Identifying Contradictions and Conflicts

Introduction
Resolving conflicts and contradictions is the single most important aspect in solving a problem. Without a thorough understanding of those issues obtaining a good solution to the problem is likely to be impossible.


The technique discussed here is an excellent process to elicit those conflicts and contradictions.

Earlier, a system model was developed that described the components of the problem and what functions are being carried out. A Conflict Resolution Diagram (CRD) takes this system model one step further with the aim of identifying any conflicts in the system. Whilst you can use the system model and embellish, it is often better to produce a separate diagram of the conflicts in order to simplify what will, undoubtedly, be a complicated diagram.

The process is as follows:
Step 1: Identify the Objective
Step 2: Determine the Requirements.
Step 3: Determine the Pre-Requisites
Step 4: Identify the Conflicts
Step 4: Identify Focus Areas

Note, steps 1 through to 4 can be carried out in any order. Sometimes, the conflicts are clear but other aspects aren’t. Sometimes it might not be clear what is the objective. You shouldn’t be too rigid, only to be sure that all the steps have been done.

Objective
The objective clarifies the main purpose: what is it that you are trying to achieve? Place a box to the left hand side and articulate the objective.

Requirements
Requirements are the necessary conditions in order to satisfy the objective. Although the example only shows two boxes; this is for simplicity and most objectives will have many requirements. Please note that requirements are “essential” (Needs) and not just “nice-to-haves” (Wants). Place each requirement in a box to the right of the objective.

Draw an arrow from the Requirement box to the Objective box. It is good practice to write each relationship in the form of: “In order to have (OBJECTIVE) we must have (REQUIREMENT). You don’t need to display the text but it helps to clarify to everyone the thinking behind the requirements.

Pre-Requisites
Pre-requisites are the necessary conditions to satisfy the Requirement. This is usually described as an action (verb) and is the place where conflicts occur. Place these in boxes to the right of the Requirements.

Draw an arrow from the Pre-Requisite box to the Requirements box. Here, there are two things worth adding to the line. The first is to write down the relationship in words using the form: “In order to have (REQUIREMENT) we must have (PRE-REQUISITE). Again writing the words clarifies the diagram. Secondly, you should list all the assumptions being made in determining that this particular pre-requisite is needed for the requirements. Assumptions are the “why something is needed”. If you wish, once you’ve listed all the assumptions, you can extend the words used to describe the line thus: “In order to have (REQUIREMENT) we must have (PRE-REQUISITE) because (ASSUMPTIONS)”.

 Listing assumptions is a tricky part and you need to be very careful to make sure they are, in fact, valid. Assumptions are particularly vulnerable to bias, prejudice and misunderstanding. They vary considerably depending on people’s value systems, which has been derived from the previous experiences and culture.

Conflicts
On the diagram, identify any pre-requisites that are competing against one another. These are usually called “Conflicts” or “Contradictions” There are two different ways they could compete. One is that you can’t have both pre-requisites at the same time; a sort of “A or B but not both”. The second is that as you improve one pre-requisite the other one gets worse; a sort of trade off situation.

For each pre-requisite that is competing, draw a line between the boxes. In Promax there are line shapes for the two different types In summary:

• Technical Contradictions: used for trade offs where as one pre-requisite improves the other gets worse
• Physical Contradiction: use where you can have A or B but not both. 

As in the previous steps it is good practice to write the rationale behind the conflict in the relationship line. A suitable form could be: “On one had we must have (PRE_REQUISITE #1) but on the other hand we must have (PRE-REQUISITE #2).

In some cases, the conflicts appear easy to see and articulate. Sometimes less so. Often they are a combination of “hard” facts and “soft” opinions. Hard facts are things where the contradiction is based on an evidence-base such as a limited resource or plain and simple physics. Soft opinions are based on peoples perceptions and values that are harder to establish. It is worth spending some time separating the two and to not dismiss the soft opinions because they go against your (or your organisation's) opinion. This is the single biggest cause of failure in solving problems where people are involved; the solution might be more that simply changing a process step – it might require significant cultural change.

Identify Focus Areas
From the conflict resolution diagram, it is likely that there may be several, or even many, areas of conflict. We need to focus in on the ones we believe would make the biggest difference to solving the problem. We call these “Focus Areas”.

List all the areas that you wish to focus on for the next stage where you want to generate ideas. The Focus Areas can be broad or narrow but it does need to be clear what it is you want to focus on.

