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Intelligent Tool Management in a Multiple Supplier Network
Intelligent Tool Management in a Multiple Supplier Network D. D'Addona, R. Teti (1) Department of Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio, Naples, 80125, Italy
Abstract The development and implementation of an intelligent Flexible Tool Management Strategy (FTMS), based on Fuzzy Logic (FL) theory and integrated in a Multi-Agent Tool Management System (MATMS) for automatic tool procurement in a supply network, is presented. The MATMS operates in the framework of a negotiationbased, multiple-supplier network where a turbine blade producer requires dressing jobs on worn-out CBN grinding wheels from external tool manufacturers. The main characteristics of the intelligent FTMS approach is the use of fuzzy set theory to model the uncertainty associated with tool demand rate and the employment of fuzzy reasoning to expand the strategy operational flexibility in comparison with traditional tool management and previously developed crisp FTMS paradigms. Keywords: Tool management, Supply networks, Intelligent systems
1 INTRODUCTION Today's manufacturing systems, under the pressure of stringent market demands and customer requirements, are increasingly characterised by a growing organisational and management complexity [ I , 21. The growth of system complexity with the number of system components is the source of uncertainty increase in system response [3]. In highly complex manufacturing systems, it is very hard to define not only the operation performance and service quality, but also the characteristics of customer-supplier relations in supply networks, such as order reliability and lead time [4, 51. Recently, a novel software architecture to manage supply networks at tactical and operational level has emerged: the supply network is viewed as a system made of a set of intelligent (software) agents, each in charge of one or more network tasks and interacting with other agents in planning and executing their duties [5-71. This work is part of a wider scope research on the development of a Multi-Agent Tool Management System (MATMS) for tool procurement in the framework of a negotiation-based, multiple-supplier network where a turbine blade producer requires worn-out CBN grinding wheel dressing jobs from external tool manufacturers. The MATMS model, based on intelligent agent technology, integrated with a Flexible Tool Management Strategy (FTMS) for optimum tool inventory sizing and control was first presented in [8, 91 and two crisp FTMS paradigms based on Planned Demand Rate (PDR) [8] and Adaptive Demand Rate (ADR) estimates [9] were illustrated. In this paper, a Fuzzy Logic (FL) based FTMS approach, proposed in [ l o ] as alternative to traditional tool management and previous crisp FTMS methods, is implemented and applied to a real industrial case of tool management. 2 CBN GRINDING WHEEL TOOL MANAGEMENT Turbine blades are manufactured along several production lines, each for one aircraft engine model requiring a set of CBN grinding wheel types (part-numbers). Each partnumber is planned to work a maximum number of blades: when it reaches its end of life, it is sent for dressing to an external supplier in a supply network and remains unavailable for a time defined as dressing cycle time. For each part-number, a sufficient number of wheels must be always available (on-hand inventory) to prevent production breakage due to tool run-out. The part-number on-hand inventory size, I, depends on: # of piecedmonth, P; # of
piecedwheel, G; # of months required without new or dressed wheel supply, C (coverage period) heuristically selected. The wheel demand, D, for each part-number is given by D = (P/G) * C - lo, where: P/G = tool demand rate (# of wheels/month); lo = initial part-number inventory size. Traditional tool management consists in the strategic planning of wheel inventory size based on the selection of a coverage on-hand inventory for each part-number (# of wheels for production needs in the coverage period C). This procedure does not always prove adequate; the producer, aware of this drawback, increases or reduces the part-number inventory level on the basis of experience. The results of this policy, founded on skilled staff knowledge, are the historical inventory size trends: in some cases, the expected trend matches the historical one; in other cases, it is underestimated, with risk of stock-out, or overestimated, with excessive capital investment [ I I ] . The historical trend is a fit solution that prevents tool run-out and useless investment: it can be used as a reference for assessing alternative tool management strategies. 