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Indicators for measuring performances of morphology and material handling systems in flexible manufacturing systems
Int. J. Production Economics 64 (2000) 209}218
Indicators for measuring performances of morphology and material handling systems in #exible manufacturing systems Olivier Devise*, Henri Pierreval E! quipe de Recherche en Syste% me de Production de l'IFMA, Laboratoire d'Informatique de Mode& lisation et d'Optimisation des Syste% mes, Institut Franc7 ais de Me& canique Avance& e, Campus des Ce& zeaux, B.P. 265, F-63175 Aubie% re Cedex, France
Abstract The aim of this paper is to present some existing and several new indicators of performances useful to help the designer to "nd a good solution for morphology and choice of material handling systems in #exible manufacturing systems. Our purpose here is to focus on the evaluation of the pair morphology}material handling systems, studied concurrently due to their strong interdependence. As a result of a survey of literature in this area, we present in this paper the indicators we have retained as suited to this purpose and easily implemented. New indicators related to the performances of these systems, such as the #exibility, are also suggested. A classi"cation of indicators is introduced: (1) the operational indicators, which characterise the dynamic behaviour of the studied FMS such as the mean #ow-time of jobs or the utilisation rates of machines; (2) the strategic indicators which measure the capacity of the system to evolve toward manufacturing new products such as the #exibility on which the emphasis is put; (3) the economic indicators such as the purchasing cost, the functioning cost or the maintenance cost. To better introduce the role, the usefulness of each indicator and their practical use, an illustrative example is presented. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Material handling systems; Morphologies; Performance indicators; Flexible manufacturing systems
1. Introduction Nowadays manufacturing systems have become more and more complex. The design or the reorganisation of manufacturing systems is a very di$cult activity. That is why it is essential that decision makers possess decision tools and assistances necessary to manage this activity. For these reasons, we are interested in the evaluation of the performances of physical part of the #exible manufactur-
* Corresponding author. Tel.: #33-473-288-101; fax: #33473-288-100. E-mail address: [email protected] (O. Devise)
ing system (FMS). It is widely known that the material handling systems (MHSs) now represent a major part of the total manufacturing cost [1}3]. This fact highlights the necessity to choose adequately the MHSs when a manufacturing system is designed. Indeed this choice greatly a!ects the performances and is complex for several reasons [4,5]. Firstly, there are considerable interactions between machines and MHSs; secondly the workshop morphology exerts a major in#uence over it [6]; thirdly many various MHSs are available. The design of an FMS is also a very di$cult activity because existing methods only evaluate speci"c aspects of the solutions proposed by designers [7]. In order to help the designer and/or the decision
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makers in their work, it would be very useful to have indicators which could measure the performance of the various solutions. A few useful indicators have been suggested in the literature related to FMS design [8}11]. Our purpose here is to focus on the evaluation of the morphology and the MHS, studied concurrently due to their strong interdependence. As a result of a survey of literature in this area, we present in this paper the indicators we have retained as suited to this purpose and easily implemented. New indicators related to the performances of these systems, such as the #exibility, are also suggested. This paper is organised as follows. First, the main features of morphology and MHSs are introduced. The choice of MHSs and the interactions between the morphology and the MHSs are pointed out. Then, we use the classi"cation proposed by [12] to describe in detail each new indicator that we propose. To better explain the bene"ts of indicators, we present a simple application example, in which the application of each indicator allows its role and its usefulness to be more precisely understood.
2. MHSs and morphology evaluation in FMS An FMS can be de"ned as basically a production facility consisting of a number of #exible machines or workstations connected by an automated material handling system, all under the control of one or more computers [13]. The related papers show that the design of a workshop is based on the choice of machines, control systems, MHS and morphology, on which emphasis is put in the following. 2.1. Morphology The morphology of a workshop, a cell or an FMS is de"ned by the forms and the main structure of the workshop relative to the machines and the MHS [14]. Some authors [15,16] have proposed a classi"cation of the various morphologies (see Fig. 1): In related works, others kinds of morphologies may be found such as T, X, H or L form. Each
Fig. 1. Most common morphologies of a workshop.
morphology possesses its advantages and disadvantages, which are summarised in Table 1. The various criteria introduced in Table 1 are useful to choose the morphology. Among the main factors to take into account, in addition to #ow and production analysis [17], we "nd the number of machines, the bulkiness (i.e. number of machines in the volume hull), the management of MHSs (e.g. control and scheduling of automatic guided vehicles) and the number of operators. The most important of them is probably the bulkiness which represents a strong constraint, that has to be satis"ed. 2.2. Choice of the MHS The MHSs represent a key issue in the design of FMS. In several works related to the FMS design, a special attention has been given to the selection and optimisation of a kind of MHSs. Unfortunately, these works do not take into account the morphology while in fact, the contribution of MHSs to the FMS functioning is very important. Tompkins and White [3] argue that the MHSs cannot be neglected since their costs represent between 10% and 80% of the total production cost. The choice of MHSs is crucial for many reasons, such as its impact on the number of job in-process (queue lengths), the utilisation rate of machines, the makespan, etc. Unfortunately, this choice is very di$cult because MHSs cover a wide area including many possible technological solutions, from workers to
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
211
Table 1 Advantages and disadvantages of some morphologies Morphologies
Advantages
Disadvantages
Single circular line
The machines are closed Input and output are closed Facility access for operators Facility of implementation Facility of MHS management The machines are closed Input and output are closed Limited bulkiness The machines are closed Facility of MHS management Limited bulkiness Input and output may be closed Facility of MHS management Access facility for operators The machines are closed Many machines
Few machines Bulky
Single straight line Single line in U form
In S form
Ring
Multilines
rolled-bridges and automatic guided vehicles (AGVs). Furthermore, these systems possess many di!erent functions: some are used for stocking, other for transferring, etc. But Chu et al. [18] distinguish four main functions in the MHS: transfer, stocking, positioning and lot formation. The complexity of MHSs has led several authors to classify the existing systems [15,18,19]. Several research works [18,20}22] have proposed various solutions based on knowledge based systems, to provide assistance in the choice of MHS. Their systems use the following data: f f f f f
the the the the the
weight and the dimensions of parts, number of parts, number of machines and workstations, distance of transfer, dimension of transfer (2D, 3D, etc.).
Several other criteria can be used. They depend on each application and are often speci"c to a class of MHS. They can be found in [20]. 2.3. Interaction between the morphology and the MHS As reported in several research works [16,17,23}26], the morphology and the MHS are
Removal of input and output Long transfer for parts and operators Di$cult access for operators
The access to machines is di$cult
Bulky Few machines Bulky Complexity of MHS management Motions of operators are not easy
strongly linked. Thus, the interaction between the choice of a morphology and an MHS is an important additional di$culty for the designer. Indeed, it seems clear that in the case of a single straight line morphology the choice of a robot is not a good idea, but in the case of a single line in U form a robot could be useful. Moreover, between two closed organisations, such as a ring with a bi-directional AGV and a line with a bi-directional shuttle, the choice of the designer is not easy. Due to these di$culties, a designer should be very interested in indicators which would provide him/her some information on the dynamic behaviour of the system, its #exibility, its functioning cost, etc. These indicators would help him/her with the evaluation of the ability of the system to ful"l the requirements and the evaluation of its performance.
