Principles of Information Systems Session 07 Problem Identification and Solving
Problem Identification and Solving Chapter 6
Overview Learning objectives 1. What is a problem? 2. Structure and complexity in problems 3. Puzzles, problems and messes 4. General methods for solving problems 5. From problems to solutions 6. Creative problem solving strategies 7. Summary
Learning objectives • Identify different kinds of problems and approaches to their solution • Distinguish problems, symptoms and problem situations • Explain the difference between puzzles, problems and messes • Apply the various problem-solving methods in appropriate solutions • Recognize wicked, intractable and insoluble problems • Describe some techniques for creative problem solving
1. What is a problem? 2. Structure and complexity 3. Puzzles, problems and messes 4. General methods 5. From problems to solutions 6. Creative problem solving strategies 7. Summary What is a problem? • Examples for people, organisations, society Problem or symptom? • Irritant or sign e.g. Ibises in suburbs –nuisance or sign of drought • Problem analysis - an important skill
Identifying the real problem • Distinguishing symptoms from deeper problems • tingling hands may seem a trivial problem but may be a symptom of a stroke or diabetes • high staff turnover may lead to extra recruitment and training costs. Underlying problem may be low morale and people are leaving because of bad managers • Problem analysis aims at finding deeper problems that underlie or cause an apparent problem.
Problem situations • Can be a set (or system) of related problems • Losing your job • Can’t pay for house • Partner leaves you • Stress from all this … • Which do you fix first?
Problems I’m Winston Wolf, I solve problems. Jimmie: Good, ‘cause we got one. Givens : what you have at the start Operations : what you can do with what you have Goals : what you are trying to achieve (Wayne Wickelgren)
Examples • Given: and • Operation: Insert a vowel • Goal: Make a complete English word • Given: • Operations: arithmetic • Goal: Combine to make 20 S _ C K I A E O U 3 2 4 + / - x
Example Given: an incomplete chessboard and 31 dominos Operation: place dominos on board Goal: until board is covered
Problems worthy of attack Prove their worth by hitting back Problem analysis • Wickelgren’s idea applies widely: puzzles … organisational strategy … warfare… • Analysis involves: identifying components and regularities whether there is enough information • Some problems are intractable: (not easily controlled or directed; not docile or manageable; stubborn; obstinate.) • They need other types of approach for a solution
Recap Problems can range from simple puzzles to complex and messy situations. Problem analysis and problem identification are important skills. All problems have givens, operations and goals
1. What is a problem? 2. Structure and complexity 3. Puzzles, problems and messes 4. General methods 5. From problems to solutions 6. Creative problem solving strategies 7. Summary Structure and complexity • Amount of formal structure • the more structure a problem has, the easier is a generalised solution. • Amount of complexity • more complex problems are less tractable
Structure - examples • Abdul is older than Bob • Bob is older than Christine • age is structured (transitive) Equivalently • Abdul is taller than Bob • Bob is taller than Christine • “who is tallest” has same structure A B C
Problem: Where does John live? John, Val and Diarmuid all live in the Perth area • Val lives northeast of John • Meeting at Diarmuid’s house is most convenient
Degrees of structure • Structured problems: routine, readily solved with known methods. Suited to computer analysis. • Semi-structured problems: part of the problem is structured. This part may be solved in a familiar way, then can support judgement • Unstructured problems: no ready method of solution, may need to be structured somehow for solving or management.
Examples • Structured problem – sudoku • Semi-structured problem • Choosing which car to buy within your budget • Unstructured problem – should we build a dam?
Complexity • How many things are involved? • How do they interact? • Do they get messier over time? • Are they combined with other problems in the wider situation? • Problem structuring can help reduce complexity.
Three levels of complexity • Puzzles: well-defined whose fixed solution is readily worked out. (e.g Sudoku, FreeCell). • Problems: well defined, but different exclusive solutions are possible. (e.g choosing a home computer, designing your garden) • Messes: complex issues, not well defined, or without agreed problem definition. (e.g. dams, bypasses). Solutions must address the whole mess: ignoring relationships to other parts of the mess will lead to failure.(Ackoff)
Structure and Complexity are similar Dragon Curve by Solkoll with extract
Recap Structure and complexity help define problems. The more structure a problem has, the easier is a generalised solution. More complex problems are less tractable.
What is a problem? Structure and complexity Puzzles, problems and messes General methods From problems to solutions Creative problem solving strategies Summary Puzzles, problems & messes • Puzzles • Problems Constraint problems Optimisation, maximisation and minimisation problems Search space and NP-completeness • Messes
1. Puzzles • Simple problems, commonly quantifiable or logical, with well understood methods • What discount applies for cash now, rather than over a three-year term? • How much feed to maintain yield from a stock of cattle? How many animals should I graze on this land to maximise productivity? • Discipline-specific methods/formulae apply. • F = C/5 * 9 + 32 given 100°C – what is Fahrenheit? • Solution usually unambiguous: exact numbers.
2. Problems • Some quantification, but also unknowns. (semi-structured). • How many prisons/hospitals should we have? • What export price to allow for tariffs and legal compliance costs in unpredictable market? • How much should I spend on marketing, compared with research and development? Possible approach: • Identify assumptions, work out a numerical answer, then consider wider feasibility.
How many hospitals? • Work out the population to be served by the hospitals, the average percentage in hospital at any one time, and their average stay. • Other information shows that: • The population is expanding • people are living longer • health problems increasingly manageable at home • a policy trend towards keeping people out of hospital where possible. • Assumptions moderate original number up or down. Answers more approximate than exact.
A general class:Constraint- satisfaction problems • Set limits on what solutions are possible • May be quantifiable or qualitative in nature. e.g. Decision problems with two alternatives or many • Where to place the next O • Where should my family live? • How should I vote? • Some have no right answer, or many equally good or bad answers.
