KEY PERFORMANCE INDEX DESCRIPTION

The six KPI indices used by MTI are depicted in Table 1. The six processes are described as follows:

Table 1 Key Performance Index Description

KPI # KPI name KPI Definition To-Be KPI Sponsor

Y1 Percentage of order confirmed

The percentage of purchase orders confirmed that could be delivered within 3 days.

PC, MC,

Y2 Percentage of inbound operation complete

The number of inbound orders/lines that are operated divided by the total inbound orders/lines in the measurement period

Y3 Percentage of work order material planning & kitting orders/lines processed (planning, picking & material kitting) complete

The number of work order material kitting orders/lines that are kitted on-time to demand requirements divided by the total work order material kitting orders/lines requested in the measurement period

Y4 Percentage of delivery performance to first committed date

The percentage of orders that are fulfilled on or before the first committed date.

All

X1 ECO (engineering change order) cycle time

The total time for request for change from customer engineering, production or quality control to revising a blueprint or design released by engineering, and implement the change within the make operation.

SM and Engineer

X2 Total build time Total build time is the average time for MTS, MTO semi-products from when production begins on the released work order until the build is completed and unit is ready to be inspected.

Y

1: Purchase order (PO) schedule evaluation

MTI is set up in such a way that each customer order should be fulfilled within no more than three days. The production controller (PC) is informed of any order coming into the sales department. PC would commit the order if work-in-process (WIP) status and production capacity available for the required order. Then PC informs order administration (OA) and the order evaluation process is completed. Otherwise, PC will pass the work order to material control (MC) and purchasing section. Purchasing section will confirm the material schedule and make a feedback to MC.

Y

₂: Inbound operation

The inbound operation process starts as the warehouse receives an arrival material. Time spent on the material for unloading, receiving, inspecting, and moving to points to be used and storage locations are recorded. The necessary bookkeeping for system control is also performed.

Y

₃: Work order preparation and W/H material hand over

Stopwatch is pressed as PC releases a work order to warehouse. Then, W/H spends time for launching the plan for material kitting task, generating dispatching assignment, picking, kitting, packing, and handling the material to production lines.

Y

4: Outbound operation

The outbound operation KPI is initialized by the production line releasing the packing list and transferring to OA. OA will follow the packing list to generate the shipping notice and then

transfer to logistic department. After the logistic department gets the shipping notice they arrange transportation and prepare all the freight information and documentation. When everything is ready, they will pass all related documents to W/H. The shipment is ready when W/H gets the product from the production line and documentation from logistic department.

Total KPI is responsibility by Production line, OA, Logistic and W/H. The other KPI for manager review are OTD for first commit date and customer required date. The OTD is the most important index for customer satisfaction and should be tracked monthly.

X

1: Engineering change order

The purpose of this KPI is evaluating the engineering change process (ECP). The process is initiated as a customer releases engineering change request to document control center (DCC).

The process is completed as OA feedbacks to the customer.

X

2: Production & testing

This KPI is to evaluate the efficiency and productivity of a production line. The collection of KPI is from shop floor control and analyzed by the system. Two separate sets of data are collected: ‘total build time’ and ‘work order completed ratio’. ‘Total building time’ is the average time for the line spends on production of customer orders. The process includes surface mount technology (SMT) production, semi-product staging, product integration, test, packaging, shipping inspection to put away finished goods in the assigned staging area. We can evaluate the test time and efficiency for each work center and test station. “Work order complete ratio” begins on the released work and end by the work order been closed. The work order completed ration will impact the on time delivery (OTD).

3 The performance data

The nine production lines of MTI are denoted as Line 1, 2,.., and 9. Their data on the six indices are depicted in the following table. For each line, say Line j, yrj denotes the data on index

Y

_r, r = 1, 2, 3 and 4, and xij denotes the data on index Xi, i = 1 and 2. As the six KPIs are defined, larger values at Y1,

Y

3 and

Y

4 smaller values on X1 and X2 indicate the better performance of the production line. Therefore, one may use the following equation to measure the efficiency of each

Line j.

∑

₌⁴₁ ^/ ₌²₁

= r rj r i ij i

y u x v

P

(1)

The notations ur and vi are the weights that should be assigned to index Yr and Xi, respectively.

It is a challenge to have a set of proper weights of the indices to measure the relative performance of production lines. We employ the theory of DEA to assess the relative efficiencies of the nine lines.

Table 2 KPI data for the production lines KPI

4 Implement Data Envelopment Analysis models

The relative efficiency of Line k is evaluated by following input-oriented CCR-I model.

[CCR-I-FP

]

εis an Archimedean infinitesimally small number.