3. Indicators In this section a special attention is given to indicators related to the physical part of an FMS. The emphasis is put on the indicators which give an evaluation of the pair morphology}MHSs. These indicators have been classi"ed into three classes [12,27]:
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f Operational indicators: they generally come from simulation results and characterise the dynamic behaviour of the system studied. f Strategic indicators: they measure the capacity of the system to evolve toward manufacturing new products. The main indicator of this class is the #exibility indicator. f Economic indicators: these indicators include such factors as the purchasing cost, the functioning cost, the maintenance cost, the depreciation cost, etc., of the pair morphology}MHS.
3.1. Indicators for operational data Simulation is a technique widely used to obtain reliable data about the dynamic behaviour of an FMS, and especially about the pair morphology} MHS. Simulation provides many measures that represent useful indicators about the system performances [8,28}34]. These indicators can be classi"ed into two groups. They include but are not limited to: f indicators that measure global performances and are related to the workshop, such as the mean #ow-time of jobs, the mean number of jobs inprocess, etc.; f indicators measuring local performances and which are related to a machine, bu!er, a particular cell, such as the maximum queue length, the utilisation rate of machines, of workstations or of material handling equipment, etc.; Mellichamp et al. [13] argue that some indicators are more important than others. Some constraints on the FMS have to be ful"lled, such as the number of parts to be manufactured in a given time. The goal is to satisfy these constraints and to keep a good level of satisfaction for others. For example, a "rm must be able to respond to market needs: the number of parts and/or lots of parts processed during a simulation have to be greater than the real forecasts of the production volume. The other indicators allow the designer to distinguish between the various possible solutions.
3.2. Indicators for strategic data The main indicator of this class is related to the #exibility of the system. The #exibility of the pair morphology}MHS contributes to the agility of a "rm, since the agility is the ability of a producer of goods or services to thrive in the face of continuous change [35,36]. More precisely, we focus on the evaluation of the capacity of pairs morphology} MHS to adapt quickly to the introduction of new products, to machines or MHSs breakdowns or to #uctuation in the production volume. The introduction of a new product means a new process-plan and maybe new transfers. An occurrence of breakdowns on a machine or on an MHS means a modi"cation of process-plans and the introduction of new transfers too [37]. An increase in production volume may cause the appearance of alternative or multiple process-plans and new transfers. It appears that the #exibility implies to be able to o!er various possibilities for the part transfer [38]. Thus, it seems clear that the measure of the adaptability to new #ow-path is relative to #exibility of the pair morphology}MHS. Chattergee et al. [39] have de"ned an indicator related to the #exibility of material handling equipment. Unfortunately, they take into account only the distances of transfer carried out by each MHS and not the morphology. It appears more interesting to evaluate the transfer time between machines. Thus, we propose the following indicators. Let us de"ne t which represents the transfer i,j time from workstation i to workstation j (the shortest time if several paths exist). The value R means that no transfer is possible from i to j. If i"j, then t "0. If M is the set of machines, t may be i,j i,j described by M]MPR ,
(1)
f : (M , M ) C t . i j i,j
(2)
A transportation matrix T is used to describe the transfer time between machines or workstations. The elements of T are t . Then we obtain the i,j following matrix (see Eq. (3)) if N is the number of M
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
machines: 0
2
F
t
1,j F
2 t 2
}
t i,j F
2
0
2
F
F
}
2
}
1,i F
t i,1 T" F
2
0
2
F
F
t j,1 F
2
j,i F
F
t
F
t
F
1,NM F
t
F
2 t M 2 t M 2 t M N ,i N ,j N ,1
t
i,NM F .
j,NM F 0 (3)
We call N the number of elements of T which %9*45 are di!erent from R and we denote by N the .!9 number of elements of T, minus its diagonal: N "cardM(M , M )3M]M Dt ORand iOjN, i,j %9*45 i j (4) N "cardM(M , M )3M]M DiOjN"N .(N !1). M M .!9 i j (5) First it is interesting to compute the rate R be53!/4&%3 tween the number of existing paths N and the %9*45 maximum number of paths N in a system with .!9 N machines: M N R " %9*45 , (6) 53!/4&%3 N .!9 R 53!/4&%3 cardM(M , M )3M]M Dt OR and iOjN i,j i j . " N .(N !1) M M (7) This indicator measures the ability of the system to o!er a path for carrying out a transfer between two machines: with this point of view, a great di!erence exists between a unidirectional MHS such as a conveyor and a bi-directional AGV. Then, the closer the R rate is to 1, the more the studied system 53!/4&%3 will provide various paths to carry out new #ows. The system (the pair morphology}MHS) must not only o!er new possible paths between two machines, but also o!er an e$cient path. Let us compute the average transfer time between machines. This indicator allows the quickness of the studied pair morphology}MHS to be evaluated. The quickness of a transfer is important since there is often no
213
added-value on the transported product during its transfer. A longer transfer time means a more important delay. Consequently the transfer must be fast with a low cost. Eq. (8) measures the average quickness ¹ of a pair morphology}MHS: !7%3!'% 1 ¹ " t . (8) + !7%3!'% N i,j %9*45 iEj (Mi , Mj)|G If the purpose of each workstation is taken into account, we can propose a more accurate indicator. For example, in the mechanical manufacturing area, some transfers will not occur. Usually no part will require a transfer from a "nishing machine to a roughing machine. Thus, let us de"ne a restriction G of M]M which describes only the future interesting paths from a machine i to another j. Let us de"ne N and N as follows: 3%!*/5%3%45*/' N "cardM(M , M )3GDt OR and iOjN, (9) 3%!i j i,j N "cardM(M , M )3GDiOjN. (10) */5%3%45*/' i j Now we can introduce (Eqs. (12) and (13)) to our two "nal indicators, the indicator of #exibility I and the indicator of quickness I : F-%9*"*-*5: Q6*#,/%44 N 3%!- , I " (11) F-%9*"*-*5: N */5%3%45*/' cardM(M , M )3GDt OR and iOjN i,j i j , I " F-%9*"*-*5: cardM(M , M )3GDiOjN i j (12) 1 " Q6*#,/%44 N */5%3%45*/'
t . (13) + i,j iEj (Mi , Mj)|G These two strategic indicators appear to be very useful, but the economical dimension has also to be taken into account. This is the aim of the following section.
