By - Munish Moudgil IAS, Commissioner, Survey Settlement and Land Records, Revenue Department, Government of Karnataka

1. 0 Introduction

The Public Services form the core in the gamut of Citizen-Government interactions. In fact, in case of “Public Services” a formal contractual or legal “Customer-Service Provider” relationship exists between Government and the citizen. In other words, the Government Public Services are the legal entitlements of the citizen.

It may be noted that a citizen interacts with government in broadly four contexts

(i) Services

(ii) Grievances/Complaints

(iii) RTI (Right to Information) Act

(iv) Any other correspondence/interaction (for example a citizen writes to government sharing some of his “ideas” or thoughts on governance issues etc)

The concept of Disposal Index as a measure of performance of delivery is a general concept which can be equally used for each of the four broad categories mentioned above; however, idea is elaborated below in context of “Public Services”.

Starting with “Citizen’s Charter” in early 1990s (Britain under John Major), today, the concept has evolved and led to conferment of statutory and legally enforceable rights to the citizens in the form of “Right to Service Delivery Acts” which mandate public service delivery in a time-bound manner.

The measurement of the performance of delivery of Public Service in an (i) objective, (ii) intuitive, (iii) rational, (iv) scalable, and, (v) transparent manner has remained a challenge. “DISPOSAL INDEX” (DI) meets the said need.

2.0 The Idea

The simplest and the most intuitive way a citizen evaluates delivery of service is whether she gets it in the time it is supposed to be delivered. “Is my train going to reach my destination in-time?”, a question that haunts every traveler. The service seeker is no different.

The Governments through Citizen’s Charter, or, through “In-Time Service Delivery Act” or through relevant Law/Rules/Circulars/Guidelines prescribe time for delivery of the public services. The citizen wants them be delivered within the said prescribed time. Period. DI is a mathematical measure of this performance of a department/unit/officer/staff/service.

In layman terms, DI is a measure of “How many times faster is the actual processing of Service Requests as compared to the prescribed processing time”

3.0 Mathematical Formulation of “Disposal Index” 3.1 The Concept of DI

Disposal Index (DI) is calculated for each individual service request received from the citizen and it measures the status of delivery of the said service request at a given point of time. The time of receipt of a service request is T=0, the DI at time T=T1 measures the status of delivery of the said service request at time T1.

Conceptually, DI for i-th Service Request for a specific service S1 at time T = T1 (T=0 is the time of receipt of the i-th service request) is

DI (S1)(i) (T1) =

[At what stage of delivery the Service Request (i) IDEALLY is at time T=T1]

divided by

[At what stage of delivery the Service Request (i) ACTUALLY should be at time T=T1]

In other words, imagine a train travelling from point A to B, say 100KM apart, and, in case the ideal time of travel is 10 hours; then at 5th hour it is expected ideally at 50KM from point A. Let it be ACTUALLY be at X-KM at 5th hour; then

DI (Train Travel)(5hour) = [X/50]

In exactly the same manner, the DI of an individual service request for any Public Service (with a prescribed time for delivery) can be calculated. This way a number gets associated with each service request pending/disposed off in a system at a given point of time. This number is called the DI of the said service request at the said time. The sum total of all such DIs of all the relevant service requests at a given point of time upon division by total number of such service requests gives the DI of the whole system/office/unit.

3.2 Analog and Digital variation of the Disposal Index

The above formulation is essentially analog or continuous method of DI calculation. However, most of the Public Services disposal process is digital. In other words, the Service Requests move from one official to another while spending some time in the hands of each such official (called “Dealing Hands”). In such a step-by-step or table-to-table movement, the method to calculate Disposal Index is explained below (as when the Service Request is at a particular step, it apparently just sits there)

3.2.1 “Workflow” Information is Available for Service Delivery:

Conventionally, each step from receipt of a Service Request to its final disposal is called a “Step” in the “Workflow”. Therefore, in case, say, 20 days are assigned for delivery of a particular Service which has 10 steps in its “Workflow”. Then, in order to deliver the Service in 20 days all the 10 steps ought to be completed within 20 days. In turn, this means that each step of the Workflow ought to get completed in much less than 20 days such that sum total of days assigned to each Step in the Workflow equals 20 days (or less). The DI shall be, therefore, calculated as follows –

Disposal Index (DI) =

{Step of Workflow in terms of days where an application actually is after N days} divided by “N” For example, “Caste Certificate” ought to be delivered in 21 days time. Let’s say there are following 5 workflow steps in its disposal (with time assigned to each workflow step). Let the actual and ideal requirement be represented by table below (for an application which has been received three days ago)

It can be seen that in 3 days, ideally, the application should have been at step 2 while it is at step 4 and it came to step no 4 after 1 day and is pending there for two days when this DI evaluation is being done

DI of this Service Request/Application =

{Ideal “In” day of step where application actually is + no of days at this step} / No of days since receipt

= {8 + 2}/3 = 3.33

Naturally, the DI for a Service Request/Application can equally well be calculated using “hours/minutes” (instead of “days”).

