computer skills advanced problem solving and decision making · 2013. 1. 11. · 1 computer skills...

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Computer skills advancedProblem solving and decision making

Prof. Raffaella FOLGIERI

DEMM, Department of Economics, Management and quantitative Methods

aa 2012/2013

•Problem solving– Introduction– Simple and complex problems– Reasoning abilities– Problem solving in psychology– Different contexts

•Problem solving and decision making– Interrelations– Decision making techniques

•Well-conditioned problems•The Pareto's principle

Outline

Prof. Raffaella Folgieri –aa 2012/2013

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The PROBLEM SOLVING approach (easy)

• Approach to the problem from the solution point of view (as at primary school!!!)

• to detect:

! Data at disposition

Data (and problem) characteristics

IT tools supporting operations needed to achieve the solution

? Requirements & final objective


Problem solving: a definition

• Cross-curricular, interdisciplinary character:• It defines way and means to solve a problem

which solution is not immediate, but– Needing superior cognitive processes to

solve real and interdisciplinary situations– Concerning situations which solution is not

immediately evident– Belong to contexts going beyond a single

competence, but involving more disciplines.


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Simple and complex problemsSimple problems

• Time: defined

• Aims and steps are defined in a clear way

• Few variables and simple dependencies

• A single solution or correct answer

Complex problems• Dynamics

• Not clear definition

• Many variables or complex dependencies

• More than onesolution or answer

Is it possible to transform a complex problem in a simple one?

– YES, using the correct approach and the right means.

– Help from Problem Solving


Face a problem: from complex to simple

• From the Problem Solving point of view– Comprehension– Detection of characteristics– Problem representation

– Possible subdivision in sub-problems

– Elaboration of a solution strategy– Verification of the solution– Communication of the solution

• Each point can be supported by toolsand techniques

COMPLEX

SIMPLY


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Reasoning abilities• Analytic Reasoning:

– Application of reasoning through formal logic:

– Needed and sufficient conditions

– Relationship between constraint causality and problem conditions

quantitative

analytic

• Quantitative reasoning:

– Application of mathematics/operational/quantitative properties and procedures

• Analogic reasoning:

– Reduction of known problems and related solutions

– Evaluation of previous experiences, independently from current context

• Combinatorial reasoning:

– Evaluation of a multiplicity of factors and of all the related combinations

– Evaluation of combinations on the basis of objective limits

– Selection or ordering of the possibility


Behaviourism and problem solving

• Problem solving as the result of beaviours

learned from trial and errors or from the

repetition of already known answers (Thorndike,

1930).


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Gestalt psychology and problem solving

• An individual can find the solution of a problem

• NOT through a trial-and-error approach

• BUT through INSIGHT

(Köhler et al., 1935)

• Insight: intuition of the structure of the problemleading a restructuring to achieve the solution


Gestalt psychology: productive problem solving

• Characterized by the presence of an insight phase of

the problem structure and by its productive

restructuring

• Insight is unpredictable (the moment of)


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Gestalt psychology: reproductive problem solving

• It implies the re-use of the past experience

• Sometimes it could avoid the satisfactory solution of

the problem (the so-called Functional fixedness

phenomenon)

• Functional Fixedness: inability to see the new

functions of objects compared to already known ones;

unability in going beyond predefined schemata,

breaking a mental set.


Scheerer (1963): 9 points problem

Trace 4 straight continue lines linking all the 9 points, without leaving the pen from the paper.

Functional fixedness: an example


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Solution

Many persons aren’t able to find a solutionbecause they think that the 4 lines can’t go outof the square delimited by the 9 points.(functional fixedness).


Cognitivism and problem solving

• Cognitivism proposes a vision of the world foundedon the continuous feedback individual-environment

• Explicit models of external factors influence onbehaviours

• Information flow, elaborated at different levelsduring their transition in the organism

• Solving a problem requires: understanding it,detecting the needed operations, executing them,controlling the results. If the final objective has notbeen achieved, then modify some steps.


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Computational approach: the space of the problem (1)

• Newell and Simon: Problem Space theory• Problems can be solved through the exploration of

different paths allowing the achievement of the solution• The Problem Space:

• The set of all the possible states and all the possible pathsallowing to achieve the solution. Only some of them couldsolve the problem.