2.1 Flexible Tool Management Strategy Tool inventory control is carried out by the MATMS Resource Agent (RA) by minimizing tool management cost and stock-out risk on the basis of dressing time predictions issued by the MATMS Dressing Time Prediction Agent (DTPA) through an Adaptive Neuro-Fuzzy Inference System based on historical dressing times of the network suppliers [II-131. The RA uses a FTMS whose rationale is to make sure that the part-number on-hand inventory level, I, remains within two real time control limits: ,,I = partnumber demand during purchase order lead time, Tpur; ,,,I = part-number demand calculated using the dressing time predictions. The on-hand inventory level, I, is left free to vary within the limits [I, ,]I otherwise: - if I < ,,I additional tools must be provided; - if I >,,,I the part-number on-hand inventory level is reduced by suspending the dressing operations. Two crisp methods to evaluate [I, ],,,I were developed: - Planned Demand Rate (PDR) approach [ I I ] ; - Adaptive Demand Rate (ADR) approach [9]. Planned Demand Rate (PDR) Approach The part-number demand rate P/G is kept constant during the tool management period. The control range lower limit is constant and given by ,,I = PIG * Tpur,where Tpuris a
constant as its historical records are only slightly variable. The control range upper limit, lmax,varies each time a tool wear-out event occurs as a function of the dressing time predictions, @+I), provided by the DTPA: lmax(j)= PIG * [(;[lj+l) + Tint]where j is the counter of worn-out wheels and Tintis the time to transfer the tool to its production line. Adaptive Demand Rate (ADR) Approach Actual tool demand rates can be higher/lower than P/G due to higher/lower production volumes or unexpectedly shorter tool life. Thus, in the ADR method the concept of adaptive tool demand rate, dR(j), is introduced: P/G, if t(j) 5 1 j/t(j), otherwise
Hex (x,a,b,c,d,e,f)=
0 x5a +1/2[(x-a)/(b-a)] a < x< b +1/2[(~+~-2b)/(c-b)]b < x 5 c -1/2[(x+d-2e)/(e-d)] d < x s e (7) -1/2[(x-f)/(f-e)] ecx5f 0 x>f
where t(j) is the time computed from the start of the FTMS. The control limits are now given by: lmin(j)
= &(j) * Tpur;
lmax(J) = ddj) * [%+I)
+
Tint]
(2)
3 INTELLIGENT TOOL MANAGEMENT STRATEGY An intelligent FL based FTMS paradigm is proposed as alternative to traditional tool management and previous crisp FTMS methods. Two main ideas characterise the intelligent approach: the use of fuzzy set theory to model the tool demand rate uncertainty and the utilisation of fuzzy reasoning to implement a tool management strategy with further expanded operational flexibility. As shown in [lo], uncertainty spreading across manufacturing environments makes historical data, especially those related to tool demand rate, unreliable even when available. Moreover, the adoption of a fuzzy inference architecture is well suited to process knowledge in form of linguistic statements.
3.1 Fuzzy Demand Rate and Fuzzy Control Limits A triangular asymmetric membership function (MF) is used to model a structurally uncertain tool demand rate as a fuzzy set (Figure l a ) . This Fuzzy Demand Rate (FDR) approach requires the estimate of tool demand rate values that do or do not belong to the dR variable domain in order to find the fuzzy set lower and upper limits, & and u, and the value, r, that best represents the set. An equivalent linguistic expression may be: "the demand rate is likely to be about r, ranging from & to u". Hence, it can be assumed: & = min, dR(j), r = mean, dR(j), u = max, dR(j) (3) and the fuzzy tool demand rate is set equal to: fR(j) = Tri (dR, &, I,U) (4) where Tri (dR, &, r, u) is a triangular MF of the independent variable dRwith parameters &, r, u; this MF is asymmetrical in the general case. Likewise, the concept of real-time variable control range applied to the on-hand inventory level, I, can be represented as fuzzy sets for control limits lmln and lmax (Figure Ib). The triangular MF parameters describing lmlnand lmaxcan be derived by:
{
{
A = & *Tpur
A = & * [ a + l ) + Tint] P = * Tpur ; lmax P = r * [ a + l ) + Tint](5) Y = u * [$j+l) + Tint] v = u * Tpur Accordingly, lmln and lmax are reshaped through multiplication of the fuzzy tool demand rate defined in eq. 4 by the temporal coefficients indicated below: lmin
I
I d ) = ~RU) * Tpur lmax(j)=fR(j) * [ @ + I ) + Tint]
~
I
lmin(j) = ~ r(1, i h, p, v) lmax(j)= Tri (I, A, P, Y)(6)
3.2 Hexagonal Membership Function An hexagonal-shaped MF is used for input and output variables. The hexagonal curve is a piecewise linear function of a positive real variable, x, and depends on six scalar parameters a, b, c, d, e, f:
4 FUZZY FTMS OPERATION In Figure 3, the on-hand inventory control of a generic partnumber is presented to explain the FDR FTMS functioning. At time t = 0, the part-number inventory size is lo and the control limits assume single values (eq. 6). As Tintand Tpur are constant and P/G is updated yearly, lmaxis a function of the current fuzzy demand rate fR(j) and predicted dressing time @+I), and lmlna function of the current fR(j) value. Each time tools wear out (w-events), the counter of wornout wheels, j, increases; the inventory level, I, decreases; the fR(j) value is updated; dressing time predictions, @+I), are issued; and lmln and lmax are recalculated.
