Business Analyatics Cases

8/10/2019 Business Analyatics Cases

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Case 1: Banking on Bank

Every investor must tradeoff return versus risk in deciding how to allocate his or heravailable funds. The opportunities that promise the greatest profits are almost always the

ones that present the most serious risks. Commercial banks must be especially careful in balancing return and risk because legal and ethical obligations demand that they avoidundo hazards, yet their goal as a business enterprise is to maximize profit. This dilemmaleads naturally to multiobjective optimization of investment that includes both profit andrisk criteria.

After working for 10 years as a finance manager in various companies, you get an offerin City Co-op Bank who is looking for a dynamic Finance Head who needs to take callon investments to maximize profits. City Co-op Bank has a modest Rs. 20 crores

capital, with Rs. 150 crores in demand deposits (current accounts) and Rs. 80 crores intime deposits (savings accounts and fixed deposit). The table below displays thecategories among which the bank must divide its capital and deposited funds as per RBIregulations. Rates of return are also provided for each category together with otherinformation related to risk.

City Co-op Bank Investment Opportunities

Investment Category ( j)Return Rate

(%)

LiquidPart(%)

RequiredCapital

(%)

Risk Asset?

(%)1. Cash 0.0 100.0 0.0 No

2. Short Term 4.0 99.5 0.5 No

3. Government: 1 to 5 years 4.5 96.0 4.0 No

4. Government: 5 to 10 years 5.5 90.0 5.0 No

5. Government: over 10 years 7.0 85.0 7.5 No

6. Personal loans 10.5 0.0 10.0 Yes

7. Housing loans 8.5 0.0 10.0 Yes

8. Commercial loans 9.2 0.0 10.0 Yes

Your predecessor was a finance head who raised to the position over thirty years afterstarting his career as a cashier. He being just commerce graduate did not know OR tools.He has been taking investment decisions based on his subjective judgment using his


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The above goals may be thought of as soft constraints. Soft constraints such as thecriteria targets of goal programming specify requirements that are desirable to satisfy butwhich may still be violated in feasible solutions. Once target levels have been specifiedfor soft constraints, we proceed to a more familiar mathematical programming

formulation by adding constraints that enforce goal achievement. However, we cannot just impose the constraint that each objective meet its goal. There may be no solution thatsimultaneously achieves the desired levels of all soft constraints. Instead we introducenew deficiency variables. Nonnegative deficiency variables are introduced to model theextent of violation in goal or other soft constraints that need not be rigidly enforced. Witha target, the deficiency is the under achievement. With a target, it is the excess. With= soft constraints, deficiency variables are included for both under- and overachievement.

In the three-objective Bank Three example, we enforce goal levels with deficiencyvariables:

d1- = amount profit falls short of its goald2+ = amount capital-adequacy ratio exceeds its goald3+ = amount risk-asset ratio exceeds its goal


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Case 2: Solar Energy Installation Model

An experimental solar energy system for residential heating consists of three majorcomponents; a solar collector made up of plate glass that is oriented toward the sun; awater tank for storing thermal energy and a piping control system for regulating flows,

pressure and temperature.

Suppose that three surface areas for the collector are under consideration: 500, 600, and700 sq ft. Engineering tests show that the area of collector directly affects its ability toincrease average ambient (outdoor) temperatures. The 500 sq ft collector increasesambient temperature by a factor of 6; the 600 sq ft collector by a factor of 7; and 700 sq ftcollector, by a factor of 8. For example, given an average ambient temperature of 30 0 F,the 600 sq ft collector has the capacity of sending water into the storage tank, which is

heated to 210 0 F (i.e. 30*7). Over the life of a typical home (estimated at 40 yrs), theamortized cost of the collector is $0.50 per sq ft per yr.

Two choices are available for the size of the storage tank: 800 gallons and 1000 gallons.Generally, the tanks have a greater ability to store thermal energy for use during the nighttime or during cloudy weather. The effective heat retention of the smaller tank is 0.7 , andthat of the larger tank is 0.8. For example, the larger tank is capable of effectivelymaintaining the water at 168 0 F, when the collector delivers water at 210 0 F (210*0.8).The amortized cost of the storage facility is $0.15 per gallon per yr.

Two choices also are available for the piping and control system. These are amortized at$50 per yr and $100 per yr. The efficiency factor for the cheaper alternative is 0.4 andthat for the more expensive alternative is 0.5. For example, if the effective temp of waterin a tank is 168 0 F, then an efficiency factor of 0.5 means that the effective temp that can

be delivered to the residence is 84 0 F (168*0.5).

The effective delivery temp is important because it determines the average cost ofsupplying conventional heat to supplement the solar system. For a 2000 sq ft residenceheated to 70 0 F, the average annual cost of the conventional heating system has been

estimated by the following relationship:

h = 150 + 10 (70 Effective delivery temperature).

