Paper II — Q2
(a) (i) 'A' can hit a target 4 times in 5 shots, 'B' 3 times in 4 shots and 'C' twice in 3 shots. Calculate the probability…
'A' can hit a target 4 times in 5 shots, 'B' 3 times in 4 shots and 'C' twice in 3 shots. Calculate the probability :
(A) 'A', 'B', 'C' all may hit the target. 2 marks
(B) 'B' and 'C' may hit the target, but 'A' may not hit it. 2 marks
(C) 'C' and 'A' may hit the target, but 'B' may not hit it. 2 marks
A decision problem has been expressed in the following payoff table :
| States of Nature | Alternatives | ||
|---|---|---|---|
| A₁ | A₂ | A₃ | |
| E₁ | 190 | 186 | 182 |
| E₂ | 164 | 162 | 166 |
| E₃ | 142 | 144 | 174 |
Which alternative will be selected if the following criterion is used ?
(A) Maximax criterion 3 marks
(B) Maximin criterion 3 marks
(C) Hurwicz's criterion 3 marks
(Assume degree of optimism is 0·7)
"Decision Support System (DSS) and Management Information System (MIS) are very helpful for managers in taking decisions." Comment and support your answer. 5 marks
How can DSS be differentiated from MIS ? 5 marks
What are the components of DSS ? 5 marks
What are the similarities and dissimilarities between data-driven and document-driven DSS ? 5 marks
A firm is considering replacement of an equipment, whose first cost is ₹ 4,000 and the scrap value is negligible at the end of any year. Based on experience, it was found that the maintenance cost is zero during the first year and it is ₹ 1,000 for the second year. It increases by ₹ 300 every year thereafter.
(A) When should the equipment be replaced if the interest rate is 0% (zero percent) ? 5 marks
(B) When should the equipment be replaced if the interest rate is 12% ? 5 marks
"Inventory Control is a rational process in which decision-making is often done irrationally." Explain. 5 marks
हिंदी में प्रश्न पढ़ें
'ए' किसी लक्ष्य पर 5 में से 4 बार निशाना लगा सकता है, 'बी' 4 में से 3 बार एवं 'सी' 3 में से 2 बार निशाना लगा सकता है । प्रायिकता की गणना कीजिए :
(A) 'ए', 'बी', 'सी' तीनों निशाना लगा सकते हैं । 2 अंक
(B) 'बी' और 'सी' तो निशाना लगा सकते हैं, पर 'ए' चूक सकता है । 2 अंक
(C) 'सी' और 'ए' तो निशाना लगा सकते हैं, पर 'बी' चूक सकता है । 2 अंक
निम्नलिखित भुगतान सारणी में एक निर्णय समस्या को व्यक्त किया गया है :
| प्रकृति की स्थितियाँ | विकल्प | ||
|---|---|---|---|
| ए₁ | ए₂ | ए₃ | |
| ई₁ | 190 | 186 | 182 |
| ई₂ | 164 | 162 | 166 |
| ई₃ | 142 | 144 | 174 |
यदि निम्नलिखित मापदण्ड उपयोग किए जाते हैं, तो कौन-सा विकल्प चयनित होगा ?