a ? w
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Figure 1: (a) Triangular membership function (MF) for fuzzy demand rate, fR, vs. demand rate, dR; (b) Triangular MF for fuzzy control limits, lmlnand lmax,vs. on-hand inventory level, I; (c) Hexagonal MF, Hex (x, a, b, c, d, e, f), for input and output variables vs. on-hand inventory level, I a 2 w
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Figure 2: Membership functions for (a) input variable Inventory, (b) output variable Purchase, (c) output variable Dressing, vs. on-hand inventory level, I. S = Short; C = Controlled; L = Large, N = Necessary; U = Unnecessary. w-event, wl: j = 1, Iwl < lo, dR(l) = PIG (eq. I ) , At the Ist and t = r = u = dR(l) (eq. 3). The fR(1) triangular MF degenerates to a singleton (eq. 4) and lmln(l),lmax(l)take on single values (eq. 6), reported at w1 in Figure 3. As Iwl falls within the updated fuzzy control range, the worn-out tools are sent to dressing but no new tool is purchased. Each time new or dressed tools are delivered by suppliers (d-events), the on-hand inventory, I, grows but Iml and lmax are not affected. This is what happens at the 1” delivery event, dl: Id1 > Iwl, lmln= lmln(l)and lmax= lmax(l). At the w-event, w2: j = 2, < I d l , dR(2) = 2/t(2), t = min [dR(1 dR(2)1, u = max [dR(1 dR(2)1, = mean [dR(1 dR(2)I = (& + u)/2. The fR(2) MF is an isosceles triangle. The fuzzy limits lmln(2),lmax(2)are defined by a max (u, Y), min ( h ,A), and symmetrical mean (p, P), reported at w2(Figure 3). The 2ndd-event, d2, represents a case where I crosses the upper control limit: Id2 > lmax(hl in Figure 3). At the next wevent, w3, a number of worn-out tools, equal to the fuzzy difference Id2 - lmax,will remain on-hold in the warehouse. At w3: j = 3, la < ld2, dR(3) = 3/t(3), and &, r, u are given by eq. 3. The fR(3) MF is a scalene triangle. The fuzzy control limits lmln(3), lmax(3) are defined by a max, min, and asymmetrical mean, reported at w3 (Figure 3). As la falls within the fuzzy control range, the worn-out tools are sent to dressing, except for Id2 - lmaxwheels that remain on-hold. The next w-event, w4, represents the case where I crosses the lower control limit: lw4 < lmln(h2 in Figure 3). The wornout wheels must be sent to dressing and a further number of tools, equal to the fuzzy difference lmln - lw4, must be provided. If there are worn-out tools on-hold, they are sent to dressing in partial or total substitution for tool purchases. In any event, the number of required tools exceeding the worn-out wheels on-hold must be newly purchased. At w4, the fR(j) MF is a scalene triangle. The fuzzy control limits lmln(j), lmax(j) are defined by a max, min, and asymmetrical mean, reported at w4 (Figure 3). )I
)I
)I
The last d-event, d3, brings the inventory level entirely within the fuzzy control range, lmln< ld3< lmax,and so on.
4.1 Crisp and Fuzzy FTMS Test Case The flexible tool management of a real CBN grinding wheel part-number, M8110855, was simulated as test case application for the crisp PDR, ADR and fuzzy FDR FTMS paradigms using one year historical data. In Figure 4, the historical and simulated inventory level trends are reported vs. time (one year), along with the historical tool supply cost and percent cost variation of the simulated trends. It is worth recalling that the historical inventory level trend, IHIST, is the result of experienced staff tool management activity. Though this management approach based on expert knowledge has the drawback of depending on skilled staff, it is robust and reliable and can be used as a reference to assess alternative intelligent computation procedures of tool management, operating without human expert support.
Figure 3: Generic part-number on-hand inventory level, I, vs. time, t, for the FDR FTMS; w = wear-out event ( 0 ) ; d = delivery event ( 0 ) ; red lines: fuzzy control limits; hl, h2: fuzzy control limit crossings (x).