It is in the next phase (Ideas Generation) that we generate ideas that could be used to solve the conflict (called “Injections” in the Theory of Constraints). We use the Triz tools “Technical Contradictions” and “Physical Contradictions” to help identify potential solutions to the conflicts. These are extraordinary powerful techniques and are significantly better than simply brainstorming and will be discussed in later blogs.

At this stage, it is true that it is difficult to prioritise which of the Focus Areas are most important since you don’t know what the effect will be on the objective if that particular conflict is resolved. However, if you have used most of the techniques from the Framing Stage, you will certainly have an excellent understanding of the problem and will be able to have an informed opinion. However, it is also true that you may need to work through more of the Focus Areas in an iterative manner, gradually resolving all the conflicts until you reach the “Ideal Final Result”.







References
"Goldratt's Theory of Constraints", H. William Dettmer (1997) is an excellent book on TOC.

Mapping the Problem

It is almost always worth trying to draw a diagram of your problem. A visual representation can often uncover “hidden” aspects that are often missed or misunderstood. As well as providing a mechanism to get to the heart of the problem it can also be a good way to identify solutions.

There are many different ways to map the problem. Promax focuses on “Functions” because we can use systematic tools later on in the process to analyse the functions and generate ideas on how to solve the problem. Other techniques for mapping rely on trial and error for solving problems, which is less efficient.

The process is quite simple. First identify all the elements and components of the problem. The components within this “system” are then linked to reflect the interactions occurring. The function is then written alongside the link.

There is therefore always three parts to any link – the Subject, the Action being carried out and the Object. Actions are always verbs.

Different colours are often used to represent the different components of the problem. In the example, drawn in Promax, the boxes are either items (grey), inputs (black) or objectives (green). Promax has seven different line types of which the following are shown; dependency (black arrow), useful (green arrow), insufficient (dashed green arrow), wasteful (red arrow) and excessive (double green arrow).

By colour coding in this way it is easier to hone in on where the problem lies. 

There are other types of mapping commonly used including;
* Value Stream Mapping (VSM)
* Process Flow Diagrams (PFD)
* Su-Field Analysis (Su-F)
* Southbeach Notation
* Systems Dynamics (SD)
* Simulation Modelling

They all have a similar objective – to explain pictorially how the different items within the system interact with each other. Sometimes the information is used to calculate time, quantities and volumes within the system. They vary somewhat in what is represented and how they are represented and are often used by different groups of professionals depending on their background and training.

Value Stream Mapping (VSM) is used in Lean Six Sigma. It differs from functional mapping in that the function and the item are listed in the same box. Arrows are used purely to indicate the movement from one box to another.

Process Flow Diagrams (PFD), often called flowsheets, are used by chemical and process engineers. These list the main components of a systems. Product Flow Diagrams are also called PFD’s and are mostly used by Project Managers to illustrate how the different products of a project are related.

Su-Field Analysis (Su-F) is used by Triz practitioners.

Southbeach Notation is a nomenclature for most types of modelling using colours and shapes to express some of the Triz terms.

Systems Dynamics (SD) is used by social scientists and often has a calculation component included within it. Unlike spread sheets you can model "circular arguments" where things in the systems can continually increase.

Simulation Modelling is used by operational research professionals on specific problem types. It is rarely purely a visual representation but the components and relationships between them is written in computer code with the aim of carrying calculations on the whole system such as throughput.

Root Cause Analysis

 Root Cause Analysis is the method by which you look for reasons as to why you have the problem in the first place.

Root cause Analysis runs through many methods from the simplest “Five Whys” to the “Ishikawa Fishbone” to the “Root Cause Analysis” method above.

The Five Whys is a technique where you are “why” five times. The rationale being that as you keep asking “why something happens” you gradually get to the point where you’ve found the root cause of the problem. Of course, you might get there in less than five or it might take more - please don’t stop just because you done the five prescribed!

The 5 Whys is included in Promax as part of the 5W’s + H method which has been covered in a separate blog. The difficulty with this method is that, in most practical examples, the cause and effects are much more complex than a simple linear flow. There may be lots of possible causes and these are awkward to capture without creating multiple 5 Why’s with links between them.