[CCR-I-FPk] tries to maximize the efficiency score for the object Line k while keeping the efficiency scores for each Line j being no greater than one. [CCR-I-FPk] is a fractional programming model and is transformed into a linear programming model as shown below. The lower bound conditions for the decision variables ur and vi would guarantee the proper transformation given the data of a line are non-negative and at least one is positive.

[CCR-I-LP

]

Maximize _r

r rk

y u

P

⁼

∑

₌⁴₁

Subject to

∑

_r₌⁴₁

y

u

r^-

∑

_i₌²₁

x

v

i ^≤⁰^,

j

=1,...,9;

are the excess of the to-be-minimized index Xi and shortfall of the to-be-maximized index Yr

of this expression, respectively, and are called slacks. We add the superscript “” on the*

variable to represent its optimal value of the model. According to the solution of the model Line

k’s performance could be one of the following categories.

Pure efficient:

s

⁴

s 0

The [CCR-I-FPk] model assumes constant returns-to-scale. To identify the property of Line k, increasing or decreasing returns-to-scale, Banker, Charnes, and Cooper (BCC) (1984) proposed a model that measures so-called pure technical efficiency and scale efficiency. It is called the BCC model. Starting out from Shephard’s definition of a production possibility set, BCC-I assumes that this set satisfies basic axioms of convexity, inefficiency, ray unbounded and minimum extrapolation,

λ

_j ≥0,

j

=1,2,...,9 and

∑

_j⁹₁ ^*j

1 λ

= .

BCC-I used the axioms and Shephard’s distance function to drive a model that measures Pure

Technical Efficiency.

[BCC-I-DLP

]

The dual form of above [BCC-I-DLPk] is expressed as follows:

[BCC-I-LP

]

Measure by the intercept

u its sign, positive or negative, allows one to determine the

^*_0k magnitude of the returns-to-scale whether Line k currently evaluated is operating under increasing or decreasing returns-to-scale. Thus

u

₀^*_k >0,

u

^*₀_k =0 and

u

^*₀_k<0 imply Line k is operating under conditions of decreasing (DRS), constant (CRS), and increasing (IRS) returns-to-scale, respectively.

Tone (2000) introduced the slack-based measurement model. We consider an expression for describing the data for Line k as

i r rk

It can be verified that

ρ

_k satisfies properties (i) units invariant and (ii) monotone decreasing in input/output slack. Furthermore, from (1), it holds0<

ρ

_k ≤1.

Another variation of SBM model [SBM-I] is also introduced to estimate the efficiency of Line k.

[SBM-I]

[SBM-I] can be transformed into a linear program using the Charnes-Cooper transformation in a similar way to the CCR model. Refer to Tone (2001) and Cooper et al. (2000) for details.

Let and optimal solution for [SBM-I] is

( ρ

^*_k

, λ

^*_j

, s

_i^-^*

, s

_r⁺^*

)

. Based on this optimal solution, we define Line k as being SBM-efficient as follows:

(SBM-efficient) Line k is efficient if

ρ

_k^* =1. This condition is equivalent to

s

_i⁻^* =0 and

s

_r⁺^* =0, i.e. no excesses and no shortfalls in any optimal solution.

Cross-sectional results

Banker, Charnes and Cooper (1984) suggested splitting the overall CCR efficiency-global technical efficiency (

θ

_k^*) into two factors, pure technical efficiency (

η

^*_k) and scale efficiency (

S )

_k^* in the following manner:

The BCC efficiency used the axioms and Shephard’s distance function to drive a model that measures pure technical efficiency. The scale efficiency (

S ) can’t exceed one. When the scale

^*_k efficiency of a line is less than one, a further step can be taken to decide whether it is located at a

stage of increasing returns-to-scale or decreasing returns-to-scale.

The calculations of economies of scale

u have a direct interpretation in terms of the

_0k^* underlying dynamic evolution. In an obvious sense, a production line with decreasing returns-to-scale has pushed its expansion too far, and management can be expected to consider the possibility of downsizing and reducing its scale of operation. Conversely, a production line with increasing returns-to-scale will typically be engaged in rapid economic growth. The mix efficiency, M^*_k, is not great than one and we have a decomposition of the non-radial efficiency into radial and efficiency as

5 Interpretation to the efficiency scores

Apply the models, [CCR-I-LPk

], [BCC-I-LP

] and [SBM-I] for the data depicted in table

2, the objective function values and the cross section results are listed in table 3.

Table 3 Efficiency scores

Line k θ

^*_k

η

^*_k

S

_k^*

ρ

^*_k

M

_k^*

u

_0k^* RTS

From table 3, we can see Lines 7, 8, and 9 exhibit high efficient performances at any scale.