3.2.2 “Workflow” Information is NOT Available for Service Delivery:

However, above method needs to be modified in case workflow step-wise information is not available. The same is explained below

Assuming, information for none of the workflow steps is available. Then we simply know the receipt date and disposal dates of individual applications. Then Disposal Index of Nth Service Request for a particular service in an office will be calculated as follows –

(Nth Service Request for Service S1 in an office) =

{Ideal Prescribed Time Limit for Service S1}

divided by

{Actual Disposal Time of Nth Service Request for S1}

3.3 DI of an Individual Service Request and DI of a {Set of Service Requests}

The DI of each individual service requests can be clubbed together in any permutation and/or combination to form of “set of service requests” which can then be used to calculate the

(i) DI of a specified Service in specified office/unit

(ii) DI of any individual officer/official

(iii) DI of a specified group of service requests

(iv) DI of a district, block, state or any administrative unit, ect..

Each such cumulative DI, in turn, is a mathematical score which measures the average performance of disposal at a given time with respect to the {Interested Set of Service Requests}. As DI at a given point of time is a number associated with each service request; therefore, DI for any type of Interested Set of service request can be calculated.

3.3.1 Cumulative DI when Workflow Step Information is Known

For example, once DI of each individual Service Request has been calculated and tagged to each one of them in the system. Now, using the DI of each Service Request in a service or in an office, the DI of service and office can be calculated as follows –

DI of a Service (wrt {Set of Service Requests} at a given point of time) =

(Sum of DI of all Service Requests in the {Set of SRs} of interest)

divided by

No of all Service Requests in the {Set of SRs} of interest

Similarly,

DI of an Office = Weighted average of DI of Services of that office

DI of an Officer = Weighted average of DI of services handled by him

DI of a Senior Officer = Weighted average of DI of Offices under him

3.3.2 Cumulative DI when Workflow Step Information is Not Known

In this case DI of pending Service Requests is not known. Therefore, DI of only the disposed off individual Service Request has been calculated and tagged to each one of them in the system. Now, using the DI of last N Service Requests in a service or in an office, the DI of service and office can be calculated as follows –

DI of a Service (at a given point of time) =

{Sum of DI of last N Service Requests of Service}

divided by

Instead of using last N Service Requests, it is equally plausible to use, say, all disposed off Service Requests over the last N-days. In either case the DI of a “Service” or of a given {Set of Service Requests} becomes the MOVING AVERAGE of individual DIs of Service Requests which constitute the said “Service” or fall under the given {Set of Service Requests}.

4.0 DI – Some Variants

4.1 Version 1:

The DI of each individual Service Request calculated using above formulae is logically consistent. However, while calculating Cumulative DI where arithmetic averages are taken for a given {Set of Service Requests}; the above formulae lead to under-representation of the poor performance in service request delivery. This happens as explained in example below

Problem with Version 1:

Let,

No of Service Requests = 10

Assume that each of the 5 Service Requests have been delivered in half the assigned time. Then DI of each of these 5 Service Requests = 2

Assume that each of the 5 Service Requests have been delivered in twice the time. Then DI of each of these 5 Service Requests = 0.5

Together, the 10 Service Requests, on average shall have DI = 1.0

However, upon using formula given in 3.3.2,

DI of 10 Service requests = [2+2+2+2+2+0.5+0.5+0.5+0.5+0.5]/10

= 12.5/10

= 1.25

Therefore, the formula gives more weightage to DIs which are >1.

The above problem can be solved by defining DI for individual Service Request as follows

4.2 Version 2:

4.2.1 Workflow Step Information is Available

Let DI be measured at time T=T1 (where at T=0, the Service Request was received)

Let

X = [Stage of delivery the service request ACTUALLY is at time T=T1]

Y = [Stage of delivery the service request IDEALLY should be at time T=T1]

DI (Service Request at T=T1)= = [X] / [Y] (if X > or equal to Y)

(–) [Y] / [X] (if X < Y)

4.2.2 Workflow Step Information is NOT Available

Let DI be measured for the N-th Service Request which has been delivered already.