• The objective structure of a problem described as a set ofstates:– Initial state (example: the beginning of a path);– Final state (example: the end of a path).– We need to apply some operators, which result is the

transition from a state to the following


• Newell and Simon hypothesize that people solve a problemexploring in their mind different "knowledge states": froman initial state, through a space composed of alternativestates, till the final knowledge state is reached.

• Transitions from a state to the following obtained with theapplication of Mental Operators.

• Mental operators: coding the allowed steps and therestrictions avoiding a step in specific conditions.

• The processes act within the limits of a specific cognitivesystem (example: there are limitation in the workingmemory)

Computational approach: the problem space (2)


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The first and most famous of these computationalmodels for problem solving: GPS

General Problem Solver by Newell, Simon &Shaw (1958), applied to the brain-teaser of theHanoi Tower (by the French mathematician EdouardLucas in 1883).

The legend: in an Indù temple some monks areinvolved in moving 64 gold disks on 3 columns,following the Hanoi tower’s rules. When they willcomplete the work, the World will end. This legend hasbeen created by the first Company selling the brain‐teaser.

The Hanoi towerProf. Raffaella Folgieri –aa 2012/2013

The game start with all the disks on the same columnin a decreasing order, as a cone.

The Hanoi tower

The aim consists inputting all the diskson the last column,moving only onedisk each time andputting a disk onlyon a bigger one(never on a smallerone).


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Problem solving: heuristic methods

• Often when facing problems similar to the Hanoi Tower,people use solution strategies based on heuristic models:

• This method implies approximated rules, not ensuring thesolution of the problem (but if a solution is achieved, aperson could save time and efforts)

• Newell and Simon state that the means‐aims analysis is a veryused heuristic method:

• It consists at first in observing the difference between theinitial state and the final objective and, after, in creating asub‐objective to reduce the difference between the twostates, selecting an operator to solve this sub‐task.

• The past experience often allows to detect more easily thesub‐tasks.


• Expertise stand for a specific knowledgecorresponding to a given domain

• An apprentice is who faces, for the first time, the tasksrelated to a specific domain.

• The chess game has been one of the first domainswhere the differences between experts and apprenticehas been studied.

• Initial state of a game: the disposition of the pieces onthe chessboard: 8 pawn, 2 horses, the king, the queen,the 2 towers and the 2 bishops

• Final state: the check-mate to the opponent

Problem solving: heuristic methods – expertise


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The expertise in the chess game – De Groot (1)

• Allowed moves are clear:1. You can move one of the 8 pawns or2. You can move one of the horses

• Soon the number of moving possibilities to evaluate gobeyond the possibility to count them, because thepossibilities explode exponentially and the number of pathsgrows exponentially.

• De Groot hypotheses that the best performance of the expertscompared to beginners are due to the knowledge of thedifferent positions of the pieces on the chessboard (based onthe experience). This fact allows them to remember the bestmoving to do, starting from the current positions (someoneaffirm that when playing chess, people imagine the 3 followingconfigurations and their effects)


The expertise in the chess game – De Groot (2)

• As a consequence of the confirmation of thehypothesis done by De Groot this knowledge shouldreflect also in specific mnemic tasks:

• In the experiment both experts and non-experts saw(for a few seconds) several configurations of the piecestaken from selected chess games. After, expert andnon-experts had been required to recreate the positionof the pieces on the chessboard. Experts were able torecreate accurately the configurations, while beginnersmade more errors.

• On the contrary, if the pieces were placed randomly onthe chessboard, both experts and beginners weren’table to recreate the configurations, demonstrating thatall they haven’t the specific knowledge required tocodify the configurations.


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Anderson and the ACT modelReciprocal interconnection of 3 components:

1. Declarative memory

2. Procedural memory

3. Working memory

In this model there are 2 key-processes for the cumulative

construction of the knowledge:

1. Proceduralization that is the transition from the declarative

memory to the procedural memory.

2. Composition: the unnecessary rules are eliminated.


Problem solving through analogy

• Some authors hypothesized that past experiences can'tbe directly applied to the current context and that inthere is an indirect process, based on analogy.