I
3.3. Indicators for economical data There are varied data for the "nancial cost. First, the initial investment I has to be taken into */*5 account. Then the following constraint (see Eq. (14)) must be satis"ed: I
NM NC NMHS * + C i# + C j# + C k , */*5 M C MHS i/1 j/1 k/1
(14)
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O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
where N is the number of machines or workstaM tions, N the number of control systems, N the C MHS number of material handling systems, C i the cost M of machine i, C j the cost of control system j, and C C k the cost of material handling system k. MHS The morphology cost C may be approxi.031)0-0': mated by the area occupied by the system. Thus, this area depends on the chosen morphology. If C is the cost of 1 m2 of the workshop and !3%! S is the surface occupied by the system: .031)0-0': C "S C . (15) .031)0-0': .031)0-0': !3%! The cost of an MHS has been studied in [4,40,41]. These authors propose a method to compute the cost per hour of a material handling system. We suggest to extend their work in order to take into account the cost per hour of machines and workstations as follows: (F !d )(ADP, i , c )#n k 0 k k, U" k k H
(16)
where F the cost of the system (MHS or machines), k d the cost of resale, ADP, i , c "((1#i )ck~1/ k 0 k 0 i (1#i )ck), i the annual interest rate, c the life0 0 0 k time of system, n the cost of the maintenance unit, k and H the number of working hours per year. We now de"ne the cost by manufactured product unit C (see Eq. (17)). This cost is composed of the 6/*5 cost of the morphology C , the cost per .031)0-0': hour of each piece of material handling equipment
multiplied by its utilisation duration and the cost per hour of each machines multiplied by its period of utilisation. Then, we obtain the following cost: +NMHS U t #+NM U i t i#C .031)0-0': , i/1 M M C " k/1 MHSk MHSk 6/*5 N 1!35 (17) where C is the cost of the morphology, .031)0-0': U k the cost per hour of the MHS number k, U i the MHS M cost per hour of the machine number i, t k MHS the period of utilisation of MHS number k, t i the M period of utilisation of machine number i, N the MHS number of MHS, N the number of machines, M N the number of produced parts. Certain data 1!35 such as N , t i or t k may be obtained from 1!35 M MHS simulation results.
4. Illustrative example In this section, we will illustrate the various indicators that we have de"ned. As shown in Fig. 2, three di!erent solutions with six machines and only one piece of material handling equipment are compared. All these simple solutions allow the bene"ts of the di!erent indicators to be illustrated. We assume that machine numbers 1 and 2 are roughing machines, numbers 3, 4 and 5 are xnishing machines, and number 6 is a super xnishing machine.
Fig. 2. The three cases to study.
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
4.1. Description of the three cases The three di!erent solutions are f Example 1 is a single circular line. The MHS is an AGV with a capacity of 1 palette of 100 parts. The load/unload systems of the six machines are automatic. Their duration follows a triangular distribution (minutes: 0.1 minutes, mode: 0.3 minutes, max.: 0.5 minutes). The queues in the front of each station have a capacity of two palettes. The mean transfer times from the input to the machines 1 or 6 are 6 seconds. The mean transfer times between machines 1 and 6 and the output are the same (the standard deviation is 10%). The mean transfer times between machines for example 1 are given below (in seconds). The durations are normally distributed with a standard deviation of 10%:
C
D
0 10
10 0
20 10
30 20
20 30
10 20
20 T " 30 1 20
10 20 30
0 10 20
10 0 10
20 10 0
30 . 20 10
10
20
30
20
10
0
f Example 2 is a single straight line. Its MHS is a bi-directional shuttle operating on a railtrack. Its capacity is 1 palette of 100 parts. The load/unload systems are the same as in example 1. The input and output are separated and are opposite, respectively, to machines 3 and 4. The means transfer times between machines in example 2 are given below (in seconds). The durations follow normal distribution with a standard deviation of 10%:
C
D
0 10
10 0
20 10
30 20
40 30
50 40
20 T " 30 2 40
10 20 30
0 10 20
10 0 10
20 10 0
30 . 20 10
50
40
30
20
10
0
f Example 3 is a single straight-line morphology with a belt conveyor without accumulation. The
215
palettes have a capacity of only 25 parts. The load/unload system is the same as for examples 1 and 2, but it is three times faster. The conveyor may be loaded in input with one palette every 2 seconds (maximum). f The mean transfer times between machines for example 3 are given below (in seconds). The durations are normally distributed with a standard deviation of 10%:
C
0 R
3 0
6 3
9 6
12 9
15 12
R T " R 3 R
R R R
0 R R
3 0 R
6 3 0
9 6 3
R
R
R
R
R
0
D
.
Machines are subjected to breakdowns. We assume that they are normally distributed. Their MTBF and MTTR are given in Table 2. 4.1.1. The production Three di!erent parts A, B and C are processed. The process-plans and the mean process times (in min) are given in Table 3 (standard deviations are 5%). The production is divided as follows: parts A 30%, parts B 35%, and parts C 35%. We will study the introduction of a new part D. The previous indicators will allow us to measure Table 2 Resources data Kind of resources
Number
MTBF MTTR (in days) (in hours)
Roughing NC 2-axis turning machine Roughing NC 3-axis milling machine Finishing NC 3-axis milling machine Finishing NC 3-axis turning machine Finishing NC 5-axis milling machine Super"nishing milling machine AGV Shuttle Conveyor
1
80
4
2
60
4
3
40
8
4
45
8
5
30
24
6 20 Example 1 20 Example 2 60 Example 3 70
8 1 2 2
216
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
Table 3 Process plans and process times of parts A, B, C and D
Table 4 Utilisation rates of each equipment
Parts
Machines
Process times
Part A
Machine 1 Machine 4 Machine 6
2.50 3.00 6.00
Machine Solution 1 Solution 2 Solution 3 number Without With Without With Without With part D part D part D part D part D part D
Part B
Machine 2 Machine 3 Machine 5
2.40 3.00 2.00
Part C
Machine Machine Machine Machine
1 4 5 6
1.80 2.40 1.40 3.00
Part D
Machine Machine Machine Machine
2 1 4 6
2.50 1.50 3.20 1.60
the sensitivity of the workshop to the introduction of this new product. With part D, the production is divided as follows: parts A 30%, parts B 25%, parts C 35% and parts D 10%. In case 3, the mean transfer time of a palette of 25 parts of D type from machine 2 to machine 1 takes 3 minutes with a standard deviation of 1 minute. This full manual operation requires an operator. 4.2. Results The simulation model has been developed with ARENA. Due to the random variable used in the model, 15 long replications have been performed. Statistics related to the initial period of each run have been truncated in order to reduce the initial bias. 4.2.1. Operational indicators The simulation experiments provide the estimated utilisation rates of each equipment. These results are given in Table 4. These estimated utilisation rates depend on the capacity of each material handling equipment and on the morphology. In fact, Table 4 shows that the introduction of the new part D causes a major perturbation on each system. Example 3 (with the conveyor) is the most sensitive and perturbed: the machines 1, 2 and 4 have an utilisation rate too high, whereas machines 3, 5 and 6 are insu$ciently supplied.
1 2 3 4 5 6
0.87 0.35 0.47 0.86 0.58 0.86
0.87 0.96 0.33 0.85 0.27 0.89
0.87 0.48 0.60 0.83 0.65 0.84
0.87 0.98 0.20 0.80 0.27 0.84
0.25 0.14 0.28 0.32 0.22 0.52
0.95 0.95 0.10 0.95 0.10 0.10
4.2.2. Indicators of yexibility and quickness The restriction G is given by the matrix R where the value 1 means that the pair (M , M ) is in G and i j 0 otherwise:
C
D
1 1
1 1
1 1
1 1
1 1
1 1
R" 0 0 0
0 0 0
1 1 1
1 1 1
1 1 1
1 . 1 1
0
0
0
0
0
1
The results for the various indicators are presented in Table 5. It seems clear that the solution number 3 is the fastest. Its average transfer time rises only at 2.3 seconds. However solutions number 1 and 2 are more #exible if the indicators I are conF-%9*"*-*5: sidered. This indicator is important in certain situations. For example, if machine 3 is a 2-axis turning machine and machine 4 is a 3-axis milling machine, solution 3 does not allow us to "nish a part "rst on the milling machine before performing the "nishing pass on the turning machines. This problem appears with the introduction of part D. This part will be able to be produced with solution 3 only if the process planning may be modi"ed in such a manner that the turning pass is made before the milling pass. Otherwise, a manual transfer will occur. 4.2.3. Financial cost The cost per hour of each machine is given in Table 6 below. For each solution, the period of utilisation of machine number i is the same.
