityjeld is something used in literature (Dittmayer, 1981, p. 37). In this diagram, the x-axis represents the operation time and the y-axis the number of units to be produced. To receive the capacity requirements of the production system, two lines have to be drawn in the diagram. One line is parallel to the x-axis and crosses the y-axis at the number of units that have to be produced in the planned production system. The other line is parallel to the y-axis and crosses the x-axis at the value of the expected operation time that probably would be necessary to produce the product (see Fig. 5). These lines and the two axis are the edges of a rectangle, which represents the capacity
center of gravity
length of the graph /_GR = 5
level 3
number of nodes NON= 11
level 2
width of the graph BGR=4
level 1
level 0 X
I
rank 0
rank 1
rank 2
Fig. 4. Precedence
rank 3
diagram
127
rank 4
and its center of gravity
center of gravity in x-direction CPX = 0.52 center of gravity in y-direction CPY = 0.30
G. Zilch et d/M.
J. Prvductim
Economics
Y
51 (IYY7) 123-134
capacity
graph
number of units
operation time standardized
’
degree of division:
center of gravity in x-direction: center of gravity in y-direction:
Fig. 5. Capacity
field and the capacity
requirements of the whole production system. The capacity stock of each of the required workplaces can also be characterized within the diagram in form of a rectangle. In this connection, it must be noted that the area of each of these rectangles is theoretically equal while the portion of the number of produced units as well as the portion of the operation time could be different from workplace to workplace. By varying these two quantities last mentioned, alternative kinds of job division can be generated. An existing parameter to describe these different kinds is the degree of division, which represents the average proportion ofjob dioision by quantity to job division by operutions (Dittmayer, 1981, p. 61). In order to adapt this parameter to the kind of parameters pointed out earlier, which have a range of value between 0 and 1, the degree of division has to be standardized. It can be calculated applying the following formula: SDD =
NWPNUW c OTW, TNU c=l
TOT NWP’
(3)
where c is the index for workplaces, NUW, the number of units at a workplace, NWP the number of workplaces, and OTW, the operation time at a workplace
graph
SDD = 0,41 CGX= 0,44 CGY = 0,33
and their describing
parameters.
The standardized degree ofjob division SDD converges to 0, if there are production systems with almost complete job divisions by operations, otherwise, in case of production systems with a division mainly by quantity, SDD converges to 1. In order to get another possible description of the form of job division, the capacity field must be interpreted as a graph. In this graph, each node is a workplace and the edges represent possibilities for the flow of material between two workplaces. Unlike the precedence diagram or the complex graph which are both AND-graphs - that means each node has to be passed ~ the capacity graph is an exclusive OR-graph. In this kind of graph, each node will be headed for only one successor, while the other nodes are not taken into consideration. This is in accordance with the fact that one single part can be assembled at one workplace only. Imitating the parameter center of gravity of a complex graph described in section 2, the center of gravity of’u capacity graph with its coordinates in x-axis CGX and in y-axis CGY has been developed. Especially, CGX points out, if there is a high parallelity of workplaces especially at the end of the production system - in this case, CGX is close to 1 - or vice versa, if the parallelity is more at the beginning of the production system. Then CGX is approximately 1.
G. Ziilch et al. /Int. .I Production
4. Relations
51 (lYY7) 123-134
129
city graph and particularly
between the describing parameters
In order to generate a concept that allows a determination of a suitable kind of job division, several simulation studies were carried out. These studies were carried out in order to detect dependencies between a complex graph, on the one hand, and a capacity graph, on the other, taking logistical key-data into consideration. In the field of logistics, in literature as well as in industrial practice the criteria lead time, due-date deviation, loading, and work in progress are often mentioned in the role of comparison or for the evaluation of production systems (Graves, 1993, p. 25). To raise the expressiveness of these criteria, Grobel (1993, p. 87) transformed them into logistical key-data, ranging from 100% to O%, where 100% is optimal. These key-data are e.g. the goal achievement for utilization GUT and goal achievement for lead time degree GLT. GLT describes the relation between total lead time TLT and total processing time TPT. As TPT is the minimal feasible lead time GLT is a measurement for the deviation of the actual lead time from this (theoretical) optimum. GLT=-
Economics
TPT TLT ’
the degree ofjob division. In order to achieve a better comparability of the simulation models and the belonging production systems, several characteristics have been fixed. Therefore, all generated precedence diagrams consist of 40 nodes, which is particularly typical for companies manufacturing products in serial production (Fremerey, 1993, p. 142). On the other hand, the capacity graph includes 10 nodes, which represents a production system with 10 workplaces. Altogether, the number of simulation experiments reached more than 900. The basis for each investigation, the results of which are founded on statistical interpretation, is a systematical procedure. Because of this, the statistical methods of experimental design has been used. The applied methods intends to define several hypothesis that should be proved first or disproved by the investigation. For the cause of the investigation presented in this paper, two hypothesis were formulated. The first hypothesis assumes a connection between the inclination of both graphs used in this paper, which are the complex graph of a product and the capacity graph of a production system. The formulation of the hypothesis is Left inclined complex
graphs reveal better logisti-
(4)
cal key-data in right inclined capacity graphs than opposite, and vice versa
where OCS is the worked off capacity stock, TCS the theoretically available capacity stock, and TPT the total processing time. In order to execute a simulation-based investigation with the goal to find possible dependencies, as mentioned above, several simulation studies were carried out using the simulation program FEMOS (simulation program for manufacturing and assembly processes, see Ziilch and Grobel 1993; Grobel, 1994, p. 32). The models necessary for simulation were generated with the program GAMMA (generator for production systems in manual assembly, see Braun, 1995, p. 120). This program is adjusted to FEMOS allowing to build up a complete model of a production system based on a parametrical description. The used parameters are the center of gravity of the complex graph as well as of the capa-
In order to confirm the assumption described by this hypothesis several simulation runs were carried out using first a 2” fractional factorial design. From this, the influencing factors CPX and CGX could be proved like assumed in the hypothesis. For these two factors a multi-level factorial design has been carried out in order to quantify their exact influence on the used logistical key-data. For the goal achievement for lead time degree GLT, no significant influence could be proved. On the other hand, a connection of the goal achievement for utilization GUT with the gravity centers CPX and CGX could be ascertained. The regression analysis resulted in the following function:
GUT== TCS ’
GUT
= 91+5CPX+7CGX
- 22CPX CGX
(in%). (5)
130
G. Ziilch et aLlInt. J. Production
Economics
51 (1997) 123-134
goal achievement for utlllzatlon (GUT II- %)
x-centerof gravity of a complex graph (CW
x-center of grawty of a capacity graph
left
(CGX)
Fig. 6. Result of the first part of the investigation
goal achievement for lead time degree (GLT in %)
- influence
of CPX and CGX on GUT.