(A) मैक्सिमैक्स मापदण्ड 3 अंक
(B) मैक्सिमिन मापदण्ड 3 अंक
(C) हरविक्ज़ मापदण्ड 3 अंक
(यदि आशावाद का परिमाण 0·7 माना जाए)
"प्रबन्धकों द्वारा निर्णय लेने में निर्णय सहायता प्रणाली (डी.एस.एस.) एवं प्रबन्ध सूचना प्रणाली (एम.आई.एस.) बहुत उपयोगी है।" टिप्पणी कीजिए एवं अपने उत्तर के समर्थन में तर्क दीजिए । 5 अंक
डी.एस.एस. एवं एम.आई.एस. में कैसे अंतर किया जा सकता है ? 5 अंक
डी.एस.एस. के अवयव क्या हैं ? 5 अंक
डेटा-चालित एवं दस्तावेज़-चालित डी.एस.एस. के बीच क्या समानताएँ एवं असमानताएँ हैं ? 5 अंक
एक प्रतिष्ठान किसी उपकरण को प्रतिस्थापित करने पर विचार कर रही है, जिसकी प्रथम लागत ₹ 4,000 है एवं वर्षांत में स्क्रैप मूल्य नगण्य है । अनुभव के आधार पर यह पाया गया कि इस उपकरण की रखरखाव लागत प्रथम वर्ष में 0 तथा द्वितीय वर्ष में ₹ 1,000 है । तदुपरान्त यह प्रति वर्ष ₹ 300 से बढ़ती है ।
(A) यदि ब्याज दर 0% (शून्य प्रतिशत) हो, तो उपकरण को कब प्रतिस्थापित करना चाहिए ? 5 अंक
(B) यदि ब्याज दर 12% हो, तो उपकरण को कब प्रतिस्थापित करना चाहिए ? 5 अंक
"माल (इन्वेंट्री) नियंत्रण एक तर्कसंगत प्रक्रिया है जिसमें अक्सर निर्णय तर्कहीन रूप से लिए जाते हैं।" समझाइए । 5 अंक
Model answer
Drafted with AI by UPSC Answer Check against this question's marking rubric, to the expected length. UPSC does not publish answers for Mains — this is one way to score well, not an official key. How we build rubrics and answers.
(a)(i) Target-hitting probabilities
P(A) = 4/5, P(B) = 3/4, P(C) = 2/3, and the shooters are independent, so the probabilities multiply.
(A) All three hit: 4/5 × 3/4 × 2/3 = 24/60 = 2/5 = 0.40.
(B) B and C hit, A misses: 1/5 × 3/4 × 2/3 = 6/60 = 1/10 = 0.10.
(C) C and A hit, B misses: 4/5 × 1/4 × 2/3 = 8/60 = 2/15 ≈ 0.133.
(a)(ii) Decision criteria
The alternatives are the columns; each column's payoffs over E₁, E₂, E₃ are A₁: 190, 164, 142; A₂: 186, 162, 144; A₃: 182, 166, 174.
(A) Maximax: best payoffs are 190, 186, 182; the maximum is 190, so choose A₁.
(B) Maximin: worst payoffs are 142, 144, 166; the maximum of these is 166, so choose A₃.
(C) Hurwicz with α = 0.7: value = 0.7 × best + 0.3 × worst. A₁ = 0.7 × 190 + 0.3 × 142 = 175.6 A₂ = 0.7 × 186 + 0.3 × 144 = 173.4 A₃ = 0.7 × 182 + 0.3 × 166 = 177.2 Choose A₃.
(b)(i) DSS and MIS as aids to managers
The statement is largely correct. An MIS draws on transaction data to give managers structured, periodic and exception reports, which suit routine control and planned decisions such as sales or inventory review. A DSS is interactive and uses data, models and the manager's judgement to handle semi-structured problems, with what-if and sensitivity analysis, such as pricing or capacity planning. Together they improve speed, accuracy and consistency of decisions. Their value depends on data quality and user skill; neither replaces judgement, and an MIS is weak where problems are unstructured.
(b)(ii) DSS versus MIS
An MIS is built for routine, structured, mostly operational and tactical decisions, with fixed, scheduled reports from internal data and little user control. A DSS is built for non-routine, semi-structured decisions, is interactive and user-driven, uses internal and external data with analytical models, and answers what-if questions. An MIS is information-oriented and rigid; a DSS is decision-oriented and flexible. A DSS can be built on top of an MIS.
(b)(iii) Components of DSS
- Database management subsystem: internal and external data, often a data warehouse.
- Model management subsystem: statistical, financial, optimisation and simulation models.
- User interface (dialogue) subsystem: lets the user query, run models and view results.
- Knowledge-based subsystem (optional): rules and expertise that advise on choices.