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218 Table 5 Results for each solution R Solution 1 Solution 2 Solution 3
53!/4&%3
1.00 1.00 0.50
Table 7 Cost and time of each solution U
¹ !7%3!'%
I F-%9*"*-*5:
I Q6*#,/%44
Kind of solution
3.60 4.60 2.30
1.00 1.00 0.79
3.60 4.20 2.30
Solution 1: bi-directional AGV 2.50 Solution 2: bi-directional 2.90 shuttle Solution 3: unidirectional 1.20 conveyor
Table 6 Cost and time of utilisation of each machine Machine 1 number
2
3
4
5
6
U i M ¹ i M
0.80 0.45
1.00 0.35
1.10 0.80
1.00 0.80
2.20 0.40
0.70 0.40
217
The period of utilisation of the material handling equipment may be quite di!erent as it is shown in Table 6. We obtain the following results: no one solution is clearly the best. Taking the global context into account is necessary before making a "nal decision. In Table 7, it seems clear that the last solution is the best from a "nancial point of view. The designer will have to choose between a more #exible solution (solution number 1) and a more economical solution with solution 3. He/she will be guided by the context of his study.
5. Conclusion The purpose of this paper was to focus on the evaluation of morphology and MHS, studied together due to their strong interdependence. As the result of a survey of the literature related to FMS design, we have presented the indicators suited to this purpose. New indicators have also been suggested, especially to evaluate the #exibility, the quickness and the economical cost of the pair morphology}material handling systems. We have described them in detail and given an illustrative example of their practical use. Indicators represent a major issue in the evaluation of the performance of morphology and material handling systems in #exible manufacturing
MHS
¹ C C MHS .031)0-0': 6/*5 2.40 2.90
0.28 0.50
9.83 12.46
1.30
0.35
5.46
system. Indicators evaluating the pair morphology} material handling systems may be either directly used by decision makers or incorporated in decision support systems. We are now interested in improving these indicators and in designing new ones to evaluate others additional aspects. References [1] R. De Guio, M. Barth, About performance evaluation in production #ow analysis, International Journal of Production Research 35 (1997) 83}99. [2] K.H. Kim, J.M.A. Tanchoco, Economical design of material #ow path, International Journal of Production Research 31 (6) (1993) 1387}1408. [3] J.A. Tompkins, J.A. White, Facilities Planning, Wiley, New York, 1984. [4] T. Hamann, Le proble`me d'agencement des ressources a` l'inteH rieur des cellules des syste`mes de production, Ph.D. Thesis, INRIA Lorraine, 1992. [5] D. Riopel, Conception d'atelier automatiseH #exible de sous-traitance: Fonction manutention et entreposage, Ph.D. Thesis, ED cole Centrale de Paris, 1989. [6] B. Montreuil, A modelling framework for integrating layout design and #ow network design, Progress in Material Handling and Logistics 2 (1991) 95}115. [7] L. Gelders, P. Mannaerts, J. Maes, Manufacturing strategy, performance indicators and improvement programmes, International Journal of Production Research 32 (4) (1994) 797}805. [8] A. Arbel, A. Seidmann, Performance evaluation of #exible manufacturing systems, IEEE Transactions on Manufacturing Systems 1 (1984) 118}129. [9] L. Berrah, A. Haurat, Une strateH gie de mise en place d'indicateurs de performance pour le pilotage des processus de production, in MOSIM'97, ModeH lisation et simulation des syste`mes de production et de logistique, Rouen, France, June 5}6, 1997, pp. 61}69. [10] L. Berrah, P. Miquet-Sage, A. Haurat, Un mode`le d'indicateur eH leH mentaire pour l'eH valuation de la performance dans les processus de production, in GI5 } IPI, Fifth International Congress of Industrial Engineering, Vol. 2, Grenoble, France, April 2}4, 1996, pp. 11}20.
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[11] N. Marcoux, D. Riopel, A. Langevin, Quel est le moment propice pour revoir une implantation, in: International Industrial Engineering Conference, Vol. 2, MontreH al, Canada, 1995, pp. 939}948. [12] M. Khalfoun, A. Gharbi, SeH lection d'une con"guration d'un FMS: Une approche multicrite`re, in: International Industrial Engineering Conference, Vol. 1, MontreH al, Canada, 1995, pp. 469}480. [13] J.M. Mellichamp, O.-J. Kwon, A.F.A. Wahab, FMS designer: An expert system for #exible manufacturing system design, International Journal of Production Research 28 (1990) 2013}2024. [14] D.R. Sule, Manufacturing Facilities, PWS-KENT Publishing Company, Boston, 1988 (Chapter 9). [15] T. Hamann, F. Vernadat, The intra-cell layout problem in automated manufacturing systems, chapter Advances in Factories of the Future, CIM and Robotics, Elsevier Science Publishers, Amsterdam, 1993. [16] M.M.D. Hassan, Machine layout problem in modern manufacturing facilities, International Journal of Production Research 23 (1994) 2559}2584. [17] S.S. Heragu, Recent models and technics for solving the layout problem, European Journal of Operational Research 57 (1992) 136}144. [18] H.-K. Chu, P.J. Egbelu, C.-T. Wu, ADVISOR: A computer-aided material handling equipment selection system, International Journal of Production Research 33 (12) (1995) 3311}3329. [19] O. Devise, Object-oriented modelling of material handling systems in FMS, Revue d'Automatique et de Productique AppliqueH e 8 (2}3) (1995) 479}484. [20] O. Devise, H. Pierreval, Modelling by KADS methodology of the choice of material handling systems in #exible manufacturing systems, in GI5}IPI, Fifth International Congress of Industrial Engineering, Vol. 2, Grenoble, France, 2}4 April, 1996, pp. 287}295. [21] R. Karni, J. Rubinivitz, A taxonomy for the materials handling and transfer environment, International Journal of Computer Integrated Manufacturing 8 (3) (1995) 177}188. [22] P.S. Welgama, P.R. Gibson, An integrated methodology for automating the determination of layout and material handling systems, International Journal of Production Research 34 (8) (1999) 2247}2264. [23] I.J. Chen, C.-H. Chung, An examination of #exibility measurements and performance of #exible manufacturing systems, International Journal of Production Research 34 (2) (1996) 379}394. [24] M.M.D. Hassan, G.L. Hogg, On constructing a block layout by graph theory, International Journal of Production Research 29 (1991) 1263}1278. [25] M.M.D. Hassan, G.L. Hogg, D.R. Smith, A construction algorithm for the selection and assignment of material handling equipment, International Journal of Production Research 23 (1985) 381}392.