80
andardized
y-center of gravity of a complex graph (CPY
0.5 rectangular
degree
0 by quantity
)
Fig. 7. Result of the second
part of the investigation
The calculated coherence coefficient was R2 = 0.75 at the significance level of CI> 95%, which indicates a high statistical significance. Fig. 6 clarifies the result of this first part of the investigation. From this figure, it is quite obvious that products having a lot of assembly operations which could be executed mainly at the beginning of the assembly process should be manufactured predominantly in right inclined assembly systems if a high utilization should be reached. On the contrary, a low utilization could be expected in the case of a production of this left inclined product in a left inclined production system.
- influence
of CPY and SDD on GLT
In a second simulation serie, the influence of the job division on the several logistical key-data has been studied. The formulated hypothesis is Linear complex graphs reveal stronger logistical effects in unfavourable forms of job division than branched complex graphs.1 Using again methods of factorial experimental design a certain influence on the goal achievement for lead time degree GLT has been detected. By regression analysis the coherence could be described mathematically as GLT = 0.89. 0.85cpy. 0.76SDD (in%)
(6)
G. Ziilch et al./Int.
J Production
The coherence coefficient reached R2 = 0.65 at a significance level of a > 95%. In Fig. 7 this connection between GLT, CPY, and SDD is depicted. An interpretation of the diagram shown in Fig. 7 clarifies that there is a connection between the parallelity of a graph ~ represented by the parameter CPY ~ and the lead time, which is much stronger in assembly systems with a job division by quantity than in those having a job division by operation. This is going to be obvious by looking at the extreme points in this diagram which are marked as Pl-P4: the difference between GLT at the points Pl and P2 (assembly system with a complete job division by quantity) is larger than the difference between GLT at the points P3 and P4 (assembly system with a complete job division by operation). Therefore, the assumption formulated in hypothesis 2 can also be confirmed. In addition to the dependencies which were already described, some other dependencies could be detected. Most of them only caused smaller effects. Thus, they are not presented here in detail (see details, Braun, 1995, p. 148).
5. A method for determining
a suitable job division
To use several of the equations proved by the investigation and others being available in literature (see e.g. Beuche, 1981, p. 112; Matthte, 1974, p. 40) to determine the “optimum” kind of job division, an analytical approach has been developed. In principle, with this approach different goals - which sometimes might be contrary - could be taken into consideration. An example of such a kind of contradictory goals is the cost minimization because of short lead times versus the profit maximization because of a high utilization of the work places and machines within an assembly system (see Kahle, 1991, p. 58). The approach requires an analytical description of each of the goals that should be taken into consideration. For this, for each goal an equation must be available describing the dependency of the particular goal achievement and their influencing parameters. For universal description of the analytical approach depicted by the following equation, these goal achievements will be indicated by
Economics
51 (1997) 123-134
131
SGAi (single goal achievement of the goal i). Depending on the importance, each of the SGAi could be weighted by a factor wi. Afterwards, the total goal achievement TGA can be calculated by adding each weighted SGA, as follows: TGA = AN$owi
SGA,,
(7)
I where SGA, is the single goal achievement and TGA the total goal achievement.
of goal i,
In order to receive the optimum goal achievement, this equation has to be differentiated mathematically. Due to the fact that in most cases a multi-criterion and not a one-dimensional goal function might be on hand, the result of the differentiation will be a gradient vector. By equating the coordinates of this vector with zero, the optimal expression of the variable parameters ~ describing the production system in this case - can be calculated. In order to clarify this approach, a simplified example will be given. As described further up, one possible goal pursued by executing the planning of a production system could be to achieve lead times that are as short as possible. For the sub-step of the production planning, which is the determination of the job division, this goal can be described by the parameter goal achievement for lead time degree in dependency of the parameters CPY and SDD. Another goal, which has been exemplary derived by an investigation carried out in a company of the automotive branch, describes a connection between the frequency of the repetition of an operation and the time necessary to execute it (see Chaffin and Hancock, 1966; Braun, 1995, p. 160). In this connection, it could be observed that with a decreasing degree of repetition the required operation time is going to increase. This result is not in contradiction to the assumptions of the well-known systems of pre-determined times (SPT) like MTM, WF, or MOST. To be more precise, these SPT-rules are already taking this into consideration. For example, the time assigned to the identical motion “picking up an object and placing it on a table 20 cm away” (AAl) is different in MTM-UAS (Universal Analysing System) and in MTM-MSS (MTM for Single and Small Series). So UAS assumes an operation
G. Ziilch et al.jlnt. J. Production Economics 51 (1997) 123-134
132
GOD
100
GLT TGA
90
,’
,/’
,I
_/-
_/- _--
____---
___________--------
___-_____--__________. GOD
TGA
a
in % 80
-1
high reference
point
60 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
SDD --------
GOD
--------------.. GLT TGA Fig. 8. Visualization SDD.