Figure 4: Historical (IHIS), crisp (IpDR, IADR) and fuzzy (IFDR) FTMS simulated on-hand inventory level vs. time (one year), for part-number M8110855. All FTMS approaches are shown to provide an economy over the historical cost. The crisp PDR paradigm yields a saving of 18%, the crisp ADR method a saving as high as 88%, and the fuzzy FDR scheme an saving of 79%. The notable cost reduction of the ADR and FDR methods versus the PDR approach is due to the initial planned tool demand rate for this part-number (dR(l) = P/G = 7.10) being much lower than the on-hand inventory level during the Ist month of tool management where no wear-out events occur (19 5 I 5 20, Figure 4). This results in no new tool purchase when the first wear-out event occurs at the end of the Ist month. Afterwards, the PDR simulation provides for new purchase orders at all occasions when, due to multiple worn-out wheels, the on-hand inventory level drops lower than the constant lower control limit, I < Imln. Conversely, in the ADR simulation no tool purchase orders are issued for the whole period because the actual tool demand rate drops to dR(2) < 2.70 as early as the month of tool management and remains very low for the rest of the period. Finally, the FDR simulation follows closely the ADR trend till the 6th month of tool management when its higher sensitivity to tool shortage yields a slightly higher fR(j) that generates a few new tool purchase orders. This reaction of the fuzzy FDR paradigm produces a modest tool supply cost increase versus the crisp ADR approach (88% - 79% = 9%), but it yields a positive reduction of stock-out risk: lFDR is never lower than 7 units whereas lADR gets as low as 3 units (Figure 4). 4.2 Functional Advantages of the Intelligent FTMS The main features of the MATMS integrated intelligent FTMS are the utilisation of fuzzy set theory to model the uncertainty of tool demand rate and the use of fuzzy reasoning to expand the operational flexibility of the tool management strategy in the supply network [14]. In terms of functional advantage, it is worth considering that in prior crisp FTMS approaches, once a tool purchase or dressing job was evaluated, it had to be either thoroughly carried out or completely neglected. In the fuzzy FTMS method, a decision may be taken in proportion to its necessity degree: e.g., if a purchase order of 10 wheels is judged necessary by 70%, a purchase order of only 7 new tools can be issued. This can provide for an actual economy and practical benefit in the management of CBN grinding wheels. 5 SUMMARY The implementation of an intelligent Flexible Tool Management Strategy (FTMS), based on Fuzzy Logic (FL) theory and integrated in a Multi-Agent Tool Management System (MATMS) for CBN grinding wheel procurement in a supply network, was presented. The intelligent FTMS is the problem solving function of the MATMS agent whose
task is the optimum tool inventory sizing and control. It operates on account of running turbine blade production plans, tool capacity and dressing time predictions. Its rationale is to let the tool inventory level vary within a real time variable control range to achieve the minimisation of tool management cost and stock-out risk. The principal characteristics of the intelligent FTMS approach are the use of fuzzy set theory to model the uncertainty of the tool demand rate and the adoption of fuzzy reasoning to expand the strategy operational flexibility versus traditional tool management and prior crisp FTMS paradigms. A test case application of the previous crisp FTMS approach and new fuzzy FTMS formulation to a real CBN grinding wheel part-number illustrated the functional advantages and practical benefits of the fuzzy FTMS paradigm in terms of tool supply cost saving and tool stock-out risk minimisation. 6 ACKNOWLEDGEMENTS This research work was carried out with support from the FP6 EC NoE on I*PROMS. The paper draws on the thesis work of A. Bontempi whose contribution is acknowledged. REFERENCES Wiendahl, H.-P., Helms, K., Hobig, M., 1998, Management of Variable Production Networks: Vision, Management & Tools, Annals of CIRP, 47/2: 549-555. EIMaraghy, W.H., Urbanic, R.J., 2004, Assessment of Manufacturing Operational Complexity, Annals of CIRP, 53/1: 401-406. Monostori, L., Csaji, B.Cs., Kadar, B., 2004, Adaptation and Learning in Distributed Production Control, Annals of CIRP, 53/1: 349-352. Wiendahl, H.-P., Scholtissek, P., 1994, Management and Control of Complexity in Manufacturing, Annals of CIRP, 43/2: 533-540. Wiendahl, H.-P., Lutz, S., 2002, Production in Networks, Annals of CIRP, 51/2: 573-586. Fox, M.S., Barbuceanu, M., Teigen, R., 2000, AgentOriented Supply-Chain Management, Int. J. of Flexible Manufacturing Systems, 12: 165-188. Scholz-Reiter, B., Hoehns, H., Hamann, T., 2004, Adaptive Control of Supply Chains: Building Blocks and Tools of an Agent-Based Simulation Framework, Annals of CIRP, 53/1: 353-356. Teti, R., D'Addona, D., 2003, Agent-Based Mulptiple Supplier Tool Management System, 36th ClRP Int. Sem. on Manufacturing Systems - ISMS 2003, Saarbrucken, 3-5 June: 39-45. Teti, R., D'Addona, D., Segreto, T., 2004, Flexible Tool Management in a Multi-Agent Modelled Supply Network, 37th ClRP Int. Sem. on Manufacturing Systems - ISMS 2004, Budapest. 19-21 May: 351-356. [ l o ] Teti, R., D'Addona, D:, 2004, FL based Tool Management in a Multiple Supplier Network, 4th ClRP Int. Sem. on Intelligent Computation in Manufacturing Eng. - ICME '04, Sorrento, 30 June - 2 July: 555-562. [ I l l Teti, R., D'Addona, D., 2003, Grinding Wheel Management through Neuro-Fuzzy Forecasting of Dressing Cycle Time, Annals of CIRP, 52/1: 407-410. [I21 D'Addona, D., Teti, R., 2003, Multiple Supplier NF Delivery Forecasting for Tool Management in a Supply Network, 6thAITEM Conf., Gaeta, 8-10 Sept.: 127-128 [I31 Teti, R., D'Addona, D., 2004, Adaptive NF Tool Delivery Forecasting for Flexible Tool Management in a Supply Network, 5th Int. Workshop on Emergent Synthesis - IWES '04, Budapest, 24-25 May: 41-50. [I41 Zhang, H.C., Li, J., Merchant, M.E., 2003, Using Fuzzy Multi-Agent Decision-Making in Environmentally Conscious Supplier Management, Annals of CIRP, 52/11385-388.