Note that effective delivery temperatures above 70 0 F reduce h below $150 per year.Moreover, if a calculation yields h


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Identify the DP structure for this problem. Determine the optimal design by DP. ( tosimplify the problem round off the effective temperature to the nearest 10 0 F)

Case 3: Investment Banking

A trust officer for a major banking institution is planning the investment of $1 millionfamily trust for the coming year. The trust officer has identified a portfolio of stocks andanother group of bonds that might be selected for investment. The family trust can beinvested in stocks or bonds exclusively, or a mix of the two. This trust officer prefers todivide the funds in the increments of 10 percent; that is the family trust may be split as100% stock& 0% bonds, 90% stocks and 10% bonds, 80% stocks and 20% bonds and soon.

The trust officer has evaluated the relationship between the yields on the differentinvestment and general economic conditions. Her judgment is as follows:

(1) If the next year is characterized by solid growth in the economy then bonds willyield 12% and stock will yield 20%.

(2) If the next year is characterized by inflation, then bonds will yield 18% and stockwill yield 10%.

(3) If the next year is characterized by stagnation, then bonds will yield 12% andstock will yield 8%.

a. Formulate a payoff table where payoffs represent the annual yield, in dollars,associated with the different investment strategies and the occurrence of variouseconomic conditions.

b. Determine the optimal strategy using the maxmax, maxmin, Hurwicz(=0.40),equally likely and regret criteria.

c. Suppose that, p (solid growth) =0.4, p (inflation) =0.25 and p (stagnation) =0.35then use the expected value criterion to select the appropriate strategy.

d. What is the expected value of perfect information?e. If the forecasting firm projects following conditional probabilities of the forecast

of economy, revise the decision with posterior probabilitiesStates ofnature

Conditional probabilitiesX1 X2 X3

Solidgrowth

0.7 0.2 0.1


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Inflation 0.1 0.8 0.1Stagnancy 0.05 0.05 0.9

WhereX1: Forecast of solid growth.X2: Forecast of inflation.X3: Forecast of stagnancy.

Case 4: Pipeline Construction Model

The installation of an oil pipeline which runs from an oil field to a refinery requires thewelding of 1000 seams. Two alternatives have been specified for conducting the welding.

1. Strictly use a team of ordinary and apprentice welders (B-Team)2. Use a team of master welders (A-Team) who check and rework (as necessary) the

works of the B team.

If the B team is strictly used, it is estimated from past experience that 5% of the seamswill be defective with probability 0.30, or 10% will be defective with probability 0.50, or20% will be defective with probability 0.20. However if the B team is followed by Ateam, a defective rate of 1% is almost certain.

Material and labour costs are estimated at $400,000 when the B-Team is used strictly,whereas these costs rise to $530,000 when the A-Team is also brought in. Defectiveseams result in leaks, which must be reworked at a cost of $1,200 per seam, which

includes the cost of labour and spilled oil but ignores the cost of environmental damage.a. Determine the optimal decision and its expected cost. How might environmental

damage be taken into account? b. A worker on the pipeline with a Baysian inclination (from long years of wagering

on sporting events) has proposed that management consider X-ray inspections offive randomly selected seams following the work of the B-Team. Such aninspection would identify defective seams, which would provide the managementwith more information for the decision on whether or not to bring the A-Team,. Itcosts $5000 to inspect the five seams.Finally is it worthwhile to carry out the inspection? If so, what decision should bemade for each possible result of the inspection?


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Case5: Vehicle Insurance. 'Profit from Accidents'.

In most of Europe and Asia annual automobile insurance premiums are determined byuse of a Bonus Malus (Latin for Good-Bad) system. Each policyholder is given a positive

integer valued state and the annual premium is the function of this state (along, of course,with the type of car being insured and the level of insurance). A policyholder's statechanges from year to year in response to the number of claims made by that policyholder.Because lower numbered states correspond to lower annual premiums, a policyholder'sstate will usually decrease if he or she had no claims in the preceding year, and willgenerally increase if he or she had at least one claim. (Thus, no claims is good andtypically results in a decreased premium, while claims are bad and typically result in ahigher premium.)

If we suppose that the number of yearly claims made by a particular policyholder is aPoisson random variable with parameter >-, then the successive states of this policyholderwill constitute a Markov chain with transition probabilities

Pi,j = e- (k / k! ) j >= 0

k: s j (k) = j

State Annual premium ($)

Next state if0 claims 1 claim 2 claims >=3 claims

1 200 1 2 3 42 250 1 3 4 43 400 2 4 4 44 600 3 4 4 4

Write a transition matrix for Markov Chain.

If average number of accident claims is 1.2 per year, is this rate of premium ok for thecompany? If not what premium would you propose for your company? Can you suggestany variation in the method to make your policy more attractive?

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Business Analyatics Cases