of different goal functions
(goal achievement for operation time deviation) (goal achievement for lead time degree) (total goal achievement)
in dependence
of the standarized
of 20 TMU (1 TMU = 0.036 s) while MSS assumes 30 TMU. This increased operation time results from the fact that in production systems with a single and small series character the degree of repetition is lower than in production systems with high volume production. On closer examination of the repetition of operation, it could be noticed, that the degree of repetition is directly depending on the degree of job division (Braun, 1995, p. 163). While in production systems made out of 10 workplaces and having a complete job division by quantity, the DRE is e.g. 60 per hour, the same operation is going to be repeated in a production system with complete job division by operation only 10 times per hour. This clarifies that production systems with a SDD = 1 are optimal in the case of taking the time extending facts just described into consideration, while production systems with SDD z 0 would be optimal if short lead times are the only goal. But considering both opposing goals within an analytical approach, a ceratin kind of job division represented by SDD can be derived. The optimal solution is depicted in time
degree ofjob
division, and determination
of an optimal
Fig. 8 and can be calculated by differentiation of the equation describing TGA. This is feasible as the equations describing the analytical interrelationship between the planning goals, on the one hand, and the structure of the assembly system and assembly task, on the other, are based on regression models what means that they are continuous and differentiable. In this figure, it is obvious that the total goal achievement is optimal in the case of a production system with a standardized degree of job division close to 0.54. With this graphical representation, GOD (goal achievement for operation time deviation) has been weighted by 0.3 while GLT (goal achievement for lead time degree) has been weighted by 0.7.
6. Conclusion
and recomandation
This paper describes an analysis for the determination of job division. Basis is a parametric description of the main elements of the planning problem. In a second step, this approach has been
G. Ziilch et al
Fig. 9. Dynamic
Int. J. Productiotl
evaluation
transferred into a computer aided planning tool called RAMONA (computer-aided determination of the job division, see Ziilch et al., 1995). At present this CAP-system is being completed by a dynamic evaluation and improvement component. The aim is to anticipate the dynamic characteristics of the assembly system being planned. For this purpose, an interface to a standard simulation program has been developed, that generates a simulation model automatically. Depending on the values of the calculated key data, improvement hints are suggested or carried out automatically. By running this improvement process for several times within an open-loop (see Fig. 9) the planning results meet the goal system in a pre-eminent way.
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51 (1997) 123-134
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J. Production
DIN 69900, 1987. Netzplantechnik, Part 1 (German standard). Dittmayer, S., 1981. Arbeits- und Kapazitatsteilung in der Montage. IPA-IA0 Forschung und Praxis, vol. 55. Springer, Berlin. Eversheim, W., Witte, K.-W., Pfeflekoven, K.-H., 1981. Montage richtig planen VDI-Verlag, Dusseldorf. Fremerey, F., 1993. Erhiihung der Variantenflexibilitat in Mehrmodel]-Montagesystemen durch ein Verfahren der Leistungsabstimmung, IPA-IA0 Forschung und Praxis, vol. 173 Springer, Berlin. Graves, SC., 1993. Logistics of Production and Inventory Handbooks in operations research and management science, vol. 4) North-Holland, Amsterdam. Grobel, T., 1993. Analyse der Einfliisse auf die Aulbauorganisation von Produktionssystemen. Doctoral Thesis, University of Karlsruhe (ifab-Forschungsberichte aus dem Institut fur Arbeitswissenschaft und Betriebsorganisation der Universitat Karlsruhe, vol. 6) Grobel, T., 1994. Influences on the organizational structure of production systems In: G.E. Bradley, H.W. Hendrick (Eds.). Human Factors in Organizational Design and Management. North-Holland, Amsterdam, pp. 29-36. Griinwald, H., Striekwold, P.E.T., Weeda, P.J., 1989. A framework for quantitative comparison of production control concepts. Int. J. Prod. Res. 27(2), 281-292. Jackson, J.R., 1956. A computing procedure for a line balancing Problem. Mgmt. Sci. 2(2), 261-271. Kahle, E., 1991. Produktion, Oldenbourg, Munich (Oldenbourgs Studienlehrbiicher der Wirtschaftsund Sozialwissenschaften) Kohler, F., 1989. Montageplanerstellung mit Expertensystemen. Verlag TUV Rheinland, Koln. Matthte, R., 1974. Entwicklung eines EDV-orientierten Verfahrens zur Ermittlung der kostenoptimalen Arbeitsteilung in metallverarbeitenden Betrieben der Einzel- und Kleinserien-
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fertigung. Doctoral Thesis, University of Technology, Aixla-Chapelle. Neumann, K., 1975. Operations Research Verfahren: vol. 3, Graphentheorie, Netzplantechnik. Carl Hanser, Munich, Vienna. Philipoom, P.R., Markland, R.E., Fry, T.D., 1989. Sequencing rules, progress milestone and product structure in a multistage job shop. J. Oper. Mgmt. 8(3), 2099229. Prenting, T.O., Battaglin, R.M., 1964. Precedence diagram ~ a tool for analysis in assembly line balancing. J. Ind. Eng. 15(4), 208-213. REFA-Verband fur Arbeitsstudien und Betriebsorganisation (Ed.), 1990. Grundlagen der Arbeitsgestaltung, Hanser, Munich, Vienna. Ritzman, L.P., Krajewski, L.J., 1986. Comparison of material requirements planning and reorder point systems. In: H. Bekirioglu (Ed.), Computer Models for Production and Inventory Control. Society for Computer Simulation, La Jolla CA, 41-54. Thaler, K., 1993. Regelbasiertes Verfahren zur Montageablaufplanung in der Serienfertigung. Springer, Berlin. Thomopoulos, N.T., 1970. Mixed model line balancing with smoothed station assignments. Mgmt. Sci. 16(9), 593-603. Tonge, F.M., 1965. Assembly line balancing using probabilistic combinations of heuristics, Mgmt. Sci. 1 l(7), 727-735. VDI, 1989 Montage mit CIM meistert Modernisierungspotential. VDI-Nachrichten 43(4), 19. Zilch, G., Braun, W.J., 1995. Regelbasierte Strukturierung in der manuellen Montage. wt-Prod. Mgmt. 85(l), 4146. Ziilch, G., Grobel, T., 1993. Simulating alternative organizational structures of production systems. Prod. Planning and Control 4(2), 128-138. Ziilch, G., Braun, W.J., Schiller, E-F., 1995. Montageplanung. Arbeitsvorbereitung. 32(2), 131-135.