• Analogic thinking: the result of a process that transferthe conceptual structure of ideas (base dominion) onanother set of ideas (target dominion)

• Gick and Holyoak (1980) studied the phenomenon ofthe analogic transfer in problem solving application

• The participants in the study had to solve the radiationProblem (Duncker, 1945)


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The radiation problemProblem:

• A doctor must destroy a tumour for which it is not possible toperform a surgery operation.

• There is a kind of ray able to destroy the tumour, in a singleshot and only at a specific intensity.

• Despite of this, if high intensity is used, the rays surely willdestroy also the tissue around the tumour, while, if low intensityis used, the tissue will not be damaged. Despite of this, if highintensity is used, the rays surely will destroy also the tissuearound the tumour, while, if low intensity is used, the tissue willnot be damaged, but the tumour could not be destroyed.

Solution:

• Convergence: the doctor sends a low intensity ray from manydifferent directions, converging them on the tumour: the raysum till such an intensity sufficient to destroy the tumour.


The radiation problem: discussion

• Only the 10% of the individuals were able to solve theproblem on their own

• If they were provided, as a suggest, the story of theGeneral who must attack a fortress with his army, thepercentage of correct solution was 80%, demonstratingthat the analogy process constitutes a reinforcement.

• Moreover, if participants in the experiment wereprovided by the story of the General withoutspecifying that it could be useful to solve the radiationproblem, only the 40% achieved the correct solution.


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The story of the General

• A General could not use the entire army to attack the fortressbecause the access roads were mined and could explode if alarge number of soldiers passed on the mines.

• He divided his copious army in many small groups positioned atseveral points around the fortress.

• The soldiers had to converge on the fortress to conquer it.


Let's come back to our aims

After facing the problem solving and the techniques

and methods by the different current psychological

point of view, let us see how, practically, we could

apply problem solving corresponding to the argument

of this course.


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Problem solving: typologies

• Problem solving and decision making

• When we treat a problem, how can we take

the right decision?

• Algorithmic Problem solving

• Problem solving and creativity

• Problem solving and project management…

• Computational thinking


We can distinguish 5 phases:

1. Well-disposed context

2. Problem definition

3. Creation of alternatives

4. Evaluation of alternatives

5. Choice of an alternative (solution)

The decision making process


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Creation of the context

• Right for taking efficient decisions

• Where there aren’t personal interests

• Without waste of resources

Decision making: 1. well-disposed contextProf. Raffaella Folgieri –aa 2012/2013

(this is the main position of problem solving)

Definition of the problem:

• requirements, needs, objectives

• dispassion

• limits

• constraints

Decision making: 2. problem definition


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Important for decision making process

• In absence of alternatives we couldn’t have

decisions to take!

• The alternatives are not necessarly intrinsic

– for this reason we need to create

alternatives

• Alternatives must be:

– feasible

– accurately described

Decision making: 3. creation of alternativesProf. Raffaella Folgieri –aa 2012/2013

The found alternatives must be evaluatedconsidering:

• Validity• Feasibility• Realistic aspect• Risks• Potentialities• Pro and cons● Costs and benefits● Financial impact● Intangibles● Time● Resources

Decision making: 4. evaluation of the alternatives


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• The choice of the best alternative completes

the cycle of the decision making process

• After this phase, we will need to practice the

chosen alternative

• This phase is strongly related to the previous

one

• Both the phases are linked to the problem

solving process

• We can use decision making techniques

Decision making: 5. choice of the best alternativeProf. Raffaella Folgieri –aa 2012/2013

• From Japan• For group decisions• Aims: involved people must

– Feel part of the decision– Make themselves free from prejudices or

external conditioning• Each person involved in the decision takes care

of an alternative and work for its improvement• After he/she passes the alternative to the other

involved person who will improve again the alternative

Decision making techniques: chatchball


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• For groups

• Expert panel geographically distant

• A set of of questionnaires is sent (by mail, email or by computer systems) to a group of preselected experts

• The questionnaire is formulated to solicit and deepen individual answers to the problem– Experts refine the own point of view at each passage