The three production lines could be the benchmark of all the others. Scale efficiency

S is equal

_k^*

to (

θ

_k^*/

η

^*_k). If

S =1, then the Line k is operating at constant returns-to-scale which is the

_k^* optimal level.

Line 1 and Line 4 have a fully efficient η

₁^* and

η

₄^* score and low efficiency of

θ

₁^*(0.423) and

θ

₄^*(0.722). The low efficiency is caused by scale0<

S

_k ≤1. The lines operate at an inappropriate scale either increasing or decreasing returns-to-scale. The values of

u and

₀₁^*

u

₀₄^* for production Line 1 and Line 4 are negative, indicating that they are increasing return-to-scale;

this shows that it is possible for them to improve their efficiency by scaling up their production activities.

It is observed that production Line 5 with low

ρ

₅^*(0.783) is caused by

M (0.877), and

₅^*

S

₅^* (0.920). Also, it is observed that production Line 6 with low

ρ

₆^*(0.539) is caused by

M

₆^* (0.817), and

S (0.715). Both

₆^*

u and

₀₅^*

u

^*₀₆ values are positive, which indicate that they are decreasing return-to-scale, showing that they can improve their efficiency by scaling down their production activities.

The production Line 2 low efficiency of

ρ

₂^*(0.407) is caused by

S (0.923) and

₂^*

η

₂^*(0.447).

The production Line 3 low efficiency of

ρ

₃^*(0.423) is caused by

S (0.690) and

₃^*

η

₃^*(0.632). Both of

u and

^*₀₂

u values are negative ones show that they have a possibility to improve their

^*₀₃ efficiency by scaling up their production activities.

η

^*_k is pure technical efficiency and low efficiency caused by technical and management. So, we can improve the efficiency by increasing scale, improving operation and management.

6 Conclusions

In this paper, we illustrate the KPI target and definition in the order fulfillment cycle. We list several KPIs and evaluate the nine production lines of MTI. The method introduced can also be used in assessing the performance of different companies. We provide example and interpretation intending to indicate direction of improvement. We decompose the efficiency score of each production line into technical, pure, scale, and mix efficiencies. DEA is successfully implemented on the assessment of the production lines. It can also be provided to assess the efficiency of management and other operation processes.

References

Banker, R.D., Charnes, A. and Cooper, W.W., 1984, Some Models for Estimating Technical and Scale Inefficiencies in DEA, Management Science, 30(9), 1078-1092.

Callan, S.J., 1991, The Sensitivity of Productivity Growth measures to Alternative Structural and Behavioural Assumptions: An Application to Electric Utilities, 1951-1984, Journal of

Business and Economic Statistics, 9(2), 207-213.

Chavas, J.P. and Cox, T.L., 1990, A Non-Parametric Analysis of Productivities: The Case of U.S.

and Japanese Manufacturing, American Economic Review, 80(3), 655-666.

Cooper, W.W., Seiford, L.M., Tone, K., 2000, Data Envelopment Analysis – A Comprehensive Text with Models, Applications, References and DEA-Solver Software, Kluwer Academic

Publishers, Dordrecht.

Farrell, M.J., 1957, The Measurement of Productive Efficiency, Journal of the Royal Statistical

Society, 120, 253-281.

Gaves, D.W., Christensen, L.R. and Diewert, W.E., 1982, The Economic Theory of Index Numbers and The Measurement of Input, Output, and Productivity, Econometrica, 50(6), 1393-1414.

Tone, K., 2002, A slacks-based measure of super-efficiency in data envelopment analysis,

European Journal of Operational Research, 143, 32-41.

在文檔中生產線訂單履行週期之績效評比-以微波通訊廠為例 (頁 12-21)

Y

Y

Y

Y

X

X

3 The performance data

Y

Y

Y

Y

Line j.

∑

∑

y u x v

P

4 Implement Data Envelopment Analysis models

[CCR-I-FP

]

[CCR-I-LP

]

y u

P

∑

∑

y

u

∑

x

v

j

of this expression, respectively, and are called slacks. We add the superscript “*” on the

k’s performance could be one of the following categories.

s

s 0

λ

j

∑

1

λ

Technical Efficiency.

[BCC-I-DLP

]

[BCC-I-LP

]

u its sign, positive or negative, allows one to determine the

u

u

u

ρ

ρ

[SBM-I]

( ρ

, λ

, s

, s

)

ρ

s

s

Cross-sectional results

θ

η

S )

S ) can’t exceed one. When the scale

u have a direct interpretation in terms of the

5 Interpretation to the efficiency scores

], [BCC-I-LP

] and [SBM-I] for the data depicted in table

Line k θ

η

S

ρ

M

u

S is equal

θ

η

S =1, then the Line k is operating at constant returns-to-scale which is the

of this expression, respectively, and are called slacks. We add the superscript “” on the*