production kconomics
ELSEVIER
Int. .I. Production
Economics
51 (1997) 123-134
Analytical approach of determining job division in manual assembly systems Gert Zdch, {fab ~ Institute
Wolfgang
J. Braun, Emmerich
of Human and Industrial Engineering (Institut fir Arbeitswissenschaft KaiserstraJe
12. D-76128 Karlsruhe,
F. Schiller*
und Betriebsorganisation). Germany
University of Karlsruhe.
Abstract Requirements upon modern production systems have changed considerably. One of the main results of these changes is that organizational improvements have become more and more important. In contradiction to this, the available approaches to support adjusted design of production systems in an early planning stage - especially regarding manual assembly systems - are deficit. Particularly, the consideration of process organizational effects by determination of the job division fails because the planning knowledge is limited to rather vague hints than based on precise planning rules. An analytical approach for the determination of job division in assembly systems under different goals has been developed to overcome this weakness. Basis is a parametric description of the important factors of the planning problem. Set up on this, a simulation-based investigation has been carried out to detect dependencies between the goal system and the assembly tasks. The result is an analytical approach based on regression models to determine a suitable form of job division for a clear-cut assembly task. Keywords:
Analytical
1. Tendencies
approach;
Job division; CAP; Center of gravity of a graph; Simulation study
in production systems
Decreasing lifecycles of industrial products, appropriate consideration of customers wishes, increasing complexity of products and the number of variants coming along with high-quality standards are forcing the industry to accept short developing times for their products as well as for the corresponding production systems. Taking this and the fact of low-manufacturing penetration into account, the central point of all planning efforts
*Tel.: + 49 721 608 4250; fax: + 49 [email protected]. 0925-5273/97/$17.00 Copyright PII so925-5273(97)00075-3
0
721
694557;
e-mail:
should be in the field of assembly, in which almost 50% of all manufacturing costs accrue meanwhile (VDI, 1989, p. 19). For all this, requirements concerning planning accuracy and planning reliability are extremely high and pressed for time. Therefore, it is obvious that traditional, usually manual planning approaches do not achieve those goals. For that reason many analytical approaches and computer-aided planning tools in the field of assembly planning were developed in the last years. Examples are precedence diagram derivation (Ammer, 1984, p. 42), standard time fixing (Kohler, 1989, p. 81), line balancing programs (a comprehensive survey of line balancing approaches is given in Brybars, 1986), process order determination
1997 Elsevier Science B.V. All rights
reserved
124
G. Ziilch et al. ilnt. J. Pxxluction
(Thaler, 1993, p. 39) or computer-aided workplace design (Braun et al., 1996). The attention is set on supporting the planning engineer mainly in his routine work with a focus on single detail tasks in order to give him more scope for the creative aspects of the planning process. Typical problems within this creative planning process are, for example, the selection of a suitable flow principle, the rating of the degree of automation, the planning of the assembly system structure or the determination of the job division. Analytical approaches supporting this process are not known, so that the results of these planning steps are mainly depending on the knowledge, experience and intuition of the planning engineer.
2. Procedures for the design of assembly systems Besides the technical and ergonomical aspects, organizational questions in connection with the design of production systems are becoming more and more important. In contradiction to this, the developing of adjusted planning approaches and methods has not kept up sufficiently with these changes. Especially, the consideration of process organizational aspects within the early planning process in the form of an arithmetical approach turns out extremely difficult. The available planning knowledge in literature (e.g. Eversheim et al., 1981, p. 25; Bullinger, 1986, p. 139; REFA, 1990, p, 160) describes some hints rather than precise planning rules (Ziilch and Braun, 1995, p. 41). In addition to this, those hints mostly cover the extremes of a design parameter. In this context there are also only vague hints available for the two extremes of job division, namely job division by operations and by quantity. Information about the large number of intermediary forms cannot be found in literature. For example, more than 700 forms of mixed job divisions can be shaped within an assembly system built up of only 10 workplaces and one can suppose that they differ in meeting the planning goals, depending on the products or its variants that have to be assembled. The general job division problem now is to find the best suitable mixed form of job division.