Another extremely common technique for root cause analysis is the Fishbone Diagram – named because the original style looked rather like a fishbone. Essential it is a branched diagram with headings for each branch under which you place the possible causes. Common headings are to use 6 M’s which stand for Management, Man, Machine, Measurement, Material, Method. I think that this method has many flaws and creates more problems than it solves because rather than asking as you do in the 5 Whys, “why something is happening”, teams just place potential faults under each heading – there isn’t a logical rationale. This means you end up with a very long list of “Issues” which may or may not be actual causes of the problem. You then need to sift through the myriad of issues to find the most pertinent ones, which is time-consuming and not at all systematic. We haven’t included a Fishbone Diagram in Promax for that reason. By all means categorise your causes after identifying them to make managing their resolution easier, but not before.

Probably the best technique for more complex problems is to use a diagramming technique. This gives the ability to create multiple routes for causes and is therefore more applicable to real-world problems.

The diagramming technique is widely used in accident scenarios where trained investigators analyse everything they can. To do this properly is not a trivial exercise and a proper analysis will take weeks if not months. They are highly trained individuals and will go to the nth degree on everything.

It is unlikely that you will have the luxury of taking many weeks to carry out a root cause analysis but it is obviously worth spending some quality time on it. After all the result of the exercise will point you in the direction of how to solve your problem!

Promax has a “root-cause” diagramming tool where you can list your causes and draw links between them. We have introduced two types of lines: a solid line indicates you have “Proof” that it is causing the problem and a dotted line indicates that it is an “Opinion” that it is the cause of the problem.

Obviously it’s up to you to decide upon the burden of proof but I would hazard a guess that just sitting in a room drawing up the diagram without any reference to some evidence will not provide for a very good analysis. This is particularly the case when dealing with managerial change issues where ideology and prejudice skew the analysis considerably. So it’s worth developing the diagram using dotted lines (opinion) and then spend some time trying to get some evidence for those opinions (where the lines can be turned to solid). If you can’t find any evidence they obviously stay dotted. If you have a diagram full of dotted lines then you’re unlikely to have a good basis for trying to solve the problem. You’ll just end up randomly trying some resolutions with no realistic idea whether they will work.

The process is as follows:

Step 1: Identify the problem
Step 2: Identify the main causes of the problem
Step 3: Identify causes of the causes
Step 4: Draw the Root Cause Analysis diagram
Step 5: Determine how the causes occur.
Step 6: Identify ideas that can resolve the problems 

Just what is Ideality?

Ideality = Benefits / (Costs + Harms)

Ideality is a concept from Triz that suggests that the “Ideal” solution is one that has everything you need but is virtually free and has zero harms. Taken at its extreme, the ideal solution is a system that carries out the required function but doesn’t actually exist. This isn’t as far fetched as it might appear since there are many systems that work very well yet are extremely cheap and generate few harms: lines painted on floors or roads to demarcate where you should or shouldn’t be; angled entries into public toilets (restrooms) rather than install doors or pencils for writing in spacecraft rather than sophisticated pens. These are all examples where the function – what it is supposed to do – is the overriding factor in the design of the system.

What this means in practice is that you need to thoroughly understand what function you need before attempting to devise a solution. Hence the emphasis in the earlier blogs of framing and problem definition.

Promax has Ideality embedded and has a number of prompts to be used to help define ideality:

1. What is the objective? That is what function are you looking for?
2. What do you need/want? That is what benefits are you expecting?
3. What don’t you want? This is nearly always cost (the lower the better and free even better) but also other harmful factors (maybe environmental impact, safety, security, etc).

 The information you collect is then used in a number of ways going forward. First, the clarification of the objective ensures you have focus on what you’re trying to achieve with your solutions. This is used in the Idea Generation stage to make sure everyone has a clear focus of the problem.

The second element is that the benefits, costs and harms are used as the criteria against which the ideas generated can be evaluated. Ideas that give the greatest benefit for the least cost and fewest harms are, by definition, closer to ideal. We carry out the evaluation in the prioritisation stage of the Cogentus Framework and a blog on this will follow in due course.

In summary:

Ideality = Benefits / (Costs) + Harms

You’ll recognise that this equation is the same as that used in traditional evaluations. It’s the same as Value For Money – the more you get for the least cost the better and this is the context that ideas (which can be new innovations or continuous improvements) can be evaluated.

It’s worth remembering though that getting as close as possible to Ideality requires a thorough understanding of what function you are trying to achieve. Hence there’s little point in demonstrating that you have a value for money solution if you’re actually providing the wrong solution!