Abstract The development and implementation of an intelligent Flexible Tool Management Strategy (FTMS), based on Fuzzy Logic (FL) theory and integrated in a Multi-Agent Tool Management System (MATMS) for automatic tool procurement in a supply network, is presented. The MATMS operates in the framework of a negotiationbased, multiple-supplier network where a turbine blade producer requires dressing jobs on worn-out CBN grinding wheels from external tool manufacturers. The main characteristics of the intelligent FTMS approach is the use of fuzzy set theory to model the uncertainty associated with tool demand rate and the employment of fuzzy reasoning to expand the strategy operational flexibility in comparison with traditional tool management and previously developed crisp FTMS paradigms. Keywords: Tool management, Supply networks, Intelligent systems
1 INTRODUCTION Today's manufacturing systems, under the pressure of stringent market demands and customer requirements, are increasingly characterised by a growing organisational and management complexity [ I , 21. The growth of system complexity with the number of system components is the source of uncertainty increase in system response [3]. In highly complex manufacturing systems, it is very hard to define not only the operation performance and service quality, but also the characteristics of customer-supplier relations in supply networks, such as order reliability and lead time [4, 51. Recently, a novel software architecture to manage supply networks at tactical and operational level has emerged: the supply network is viewed as a system made of a set of intelligent (software) agents, each in charge of one or more network tasks and interacting with other agents in planning and executing their duties [5-71. This work is part of a wider scope research on the development of a Multi-Agent Tool Management System (MATMS) for tool procurement in the framework of a negotiation-based, multiple-supplier network where a turbine blade producer requires worn-out CBN grinding wheel dressing jobs from external tool manufacturers. The MATMS model, based on intelligent agent technology, integrated with a Flexible Tool Management Strategy (FTMS) for optimum tool inventory sizing and control was first presented in [8, 91 and two crisp FTMS paradigms based on Planned Demand Rate (PDR) [8] and Adaptive Demand Rate (ADR) estimates [9] were illustrated. In this paper, a Fuzzy Logic (FL) based FTMS approach, proposed in [ l o ] as alternative to traditional tool management and previous crisp FTMS methods, is implemented and applied to a real industrial case of tool management. 2 CBN GRINDING WHEEL TOOL MANAGEMENT Turbine blades are manufactured along several production lines, each for one aircraft engine model requiring a set of CBN grinding wheel types (part-numbers). Each partnumber is planned to work a maximum number of blades: when it reaches its end of life, it is sent for dressing to an external supplier in a supply network and remains unavailable for a time defined as dressing cycle time. For each part-number, a sufficient number of wheels must be always available (on-hand inventory) to prevent production breakage due to tool run-out. The part-number on-hand inventory size, I, depends on: # of piecedmonth, P; # of
piecedwheel, G; # of months required without new or dressed wheel supply, C (coverage period) heuristically selected. The wheel demand, D, for each part-number is given by D = (P/G) * C - lo, where: P/G = tool demand rate (# of wheels/month); lo = initial part-number inventory size. Traditional tool management consists in the strategic planning of wheel inventory size based on the selection of a coverage on-hand inventory for each part-number (# of wheels for production needs in the coverage period C). This procedure does not always prove adequate; the producer, aware of this drawback, increases or reduces the part-number inventory level on the basis of experience. The results of this policy, founded on skilled staff knowledge, are the historical inventory size trends: in some cases, the expected trend matches the historical one; in other cases, it is underestimated, with risk of stock-out, or overestimated, with excessive capital investment [ I I ] . The historical trend is a fit solution that prevents tool run-out and useless investment: it can be used as a reference for assessing alternative tool management strategies. 