Flexible tool management strategy for optimum tool inventory control

D. D’Addona, R. Teti

University of Naples Federico II, Naples, Italy

Introduction

The design and functioning of a Flexible Tool Management Strategy (FTMS) paradigms for optimum tool inventory sizing of CBN grinding wheels for nickel alloy turbine blade fabrication is presented
The FTMS is integrated in a Multi-Agent Tool Management System (MATMS) as a domain specific problem solving function of the intelligent agent responsible for tool inventory sizing and control
The evaluation and comparison of the performance of the FTMS was carried out with reference to two real industrial cases of CBN grinding wheel inventory management

CBN grinding wheel tool management

Tur bine blades are manufactured along several production lines, each for one aircraft engine model requiring a set of CBN grinding wheel types (part-numbers)
Each part-number is planned to work a maximum number of blades
Once a CBN grinding wheel 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

Traditional CBN grinding wheel tool management

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 pieces/month, P
# of pieces/wheel, 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 – I₀

where: P/G = tool demand rate (# of wheels/month); I₀= initial part-number inventory size

Traditional CBN grinding wheel tool management

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
The logistic staff of the turbine blade producer is aware of these drawbacks and modifies the inventory size trend by increasing or reducing the part-number inventory level based on experience
The results of this policy, founded on expert knowledge of skilled staff, are given by historical inventory size trends
In some cases, the expected trend, based on traditional tool management, corresponds to the historical one; in other cases, the expected demand is underestimated, with risk of stock breakage, or overestimated, with excessive capital investiment
The historical trend, issue of human expert activities, is a suitable solution that prevents tool stock breakage and useless investments

Flexible tool management strategy

The design, functioning and performance of a Flexible Tool Management Strategy (FTMS) integrated in the MATMS is illustrated
The FTMS paradigm is configured as a domain specific problem solving function operating within the intelligent agent of the MATMS, Resource Agent, holding the responsibility for optimum tool inventory sizing and control of CBN grinding wheels
The developed MATMS subdivided into three functional levels:

the Supplier Network Level, including the tool manufacturers in the supply network
the Enterprise Level, including the logistics of the turbine blade producer
the Plant Level, including the production lines of the turbine blade producer

Flexible tool management strategy

The Resource Agent (RA) merges the functions of tool inventory management, tool resource demand estimation and determination of tool order quantities. The RA domain specific problem solving function is the FTMS
Each time a worn-out CBN grinding wheel leaves a production line, a new part-number demand is set up as a function of the dressing cycle time
If an accurate estimate of the dressing cycle time of each worn-out CBN grinding wheel is provided by the DTPA, the demand for that part-number can be compared with the part-number on-hand inventory
Moreover, as a CBN grinding wheel purchase order issued at a certain time requires a suitable lead time (Tpur) before an actual delivery takes place, to avoid stock-out it is necessary to have available at any time a minimum stock at least equal to the part-number demand during the purchase order lead time Tpur

Tool inventory control

A FTMS was initially presented in previous work whose rationale was to make sure that the part-number on-hand inventory size, I, remains within an interval defined by two real-time control limits:

the part-number demand during Tpur (lower limit, Imin)
the part-number demand calculated using the dressing cycle time predicted by the DTPA (upper limit, Imax).

The inventory level, I, is left free to fluctuate within the limits [Imin , Imax], provided neither of them is crossed, and whenever I decreases due to a tool wear-out event, the CBN grinding wheels are sent out for dressing
When the lower control limit is crossed (I < Imin), the turbine blade producer logistics must either provide additional serial-numbers
When the upper control limit is crossed (I > Imax), the logistics reduce the part-number on-hand inventory by suspending the dressing job order allocation to bring back the stock level within the control range

FTMS procedure

An improved FTMS procedure was presented whereby the part-number demand rate was not given by the constant ratio P/G but it was expressed by an adaptive function, dR(w), of wear-out events, w
A wear-out-event was defined as an event in the tool management where a number of worn-out CBN grinding wheels with the same part-number are simultaneously proposed for dressing
The adaptive tool demand rate was defined as follows:

dR(w) = P/G if t(w) ≤ 1

dR(w) = j/t(w) otherwise

where: w = counter of wear-out events and t(w) = time (months from the start of the FTMS procedure) at which the dressing of the worn-out serial-numbers is proposed .