- The user, usually a manager or analyst, who drives the process.
(b)(iv) Data-driven versus document-driven DSS
Similarities: both are types of DSS that support decisions by retrieving and organising stored information; both have a database or repository, a user interface and often web access; both aim at semi-structured problems.
Dissimilarities: a data-driven DSS works on structured, mostly numeric data (data warehouses, time series) with queries, OLAP and analytics to analyse trends; a document-driven DSS works on unstructured text (reports, policies, web pages, e-mails) with search engines and text-mining to retrieve and summarise relevant documents. Data-driven DSS answers "how much or how many"; document-driven DSS finds "what was said or decided".
(c)(i) Equipment replacement
Cost ₹4,000, scrap nil. Maintenance: year 1 = 0, year 2 = 1,000, year 3 = 1,300, year 4 = 1,600, year 5 = 1,900, year 6 = 2,200, rising ₹300 a year.
(A) At 0% interest, average annual cost = (4,000 + cumulative maintenance) ÷ n: n = 1: 4,000; n = 2: 2,500; n = 3: 2,100; n = 4: 1,975; n = 5: 1,960; n = 6: 2,000. The average is lowest at n = 5 (₹1,960), and year 6 maintenance (₹2,200) exceeds it. Replace at the end of year 5.
(B) At 12%, with discount factor v = 1/1.12, average cost = PV of costs ÷ annuity factor: n = 4: 6,739 ÷ 3.037 = ₹2,219; n = 5: 7,817 ÷ 3.605 = ₹2,169; n = 6: 8,932 ÷ 4.111 = ₹2,173. The minimum is at n = 5. Replace at the end of year 5.
(c)(ii) Inventory control: rational process, irrational decisions
Inventory control rests on rational tools: EOQ, ABC analysis, reorder levels and safety stock, all balancing ordering, carrying and stock-out costs. Yet decisions are often irrational. Managers over-order to avoid any stock-out, ignoring carrying cost; buy large lots for a discount without costing the extra holding; keep inflated safety stock from fear of blame; and rely on rules of thumb or stale data. Departments pull in opposite directions: production wants long runs, marketing wants wide stock, finance wants low stock. Personal ties with suppliers and bounded rationality add to this. The remedy is accurate data, shared costing and clear policies.
How this answer will be evaluated
Framework: Decision Theory (Probability, Payoff Criteria) & Operations Research (Equipment Replacement, Inventory Control)
What earns full marks: Accurate calculations with clear steps; precise definitions; well-structured comparisons; logical reasoning for qualitative parts.
Evaluation rubric
Each sub-part is marked on its own, against the marks and word limit printed on the paper.
- (a)(i) Probability that all three shooters hit. 2 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Treat shots as independent and multiply
- P = 4/5 × 3/4 × 2/3 = 2/5 = 0.4
Loses marks
- Adding instead of multiplying
Earns more
- Individual probabilities 4/5, 3/4, 2/3 stated
- (a)(i) Probability that B and C hit but A misses. 2 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Use the complement 1/5 for A missing
- P = 1/5 × 3/4 × 2/3 = 1/10 = 0.1
Loses marks
- Using 4/5 for A
Earns more
- Independence stated
- (a)(i) Probability that C and A hit but B misses. 2 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Use the complement 1/4 for B missing
- P = 4/5 × 1/4 × 2/3 = 2/15 ≈ 0.133
Loses marks
- Using 3/4 for B
Earns more
- Independence stated
- (a)(ii) Choose the alternative under the maximax criterion. 3 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Take the best payoff of each alternative (190, 186, 182)
- Choose the maximum, A₁
Loses marks
- Using row maxima instead of column maxima
Earns more
- Reading alternatives as columns
- (a)(ii) Choose the alternative under the maximin criterion. 3 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Take the worst payoff of each alternative (142, 144, 166)
- Choose the maximum of these, A₃
Loses marks
- Choosing the minimum of the worst payoffs
Earns more
- Reading alternatives as columns
- (a)(ii) Choose the alternative under Hurwicz's criterion with α = 0.7. 3 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Value = 0.7 × best + 0.3 × worst
- Compute 175.6, 173.4 and 177.2
- Choose A₃
Loses marks
- Swapping α and 1−α
Earns more
- Correct best and worst payoffs