Use of Triz Resources

Promax has a number of tools to help with Framing and Problem Definition one of which is called Resources. 

Resources are anything within the environment of the problem that isn’t being directly used. Resources are basically free or very low cost items that are readily available. A resource can be anything and is could be easily visible, hidden or even derived from something else.

The rationale for understanding what free resources are available is that they may be useful in solving your problem. After all, why invest in something when you already have it to hand.

 

It is important to undertake a Site/Location visit to identify resources. Unless you can walk through the problem area you might not see everything and you might miss things that are taken for granted. This cannot be done from a meeting room.

There are typically four things to consider:

Materials and Objects: Are there any unused physical components in the system such as walls, floors, etc.? Are there components that are there but simply not seen such as air, water and the actual properties of substances? (“hidden”). Or are there components where the property of it could be easily changed? (derived)

Energy: Is there energy in the system such as electrical, thermal and magnetic that is not being used? Is there energy from the environment such as light that is not being used?

Space and Time. Is there space that is not being used? Is there idle time in machinery, equipment, documentation and people?

Knowledge & Information. Is there knowledge and information that is available yet not currently used?

Promax has these prompts in the Resource window and you simply create a list of things that sit under each category. These form the record from which you can use later in the ideas generation stage to see if anything can be used to help create a solution for your problem. 

Resources are a tool from Triz.

Framing using 5W’s+H

The importance of properly defining a problem before trying to generate a solution cannot be overemphasized. The most obvious outcome of poor definition is the solving of the wrong problem! It can also be that the problem might be easier solved once you understand the specifics.

There are many techniques available and Promax includes a good number that will ensure a robust identification of the real problem to be solved. 

The 5W’s and an H technique is a quick and easy way to define a problem. It is based on Rudyard Kipling’s poem:

I KEEP six honest serving-men:
(They taught me all I knew)
Their names are What and Why and When
And How and Where and Who.
I send them over land and sea,
I send them east and west;
But after they have worked for me,
I give them all a rest.

I let them rest from nine till five,
For I am busy then,
As well as breakfast, lunch, and tea,
For they are hungry men:
But different folk have different views:
I know a person small -
She keeps ten million serving-men,
Who get no rest at all!
She sends 'em abroad on her own affairs,
From the second she opens her eyes -
One million Hows, two million Wheres,
And seven million Whys!

The Elephant’s Child from the Just So Stories of Rudyard Kipling, 1902
 
The poem is used as a basis to ask a series of questions, which aims to identify all the key aspects of a problem to enable a solution to be developed that match the problem.

Process

Step 1
Ask “What is the problem?”
Step 2
Ask “Who has the problem?”
Step 3
Ask “When does the problem occur?”
Step 4
Ask “Where does the problem occur?”
Step 5
Ask “Why does the problem occur?”
Step 6
Ask “How does the cause occur?”


What is the problem?
The purpose of this question is to explain the problem in a clear manner. If the problem has a contradiction is should be stated here.

Who has the problem?
The purpose of this question is to identify the person or persons connected with the problem. They are the people who are directly impacted and will be the beneficiaries of any solution.

When does the problem occur?
The purpose of this question is to clearly identify the time related aspects of the problem.

Where does the problem occur?
The purpose of this question is to understand precisely where the problem takes place.

Why does the problem occur?
The purpose of this question is to find out what the cause of the problem is. This is accomplished by asking “why? five times

How does the cause occur?
The purpose of this question is to understand how the cause arises. From this the best solution can then be developed that will prevent the problem occurring in the future.

Example

 

Promax Screenshot

The scenario is that you manage a firm who provide security to factories and buildings. You provide staff with uniforms and equipment for their job. You’ve been receiving complaints from the staff that they need better torches (flashlights) as they’re not bright enough.

In Promax, the first tab provides a number of tools for Framing and the first button is the one for 5W’s+H. It provides the prompts and you simply fill in the boxes below each one:
What is the problem?
The torch/flashlight isn’t bright enough

Who has the problem?
The security guards at the factories

When does the problem occur?
At night when they are doing their rounds

Where does the problem occur?
Across the factories and building. Inside and outside

Why does the problem occur?
Why #1: Torch isn’t powerful enough
Why #2: Not enough battery power
Why #3: Limited to two batteries only
Why #4: The barrel can only take 2 batteries
Why #5: The barrel is sized to be comfortable to hold

How does the cause occur?
The user needs to be able to hold the torch/flashlight.