FTMS procedure

In the Adaptive Demand Rate approach, the control limits are given by:

Imin = dR(w) * Tpur
Imax = dR(w) * [T (j+1) + Tint]

where: j = counter of worn-out serial-numbers, T (j+1) = DTPA dressing cycle time prediction, and Tint = internal time

As Tint is a constant typical of the manufacturing plant, Tpur is considered constant on a historical basis, and P/G is updated yearly by the turbine blade producer for each one year period

the upper control limit Imax varies or stays constant as a function of the current adaptive demand rate dR(w) and the predicted dressing cycle time T (j+1)
the lower control limit Imin varies or stays constant only as a function of the current value of dR(w)

Novel FTMS procedure

Ifut is the on-hand inventory level calculated with reference to a future time (t + Trt) and is given by:

Ifut(t + Trt) = I(t) + X + Y + Z – dR(w) * Trt

In this FTMS approach, if I(t) ≥ Imin, Trt is given by the sum of the mean historical dressing cycle times dct (6 weeks) and the internal time Tint (5 weeks):

Trt = dct + Tint = 6 weeks + 5 weeks = 11 weeks

If I(t) < Imin, Trt is considered equal to the purchase time Tpur (9 weeks):

Trt = Tpur = 9 weeks

Novel FTMS procedure

The above version of the FTMS has the drawback of a “shortsighted” approach because decisions are only taken on the basis of the current inventory level, I(t), with no consideration for what will happen in the future
A “non shortsighted” version of the FTMS (NS-FTMS) procedure is proposed whereby the FTMS takes into account for tool management decision making the value of a future on-hand inventory level, I_fut(t + T_rt), instead of the current on-hand inventory level, I(t)

Test case applications

The flexible tool management of the two part-numbers was simulated as test case applications of the novel “non shortsighted” FTMS version using one year historical data
The historical and the simulated inventory level trends are reported versus time, for the reference period of one year, with the indication of the historical tool supply cost and the cost variation of the simulated trend
It is worth recalling that the inventory level historical trend is the result of the tool management activity of experienced staff
This managment approach is robust and reliable and can be utilised as a reference for assessing intelligent computation procedures of tool management, operating without the support of human experts

Test case applications results

Table 1: Yearly tool supply cost for the two test case part-numbers

Part-Number	Scenario	Supply Cost (€)	Cost Variation	Purchased Tools	Dressed Tools
M3941142-1	Historical	54.996	-	18	73
M3941142-1	Simulation	33.324	-39%	3	55
M3942462	Historical	7.326	-	0	22
M3942462	Simulation	2.706	-63%	3	3

Test case applications results

Initial tool demand rate, P/G, and average demand rate, d_R,during the tool management period for the two test case part-numbers

Part-Number	Initial demand rate P/G(units/month)	Average adaptive demand rate dR(units/month)
M3941142-1	8.1	6.3
M3942462	11.8	2.4

Test case applications results - P/N M3941142-1

Historical (black) and novel FTMS simulated (green) on-hand inventory level, I, vs. time (one year),

for part-numbers M3941142-1

Test case applications results - P/N M3942462

Historical (black) and novel FTMS simulated (green) on-hand inventory level, I, vs. time (one year),

for part-numbers M3942462

Conclusions

The design, functioning and performance of a novel Flexible Tool Management Strategy (FTMS) paradigm integrated in a Multi-Agent Tool Management System (MATMS) for automatic tool procurement was presented
The MATMS operates in the framework of a negotiation based multiple-supplier network where a turbine blade producer requires dressing jobs on worn-out CBN grinding wheels for nickel alloy turbine blade manufacturing from different tool manufacturers
The FTMS is designed as a domain specific problem solving function of the MATMS intelligent agent whose task is the optimum tool inventory sizing and control of CBN grinding wheels.
This agent performs its activities on the basis of running production plans and dressing cycle time predictions, utilising the FTMS paradigm

Conclusions

Test case applications of the novel FTMS paradigm based on tool management decision making with reference to the value of a future inventory level, Ifut(t + Trt), were presented to illustrate and assess the new FTMS performance versus traditional tool management
By comparing the historical and the FTMS simulated inventory level trends for two test case part-numbers, in both instances a notable cost reduction was obtained with the FTMS method
The development of the research activity will aim at the generalisation of the management approach to the inventory control applications other than CBN grinding wheel tool management