[26] S.S. Heragu, A. Kusiak, Experimental analysis of simulated annealing based algorithms for the layout problem, European Journal of Operational Research 57 (1992) 190}202. [27] A. Gharbi, L. Villeneuve, Conception d'un FMS: Approche inteH greH e assisteH e par ordinateur, in GI5}IPI, Fifth International Congress of Industrial Engineering, Vol. 1, Grenoble, France, April 2}4, 1996. [28] C.N. Madu, N.C. Georgantzas, Strategic thrust of manufacturing automation decisions: a conceptual framework, IEEE Transaction (1991) 138}147. [29] B. Mahadevan, T.T. Narendran, Estimation of number of AGVs for an FMS: An analytical model, International Journal of Production Research 31 (7) (1993) 1655}1670. [30] S.U. Randhawa, D. Bedworth, Factors identi"ed for use in comparing convention and #exible manufacturing systems. Industrial Engineering, June 1985, pp. 40}44. [31] R. Suri, An overview of evaluative models for #exible manufacturing systems, Annals of Operations Research 3 (1985) 13}21. [32] J.W. Troxler, L. Blank, A comprehensive methodology for manufacturing system evaluation and comparison, Journal of Manufacturing Systems 8 (3) (1989) 175}183. [33] R.N. Wabalickis, Justi"cation of FMS with analytic hierarchy process, Journal of Manufacturing Systems 7 (3) (1988) 175}182. [34] S.F. Weber, A modi"ed analytic hierarchy process for automated manufacturing decisions, Interfaces 23 (4) (1993) 75}84. [35] R. De Vor, R. Graves, J. Mills, Agile manufacturing research: Accomplishments and opportunities, IIE Transactions 29 (1997) 813}823. [36] R. Quinn, G. Causey, F. Merat, D. Sargent, N. Barendt, W. Newman, V. Velasco Jr., A. Podgurski, J. Jo, L. Sterling, Y. Kim, An agile manufacturing workcell design, IIE Transactions 29 (1997) 901}909. [37] A.K. Sethi, S.P. Sethi, Flexibility in manufacturing: A survey, International Journal of Flexible Manufacturing Systems 2 (4) (1990) 289}328. [38] P.J. Egbelu, Flexible guidepath design for automated guided vehicle systems, International Journal of Production Research 33 (4) (1995) 1135}1168. [39] A. Chattergee, M. Cohen, W.L. Maxwell, A planning framework for #exible manufacturing systems, Technical Report, University of Pennsylvania, Philadelphia, PA, July 1987. [40] P.J. Egbelu, Concurrent speci"cation of unit load sizes and automated guided vehicle #eet size in manufacturing system, International Journal of Production Economics 29 (1993) 49}64. [41] P.J. Egbelu, Economic design of unit load-based FMSs employing AGVs for transport, International Journal of Production Research 31 (12) (1993) 2753}2776.
Indicators for measuring performances of morphology and material handling systems in #exible manufacturing systems Olivier Devise*, Henri Pierreval E! quipe de Recherche en Syste% me de Production de l'IFMA, Laboratoire d'Informatique de Mode& lisation et d'Optimisation des Syste% mes, Institut Franc7 ais de Me& canique Avance& e, Campus des Ce& zeaux, B.P. 265, F-63175 Aubie% re Cedex, France
Abstract The aim of this paper is to present some existing and several new indicators of performances useful to help the designer to "nd a good solution for morphology and choice of material handling systems in #exible manufacturing systems. Our purpose here is to focus on the evaluation of the pair morphology}material handling systems, studied concurrently due to their strong interdependence. As a result of a survey of literature in this area, we present in this paper the indicators we have retained as suited to this purpose and easily implemented. New indicators related to the performances of these systems, such as the #exibility, are also suggested. A classi"cation of indicators is introduced: (1) the operational indicators, which characterise the dynamic behaviour of the studied FMS such as the mean #ow-time of jobs or the utilisation rates of machines; (2) the strategic indicators which measure the capacity of the system to evolve toward manufacturing new products such as the #exibility on which the emphasis is put; (3) the economic indicators such as the purchasing cost, the functioning cost or the maintenance cost. To better introduce the role, the usefulness of each indicator and their practical use, an illustrative example is presented. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Material handling systems; Morphologies; Performance indicators; Flexible manufacturing systems
1. Introduction Nowadays manufacturing systems have become more and more complex. The design or the reorganisation of manufacturing systems is a very di$cult activity. That is why it is essential that decision makers possess decision tools and assistances necessary to manage this activity. For these reasons, we are interested in the evaluation of the performances of physical part of the #exible manufactur-
* Corresponding author. Tel.: #33-473-288-101; fax: #33473-288-100. E-mail address: [email protected] (O. Devise)
ing system (FMS). It is widely known that the material handling systems (MHSs) now represent a major part of the total manufacturing cost [1}3]. This fact highlights the necessity to choose adequately the MHSs when a manufacturing system is designed. Indeed this choice greatly a!ects the performances and is complex for several reasons [4,5]. Firstly, there are considerable interactions between machines and MHSs; secondly the workshop morphology exerts a major in#uence over it [6]; thirdly many various MHSs are available. The design of an FMS is also a very di$cult activity because existing methods only evaluate speci"c aspects of the solutions proposed by designers [7]. In order to help the designer and/or the decision
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makers in their work, it would be very useful to have indicators which could measure the performance of the various solutions. A few useful indicators have been suggested in the literature related to FMS design [8}11]. Our purpose here is to focus on the evaluation of the morphology and the MHS, studied concurrently due to their strong interdependence. As a result of a survey of literature in this area, we present in this paper the indicators we have retained as suited to this purpose and easily implemented. New indicators related to the performances of these systems, such as the #exibility, are also suggested. This paper is organised as follows. First, the main features of morphology and MHSs are introduced. The choice of MHSs and the interactions between the morphology and the MHSs are pointed out. Then, we use the classi"cation proposed by [12] to describe in detail each new indicator that we propose. To better explain the bene"ts of indicators, we present a simple application example, in which the application of each indicator allows its role and its usefulness to be more precisely understood.
2. MHSs and morphology evaluation in FMS An FMS can be de"ned as basically a production facility consisting of a number of #exible machines or workstations connected by an automated material handling system, all under the control of one or more computers [13]. The related papers show that the design of a workshop is based on the choice of machines, control systems, MHS and morphology, on which emphasis is put in the following. 2.1. Morphology The morphology of a workshop, a cell or an FMS is de"ned by the forms and the main structure of the workshop relative to the machines and the MHS [14]. Some authors [15,16] have proposed a classi"cation of the various morphologies (see Fig. 1): In related works, others kinds of morphologies may be found such as T, X, H or L form. Each
Fig. 1. Most common morphologies of a workshop.