2.1 Flexible Tool Management Strategy Tool inventory control is carried out by the MATMS Resource Agent (RA) by minimizing tool management cost and stock-out risk on the basis of dressing time predictions issued by the MATMS Dressing Time Prediction Agent (DTPA) through an Adaptive Neuro-Fuzzy Inference System based on historical dressing times of the network suppliers [II-131. The RA uses a FTMS whose rationale is to make sure that the part-number on-hand inventory level, I, remains within two real time control limits: ,,I = partnumber demand during purchase order lead time, Tpur; ,,,I = part-number demand calculated using the dressing time predictions. The on-hand inventory level, I, is left free to vary within the limits [I, ,]I otherwise: - if I < ,,I additional tools must be provided; - if I >,,,I the part-number on-hand inventory level is reduced by suspending the dressing operations. Two crisp methods to evaluate [I, ],,,I were developed: - Planned Demand Rate (PDR) approach [ I I ] ; - Adaptive Demand Rate (ADR) approach [9]. Planned Demand Rate (PDR) Approach The part-number demand rate P/G is kept constant during the tool management period. The control range lower limit is constant and given by ,,I = PIG * Tpur,where Tpuris a
constant as its historical records are only slightly variable. The control range upper limit, lmax,varies each time a tool wear-out event occurs as a function of the dressing time predictions, @+I), provided by the DTPA: lmax(j)= PIG * [(;[lj+l) + Tint]where j is the counter of worn-out wheels and Tintis the time to transfer the tool to its production line. Adaptive Demand Rate (ADR) Approach Actual tool demand rates can be higher/lower than P/G due to higher/lower production volumes or unexpectedly shorter tool life. Thus, in the ADR method the concept of adaptive tool demand rate, dR(j), is introduced: P/G, if t(j) 5 1 j/t(j), otherwise
Hex (x,a,b,c,d,e,f)=
0 x5a +1/2[(x-a)/(b-a)] a < x< b +1/2[(~+~-2b)/(c-b)]b < x 5 c -1/2[(x+d-2e)/(e-d)] d < x s e (7) -1/2[(x-f)/(f-e)] ecx5f 0 x>f
where t(j) is the time computed from the start of the FTMS. The control limits are now given by: lmin(j)
= &(j) * Tpur;
lmax(J) = ddj) * [%+I)
+
Tint]
(2)
3 INTELLIGENT TOOL MANAGEMENT STRATEGY An intelligent FL based FTMS paradigm is proposed as alternative to traditional tool management and previous crisp FTMS methods. Two main ideas characterise the intelligent approach: the use of fuzzy set theory to model the tool demand rate uncertainty and the utilisation of fuzzy reasoning to implement a tool management strategy with further expanded operational flexibility. As shown in [lo], uncertainty spreading across manufacturing environments makes historical data, especially those related to tool demand rate, unreliable even when available. Moreover, the adoption of a fuzzy inference architecture is well suited to process knowledge in form of linguistic statements.
3.1 Fuzzy Demand Rate and Fuzzy Control Limits A triangular asymmetric membership function (MF) is used to model a structurally uncertain tool demand rate as a fuzzy set (Figure l a ) . This Fuzzy Demand Rate (FDR) approach requires the estimate of tool demand rate values that do or do not belong to the dR variable domain in order to find the fuzzy set lower and upper limits, & and u, and the value, r, that best represents the set. An equivalent linguistic expression may be: "the demand rate is likely to be about r, ranging from & to u". Hence, it can be assumed: & = min, dR(j), r = mean, dR(j), u = max, dR(j) (3) and the fuzzy tool demand rate is set equal to: fR(j) = Tri (dR, &, I,U) (4) where Tri (dR, &, r, u) is a triangular MF of the independent variable dRwith parameters &, r, u; this MF is asymmetrical in the general case. Likewise, the concept of real-time variable control range applied to the on-hand inventory level, I, can be represented as fuzzy sets for control limits lmln and lmax (Figure Ib). The triangular MF parameters describing lmlnand lmaxcan be derived by:
{
{
A = & *Tpur
A = & * [ a + l ) + Tint] P = * Tpur ; lmax P = r * [ a + l ) + Tint](5) Y = u * [$j+l) + Tint] v = u * Tpur Accordingly, lmln and lmax are reshaped through multiplication of the fuzzy tool demand rate defined in eq. 4 by the temporal coefficients indicated below: lmin
I
I d ) = ~RU) * Tpur lmax(j)=fR(j) * [ @ + I ) + Tint]
~
I
lmin(j) = ~ r(1, i h, p, v) lmax(j)= Tri (I, A, P, Y)(6)
3.2 Hexagonal Membership Function An hexagonal-shaped MF is used for input and output variables. The hexagonal curve is a piecewise linear function of a positive real variable, x, and depends on six scalar parameters a, b, c, d, e, f:
4 FUZZY FTMS OPERATION In Figure 3, the on-hand inventory control of a generic partnumber is presented to explain the FDR FTMS functioning. At time t = 0, the part-number inventory size is lo and the control limits assume single values (eq. 6). As Tintand Tpur are constant and P/G is updated yearly, lmaxis a function of the current fuzzy demand rate fR(j) and predicted dressing time @+I), and lmlna function of the current fR(j) value. Each time tools wear out (w-events), the counter of wornout wheels, j, increases; the inventory level, I, decreases; the fR(j) value is updated; dressing time predictions, @+I), are issued; and lmln and lmax are recalculated.