Discussion

From this, you can move on to generate ideas on how best to address the cause – in this case how best to hold the torch given the constraints of battery size.

It is worth noting, however, that the “cause and effect” analysis of the 5 Why’s is rather simplistic and is rarely, if ever, quite as simple as asking “why?” five times. Even in the extremely simple Torch/Flashlight example you can see that although we only identified one cause there could, in fact, be multiple causes possible at “Why #2”. It could be a faulty bulb, a dirty lens or poorly designed reflector. In this case you may need to use multiple lists of “5 whys” and then try to see if any are related.

Improving Criteria Scaling

A previous article examined how to use Promax to recreate the model for decisions involving multiple objectives as described in the book “Decision Analysis for Management Judgment” by Paul Goodwin and George Wright (1991).

In the example we used a real-world scale for some of the criteria (for example, office floor area in ft2) and a preference scale for criteria where real-world scales were difficult to define. The problem with preference scales is that they are unique to the group involved. The chances of a completely different group choosing the same preferences are remote. This means that the result cannot be adequately explained or justified and it also cannot be recreated. This may be perfectly acceptable for a decision where there is a single decision maker but it is not acceptable where there are multiple decision makers – for instance in large organisations where decisions are approved and reviewed at multiple stages.

This article looks at another type of scale that can be used for those “difficult-to-measure” criteria – namely textual scales.

Textual scales are ones where the degree of preference is explained in words rather than numbers. They are created in a similar way to preference scales except that the reasoning behind the position on the scale is explain in objective terms. See an earlier blog for the differences between objective and subjective information.

For the criteria being discussed, write, as clearly as possible, the best imaginable score. The addition of real examples that people would recognize is well worth the effort. Then consider the worst imaginable. Then imagine what lies between the best and the worst. Don’t think in terms of position (e.g. halfway between best and worst) but more in terms of discrete differences. They should be something that you can describe as being a step-change difference. Then, create as many intervals as you need that will adequately segment the scale. For example, office image could be explained thus:

T	This office compares with the best in the world. As a benchmark the TBWA Hakuhodo offices in Tokyo.
H	This office is just about the best in the area. As a benchmark the “Hatton Gardens” office block.
K	The offices in “Kent Boulevard” are the benchmark here
L	The offices along “Link Road are the benchmark here
M	The offices along “Mellor Drive” are the benchmark here
I	This office is just about the worst in the area. The offices in “India Road” and “Jason Place” are the benchmark here
P	This office compares with the worst imaginable. A dark, dingy, very run-down office which is particularly uninvited. For example you’ll smile smugly to yourself as you imagine people whose offices are much messier than yours. You’ll stretch your arms out and luxuriate in the fact that you can’t even touch both walls of your 8×8 cubicle simultaneously as you view picture of a worker toiling in a space smaller than a closet in a one bedroom apartment.

Figure 1: The Promax scorecard display once descriptions have been defined

There are some top tips in creating textual scales:

• Do not use numerical scales (e.g. 0-10) even if you explain what a 10, or a 7 or a zero is. These scales are prone to people “gaming the system”. This means that since people know that a 7 is a better score than a 5 they will persuade others that the rationale behind giving the scores makes sense. It may make sense at the time, but later on you will struggle to reconcile the scoring with the facts. So, people can quite easily generate the result they always wanted even though apparently the methodology was fair and transparent. That is why techniques using numbers such as Kepner-Tregoe, the Pugh Matrix, AHP etc. should be avoided – they appear robust and scientific but are anything of the sort.
• Do not use Very Good, Good, Average, Poor, Very Poor even if you explain what “Good” means. Again, it is too easy to game the system because you know that a Very Good is better than Good.
• Do Randomise the scale. In the same way that a well-conceived survey randomizes it’s questions in order to reduce bias so you should do this for textual scales. This means not ordering the scale from good to bad. Order them in a different way otherwise, whatever the description, you end up in the same trap as for the previous two tips – people can game the system because they know what scores will generate the result they want.

Once you have created your scale you need to value the points on it. The best imaginable is worth 100 and the worst is worth 0. The others will lie somewhere between 0 and 100. Remember, as in the mapping done for real-world scales the mapping does not need to be a linear, straight line. You may decide that anything with a better image than “Link Road” does not add any more value so you end up with more of an s-curve.

Always keep the scaling separate from the mapping. In Promax, when using textual scales you need to map the scale against the value as part of the process.