Economics
51 (1997) 123-134
-
..,
<‘ij)- -(5&+2~-/
asse&bly operation -------assembly
Fig. 1. Precedence
diagram
,
task-
of an assembly
task.
To describe this problem formally, it is necessary to give a description of all necessary parameters of an assembly task. In connection with the job division problem, these parameters are the product with its respective variants, the production program and the technical assembly system itself. Industrial products are usually made up of several parts and sub-assemblies. Variants of these products are created by changing, adding or omitting single parts. The essential question in the case of assembly is the quality of the products rather than the (joining) relations among them, e.g. the sequence in which they have to be assembled or the kind of assembly operation. A common way to depict these relations is the use of the precedence diagram (see Fig. 1). The precedence diagram, developed by Prenting and Battaglin (1964) is a directed graph where the nodes represent the assembly operations, specified by the parts which have to be assembled and the kind of assembly operation (according to DIN 8593); the arches characterize the logical and technological constraints between them. Using the precedence diagram as a basis for the job division problem, it has to be built up for each product including its variants, which form together a product family. Traditional planning approaches confine to build up a precedence diagram for only one representative product of each product family, putting up the disadvantage that all the other variants cannot be taken into account in the planning process. A complex graph has been developed, to overcome this weakness. This graph is an extension of the precedence graph, representing all variants of a product family in a single graph which are similar enough. Similar in this context means that their precedence graphs contain similar assembly that means similar sub-structures sequences,
G. Ziilch et al. lint. J. Production
Economics
(sub-graph automorphisms) within the graphs (see Fig 2). As an extension of the approach introduced by Thomopoulos (1970) this similarity is described by parameters, allowing a comparison with the help of cluster analysis. Differences between the frequency of the assembly operations are considered by using an accumulated standard time, calculated out of
precedence variant A
diagram
automorphism
diagram
Fig. 2. Derivation
of a complex
by operations
graph
q
q quantity per period time per unit
t
+ short learning time
clrr + -
mixed _.. (i.e.)
by quantities
q
q
; L
Fig. 3. Capacity
fields of different
forms of job division
125
the standard time of each operation multiplied with the frequency of its appearance in the expected production program. The frequency of the appearance of each assembly operation depends, on the one hand, on the number of variants it has to be carried out in and, on the other hand, on how often these variants have to be assembled in total. Herewith, the frequency is determined by the production program of each product family, which states how many products of type, variant or version have to be produced. Describing the assembly system, one can concentrate on describing the essential parameters. In the case of the job division problem, these parameters are the capacity of the assembly system and the distribution of this capacity onto assembly operations. To describe this, the capacity field has been developed (Dittmayer, 1981, p. 37). This two-dimensional representation of the capacity requirements is characterized by time per unit necessary for the complete assembly task and the number of products to be assembled within a period, e.g. a shift. It follows from this that each rectangle
complex graph
precedence variant B
51 (1997) 123-134
flow principle low self responsability idle time lack of flexibility
+ full product responsability + good flexibility + individual performance - high educational requirements
t inclusive
corresponding
advantages
and disadvantages.
126
G. Zilch et al. 11~. J. Production
represents a workplace which has to fulfill a defined work content (see Fig. 3). Based on these considerations, it is desirable to find a parametric description of the job division problem in order to develop an analytical approach to solve it. A feasible approach for this is described in the following section.
3. Conception of a parametric description of products and production systems As set out in the last section, the tasks necessary to design production systems, above all the design of mainly manual assembly systems, can be classified by the two objects product and production. While the concentration of the tasks assigned to the object product is placed on the analysis of available input information, the emphasis of those assigned to the object production is placed mainly on the design. In order to describe these two objects exactly, a lot of data is required. As pointed out earlier, a usual kind of representation of a product is the precedence diagram. If there are only 40 production operations required to produce a product at least 79 data are necessary to describe this precedence diagram, 40 nodes and 39 precedence relations. In addition to characterize one single assembly operation, one date is not sufficient. At a minimum three data are required to describe the two parts or components that have to be connected and the kind of assembly task, like e.g. joining by splaying (see Braun, 1995, p. 53). On this assumption, the minimal number of data necessary to describe the precedence diagram increases to 159. Since a product usually exists of several variants, the number of required data increases again. In the case of 50 product variants, what certainly is not untypical for modern products, the number of required input data concerning the object product reaches a minimum of 7950. This example already clarifies, that because of the complexity of the description, the design of product systems cannot be done neither manually nor computer aided if each date and information should be taken into consideration. One possibility to solve this problem and to simplify the planning process is to compress these
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123-134
data by describing them with a limited number of parameters. In literature, several useful parameters for describing universal graphs are listed. Examples are the length (Ritzmann and Krajewski 1986, p. 51) or the breadth (Philipoom et al. Fry 1989, p. 215), the degree of interweaving (DIN 69900, Part 1, p. 4), the relative number of edges (Neumann 1975, p. 54), the complexity (Davis 1975, p. 136) as well as the degree of complexity (Griinwald et al., 1989, p. 288) the degree of parallelity and the degree of meshing (Grobel, 1994, p. 31). As a common feature, all these parameters are not suited to describe this special kind of a graph like the precedence diagram or the complex graph. This is due to the fact that all these parameters represent a kind of ratio of the number of nodes to the number of edges. Information concerning e.g. the position of nodes within a graph cannot be received. But exactly these informations are very important. For example, it can be supposed that in connection with a precedence diagram or a complex graph, where a lot of (parallel) nodes can be found, a high flexibility exists. This flexibility probably leads to a good solution for the line balancing problem. Appropriated algorithms to solve the line balancing problems have been developed e.g. by Jackson (1956), Arcus (1966) Dar-El (1973) or Tonge (1965). This demonstrates the fact that in each line balancing step more than one operation is available for assignment. On the contrary, there are often several possible operations with different operation times existing, which can be assigned to a certain station. In order to receive a more suitable description of the precedence diagram, a new parameter has been developed. It bases on the definition of the center of gravity of a plane surface, known from mechanics and is called center of gravity of a graph. In this context, it is supposed that the precedence diagram is a two-dimensional structure consisting of several plane surfaces in the form of nodes. Each plane surface is assigned the uniform area one, where the area of the edges is not considered. Due to the fact that the value of the center of gravity of a graph depends on the arrangement of the nodes, several rules for this arrangement have to be considered. For this, the nodes must be assigned to one field within a matrix. In this matrix, the lines represent
G. Zilch et al. lint. J. Production
levels and the columns represent ranks. Because of this, the matrix is called the level-rank-matrix. First of all, in the direction of the x-axis each node is assigned to the next higher rank of its direct predecessor with the highest rank. In y-direction each node is assigned to the lowest possible level within the corresponding rank. Therefore, in the case of 4 nodes within one rank, they have to be assigned to the levels 0, 1, 2, and 3. Taking these assumptions into account, the x-coordinate CPX and the y-coordinate CPY can be calculated with the help of the following formulas: Ca”“:-’ NON,a for LGR > 1, NON(LGR - 1) (I) 1 for LGR = 1,
!?