a ? w
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Figure 1: (a) Triangular membership function (MF) for fuzzy demand rate, fR, vs. demand rate, dR; (b) Triangular MF for fuzzy control limits, lmlnand lmax,vs. on-hand inventory level, I; (c) Hexagonal MF, Hex (x, a, b, c, d, e, f), for input and output variables vs. on-hand inventory level, I a 2 w
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Figure 2: Membership functions for (a) input variable Inventory, (b) output variable Purchase, (c) output variable Dressing, vs. on-hand inventory level, I. S = Short; C = Controlled; L = Large, N = Necessary; U = Unnecessary. w-event, wl: j = 1, Iwl < lo, dR(l) = PIG (eq. I ) , At the Ist and t = r = u = dR(l) (eq. 3). The fR(1) triangular MF degenerates to a singleton (eq. 4) and lmln(l),lmax(l)take on single values (eq. 6), reported at w1 in Figure 3. As Iwl falls within the updated fuzzy control range, the worn-out tools are sent to dressing but no new tool is purchased. Each time new or dressed tools are delivered by suppliers (d-events), the on-hand inventory, I, grows but Iml and lmax are not affected. This is what happens at the 1” delivery event, dl: Id1 > Iwl, lmln= lmln(l)and lmax= lmax(l). At the w-event, w2: j = 2, < I d l , dR(2) = 2/t(2), t = min [dR(1 dR(2)1, u = max [dR(1 dR(2)1, = mean [dR(1 dR(2)I = (& + u)/2. The fR(2) MF is an isosceles triangle. The fuzzy limits lmln(2),lmax(2)are defined by a max (u, Y), min ( h ,A), and symmetrical mean (p, P), reported at w2(Figure 3). The 2ndd-event, d2, represents a case where I crosses the upper control limit: Id2 > lmax(hl in Figure 3). At the next wevent, w3, a number of worn-out tools, equal to the fuzzy difference Id2 - lmax,will remain on-hold in the warehouse. At w3: j = 3, la < ld2, dR(3) = 3/t(3), and &, r, u are given by eq. 3. The fR(3) MF is a scalene triangle. The fuzzy control limits lmln(3), lmax(3) are defined by a max, min, and asymmetrical mean, reported at w3 (Figure 3). As la falls within the fuzzy control range, the worn-out tools are sent to dressing, except for Id2 - lmaxwheels that remain on-hold. The next w-event, w4, represents the case where I crosses the lower control limit: lw4 < lmln(h2 in Figure 3). The wornout wheels must be sent to dressing and a further number of tools, equal to the fuzzy difference lmln - lw4, must be provided. If there are worn-out tools on-hold, they are sent to dressing in partial or total substitution for tool purchases. In any event, the number of required tools exceeding the worn-out wheels on-hold must be newly purchased. At w4, the fR(j) MF is a scalene triangle. The fuzzy control limits lmln(j), lmax(j) are defined by a max, min, and asymmetrical mean, reported at w4 (Figure 3). )I
)I
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The last d-event, d3, brings the inventory level entirely within the fuzzy control range, lmln< ld3< lmax,and so on.
4.1 Crisp and Fuzzy FTMS Test Case The flexible tool management of a real CBN grinding wheel part-number, M8110855, was simulated as test case application for the crisp PDR, ADR and fuzzy FDR FTMS paradigms using one year historical data. In Figure 4, the historical and simulated inventory level trends are reported vs. time (one year), along with the historical tool supply cost and percent cost variation of the simulated trends. It is worth recalling that the historical inventory level trend, IHIST, is the result of experienced staff tool management activity. Though this management approach based on expert knowledge has the drawback of depending on skilled staff, it is robust and reliable and can be used as a reference to assess alternative intelligent computation procedures of tool management, operating without human expert support.
Figure 3: Generic part-number on-hand inventory level, I, vs. time, t, for the FDR FTMS; w = wear-out event ( 0 ) ; d = delivery event ( 0 ) ; red lines: fuzzy control limits; hl, h2: fuzzy control limit crossings (x).
Figure 4: Historical (IHIS), crisp (IpDR, IADR) and fuzzy (IFDR) FTMS simulated on-hand inventory level vs. time (one year), for part-number M8110855. All FTMS approaches are shown to provide an economy over the historical cost. The crisp PDR paradigm yields a saving of 18%, the crisp ADR method a saving as high as 88%, and the fuzzy FDR scheme an saving of 79%. The notable cost reduction of the ADR and FDR methods versus the PDR approach is due to the initial planned tool demand rate for this part-number (dR(l) = P/G = 7.10) being much lower than the on-hand inventory level during the Ist month of tool management where no wear-out events occur (19 5 I 5 20, Figure 4). This results in no new tool purchase when the first wear-out event occurs at the end of the Ist month. Afterwards, the PDR simulation provides for new purchase orders at all occasions when, due to multiple worn-out wheels, the on-hand inventory level drops lower than the constant lower control limit, I < Imln. Conversely, in the ADR simulation no tool purchase orders are issued for the whole period because the actual tool demand rate drops to dR(2) < 2.70 as early as the month of tool management and remains very low for the rest of the period. Finally, the FDR simulation follows closely the ADR trend till the 6th month of tool management when its higher sensitivity to tool shortage yields a slightly higher fR(j) that generates a few new tool purchase orders. This reaction of the fuzzy FDR paradigm produces a modest tool supply cost increase versus the crisp ADR approach (88% - 79% = 9%), but it yields a positive reduction of stock-out risk: lFDR is never lower than 7 units whereas lADR gets as low as 3 units (Figure 4). 