Conclusion

The use of textual scales rather than preference scales is to be preferred for decisions involving multiple decision makers since the results can be more easily reviewed and challenged. That said, there are lessons to be learnt in creating those scales so that it is difficult for participants to game the system.

Decisions Involving Multiple Objectives

The truly excellent textbook “Decision Analysis for Management Judgment” by Paul Goodwin and George Wright (1991) explains a number of decision methodologies, one of which is for decisions involving multiple objectives. Commonly called multi-criteria decision analysis (MCDA), multi-attribute decision analysis (MADA) or multi-objective decision analysis (MODA) it involves a decision problem with a number of objectives that are often conflicting.

The textbook (chapter 2) provides a worked example of the methodology and this blog shows how to model this in Promax.

An Office Location Problem

Goodwin & Wright explain the problem thus:

A small printing and photocopying business must move from its existing office because the site has been acquired for redevelopment. The owner of the business is considering seven possible new offices, all of which would be rented. Details of the location of these offices and the annual rent payable are given below.

Location of office	Annual rent ($)
Addison Square (A)	30 000
Bilton Village (B)	15 000
Carlisle Walk (C)	5 000
Denver Street (D)	12 000
Elton Street (E)	30 000
Filton Village (F)	15 000
Gorton Square (G)	10 000

While the owner would like to keep his costs as low as possible, he would also like to take other factors into account. For example the Addison Square office is in a prestigious location and also close to potential customers, but it is expensive to rent. It is also an old, dark building which will not be comfortable for staff to work in. In contrast, the Bilton Village office is a new building which will provide excellent working conditions, but it is several miles from the center of town, where most potential customers are to be found. The owner is unsure how to set about making his choice, given the number of factors involved.

An Overview of the Analysis

There are seven stages required:

Stage 1: Identify the alternative courses of action. Options. In the example these are the office locations.

Stage 2: Identify the factors that are relevant to the decision. Criteria. In the example above some have already been mentioned such as annual rent, image, closeness to customers and staff comfort.

Stage 3: Determine how to measure the criteria. Criteria properties. In the example above, “Annual Rent” already has a measurement scale in $. However, “Image” doesn’t one readily available.

Stage 4: Determine the weight for each factor. Weight. This reflects the importance of each criterion compared to each other.

Stage 5: Assign scores on how well each option performs on each criterion. Scoring.

Stage 6: Make a provisional decision. Priorities

Stage 7: Perform sensitivity analysis to see how robust the decision is to changes in the data used.

Constructing a Value Tree

Start by creating two headings – one for costs and one for benefits. The objectives here are (a) to minimize costs and (b) to maximize benefits. Then, for each heading, identify the criteria that contribute to meeting those twin objectives. Goodwin & Wright established the following:

Minimize Costs

·       Annual Rent

·       Cost of Electricity (for heating, lighting, operating equipment, etc.)

·       Cost of Cleaning

Maximize Benefit

·       Increase Turnover

·       Improve Working Conditions

Increasing the turnover of the business will be achieved by being close to customers, being visible to the customers and having inviting premises.

Improving the working conditions for staff will be achieved by having large premises that are comfortable with adequate car parking.

The value tree that results can be represented thus

To create this in Promax use the “Criteria” tab. Double click in the workspace to add a box. Drag the boxes onto the “Value Tree” box. This turns all the boxes into “Criteria”. To create a “Topic” or “Node” (the red headings in the value tree) right click a box and turn it into a “Topic”.

Measuring How Well The Options Perform On Each Criteria

Having created the value tree the next step is to determine how best to measure each criterion.

Fixed Mapping

For the cost criteria, this is relatively simple. Costs for rent have already been provided and estimates for electricity and cleaning can be obtained. All of these will be measured in $ over the entire year and all three can be added together to give a total cost per year in $. It is also true in this case that $100 is valued at twice $50 and this relationship holds throughout.

In Promax, the measurement scales are added through “Criteria Properties”. In the criteria tab, choose the Total Cost criteria right click and choose properties. This brings up a box as below:

There are a number of areas to explain more about the criteria but we’ll focus on just a couple.

First, choose the radio button for “Cost”. This is essential.

Next, we’ll choose the “Fixed” mapping (second from the left) and then set the range – the left hand number should be zero and the right hand number 35000 (which represents the largest total cost figure). In fact, as long as this number is larger than the maximum it doesn’t matter. What this does is to create a straight-line mapping with the real-world scale (of $0 - $35000) on the x-axis and the value assigned to the scale on the y-axis (0 – 100). So $17,500 is worth 50 points.