with a being the index for ranks, LGR the length of the graph and NON the number of nodes,
1gy-’
NON,b
CPY = ’ NON(BGR
- 1)
0
for
BGR > 1,
for
BGR = 1,
(2)
with b the index for levels, BGR the width of the graph. The range of value of CPX is the interval between 0 and 1. Graphs with CPX close to 0 are left inclined. This means that most of the nodes are on the left side of the graph. Correspondingly, graphs with CPX close to unity are right inclined. The
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51 (1997) 123-134
range of value of CPY is the interval between 0 and 0.5. With this, an increasing breadth of the graph leads to increasing CPY. Using both coordinates, a sufficient description of the structure of the product is available, which allows an interpretation of a graph, on the one hand, and a classification, on the other. The classification can be carried out in the sense of the right or left inclination of the graph using the coordinate CPX and in the sense of a constant or non-constant breadth of the graph using the coordinate CPY. In Fig. 4, the center of gravity of a graph is visualized as an example. In addition to the description of the object prodtact represented in the form of a precedence diagram or in the case of product variants in the form of a complex graph, a description of the object production is also required. For a visualization of this object, the cupucityjeld is something used in literature (Dittmayer, 1981, p. 37). In this diagram, the x-axis represents the operation time and the y-axis the number of units to be produced. To receive the capacity requirements of the production system, two lines have to be drawn in the diagram. One line is parallel to the x-axis and crosses the y-axis at the number of units that have to be produced in the planned production system. The other line is parallel to the y-axis and crosses the x-axis at the value of the expected operation time that probably would be necessary to produce the product (see Fig. 5). These lines and the two axis are the edges of a rectangle, which represents the capacity
center of gravity
length of the graph /_GR = 5
level 3
number of nodes NON= 11
level 2
width of the graph BGR=4
level 1
level 0 X
I
rank 0
rank 1
rank 2
Fig. 4. Precedence
rank 3
diagram
127
rank 4
and its center of gravity
center of gravity in x-direction CPX = 0.52 center of gravity in y-direction CPY = 0.30
G. Zilch et d/M.
J. Prvductim
Economics
Y
51 (IYY7) 123-134
capacity
graph
number of units
operation time standardized
’
degree of division:
center of gravity in x-direction: center of gravity in y-direction:
Fig. 5. Capacity
field and the capacity
requirements of the whole production system. The capacity stock of each of the required workplaces can also be characterized within the diagram in form of a rectangle. In this connection, it must be noted that the area of each of these rectangles is theoretically equal while the portion of the number of produced units as well as the portion of the operation time could be different from workplace to workplace. By varying these two quantities last mentioned, alternative kinds of job division can be generated. An existing parameter to describe these different kinds is the degree of division, which represents the average proportion ofjob dioision by quantity to job division by operutions (Dittmayer, 1981, p. 61). In order to adapt this parameter to the kind of parameters pointed out earlier, which have a range of value between 0 and 1, the degree of division has to be standardized. It can be calculated applying the following formula: SDD =
NWPNUW c OTW, TNU c=l
TOT NWP’
(3)
where c is the index for workplaces, NUW, the number of units at a workplace, NWP the number of workplaces, and OTW, the operation time at a workplace
graph
SDD = 0,41 CGX= 0,44 CGY = 0,33
and their describing
parameters.
The standardized degree ofjob division SDD converges to 0, if there are production systems with almost complete job divisions by operations, otherwise, in case of production systems with a division mainly by quantity, SDD converges to 1. In order to get another possible description of the form of job division, the capacity field must be interpreted as a graph. In this graph, each node is a workplace and the edges represent possibilities for the flow of material between two workplaces. Unlike the precedence diagram or the complex graph which are both AND-graphs - that means each node has to be passed ~ the capacity graph is an exclusive OR-graph. In this kind of graph, each node will be headed for only one successor, while the other nodes are not taken into consideration. This is in accordance with the fact that one single part can be assembled at one workplace only. Imitating the parameter center of gravity of a complex graph described in section 2, the center of gravity of’u capacity graph with its coordinates in x-axis CGX and in y-axis CGY has been developed. Especially, CGX points out, if there is a high parallelity of workplaces especially at the end of the production system - in this case, CGX is close to 1 - or vice versa, if the parallelity is more at the beginning of the production system. Then CGX is approximately 1.