4.2 Functional Advantages of the Intelligent FTMS The main features of the MATMS integrated intelligent FTMS are the utilisation of fuzzy set theory to model the uncertainty of tool demand rate and the use of fuzzy reasoning to expand the operational flexibility of the tool management strategy in the supply network [14]. In terms of functional advantage, it is worth considering that in prior crisp FTMS approaches, once a tool purchase or dressing job was evaluated, it had to be either thoroughly carried out or completely neglected. In the fuzzy FTMS method, a decision may be taken in proportion to its necessity degree: e.g., if a purchase order of 10 wheels is judged necessary by 70%, a purchase order of only 7 new tools can be issued. This can provide for an actual economy and practical benefit in the management of CBN grinding wheels. 5 SUMMARY The implementation of an intelligent Flexible Tool Management Strategy (FTMS), based on Fuzzy Logic (FL) theory and integrated in a Multi-Agent Tool Management System (MATMS) for CBN grinding wheel procurement in a supply network, was presented. The intelligent FTMS is the problem solving function of the MATMS agent whose
task is the optimum tool inventory sizing and control. It operates on account of running turbine blade production plans, tool capacity and dressing time predictions. Its rationale is to let the tool inventory level vary within a real time variable control range to achieve the minimisation of tool management cost and stock-out risk. The principal characteristics of the intelligent FTMS approach are the use of fuzzy set theory to model the uncertainty of the tool demand rate and the adoption of fuzzy reasoning to expand the strategy operational flexibility versus traditional tool management and prior crisp FTMS paradigms. A test case application of the previous crisp FTMS approach and new fuzzy FTMS formulation to a real CBN grinding wheel part-number illustrated the functional advantages and practical benefits of the fuzzy FTMS paradigm in terms of tool supply cost saving and tool stock-out risk minimisation. 6 ACKNOWLEDGEMENTS This research work was carried out with support from the FP6 EC NoE on I*PROMS. The paper draws on the thesis work of A. Bontempi whose contribution is acknowledged. REFERENCES Wiendahl, H.-P., Helms, K., Hobig, M., 1998, Management of Variable Production Networks: Vision, Management & Tools, Annals of CIRP, 47/2: 549-555. EIMaraghy, W.H., Urbanic, R.J., 2004, Assessment of Manufacturing Operational Complexity, Annals of CIRP, 53/1: 401-406. Monostori, L., Csaji, B.Cs., Kadar, B., 2004, Adaptation and Learning in Distributed Production Control, Annals of CIRP, 53/1: 349-352. Wiendahl, H.-P., Scholtissek, P., 1994, Management and Control of Complexity in Manufacturing, Annals of CIRP, 43/2: 533-540. Wiendahl, H.-P., Lutz, S., 2002, Production in Networks, Annals of CIRP, 51/2: 573-586. Fox, M.S., Barbuceanu, M., Teigen, R., 2000, AgentOriented Supply-Chain Management, Int. J. of Flexible Manufacturing Systems, 12: 165-188. Scholz-Reiter, B., Hoehns, H., Hamann, T., 2004, Adaptive Control of Supply Chains: Building Blocks and Tools of an Agent-Based Simulation Framework, Annals of CIRP, 53/1: 353-356. Teti, R., D'Addona, D., 2003, Agent-Based Mulptiple Supplier Tool Management System, 36th ClRP Int. Sem. on Manufacturing Systems - ISMS 2003, Saarbrucken, 3-5 June: 39-45. Teti, R., D'Addona, D., Segreto, T., 2004, Flexible Tool Management in a Multi-Agent Modelled Supply Network, 37th ClRP Int. Sem. on Manufacturing Systems - ISMS 2004, Budapest. 19-21 May: 351-356. [ l o ] Teti, R., D'Addona, D:, 2004, FL based Tool Management in a Multiple Supplier Network, 4th ClRP Int. Sem. on Intelligent Computation in Manufacturing Eng. - ICME '04, Sorrento, 30 June - 2 July: 555-562. [ I l l Teti, R., D'Addona, D., 2003, Grinding Wheel Management through Neuro-Fuzzy Forecasting of Dressing Cycle Time, Annals of CIRP, 52/1: 407-410. [I21 D'Addona, D., Teti, R., 2003, Multiple Supplier NF Delivery Forecasting for Tool Management in a Supply Network, 6thAITEM Conf., Gaeta, 8-10 Sept.: 127-128 [I31 Teti, R., D'Addona, D., 2004, Adaptive NF Tool Delivery Forecasting for Flexible Tool Management in a Supply Network, 5th Int. Workshop on Emergent Synthesis - IWES '04, Budapest, 24-25 May: 41-50. [I41 Zhang, H.C., Li, J., Merchant, M.E., 2003, Using Fuzzy Multi-Agent Decision-Making in Environmentally Conscious Supplier Management, Annals of CIRP, 52/11385-388.