Where should my family live? Answers are needed! Often satisfactory answers are found by constraining the problem. House locations may be narrowed down by asking: • Can I get to my place of livelihood from there? • Can the children get to a good school? • Is it in an attractive area • Is transport convenient? • Can I afford it? • Does the whole family like it? • Is it near the CBD? • Can I get broadband? …
Hard vs soft constraints Such considerations constrain, but don’t determine the solution. • Hard constraints are not negotiable • I must be able to get to my work place • F = C/5 * 9 + 32 • Soft allow some tolerance • proximity to the beach is debatable or can be relaxed (i.e. loosened or dropped). • Typical solution may not meet all constraints but it may meet enough of them well enough. Not perfect but satisfies the requirements.
Optimisation, maximisation and minimisation problems Examples: • How to maximise shareholder value? • How to minimise staff turnover? • Optimal mix of products we should manufacture? • Optimal density of planting for best yield? • Stacking shipping containers at ports. • Stacking containers is an optimisation problem. Find a balance between putting through as many containers as possible to maximise profit, and minimising the throughput time to remain competitive. • Tools e.g. MS Solver
Search space problems • When many components interact this creates a very large set of possibilities. Perhaps only one combination is of interest. • Sudoku • Travelling sales rep problem. • Which way should the travelling sales rep go? • Computational complexity: • Brute force search may take forever, need more intelligent solution strategies.
3. Messes • Puzzles and problems can be tamed. They apply in idealised worlds, without social and political realities. But consider: • Should this country have the death penalty? • How should we deal with poverty? • How can we fix the university parking crisis? • Messes need managing not solving • deal with the situation vs solve the problem • Problem and possible solutions (may) be defined, but method to reach solution is arguable. Some messes are wicked problems.
Recap Puzzles, problems and messes are three classes of problems. Each has particular qualities and general approaches to solution which can be used.
1. What is a problem? 2. Structure and complexity 3. Puzzles, problems and messes 4. General methods 5. From problems to solutions 6. Creative problem solving strategies 7. Summary General methods for solving problems • Pólya’s 4-step general method • Understand the problem 2. Devise a plan • Implement the plan 4. Reflect on the outcome • Within each steps are prompts: - have you seen this before? - Solve a simpler problem. • Pólya called these heuristics. They help you guessat or partly solve a more complex problem.
Heuristic: Solve a simpler problem Sliding tiles puzzle
Herbert Simon’s model Closely related to “scientific method” but tailored to management decision problems • Intelligence: collect information, identify the problem • Design: conceive alternatives, select criteria • Choice: evaluate alternatives, select • Implementation: put decision into effect, allocate resources, control Basis for other methods and versions
Recap There are some general approaches that can be applied to all problems, e.g. Pólya's method and Simon’s model
1. What is a problem? 2. Structure and complexity 3. Puzzles, problems and messes 4. General methods 5. From problems to solutions 6. Creative problem solving strategies 7. Summary From problems to solutions Generally all aim at • understanding and defining the problem • designing a solution addressing a specifically defined problem. 5.1 Facets of problem definition 5.2 Approaches to problem solution • Puzzles • Problems • Messes and wicked problems
A problem well stated is half solved problem definition • Formulating problems: how a problem is described and represented makes it easier or harder to handle. Try these: 19+27+46+54+73+81= (1) 19+81+54+46+73+27= (2) 7x6x5x4x3x2x1 = (3) 1x2x3x4x5x6x7 = (4) • These pairs have equivalent intellectual difficulty but (2) and (4) are easier.
Problem Ownership • Who has the parking problem? • Students /staff who can’t park? • University officers? • Bus company? • Government? • Solutions can cause problems! • A rail link may affect nearby houses • Multi-storey stops library expansion…
Practice example: (from Gause & Weinberg) A road tunnel through the Swiss Alps has been built. For safety a sign is made: At a scenic viewpoint just beyond the far end of the tunnel people stop for photos and refreshment. Many then find their car batteries dead from leaving lights on! National police are fed up jump-starting cars. Tourists are upset. WHOSE PROBLEM IS IT? Tunnel ahead - please turn on headlights
WHOSE PROBLEM IS IT? • Drivers • Tunnel engineer • Gendarmes • Swiss canton president • Other • All of the above • None of the above Probably the tunnel engineer’s problem WHAT SOLUTIONS MIGHT WORK?
Possible solutions • Sign at tunnel end? • Ignore it? • Battery chargers at rest stop? • Franchise battery charging? Each solution causes new problems! Turn off your lights
Possible solutions Turn off your lights Sign at tunnel end? Problem: people should not turn off lights at night Ignore it? Problem: no changes and loss of reputation Battery chargers at rest stop? Problem: expensive, maintenance, unpopular… Franchise battery charging? Problem: commercialises rest stop, unacceptable to tourists, govt. … A better sign?
A better sign? Turn off your lights If it is daylight and if your lights are on then turn off your lights If it is dark and if your lights are off then turn on your lights If it is daylight and if your lights are off then leave your lights off If it is dark and if your lights are on then leave your lights on
Choosing which problem to solve • Which problem to solve in a problem situation? • analysing specific problem components • prioritising and scoping Medical triage at an accident. Who to treat first with the limited resources of ambulance officers and time? An organisation identifies problems in its marketing, finance, IT, and innovation departments. Business analysis suggests fixing the IT aspects is most critical.
Agreed conceptual models • With (19+81)+(54+46)+(73+27)= all information is given, operations and goal are obvious • Problem is understood so the solution is straightforward. • The conceptual model is base 10 arithmetic • Not always so clear e.g. in ethical questions.