Let

X = [Ideal Prescribed Time Limit for Service Request]

Y = [Actual Time Taken by N-th Service Request]

DI (Service Request at T=T1) = [X] / [Y] (if X > or equal to Y)

(–) [Y] / [X] (if X < Y)

Using above formulation of DI for individual Service Request will solve the issue of bias towards positive performance for cumulative DI of {Set of Service Requests} measured by taking arithmetic mean of the DIs of the individual Service Requests.

Problem with Version 2:

A DI value of “1” for an individual Service Request represents that the said individual Service Request is being disposed off or has been disposed off as per schedule/prescribed time.

However, in case of cumulative DI calculated for a {Set of Service Requests}, a DI of ZERO “0” will represent that the said {Set of Service Request} are being disposed off or have been disposed off as per schedule/prescribed time

This can be understood by taking the same example of 10 Service Requests as cited in paragraph 4.1 above.

Let,

No of Service Requests = 10

Assume that each of the 5 Service Requests have been delivered in half the assigned time. Then DI of each of these 5 Service Requests = 2 (see 4.2.2 above)

Assume that each of the 5 Service Requests have been delivered in twice the time. Then DI of each of these 5 Service Requests = (–)2 (see 4.2.2 above)

Together, the 10 Service Requests, on average shall have DI = 1.0

However, upon using formula given in 3.3.2,

DI of 10 Service requests = [2+2+2+2+2-2-2-2-2-2]/10

= 0/10

= 0

Therefore, DI Scoring Scale for individual Service Request becomes different than DI Scoring Scale for a {Set of Service Requests}.

4.3 Version 3:

4.3.1 Workflow Step Information is Available

Let DI be measured at time T=T1 (where at T=0, the Service Request was received)

Let

X = [Stage of delivery the service request ACTUALLY is at time T=T1]

Y = [Stage of delivery the service request IDEALLY should be at time T=T1]

DI (Service Request at T=T1)= =( [X] / [Y] – 1) (if X > or equal to Y)

(–) ( [Y] / [X] – 1) (if X < Y)

4.3.2 Workflow Step Information is NOT Available

Let DI be measured for the N-th Service Request which has been delivered already.

Let,

X = [Ideal Prescribed Time Limit for Service Request]

Y = [Actual Time Taken by N-th Service Request]

DI (Service Request at T=T1)= =( [X] / [Y] – 1) (if X > or equal to Y)

(–) ( [Y] / [X] – 1) (if X < Y)

Using above formulation of DI for individual Service Request will solve both the issues that afflict Version 1 and Version 2.

In this Version 3, both for individual Service Request and a {Set of Service Requests})

(i) DI = ZERO represents “on-schedule performance”.

(ii) DI > 0 represents “Ahead of Schedule Performance” (Higher the better)

(iii) DI < 0 represents “Behind Schedule Performance” (More Negative the Worse)

In layman terms, DI is a measure of “How many times faster is the actual processing of Service Requests than the prescribed processing time”

5.0 DI – Uses and Applications

DI is a very simple but powerful tool to do the following

1. It measures average speed of service delivery viz-a-viz expected speed of delivery

2. It measure how fast or slowly the service is getting delivered as compared to the prescribed time-limit

3. A DI of 3 means that service delivery is 3 Times faster than ideal speed of delivery. While DI of 0.2 means that delivery speed is merely 0.2 times or 20% of what it ideally should be.

4. DI can be used to rank offices or officials as regards their efficiency of service delivery – for a given service or department or even cutting across departments.

5. It brings different public services, different departments, etc on a single platform of performance measurement, which then can be compared with one-another. This allows comparison of different offices, departments, districts, etc with one-another. For example a police station with DI of 2.5 is better in public service delivery than a Medical Dispensary with DI of 1.4.

6. An office or a given Unit under consideration with the lowest DI is the one which is most likely to fail to deliver service in the prescribed time. Therefore, DI of an office or officer allows us to directly focus on such potential defaulters.

7. Further, the DI helps to prevent delayed disposals.

8. In case, more than one Office or Officer or Unit of Interest has the same DI, then they can be differentiated using the Standard Deviation of the DI and one with lower SD shall be ranked higher.

9. The concept of DI can be extended to directly calculate and identify bottleneck steps, identify steps of the workflow which need process re-engineering etc.

10. In fact, the gamut of uses of DI is so vast that it needs a separate monograph to reasonably talk about the same. This shall be done in subsequent blogs/monographs.