- (b)(i) Comment on the usefulness of DSS and MIS to managers and support the answer. 5 marks
comment— context → arguments both sides → judgment → close
Must cover
- Explain how MIS supports routine structured decisions
- Explain how DSS supports semi-structured decisions with models and what-if analysis
- Support with reasons or an example, noting limits
Loses marks
- Only defining DSS and MIS
- No supporting argument
Earns more
- Speed, accuracy and consistency of decisions
- Dependence on data quality and user skill
Extra mark
- A business example
- (b)(ii) Differentiate DSS from MIS. 5 marks
compare— paired headings or point-wise contrast → key differences → significance → conclusion
Must cover
- Structured routine versus semi-structured problems
- Fixed reports versus interactive, model-based analysis
- Information-oriented versus decision-oriented
Loses marks
- Treating the two as identical
- Only describing one of them
Earns more
- Internal data versus internal and external data
- DSS built on top of MIS
- (b)(iii) Components of a DSS. 5 marks
describe— define → structure or process in order → labelled diagram → significance
Must cover
- Database subsystem
- Model subsystem
- User interface subsystem
Loses marks
- Naming hardware or software only
- Omitting the model component
Earns more
- Knowledge-based subsystem and the user
Extra mark
- Example of data or models in each component
- (b)(iv) Similarities and dissimilarities between data-driven and document-driven DSS. 5 marks
compare— paired headings or point-wise contrast → key differences → significance → conclusion
Must cover
- At least one similarity (both support decisions through stored information)
- Data type difference: structured numeric versus unstructured text
- Tool difference: OLAP and analytics versus search and text mining
Loses marks
- Only similarities or only differences
Earns more
- Examples such as data warehouse versus document repository
- Typical questions each answers
- (c)(i) Replacement time of the equipment at 0% interest. 5 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Compute average annual cost for each year (4,000; 2,500; 2,100; 1,975; 1,960; 2,000)
- Identify the minimum at year 5
- Replace at the end of year 5
Loses marks
- Ignoring the purchase cost
- Wrong maintenance series
Earns more
- Compare year 6 maintenance (2,200) with the average
- (c)(i) Replacement time of the equipment at 12% interest. 5 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Discount costs with v = 1/1.12
- Divide present value of costs by the annuity factor to get average cost
- Minimum at year 5 (about ₹2,169); replace at the end of year 5
Loses marks
- Using the undiscounted method
- Arithmetic errors in discounting
Earns more
- Comparison with years 4 and 6
- (c)(ii) Explain how inventory control is rational in design but decisions are often irrational. 5 marks
explain— definition/context → points in order → small example → short close
Must cover
- State the rational tools (EOQ, ABC, reorder level, safety stock)
- Give causes of irrational decisions (over-ordering, fear of stock-outs, discounts without costing)
- Mention departmental conflict or poor data
Loses marks
- Only defining inventory control
- No link to irrational behaviour
Earns more
- Bounded rationality or behavioural biases
- Remedies
Extra mark
- A concrete example
What "Solve" is asking you to do
Choose the method, then carry it through to a final answer. Identifying what kind of problem this is and why that method applies is the first thing marked; a correct figure arrived at invisibly earns almost nothing.
Structure that answers it
Given data and what is required → method chosen, with the reason it applies → set-up (equation, circuit, free body, trial balance) → working, step by step → answer with units and any condition of validity
Where marks are lost
Doing the middle steps mentally and writing only the result. In mathematics papers, a further loss comes from giving a decimal where the exact value in surds or fractions was wanted, or from skipping the justification a part explicitly asks for.
Practice this exact question
Write your answer and it is marked point by point against the model answer above — what you covered, what you missed, what you got wrong.
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