G. Ziilch et al. /Int. .I Production
4. Relations
51 (lYY7) 123-134
129
city graph and particularly
between the describing parameters
In order to generate a concept that allows a determination of a suitable kind of job division, several simulation studies were carried out. These studies were carried out in order to detect dependencies between a complex graph, on the one hand, and a capacity graph, on the other, taking logistical key-data into consideration. In the field of logistics, in literature as well as in industrial practice the criteria lead time, due-date deviation, loading, and work in progress are often mentioned in the role of comparison or for the evaluation of production systems (Graves, 1993, p. 25). To raise the expressiveness of these criteria, Grobel (1993, p. 87) transformed them into logistical key-data, ranging from 100% to O%, where 100% is optimal. These key-data are e.g. the goal achievement for utilization GUT and goal achievement for lead time degree GLT. GLT describes the relation between total lead time TLT and total processing time TPT. As TPT is the minimal feasible lead time GLT is a measurement for the deviation of the actual lead time from this (theoretical) optimum. GLT=-
Economics
TPT TLT ’
the degree ofjob division. In order to achieve a better comparability of the simulation models and the belonging production systems, several characteristics have been fixed. Therefore, all generated precedence diagrams consist of 40 nodes, which is particularly typical for companies manufacturing products in serial production (Fremerey, 1993, p. 142). On the other hand, the capacity graph includes 10 nodes, which represents a production system with 10 workplaces. Altogether, the number of simulation experiments reached more than 900. The basis for each investigation, the results of which are founded on statistical interpretation, is a systematical procedure. Because of this, the statistical methods of experimental design has been used. The applied methods intends to define several hypothesis that should be proved first or disproved by the investigation. For the cause of the investigation presented in this paper, two hypothesis were formulated. The first hypothesis assumes a connection between the inclination of both graphs used in this paper, which are the complex graph of a product and the capacity graph of a production system. The formulation of the hypothesis is Left inclined complex
graphs reveal better logisti-
(4)
cal key-data in right inclined capacity graphs than opposite, and vice versa
where OCS is the worked off capacity stock, TCS the theoretically available capacity stock, and TPT the total processing time. In order to execute a simulation-based investigation with the goal to find possible dependencies, as mentioned above, several simulation studies were carried out using the simulation program FEMOS (simulation program for manufacturing and assembly processes, see Ziilch and Grobel 1993; Grobel, 1994, p. 32). The models necessary for simulation were generated with the program GAMMA (generator for production systems in manual assembly, see Braun, 1995, p. 120). This program is adjusted to FEMOS allowing to build up a complete model of a production system based on a parametrical description. The used parameters are the center of gravity of the complex graph as well as of the capa-
In order to confirm the assumption described by this hypothesis several simulation runs were carried out using first a 2” fractional factorial design. From this, the influencing factors CPX and CGX could be proved like assumed in the hypothesis. For these two factors a multi-level factorial design has been carried out in order to quantify their exact influence on the used logistical key-data. For the goal achievement for lead time degree GLT, no significant influence could be proved. On the other hand, a connection of the goal achievement for utilization GUT with the gravity centers CPX and CGX could be ascertained. The regression analysis resulted in the following function:
GUT== TCS ’
GUT
= 91+5CPX+7CGX
- 22CPX CGX
(in%). (5)
130
G. Ziilch et aLlInt. J. Production
Economics
51 (1997) 123-134
goal achievement for utlllzatlon (GUT II- %)
x-centerof gravity of a complex graph (CW
x-center of grawty of a capacity graph
left
(CGX)
Fig. 6. Result of the first part of the investigation
goal achievement for lead time degree (GLT in %)
- influence
of CPX and CGX on GUT.
80
andardized
y-center of gravity of a complex graph (CPY
0.5 rectangular
degree
0 by quantity
)
Fig. 7. Result of the second
part of the investigation
The calculated coherence coefficient was R2 = 0.75 at the significance level of CI> 95%, which indicates a high statistical significance. Fig. 6 clarifies the result of this first part of the investigation. From this figure, it is quite obvious that products having a lot of assembly operations which could be executed mainly at the beginning of the assembly process should be manufactured predominantly in right inclined assembly systems if a high utilization should be reached. On the contrary, a low utilization could be expected in the case of a production of this left inclined product in a left inclined production system.
- influence
of CPY and SDD on GLT
In a second simulation serie, the influence of the job division on the several logistical key-data has been studied. The formulated hypothesis is Linear complex graphs reveal stronger logistical effects in unfavourable forms of job division than branched complex graphs.1 Using again methods of factorial experimental design a certain influence on the goal achievement for lead time degree GLT has been detected. By regression analysis the coherence could be described mathematically as GLT = 0.89. 0.85cpy. 0.76SDD (in%)
(6)
G. Ziilch et al./Int.
J Production
The coherence coefficient reached R2 = 0.65 at a significance level of a > 95%. In Fig. 7 this connection between GLT, CPY, and SDD is depicted. An interpretation of the diagram shown in Fig. 7 clarifies that there is a connection between the parallelity of a graph ~ represented by the parameter CPY ~ and the lead time, which is much stronger in assembly systems with a job division by quantity than in those having a job division by operation. This is going to be obvious by looking at the extreme points in this diagram which are marked as Pl-P4: the difference between GLT at the points Pl and P2 (assembly system with a complete job division by quantity) is larger than the difference between GLT at the points P3 and P4 (assembly system with a complete job division by operation). Therefore, the assumption formulated in hypothesis 2 can also be confirmed. In addition to the dependencies which were already described, some other dependencies could be detected. Most of them only caused smaller effects. Thus, they are not presented here in detail (see details, Braun, 1995, p. 148).