Repeat for all the cost criteria with the scale going from zero to the largest in all cases. Note, that at this stage you won’t necessarily know what is the largest cost so you will need to go back and check.

Custom Mapping

In a lot of cases the relationship between the real-world scale and what it is valued is not a straight-line. Goodwin & Wright use the example of “Floor Area”.

Let us now consider the benefit attributes which can be represented by easily quantified variables. First we need to measure the owner’s relative strength of preference for offices if different sizes. The floor area of the offices is shown below:

Location of office	Floor area (ft2)
Addison Square (A)	1000
Bilton Village (B)	550
Carlisle Walk (C)	400
Denver Street (D)	800
Elton Street (E)	1500
Filton Village (F)	400
Gorton Square (G)	700

Now it may be that an increase in area from 500ft² to 1000 ft² is very attractive to the owner, because this would considerably improve working conditions. However, the improvements to be gained from an increase from 100 ft² to 1500 ft² might be marginal and make this increase less attractive. Because of this we need to translate the floor area into values. This can be achieved as follows.

The owner judges that the larger the office, the more attractive it is. The largest office, Elton Street, has an area of 1500ft2 so we can give 1500 ft² a value of 100. …… Similarly, the smallest offices (Carlisle Walk and Filton Village) both have areas of 400 ft² so we can attach a value of 0 to this area.

The technique is to then identify the mid-point. That is what floor area is about halfway between most preferred and least preferred. Then do the quarter points in between until you have the scales mapped.

In Promax, select the criteria “Area” and right click to get to the properties box. The "Benefit" button is the default. Choose “Custom” as the mapping type. In the top row add in the floor areas and in the bottom row add in the values. In this case you have 400 and 0 on the left and 1500 and 100 on the right. Then complete the intermediate points. If you need more points, go to one of the existing points and right click to insert an additional point to the right or left of the one highlighted. Click OK to accept.

Preference Scales

In many cases it is difficult (or impossible) to use real-world scales and so preference scales are often used. "Image" is one such criterion.

In Promax, go to the Image box and right click to get the properties box. Choose the “Preference” mapping type (the one in the middle). This produces a straight-line mapping of the preference on the x-axis of 0 – 100 and the value on the y-axis of 0 – 100.

The process is actually carried out in the score window. First rank the offices from the most preferred to the least preferred:

1.     Addison Square

2.     Elton Street

3.     Filton Vilage

4.     Denver Street

5.     Gorton Square

6.     Bilton Village

7.     Carlisle Walk

Then give the most preferred a score of 100 and the least preferred a score of 0.

Goodwin & Wright go on to explain that:

The owner is now asked to rate the other locations in such a way that the space between the values he gives to the offices represents his strength of preference for one office over another in terms of image.

So in the example, moving from Carlisle Walk to Gorton Square is twice as preferable to moving from Carlisle Walk to Bilton Village. Similarly moving from Carlisle Walk to Addison Square is ten times more preferable than moving from Carlisle Walk to Bilton Village.

Note that since this is an interval scale you can’t say that Gorton Square is twice as preferable as that of Bilton Village.

Determining the Weights of the Criteria

Goodwin & Wright have an excellent section on weighting and the problems associated with the typical approach of weighting by importance.

An intuitively appealing way ….. is to attach weights to each of the attributes which reflect their importance to the decision maker. For example, he might consider office area to be less important than distance from customers and therefore give a weight of only 1 to office area and a weight of 5 to distance from customers. The problem with this approach is that it may not take into account how large the range is between the most preferred and the least preferred range on each attribute.

A better way is to use swing weights. In this method you are asked to compare a change from the least preferred to the most preferred value on one criteria to a similar change on another criteria.

The process is to imagine the worst office possible – the one which scores the least on all criteria. Then ask “if you could move just one criteria to its best score which one would it be?” In this example the owner selects “Closeness to Customer”. This is assigned a weight of 100 and is the yardstick. You then compare all the other criteria against this one.

In Promax is to go to the “Weights” tab and select “Swing Weighting”. Select two criteria from the left hand side, “Closeness” and “Visibility”. This will duplicate them on the right hand side. Right click on “Closeness” and select “Set as Yardstick”.