• Usually the first questionnaire gives the problem in a general form, requiring answers and comments– the answers to the first questionnaire are synthesized from the

research team and used to create the second questionnaire

• The second questionnaire presents the results of the first one and offers the opportunity to review the first answers following the feedback on the basis of the answers of the entire group

• The process is interactive and could be repeated

Decision making technique: delphiProf. Raffaella Folgieri –aa 2012/2013

● There are other techniques, such as Brainstorming (we

will see it when we will talk about the creative problem

solving), SWOT for decision concerning

marketing/positioning, mental maps (we will see also

these last)

● Decision making techniques for individuals:

● Adaptable SWOT

● Mental map

● Pro and cons list

• F.A.R.E. (Focalizzare; Analizzare; Risolvere; Eseguire –Focus, Analyse, Resolve, Execute)

Other decision making techniques


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● Problem solving

– at the second step of the decision making

process

● If the problem is not well-conditioned, it

could be difficult

– to find the alternatives

– To evaluate the alternatives

– To achieve the correct solution

● It is important to define WELL the problem

Importance of problem solving in decision makingProf. Raffaella Folgieri –aa 2012/2013

● WHY (where the exigence come from?)

● WHO does WHAT

● HOW: what resources (not only from the economic point

of view)

● WHERE: is the localization important or not?

● WHEN: start, end, intermediate time

● HOW MUCH: are there economic constraints?

● CONSTRAINTS: consider all! (Ex. “Build a 100 meter high

palace” is different from “build a palace”)

● Enlarged Lasswell (5 W and 1 H: Who? What? Where?

When? Why? How?)

Well-defined problem


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Examples

problemCONDITIONED

problemSOLVED

Example

WELL WELL Sign for the exam having studied, so passing it

WELL WRONG Titanic

WELL WELL Discovery of America

WRONG WRONG Sign for the exam if you have not studied

Initial state, end state and operators needed to solve the problem, must be all defined in a clear way


• Vilfredo, Italian economist (1848-1923)• Studying salary distribution, noted that in a

region only a few individuals (20%) own the greater part of the richness (80%).

• This fact can be synthesized in the sentence: the great part of the effect depends on a restricted number of causes– In general the 80% of results depends on

20% of causes.• Different applications (from economy to daily

life).

Pareto’s principle (or “rule 80/20“)


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From theory to practice

Investment choices for a Company(case study #1)P

rof. Raffaella Folgieri –aa 2012/2013

A daily problem: how optimize available resourcesFinancial fonts: great difficulties in seeking and managing.

– Enlargement of the kind of offered products, new market,

– Acquisition of another company– Renovation of technology

It is necessary to evaluate– The investment profitability– The economic convenience– The sustainability respect to the patrimonial

structure or the coherence with already active business areas

Decision making in a Company


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We are interested in investment choices and we will try

to analyse the case of a Company, under specific

conditions, using the most appropriate ICT tools.

Before analysing the specific case, let’s see which

indicators and methods are used in practice.

In a company, these kinds of evaluation are generally

performed by the FINANCE function.

Decision making in a CompanyProf. Raffaella Folgieri –aa 2012/2013

• The finance function performs evaluation through appropriate methods

• There are different methods, such as (different for approach):

• VAN (it examines the cash flows)• Payback period (it concentrates on time

variable compared to the strategy)• IRR (provides an evaluation based on the

discount rate)

Decision making and the FINANCE function


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• VAN (valore attuale netto, current net value)• To calculate the economic convenience of an investment• Through the sum of the current cash flows, it allows to

detect a value that, if positive, indicates the convenience to invest. The VAN formula is:

Current (Attualizzazione): process through that it is possible to define the economic value in terms of buying power of a money sum that will be income in a future period. It is sufficient divide for the expression (1 + i)n

where i = cost~opportunity of the money (sure return that the money could have through the investment in capital warranty financial instruments); n = number of previous years that must be considered.

Valutazione degli investimenti: il VANProf. Raffaella Folgieri –aa 2012/2013

• Not easy to be used– You need to identify either the net cash flows (flussi

di cassa netti - FCN), direct and indirect, and the current rate (tasso di attualizzazione)

• Compared different investment solution must have the same reference period (duration in years)

• Flows must generate a cash variation, differential (direct or indirect consequence of the investment), including financial debts, excluding possible taxes.