morphology possesses its advantages and disadvantages, which are summarised in Table 1. The various criteria introduced in Table 1 are useful to choose the morphology. Among the main factors to take into account, in addition to #ow and production analysis [17], we "nd the number of machines, the bulkiness (i.e. number of machines in the volume hull), the management of MHSs (e.g. control and scheduling of automatic guided vehicles) and the number of operators. The most important of them is probably the bulkiness which represents a strong constraint, that has to be satis"ed. 2.2. Choice of the MHS The MHSs represent a key issue in the design of FMS. In several works related to the FMS design, a special attention has been given to the selection and optimisation of a kind of MHSs. Unfortunately, these works do not take into account the morphology while in fact, the contribution of MHSs to the FMS functioning is very important. Tompkins and White [3] argue that the MHSs cannot be neglected since their costs represent between 10% and 80% of the total production cost. The choice of MHSs is crucial for many reasons, such as its impact on the number of job in-process (queue lengths), the utilisation rate of machines, the makespan, etc. Unfortunately, this choice is very di$cult because MHSs cover a wide area including many possible technological solutions, from workers to
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211
Table 1 Advantages and disadvantages of some morphologies Morphologies
Advantages
Disadvantages
Single circular line
The machines are closed Input and output are closed Facility access for operators Facility of implementation Facility of MHS management The machines are closed Input and output are closed Limited bulkiness The machines are closed Facility of MHS management Limited bulkiness Input and output may be closed Facility of MHS management Access facility for operators The machines are closed Many machines
Few machines Bulky
Single straight line Single line in U form
In S form
Ring
Multilines
rolled-bridges and automatic guided vehicles (AGVs). Furthermore, these systems possess many di!erent functions: some are used for stocking, other for transferring, etc. But Chu et al. [18] distinguish four main functions in the MHS: transfer, stocking, positioning and lot formation. The complexity of MHSs has led several authors to classify the existing systems [15,18,19]. Several research works [18,20}22] have proposed various solutions based on knowledge based systems, to provide assistance in the choice of MHS. Their systems use the following data: f f f f f
the the the the the
weight and the dimensions of parts, number of parts, number of machines and workstations, distance of transfer, dimension of transfer (2D, 3D, etc.).
Several other criteria can be used. They depend on each application and are often speci"c to a class of MHS. They can be found in [20]. 2.3. Interaction between the morphology and the MHS As reported in several research works [16,17,23}26], the morphology and the MHS are
Removal of input and output Long transfer for parts and operators Di$cult access for operators
The access to machines is di$cult
Bulky Few machines Bulky Complexity of MHS management Motions of operators are not easy
strongly linked. Thus, the interaction between the choice of a morphology and an MHS is an important additional di$culty for the designer. Indeed, it seems clear that in the case of a single straight line morphology the choice of a robot is not a good idea, but in the case of a single line in U form a robot could be useful. Moreover, between two closed organisations, such as a ring with a bi-directional AGV and a line with a bi-directional shuttle, the choice of the designer is not easy. Due to these di$culties, a designer should be very interested in indicators which would provide him/her some information on the dynamic behaviour of the system, its #exibility, its functioning cost, etc. These indicators would help him/her with the evaluation of the ability of the system to ful"l the requirements and the evaluation of its performance.
3. Indicators In this section a special attention is given to indicators related to the physical part of an FMS. The emphasis is put on the indicators which give an evaluation of the pair morphology}MHSs. These indicators have been classi"ed into three classes [12,27]:
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f Operational indicators: they generally come from simulation results and characterise the dynamic behaviour of the system studied. f Strategic indicators: they measure the capacity of the system to evolve toward manufacturing new products. The main indicator of this class is the #exibility indicator. f Economic indicators: these indicators include such factors as the purchasing cost, the functioning cost, the maintenance cost, the depreciation cost, etc., of the pair morphology}MHS.
3.1. Indicators for operational data Simulation is a technique widely used to obtain reliable data about the dynamic behaviour of an FMS, and especially about the pair morphology} MHS. Simulation provides many measures that represent useful indicators about the system performances [8,28}34]. These indicators can be classi"ed into two groups. They include but are not limited to: f indicators that measure global performances and are related to the workshop, such as the mean #ow-time of jobs, the mean number of jobs inprocess, etc.; f indicators measuring local performances and which are related to a machine, bu!er, a particular cell, such as the maximum queue length, the utilisation rate of machines, of workstations or of material handling equipment, etc.; Mellichamp et al. [13] argue that some indicators are more important than others. Some constraints on the FMS have to be ful"lled, such as the number of parts to be manufactured in a given time. The goal is to satisfy these constraints and to keep a good level of satisfaction for others. For example, a "rm must be able to respond to market needs: the number of parts and/or lots of parts processed during a simulation have to be greater than the real forecasts of the production volume. The other indicators allow the designer to distinguish between the various possible solutions.
3.2. Indicators for strategic data The main indicator of this class is related to the #exibility of the system. The #exibility of the pair morphology}MHS contributes to the agility of a "rm, since the agility is the ability of a producer of goods or services to thrive in the face of continuous change [35,36]. More precisely, we focus on the evaluation of the capacity of pairs morphology} MHS to adapt quickly to the introduction of new products, to machines or MHSs breakdowns or to #uctuation in the production volume. The introduction of a new product means a new process-plan and maybe new transfers. An occurrence of breakdowns on a machine or on an MHS means a modi"cation of process-plans and the introduction of new transfers too [37]. An increase in production volume may cause the appearance of alternative or multiple process-plans and new transfers. It appears that the #exibility implies to be able to o!er various possibilities for the part transfer [38]. Thus, it seems clear that the measure of the adaptability to new #ow-path is relative to #exibility of the pair morphology}MHS. Chattergee et al. [39] have de"ned an indicator related to the #exibility of material handling equipment. Unfortunately, they take into account only the distances of transfer carried out by each MHS and not the morphology. It appears more interesting to evaluate the transfer time between machines. Thus, we propose the following indicators. Let us de"ne t which represents the transfer i,j time from workstation i to workstation j (the shortest time if several paths exist). The value R means that no transfer is possible from i to j. If i"j, then t "0. If M is the set of machines, t may be i,j i,j described by M]MPR ,
(1)
f : (M , M ) C t . i j i,j
(2)
A transportation matrix T is used to describe the transfer time between machines or workstations. The elements of T are t . Then we obtain the i,j following matrix (see Eq. (3)) if N is the number of M
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
machines: 0
2
F
t
1,j F
2 t 2
}
t i,j F
2
0
2
F
F
}
2
}
1,i F
t i,1 T" F
2
0
2
F
F
t j,1 F
2
j,i F
F
t
F
t
F
1,NM F
t
F
2 t M 2 t M 2 t M N ,i N ,j N ,1
t
i,NM F .