Drag the “Visibility” part up and down until the most preferred is equivalent to the yardstick. In this case the decision maker believes that the best in visibility is worth about 80% of the best in closeness to customers.

This is carried out for all criteria until all the weights have been done.

Note that in the example, weighting has been done only on the benefit criteria. This is so you can compare costs with benefits in a specific way. It is possible to include costs in weighting but as Goodwin & Wright explain

Our owner does have difficulties in judging the cost-benefit trade-off.

Aggregating the benefits using the additive model

Goodwin & Wright explain the calculations involved which is adding an office’s weighted value scores together to obtain a measure of the overall benefits, which that office has to offer.

Promax does all the arithmetic for you of course.

Firstly here are the scores used.

Costs

Benefits

Scores

Second, here are the mapped and mapped & weighted values.

Mapped Values

Mapped & Weighted Values

Results Chart
After choosing the criteria, weighting them and the scoring each alternative you can look at which one is preferred.

Click the “Priorities” tab to give you the results. Addison Square provides the best benefit.

By default, Promax places the options in order. If you want to look at the result alphabetically sort alphabetically.

Strengths & Weaknesses

Another way of looking at the results (not discussed by Goodwin & Wright) is strengths & weaknesses. Choose this from the “Priorities” tab and select the options you want to compare.

The length of the white background line is the weight of each criterion and the coloured lines reflect how well each option performs against each criterion.

Trading Benefits Against Costs

Goodwin & Wright use a graph to compare costs against benefits. You can do the same in Promax.

Firstly we need to create a new weight set where costs have a weight (at the moment, costs are weighted as zero as we’re only comparing the benefits).

Go to the “Weights” tab and select “Add” from the weight sets block. Give it a name and copy from “Initial Weights”. You’ll end up with a table with an additional row. Put in a weight for Total Cost and make sure all the other costs are zero weighted. Note, it doesn’t matter what value you pick for a cost weight since costs and benefits will be kept separate. It does matter that the other costs are zero weighted since, if they weren’t, you’d be double counting some of the costs.

Then to look at the graph go to the Priorities tab and select “Scatter” from the drop down on the left hand side.

By default, the display plots costs on the x-axis with the cheapest costs (better) to the left. Benefits are on the y-axis with the greatest benefits towards the top.

To mimic the Goodwin & Wright graph you need to make the cheapest cost go to the right so click “Reverse Cost Axis” in the ribbon. Click the frontier button and you end up with the following:

Note, only the mapped values are shown for costs rather than the actual $ amounts.

Clicking on table and then each of the options on the frontier, highlights each option.

The B/C ratio gives the benefit score (mapped & weighted) divided by the costs, which are positively mapped (i.e. a high cost is a high score).

The graph provides some interesting insights. The Addison Square office provides the greatest benefits but also has the highest cost. The only options worth considering are those on the frontier i.e. Addison Square, Gorton Square and Carlisle Walk. If (and only if) all the options meet the minimum benefit required then the decision maker should choose the option with the best benefit to cost ratio – in this case Carlisle Walk.

Sensitivity Analysis

Gordon & Wright’s definition of sensitivity analysis is:

Sensitivity analysis is used to examine how robust the choice of an alternative is to changes in the figures used in the analysis.

This is a fine definition but they then go on to describe the variation of only one element of the data – weights. Clearly there are other factors can also vary, especially the scores (uncertainty in the costs for instance) and in the value mapping (uncertainty in whether a floor area of 1000ft² is valued at 75% that of 1500ft².

However, to look at the uncertainty of weights on the results choose the “Sensitivity” graph from the Priorities tab. By default, it will plot the top options at different weights. As it suggests in their example the owner is most concerned about the effect of turnover and whether a change in weight would affect the choice.

Select “Turnover” as the filter and the graph below will appear. The current weight is shown by vertical the red line (81). The top lines in yellow and blue reflect the top options as the weight of “Turnover” changes. It can be seen that the top option is Addison Square until the weight drops to around 50 whereupon Elton Street is the most preferred. Choosing the “What If” button in the ribbon allow you to see exact figures and test out different weights. In this case it would take a substantial change in weights for a different option to become more favoured and the decision can be considered robust.

This needs to be done for all criteria to determine whether the result is sensitive to a small change in one of them.

Future blogs will consider:

• How to use scales other than preference scales, for difficult to measure criteria
• Integrating cost criteria into weighting using swing weights, and
• Considering additional uncertainties in scores and value mapping.