• Current rate composed of two parts: one without risks, related to the returns curve for the warranted capital at the deadline, and one allowing the evaluation of the premium for the risk.

Investment evaluation: comments on VAN


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• Indicates the number of periods needed to achieve the initial capital with the returns of investments

• Evaluation given by the duration of the financialexposition and to related expenses

• An investment with positive return can be saved if the payback period is greater than the cutoff.

• The payback period formula is:

• where N is minor than the previously determined cutoff.• Cutoff: maximum period for the return of an investment. The

detection method is arbitrary but influenced by some structural variables of the company (es. finance fonts, investment strategy, company complexity and dimension).

Investment evaluation: payback periodProf. Raffaella Folgieri –aa 2012/2013

Comments• The method offers a greater informative contribution

offers a greater informative contribution• It allows an accurate evaluation of the opportunity

cost of the used financial resources and of the alternative investment for the same resources.

• The payback period does not give an evaluation of the total opportunity of the investment.

Investment evaluation: payback period


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• Internal rate of return: measures the return of a project

• Variables influencing the calculus: investment amountand number of periods for the investment

• Allows the detection of a discount rate applied to the cash flow generated by the investment and a current net value equal to zero. The discount rate is the risk rate associated with the investment.

• The choice to do or not the investment: obtainedcomparing the IRR with the opportunity cost of the capital. It represents a financial cost for the project. The formula to calculate IRR is:

• The opportunity cost represents the return expected from a financialactivity with a risk equivalent to the project we are evaluating.

The decision making in a company: IRRProf. Raffaella Folgieri –aa 2012/2013

• Not all the flow-series have a current net value

diminishing while improving the discount rate

• The project can have multiple IRR (depending on the

mathematical function) or in other cases it could be not

calculable if we do not predict negative flows

• In the evaluation of alternative projects, both with a

convenient IRR, the right choice consists in doing another

comparison stressing the incremental project's IRR.

The decision making in a company: IRR-comments


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• If we can detect all the variables influencing the investment, the best solution to evaluate a project consist in using the VAN.

• If we aim to reach the company's financial equilibrium (small companies, difficulties in finding founds) we will prefer to use the payback period.

• The IRR is the most used methods in alternative low-economic-impact projects, for its characteristic consisting in underlining a greater or less capability in generating returns.

The decision making in a company: conclusionsProf. Raffaella Folgieri –aa 2012/2013

• We will come back to IT tools supporting problem solving in general.

• Final decision making techniques, in this case concerning investment choices, can be supported by ICT tools. You need to choose the right ones…

• If we have great numeric quantity of data to manage: Electronic data sheets (i.e. MS Excel)

• If we have a great alphanumeric quantity of data to save and manage: DataBase management systems (MS Access, MySQL)

• If we need any statistical operations on data: MS Excel or specific statistic tools (i.e. R, Mathlab,

Statistica and so on)

IT tools supporting investment choices


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We need

• A worksheet.

• We can use Excel or OpenCalc (free in Open office suite).

• You can download it here:

http://it.openoffice.org/download/3.3.0/download330.html

Case study 1IT tools for our problem


• It is a decision making problem

• Remember the 5 phases of the decision making process:

1. Favourable context (no loss of resources)

2. Problem definition (problem solving: we must analyse the problem

characteristics, define the objectives and intermediate steps – for

example useful technologies)

3. Creation of alternatives (after problem analysis, identify the

alternatives)

4. Evaluate the alternatives (what is the alternative that satisfy

requirements and objectives?)

5. Chose the alternative (solution)

How to solve the first case study


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Assumptions (problem characteristics):• The Company:

produces just one deteriorable product uses a technology based on a not-increasing scale acquires and sales in full competitive-based market uses the capital as the only productivity factor operates in absence of uncertainty

• Such a kind of Company plans for a period window the quantity of capital it needs to maximize the profit, once evaluated the market prices and the technology at disposition.