5. A method for determining
a suitable job division
To use several of the equations proved by the investigation and others being available in literature (see e.g. Beuche, 1981, p. 112; Matthte, 1974, p. 40) to determine the “optimum” kind of job division, an analytical approach has been developed. In principle, with this approach different goals - which sometimes might be contrary - could be taken into consideration. An example of such a kind of contradictory goals is the cost minimization because of short lead times versus the profit maximization because of a high utilization of the work places and machines within an assembly system (see Kahle, 1991, p. 58). The approach requires an analytical description of each of the goals that should be taken into consideration. For this, for each goal an equation must be available describing the dependency of the particular goal achievement and their influencing parameters. For universal description of the analytical approach depicted by the following equation, these goal achievements will be indicated by
Economics
51 (1997) 123-134
131
SGAi (single goal achievement of the goal i). Depending on the importance, each of the SGAi could be weighted by a factor wi. Afterwards, the total goal achievement TGA can be calculated by adding each weighted SGA, as follows: TGA = AN$owi
SGA,,
(7)
I where SGA, is the single goal achievement and TGA the total goal achievement.
of goal i,
In order to receive the optimum goal achievement, this equation has to be differentiated mathematically. Due to the fact that in most cases a multi-criterion and not a one-dimensional goal function might be on hand, the result of the differentiation will be a gradient vector. By equating the coordinates of this vector with zero, the optimal expression of the variable parameters ~ describing the production system in this case - can be calculated. In order to clarify this approach, a simplified example will be given. As described further up, one possible goal pursued by executing the planning of a production system could be to achieve lead times that are as short as possible. For the sub-step of the production planning, which is the determination of the job division, this goal can be described by the parameter goal achievement for lead time degree in dependency of the parameters CPY and SDD. Another goal, which has been exemplary derived by an investigation carried out in a company of the automotive branch, describes a connection between the frequency of the repetition of an operation and the time necessary to execute it (see Chaffin and Hancock, 1966; Braun, 1995, p. 160). In this connection, it could be observed that with a decreasing degree of repetition the required operation time is going to increase. This result is not in contradiction to the assumptions of the well-known systems of pre-determined times (SPT) like MTM, WF, or MOST. To be more precise, these SPT-rules are already taking this into consideration. For example, the time assigned to the identical motion “picking up an object and placing it on a table 20 cm away” (AAl) is different in MTM-UAS (Universal Analysing System) and in MTM-MSS (MTM for Single and Small Series). So UAS assumes an operation
G. Ziilch et al.jlnt. J. Production Economics 51 (1997) 123-134
132
GOD
100
GLT TGA
90
,’
,/’
,I
_/-
_/- _--
____---
___________--------
___-_____--__________. GOD
TGA
a
in % 80
-1
high reference
point
60 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
SDD --------
GOD
--------------.. GLT TGA Fig. 8. Visualization SDD.
of different goal functions
(goal achievement for operation time deviation) (goal achievement for lead time degree) (total goal achievement)
in dependence
of the standarized
of 20 TMU (1 TMU = 0.036 s) while MSS assumes 30 TMU. This increased operation time results from the fact that in production systems with a single and small series character the degree of repetition is lower than in production systems with high volume production. On closer examination of the repetition of operation, it could be noticed, that the degree of repetition is directly depending on the degree of job division (Braun, 1995, p. 163). While in production systems made out of 10 workplaces and having a complete job division by quantity, the DRE is e.g. 60 per hour, the same operation is going to be repeated in a production system with complete job division by operation only 10 times per hour. This clarifies that production systems with a SDD = 1 are optimal in the case of taking the time extending facts just described into consideration, while production systems with SDD z 0 would be optimal if short lead times are the only goal. But considering both opposing goals within an analytical approach, a ceratin kind of job division represented by SDD can be derived. The optimal solution is depicted in time
degree ofjob
division, and determination
of an optimal
Fig. 8 and can be calculated by differentiation of the equation describing TGA. This is feasible as the equations describing the analytical interrelationship between the planning goals, on the one hand, and the structure of the assembly system and assembly task, on the other, are based on regression models what means that they are continuous and differentiable. In this figure, it is obvious that the total goal achievement is optimal in the case of a production system with a standardized degree of job division close to 0.54. With this graphical representation, GOD (goal achievement for operation time deviation) has been weighted by 0.3 while GLT (goal achievement for lead time degree) has been weighted by 0.7.
6. Conclusion
and recomandation
This paper describes an analysis for the determination of job division. Basis is a parametric description of the main elements of the planning problem. In a second step, this approach has been
G. Ziilch et al
Fig. 9. Dynamic
Int. J. Productiotl
evaluation
transferred into a computer aided planning tool called RAMONA (computer-aided determination of the job division, see Ziilch et al., 1995). At present this CAP-system is being completed by a dynamic evaluation and improvement component. The aim is to anticipate the dynamic characteristics of the assembly system being planned. For this purpose, an interface to a standard simulation program has been developed, that generates a simulation model automatically. Depending on the values of the calculated key data, improvement hints are suggested or carried out automatically. By running this improvement process for several times within an open-loop (see Fig. 9) the planning results meet the goal system in a pre-eminent way.
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