j,NM F 0 (3)
We call N the number of elements of T which %9*45 are di!erent from R and we denote by N the .!9 number of elements of T, minus its diagonal: N "cardM(M , M )3M]M Dt ORand iOjN, i,j %9*45 i j (4) N "cardM(M , M )3M]M DiOjN"N .(N !1). M M .!9 i j (5) First it is interesting to compute the rate R be53!/4&%3 tween the number of existing paths N and the %9*45 maximum number of paths N in a system with .!9 N machines: M N R " %9*45 , (6) 53!/4&%3 N .!9 R 53!/4&%3 cardM(M , M )3M]M Dt OR and iOjN i,j i j . " N .(N !1) M M (7) This indicator measures the ability of the system to o!er a path for carrying out a transfer between two machines: with this point of view, a great di!erence exists between a unidirectional MHS such as a conveyor and a bi-directional AGV. Then, the closer the R rate is to 1, the more the studied system 53!/4&%3 will provide various paths to carry out new #ows. The system (the pair morphology}MHS) must not only o!er new possible paths between two machines, but also o!er an e$cient path. Let us compute the average transfer time between machines. This indicator allows the quickness of the studied pair morphology}MHS to be evaluated. The quickness of a transfer is important since there is often no
213
added-value on the transported product during its transfer. A longer transfer time means a more important delay. Consequently the transfer must be fast with a low cost. Eq. (8) measures the average quickness ¹ of a pair morphology}MHS: !7%3!'% 1 ¹ " t . (8) + !7%3!'% N i,j %9*45 iEj (Mi , Mj)|G If the purpose of each workstation is taken into account, we can propose a more accurate indicator. For example, in the mechanical manufacturing area, some transfers will not occur. Usually no part will require a transfer from a "nishing machine to a roughing machine. Thus, let us de"ne a restriction G of M]M which describes only the future interesting paths from a machine i to another j. Let us de"ne N and N as follows: 3%!*/5%3%45*/' N "cardM(M , M )3GDt OR and iOjN, (9) 3%!i j i,j N "cardM(M , M )3GDiOjN. (10) */5%3%45*/' i j Now we can introduce (Eqs. (12) and (13)) to our two "nal indicators, the indicator of #exibility I and the indicator of quickness I : F-%9*"*-*5: Q6*#,/%44 N 3%!- , I " (11) F-%9*"*-*5: N */5%3%45*/' cardM(M , M )3GDt OR and iOjN i,j i j , I " F-%9*"*-*5: cardM(M , M )3GDiOjN i j (12) 1 " Q6*#,/%44 N */5%3%45*/'
t . (13) + i,j iEj (Mi , Mj)|G These two strategic indicators appear to be very useful, but the economical dimension has also to be taken into account. This is the aim of the following section.
I
3.3. Indicators for economical data There are varied data for the "nancial cost. First, the initial investment I has to be taken into */*5 account. Then the following constraint (see Eq. (14)) must be satis"ed: I
NM NC NMHS * + C i# + C j# + C k , */*5 M C MHS i/1 j/1 k/1
(14)
214
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
where N is the number of machines or workstaM tions, N the number of control systems, N the C MHS number of material handling systems, C i the cost M of machine i, C j the cost of control system j, and C C k the cost of material handling system k. MHS The morphology cost C may be approxi.031)0-0': mated by the area occupied by the system. Thus, this area depends on the chosen morphology. If C is the cost of 1 m2 of the workshop and !3%! S is the surface occupied by the system: .031)0-0': C "S C . (15) .031)0-0': .031)0-0': !3%! The cost of an MHS has been studied in [4,40,41]. These authors propose a method to compute the cost per hour of a material handling system. We suggest to extend their work in order to take into account the cost per hour of machines and workstations as follows: (F !d )(ADP, i , c )#n k 0 k k, U" k k H
(16)
where F the cost of the system (MHS or machines), k d the cost of resale, ADP, i , c "((1#i )ck~1/ k 0 k 0 i (1#i )ck), i the annual interest rate, c the life0 0 0 k time of system, n the cost of the maintenance unit, k and H the number of working hours per year. We now de"ne the cost by manufactured product unit C (see Eq. (17)). This cost is composed of the 6/*5 cost of the morphology C , the cost per .031)0-0': hour of each piece of material handling equipment
multiplied by its utilisation duration and the cost per hour of each machines multiplied by its period of utilisation. Then, we obtain the following cost: +NMHS U t #+NM U i t i#C .031)0-0': , i/1 M M C " k/1 MHSk MHSk 6/*5 N 1!35 (17) where C is the cost of the morphology, .031)0-0': U k the cost per hour of the MHS number k, U i the MHS M cost per hour of the machine number i, t k MHS the period of utilisation of MHS number k, t i the M period of utilisation of machine number i, N the MHS number of MHS, N the number of machines, M N the number of produced parts. Certain data 1!35 such as N , t i or t k may be obtained from 1!35 M MHS simulation results.
4. Illustrative example In this section, we will illustrate the various indicators that we have de"ned. As shown in Fig. 2, three di!erent solutions with six machines and only one piece of material handling equipment are compared. All these simple solutions allow the bene"ts of the di!erent indicators to be illustrated. We assume that machine numbers 1 and 2 are roughing machines, numbers 3, 4 and 5 are xnishing machines, and number 6 is a super xnishing machine.
Fig. 2. The three cases to study.
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
4.1. Description of the three cases The three di!erent solutions are f Example 1 is a single circular line. The MHS is an AGV with a capacity of 1 palette of 100 parts. The load/unload systems of the six machines are automatic. Their duration follows a triangular distribution (minutes: 0.1 minutes, mode: 0.3 minutes, max.: 0.5 minutes). The queues in the front of each station have a capacity of two palettes. The mean transfer times from the input to the machines 1 or 6 are 6 seconds. The mean transfer times between machines 1 and 6 and the output are the same (the standard deviation is 10%). The mean transfer times between machines for example 1 are given below (in seconds). The durations are normally distributed with a standard deviation of 10%:
C
D
0 10
10 0
20 10
30 20
20 30
10 20
20 T " 30 1 20
10 20 30
0 10 20
10 0 10
20 10 0
30 . 20 10
10
20
30
20
10
0
f Example 2 is a single straight line. Its MHS is a bi-directional shuttle operating on a railtrack. Its capacity is 1 palette of 100 parts. The load/unload systems are the same as in example 1. The input and output are separated and are opposite, respectively, to machines 3 and 4. The means transfer times between machines in example 2 are given below (in seconds). The durations follow normal distribution with a standard deviation of 10%:
C
D
0 10
10 0
20 10
30 20
40 30
50 40
20 T " 30 2 40
10 20 30
0 10 20
10 0 10
20 10 0
30 . 20 10
50
40
30
20
10
0
f Example 3 is a single straight-line morphology with a belt conveyor without accumulation. The
215
palettes have a capacity of only 25 parts. The load/unload system is the same as for examples 1 and 2, but it is three times faster. The conveyor may be loaded in input with one palette every 2 seconds (maximum). f The mean transfer times between machines for example 3 are given below (in seconds). The durations are normally distributed with a standard deviation of 10%:
C
0 R
3 0
6 3
9 6
12 9
15 12
R T " R 3 R
R R R
0 R R
3 0 R
6 3 0
9 6 3
R
R
R
R
R
0
D
.