• Scope: to know future values of: Prices (or interest rate) of the capital market Sales prices for the Company product

Case study 1: investment choices for a companyProf. Raffaella Folgieri –aa 2012/2013

Step 1: the right conditions

• Not-increasing scale yields hypothesis (gains) are aligned with the assumption of a concurrent (full competitive) market. This fact implies that: a single Company doesn’t influence the market

variables (quantities and prices exchanged)• The product deteriorability implies that the Company

can accumulate only the capital, without problems for product escorts storage

• The hypothesis of a single factor simplify the problem. In fact a single rule regulates both production decisions and investment and accumulation plans.

These conditions determine also constraints simplifiesthe detection of alternatives.

Case study 1


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• A Company can choose among different investment plans, each characterized by a specific investment level and by a gross yield.

• To take a decision and chose the level satisfying the requirements, we need to compare market data at disposition.

• Only in this way we could have several alternatives at disposition (step 3, creation of alternatives) and we could go on with the evaluation (step 4)

• (Numeric) data at disposition can be several and usually they will be not saved (because they vary every year), so, if we want to use IT tools for the intermediate steps, the best choice consists in electronic datasheet such as Excel, Open Calc, and similar…

Case study 1Step 2: problem definition


• We must organize data in a table (founds offer/supply and aggregated demand) in which columns represent the market capital demand (r di domanda, inverse) and supply (r di offerta):

• r di domanda represents the marginal average yield for the capital in Economy.

• r di offerta represents the supply curve for the capital, influenced by the saving decisions made by the operators



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• To use the chosen IT tool we must prepare several tables.

One is that already seen (table 1).

• On another sheet we will prepare other columns to

complete the evaluation. Table 2 presents the possible

investment level amount that the Company can choose,

evaluated on the (year) value of the total cost C.

• Remember that the Company produces without work

effort [Y = f(C)] and chooses how much produce to

maximise the profit




Table 2


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• We aim to complete the table 2 to find the optimal level for the Company, that means we have to:1. determine the interest level for which we could have an

equilibrium between demand and aggregated offer of founds (r Equilibrio), in the table 1 (step 3: creation of alternatives)

2. After that we will find (table 2) the maximum sustainable interest rate (constant) for a company, that is the minimum return rate of the capital required by the company to make the investment (step 4 : alternatives evaluation). We will have to satisfy the formula

3. To complete the analysis (that means to find the solution – step 5 – chose of the alternative/solution) we will calculate the optimal investment for the company.

• In this way we will apply all the step of the decision process, using problem solving techniques and the right ICT tools.


C = costo del capitale; Rt = rendimento futuro atteso al tempo t; j = tasso di rendimento o efficienza marginale del capitale in ogni periodo t; T = durata dell’investimento


• We’ll use Excel, and particularly, the functions: IF (SE) that allows to insert a condition and evaluate (true or false)

the result AND (E) that allows to combine more conditions which have to be

true contemporary• We aim to evaluate that:

r offerta = r domanda r offerta > 0

Case study 1Step 3: creation of alternatives

If the result is TRUE, we will have “r offerta”

On the contrary, we’ll have FALSE

• Once completed, only in a cell will appear a 4% (and not the word FALSE).. This will mean that the equilibrium rate is 4%


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• We must use the function RATE (TASSO), that is the passive rate paid on a rented capital. We can use it also to calculate the yield rate for each level of investing capital, modifying the function arguments.


• NUM. rate = total number of payment periods per year (ex. 12 months * 10 years)

• rate = amount payed in each period (ex. -150)

• Va = current value of a payment series (our K)

• Val.fut = final value we wish to achieve after the last payment (0, if omitted)


• The column "r Equilibrio" must simply report what we have found in table 1, so we will insert in every cell the reference to the cell containing 4% in the table 1.



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• Let's find the optimal solution for the company, that is the interest rate level making equilibrium the demand and the aggregated offer of funds.

Case study 1Step 4: evaluation of the alternatives

• This means the minimum distance between the return and the interest rate (in absolute value –function ASS) and after finding the minimum in the column (function MIN)


• This is our solution

• At this point the company have chosen the alternative– following the steps of the decision process;– using the problem solving approach;– with the support of the right ICT tool.

Case study 1Step 5: solution


computer skills advanced problem solving and decision making · 2013. 1. 11. · 1 computer skills...

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