Management Notes: Prioritisation

Abstract

Prioritization is critical for determining the sequence of decisions. There are many methods for setting priorities. Some of them will be discussed below.

For simplicity, all prioritization methods will be discussed using the example of selecting task implementations and determining the sequence for their implementation. Let’s assume that Project P has several tasks, and the project team is assigned four tasks: Task A, Task B, Task C, and Task D.

Analytic Hierarchy Process

We should begin with a method that is also highly popular and has been rated as the most effective. This tool’s effectiveness belies its complexity.

Analytic Hierarchy Process использует математический подход для выстраивания приоритета задач по шкале значимости. Для оценки потребуется выделение трех компонентов: Goal - итоговая цель; Criteria - факторы, влияющие на Goal; и Alternatives - существующие альтернативы.

The Analytical Hierarchy Process uses a mathematical approach to prioritize tasks based on their importance. The evaluation requires identifying three components: Goal (the ultimate goal); Criteria (the factors that influence the Goal); and Alternatives (the existing alternatives).

AHP steps

1. Identify the problem.

Example: Choosing a tasks priority

2. Prepare an evaluation platform. It should include: Goal - the problem itself; Criteria - how we will evaluate (by what criteria) the impact of the choice option on the Goal; Alternatives - the options themselves.

3. Define the Criteria set. List the Criteria that are most important for achieving the Goal.

Example

Criterias = Complexity (C), Schedule Index (SI), Earned Value Index (EVI), Importance (I)

4. Perform a pairwise comparison of criteria. The goal of this step is to determine the weight of each Criteria relative to the Goal. Each Criteria is compared to another Criteria, forming a matrix. Then, by simply adding the values together, the weight of each Criteria can be calculated for the upcoming assessment.

Example

Let’s assume that the Comparison Matrix for Criteria looks like this:

	C	SI	EVI	I
C	1	1.27	0.69	1.38
SI	0.79	1	2.21	1.18
EVI	1.45	0.45	1	2.08
I	0.72	0.85	0.48	1

It’s important to note how these values are obtained—they are the result of an analytical comparison of the relationship between one criterion and another. The figure can be obtained in various ways, including expert assessment, analysis of scientific papers, etc.

5. Calculate the weight of the Criteria. How does the criterion influence the achievement of the Goal?

Example

There are several methods, below 2 of them will be proposed (additional: Largest Eigenvector Method, Fuzzy Geometric Mean Method).

5.1. Eigenvector Vector Weighting Method

5.1.1. Columns arithmetic summary

	C	SI	EVI	I
C	1.00	1.27	0.69	1.38
SI	0.79	1.00	2.21	1.18
EVI	1.45	0.45	1.00	2.08
I	0.72	0.85	0.48	1.00
Summ	3.96	3.57	4.38	5.64

5.1.2. Columns normalization

	C	SI	EVI	I
C	1.00/3.96=0.25	1.27/3.57=0.35	0.69/4.38=0.16	1.38/5.64=0.24
SI	0.79/3.96=0.20	1.00/3.57=0.28	2.21/4.38=0.50	1.18/5.64=0.21
EVI	1.45/3.96=0.36	0.45/3.57=0.13	1.00/4.38=0.23	2.08/5.64=0.37
I	0.72/3.96=0.19	0.85/3.57=0.24	0.48/4.38=0.11	1.00/5.64=0.18
Summ	1	1	1	1

5.1.3. Arithmetic mean

	C	SI	EVI	I	Criteria Weight
C	0.25	0.35	0.16	0.24	(0.25+0.35+0.16+0.24)/4=0.25
SI	0.20	0.28	0.50	0.21	(0.20+0.28+0.50+0.21)/4=0.30
EVI	0.36	0.13	0.23	0.37	(0.36+0.13+0.23+0.37)/4=0.27
I	0.19	0.24	0.11	0.18	(0.19+0.24+0.11+0.18)/4=0.18
Summ	1	1	1	1	1

5.2. Geometric Mean Weighting Method

5.2.1. Column geometric mean

	C	SI	EVI	I	Geometric mean
C	1.00	1.27	0.69	1.38	(1.00*1.27*0.69*1.38)^(1/4)=1.05
SI	0.79	1.00	2.21	1.18	(0.79*1.00*2.21*1.18)^(1/4)=1.20
EVI	1.45	0.45	1.00	2.08	(1.45*0.45*1.00*2.08)^(1/4)=1.08
I	0.72	0.85	0.48	1.00	(0.72*0.85*0.48*1.00)^(1/4)=0.74
Summ	3.96	3.57	4.38	5.64	4.06

5.2.2. Rows normalization

	C	SI	EVI	I	Geometric mean	Criteria Weight
C	1.00	1.27	0.69	1.38	1.05	1.05/4.07=0.26
SI	0.79	1.00	2.21	1.18	1.20	1.20/4.07=0.29
EVI	1.45	0.45	1.00	2.08	1.08	1.08/4.07=0.27
I	0.72	0.85	0.48	1.00	0.74	0.74/4.07=0.18
Summ	3.96	3.57	4.38	5.64	4.07	1

6. Perform an assessment check using the Consistency Ratio. The step-by-step calculation is shown below:

Example

6.1. Multiply matrixes

Matrix multiplication is performed for Comparison Matrix

	C	SI	EVI	I
C	1.00	1.27	0.69	1.38
SI	0.79	1.00	2.21	1.18
EVI	1.45	0.45	1.00	2.08
I	0.72	0.85	0.48	1.00

and the weighing results:

	Criteria Weight
C	0.26
SI	0.29
EVI	0.27
I	0.18

The result is:

	Principal Eigenvalue
C	1.07
SI	1.30
EVI	1.15
I	0.74

6.2. Calculate Average Principal Eigenvalue

	C	SI	EVI	I	Criteria Weight	Principal Eigenvalue	Average Principal Eigenvalue
C	1.00	1.5	5.0	2.4	0.26	1.07	1.07/0.26=4.11
SI	0.6	1.00	3.2	0.7	0.29	1.30	1.30/0.29=4.48
EVI	0.2	0.31	1.00	2.8	0.27	1.15	1.15/0.27=4.26
I	0.4	1.4	0.35	1.00	0.18	0.74	0.74/0.18=4.11

6.3. Calculate Principal Eigenvalue

Is the average of the Average Principal Eigenvalue set. n is involved, matrix size:

$${''Principal\; Eigenvalue,\; PE''}_{}=\frac{{''\sum ''}_{\mathrm{APE}}}{{''n''}^{}}=\frac{\mathrm{4.11\; +\; 4.48\; +\; 4.26\; +\; 4.11}}{4}=4.24$$

6.4. Calculate Consistency Index

$${''Consistency\; Index,\; CI''}_{}={''APE''}_{-}={''4.24''}_{-}=0.08$$

6.5. Calculate Consistency Ratio

Finally, the Consistency Ratio is calculated:

$${''Consistency\; Ratio,\; CR''}_{}={''CI''}_{/}$$

Random Index is a special value provided by the method’s developer, Thomas Saaty, as expected inconsistency. You must select a value from a prepared table according to n, the matrix size:

Matrix size, n	Random Index, RI
1	0
2	0
3	0.52
4	0.89
5	1.11
6	1.25
7	1.35
8	1.40
9	1.45
10	1.49
11	1.52
12	1.54
13	1.56
14	1.58

Example

In our case, the Consistency Ratio value will be as follows:

$${''Consistency\; Ratio,\; CR''}_{}={''0.08''}_{/}={''0.09''}_{}$$

6.6. Consistency Ratio should be ≤0.1. In some cases, a Consistency Ratio above 0.1 may be accepted and considered a fair estimate.

Example

In our example, Consistency Ratio meets the requirements, although it is close to the critical limit. If the score is greater than 0.1, the criteria assessment should be reconsidered!

7. Evaluate the Alternatives. Evaluation is performed for each criterion based on the relationship of each Alternative to the others. In other words, “Considering Criterion A, what score can be given to Option A?”, “Considering Criterion A, what score can be given to Option B?”, …, “Considering Criterion B, what score can be given to Option A?”, etc.

Example

Let us assume that the assessment is performed as follows:

	C	SI	EVI	I
Task A	0.36	0.20	0.31	0.18
Task B	0.19	0.12	0.34	0.34
Task C	0.28	0.32	0.19	0.23
Task D	0.17	0.36	0.16	0.25

8. Calculate the evaluation results for each Alternative. This is simpler: for each Alternative, the final score is calculated for each criterion relative to its weight.

Example

	C	SI	EVI	I
Task A	0.36*0.26=0.09	0.20*0.29=0.06	0.31*0.27=0.09	0.18*0.18=0.03
Task B	0.19*0.26=0.05	0.12*0.29=0.04	0.34*0.27=0.09	0.34*0.18=0.06
Task C	0.28*0.26=0.07	0.32*0.29=0.09	0.19*0.27=0.05	0.23*0.18=0.04
Task D	0.17*0.26=0.05	0.36*0.29=0.10	0.16*0.27=0.05	0.25*0.18=0.04

9. Final decision based on the evaluation of each Alternative. Next, the sum is calculated for all criteria.

Example

	Rate
Task A	0.09+0.06+0.09+0.03=0.27
Task B	0.05+0.04+0.09+0.06=0.24
Task C	0.07+0.09+0.05+0.04=0.25
Task D	0.05+0.10+0.05+0.04=0.24

In our example, the priorities are arranged as follows: Task A, Task C, Task B, Task D.

This mechanism is quite labor-intensive, so it is more often used for critical decisions.

MoSCoW

This tool is much easier to use. The principle is very simple and is reflected in the method’s name: Must_haveShold_haveCould_haveWon’t_have.

Must have

Critical activities (project tasks, projects, products, etc.) that must be completed for the survival (of a project, company, initiative, etc.).

Should have

These are important but not mandatory activities. The results may be of interest to stakeholders, so their implementation is desirable. Their implementation can, in principle, be postponed until a later date, but they are still necessary.

Could have

Low-priority activities. These are activities that can be implemented, but only if there’s free time.

Won’t have

During the allocated time period (e.g., the sprint in question, the calendar year, the five-year development plan, etc.), the activities will not be performed. There is either no time, no resources, or both.

MoSCoW usage

This mechanism is convenient to use due to its simplicity. However, unlike the Analytic Hierarchy Process, the assessment is more subjective, meaning it is difficult to use this tool to justify business decisions.

Recomendations

1. When evaluating each activity, its significance must be fairly assessed. If all activities fall into the Must have category, then the assessment is unfair.
2. Activity assessments must be based on specific criteria. For example, Net Present Value, Earned Value Index, Schedule Index, stakeholder satisfaction, etc.
3. The MoSCoW model can be adjusted over time as priorities and the environment change.

MoSCoW process

It is somewhat similar to the Analytic Hierarchy Process:

1. Define criteria. Important criteria that impact the goal (project, company, product, etc.) are listed.
2. Create a MoSCoW Board similar to the one below:

3. Activities requiring analysis are distributed across the board according to their assessment. Various methods can be used, but some systematic approach to assessment is desirable.
4. Tracking ongoing activities
5. Updating the board

Overall, this mechanism is overly simple and is better suited for accounting and monitoring activities. To assess the weight of activities, one can use the Principal Eigenvalue calculation, which is more fundamental and transparent.