Machines are subjected to breakdowns. We assume that they are normally distributed. Their MTBF and MTTR are given in Table 2. 4.1.1. The production Three di!erent parts A, B and C are processed. The process-plans and the mean process times (in min) are given in Table 3 (standard deviations are 5%). The production is divided as follows: parts A 30%, parts B 35%, and parts C 35%. We will study the introduction of a new part D. The previous indicators will allow us to measure Table 2 Resources data Kind of resources
Number
MTBF MTTR (in days) (in hours)
Roughing NC 2-axis turning machine Roughing NC 3-axis milling machine Finishing NC 3-axis milling machine Finishing NC 3-axis turning machine Finishing NC 5-axis milling machine Super"nishing milling machine AGV Shuttle Conveyor
1
80
4
2
60
4
3
40
8
4
45
8
5
30
24
6 20 Example 1 20 Example 2 60 Example 3 70
8 1 2 2
216
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218
Table 3 Process plans and process times of parts A, B, C and D
Table 4 Utilisation rates of each equipment
Parts
Machines
Process times
Part A
Machine 1 Machine 4 Machine 6
2.50 3.00 6.00
Machine Solution 1 Solution 2 Solution 3 number Without With Without With Without With part D part D part D part D part D part D
Part B
Machine 2 Machine 3 Machine 5
2.40 3.00 2.00
Part C
Machine Machine Machine Machine
1 4 5 6
1.80 2.40 1.40 3.00
Part D
Machine Machine Machine Machine
2 1 4 6
2.50 1.50 3.20 1.60
the sensitivity of the workshop to the introduction of this new product. With part D, the production is divided as follows: parts A 30%, parts B 25%, parts C 35% and parts D 10%. In case 3, the mean transfer time of a palette of 25 parts of D type from machine 2 to machine 1 takes 3 minutes with a standard deviation of 1 minute. This full manual operation requires an operator. 4.2. Results The simulation model has been developed with ARENA. Due to the random variable used in the model, 15 long replications have been performed. Statistics related to the initial period of each run have been truncated in order to reduce the initial bias. 4.2.1. Operational indicators The simulation experiments provide the estimated utilisation rates of each equipment. These results are given in Table 4. These estimated utilisation rates depend on the capacity of each material handling equipment and on the morphology. In fact, Table 4 shows that the introduction of the new part D causes a major perturbation on each system. Example 3 (with the conveyor) is the most sensitive and perturbed: the machines 1, 2 and 4 have an utilisation rate too high, whereas machines 3, 5 and 6 are insu$ciently supplied.
1 2 3 4 5 6
0.87 0.35 0.47 0.86 0.58 0.86
0.87 0.96 0.33 0.85 0.27 0.89
0.87 0.48 0.60 0.83 0.65 0.84
0.87 0.98 0.20 0.80 0.27 0.84
0.25 0.14 0.28 0.32 0.22 0.52
0.95 0.95 0.10 0.95 0.10 0.10
4.2.2. Indicators of yexibility and quickness The restriction G is given by the matrix R where the value 1 means that the pair (M , M ) is in G and i j 0 otherwise:
C
D
1 1
1 1
1 1
1 1
1 1
1 1
R" 0 0 0
0 0 0
1 1 1
1 1 1
1 1 1
1 . 1 1
0
0
0
0
0
1
The results for the various indicators are presented in Table 5. It seems clear that the solution number 3 is the fastest. Its average transfer time rises only at 2.3 seconds. However solutions number 1 and 2 are more #exible if the indicators I are conF-%9*"*-*5: sidered. This indicator is important in certain situations. For example, if machine 3 is a 2-axis turning machine and machine 4 is a 3-axis milling machine, solution 3 does not allow us to "nish a part "rst on the milling machine before performing the "nishing pass on the turning machines. This problem appears with the introduction of part D. This part will be able to be produced with solution 3 only if the process planning may be modi"ed in such a manner that the turning pass is made before the milling pass. Otherwise, a manual transfer will occur. 4.2.3. Financial cost The cost per hour of each machine is given in Table 6 below. For each solution, the period of utilisation of machine number i is the same.
O. Devise, H. Pierreval / Int. J. Production Economics 64 (2000) 209}218 Table 5 Results for each solution R Solution 1 Solution 2 Solution 3
53!/4&%3
1.00 1.00 0.50
Table 7 Cost and time of each solution U
¹ !7%3!'%
I F-%9*"*-*5:
I Q6*#,/%44
Kind of solution
3.60 4.60 2.30
1.00 1.00 0.79
3.60 4.20 2.30
Solution 1: bi-directional AGV 2.50 Solution 2: bi-directional 2.90 shuttle Solution 3: unidirectional 1.20 conveyor
Table 6 Cost and time of utilisation of each machine Machine 1 number
2
3
4
5
6
U i M ¹ i M
0.80 0.45
1.00 0.35
1.10 0.80
1.00 0.80
2.20 0.40
0.70 0.40
217
The period of utilisation of the material handling equipment may be quite di!erent as it is shown in Table 6. We obtain the following results: no one solution is clearly the best. Taking the global context into account is necessary before making a "nal decision. In Table 7, it seems clear that the last solution is the best from a "nancial point of view. The designer will have to choose between a more #exible solution (solution number 1) and a more economical solution with solution 3. He/she will be guided by the context of his study.
5. Conclusion The purpose of this paper was to focus on the evaluation of morphology and MHS, studied together due to their strong interdependence. As the result of a survey of the literature related to FMS design, we have presented the indicators suited to this purpose. New indicators have also been suggested, especially to evaluate the #exibility, the quickness and the economical cost of the pair morphology}material handling systems. We have described them in detail and given an illustrative example of their practical use. Indicators represent a major issue in the evaluation of the performance of morphology and material handling systems in #exible manufacturing
MHS
¹ C C MHS .031)0-0': 6/*5 2.40 2.90
0.28 0.50
9.83 12.46
1.30
0.35
5.46
system. Indicators evaluating the pair morphology} material handling systems may be either directly used by decision makers or incorporated in decision support systems. We are now interested in improving these indicators and in designing new ones to evaluate others additional aspects. References [1] R. De Guio, M. Barth, About performance evaluation in production #ow analysis, International Journal of Production Research 35 (1997) 83}99. [2] K.H. Kim, J.M.A. Tanchoco, Economical design of material #ow path, International Journal of Production Research 31 (6) (1993) 1387}1408. [3] J.A. Tompkins, J.A. White, Facilities Planning, Wiley, New York, 1984. [4] T. Hamann, Le proble`me d'agencement des ressources a` l'inteH rieur des cellules des syste`mes de production, Ph.D. Thesis, INRIA Lorraine, 1992. [5] D. Riopel, Conception d'atelier automatiseH #exible de sous-traitance: Fonction manutention et entreposage, Ph.D. Thesis, ED cole Centrale de Paris, 1989. [6] B. Montreuil, A modelling framework for integrating layout design and #ow network design, Progress in Material Handling and Logistics 2 (1991) 95}115. [7] L. Gelders, P. Mannaerts, J. Maes, Manufacturing strategy, performance indicators and improvement programmes, International Journal of Production Research 32 (4) (1994) 797}805. [8] A. Arbel, A. Seidmann, Performance evaluation of #exible manufacturing systems, IEEE Transactions on Manufacturing Systems 1 (1984) 118}129. [9] L. Berrah, A. Haurat, Une strateH gie de mise en place d'indicateurs de performance pour le pilotage des processus de production, in MOSIM'97, ModeH lisation et simulation des syste`mes de production et de logistique, Rouen, France, June 5}6, 1997, pp. 61}69. [10] L. Berrah, P. Miquet-Sage, A. Haurat, Un mode`le d'indicateur eH leH mentaire pour l'eH valuation de la performance dans les processus de production, in GI5 } IPI, Fifth International Congress of Industrial Engineering, Vol. 2, Grenoble, France, April 2}4, 1996, pp. 11}20.
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