Paper II — Q3
(a) (i) List the strategic objectives of aggregate planning. 5 (ii) Describe the chase and level strategies for aggregate…
List the strategic objectives of aggregate planning. 5 marks
Describe the chase and level strategies for aggregate planning. Which one of these should be preferred? 5 marks
How does aggregate planning in service differ from aggregate planning in manufacturing? 5 marks
What is 'time and motion study'? 4 marks
Define the terms 'work study' and 'method study'. 5 marks
Describe the steps involved in work study and method study. 6 marks
Mention the characteristics of control charts. 4 marks
What is P-chart? 4 marks
The following are the inspection results of 10 lots, each lot having 300 pieces. The number of defective pieces in each lot is 25, 30, 35, 40, 45, 35, 40, 30, 20 and 50 : Calculate the average fraction defective and three sigma limits for P-chart, and state whether the process is in control. 12 marks
हिंदी में प्रश्न पढ़ें
(क) (i) संकलित (एग्रीगेट) योजना के रणनीतिक उद्देश्यों को सूचीबद्ध कीजिए। संकलित योजना के लिए आउटे (चेस) एवं स्तर रणनीतियों का वर्णन कीजिए। इनमें से किसे अधिक पसन्द किया जाना चाहिए?
सेवा के लिए संकलित योजना विनिर्माण के लिए संकलित योजना से कैसे भिन्न होती है? (ख) (i) 'समय एवं गति अध्ययन' क्या होता है?
'कार्य अध्ययन' एवं 'विधि अध्ययन' पदों को परिभाषित कीजिए।
उन चरणों का वर्णन कीजिए जो कार्य अध्ययन एवं विधि अध्ययन में संलिखित हैं। (ग) (i) नियंत्रण चार्टों की विशेषताओं का उल्लेख कीजिए।
P-चार्ट क्या होता है?
10 समूहों (लॉट), प्रत्येक समूह में 300 मदें हैं, के निरीक्षण परिणाम निम्नलिखित हैं। प्रत्येक समूह में त्रुटिपूर्ण मदों की संख्या 25, 30, 35, 40, 45, 35, 40, 30, 20 एवं 50 है : P-चार्ट हेतु एवरेज फ्रैक्शन डिफेक्टिव एवं त्री सिग्मा लिमिट की गणना कीजिए और स्पष्ट कीजिए कि क्या प्रक्रिया नियंत्रण में है।
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) Strategic objectives of aggregate planning
- Match aggregate demand with available capacity at minimum total cost.
- Decide output rate, workforce size, inventory and backlog levels.
- Stabilise employment and production, avoiding frequent hiring, firing and idle time.
- Meet customer service and delivery targets.
- Use overtime, subcontracting and inventory efficiently.
- Maximise profit and give a basis for master production scheduling.
(a)(ii) Chase and level strategies
Chase strategy varies output/capacity each period to match demand. It uses hiring, lay-off, overtime, idle time and subcontracting. It gives low inventory and close demand matching, but causes unstable workforce, morale and quality problems, and high hiring/firing costs. Level strategy keeps workforce/output constant and absorbs demand changes through inventory, backorders, queues or stockouts. It gives stable workforce and consistent quality, but creates inventory carrying, storage, obsolescence and backlog costs. Between the two, level strategy is generally preferred when demand fluctuations are moderate and inventory carrying cost is low, because it stabilises employment and quality. Chase is preferred when demand is highly seasonal and labour is flexible. In practice, a mixed/hybrid strategy based on least total cost that satisfies service policy is often best.
(a)(iii) Aggregate planning in services and manufacturing
Manufacturing aggregate planning can store output, so it uses finished-goods inventory, backorders, overtime, subcontracting and workforce changes. Service output is intangible and perishable; it cannot be inventoried except through customer waiting or appointments. Service capacity is usually labour/equipment at the point of contact, so planning uses scheduling, reservations, pricing, promotion, part-time staff, cross-training, queueing and yield management. Manufacturing can smooth production by inventory; services must manage demand and capacity at the same time. Service capacity units are rooms, seats or billable hours, not stored units.
(b)(i) Time and motion study
Time and motion study is a systematic work-measurement and method-improvement technique. Time study determines the standard time for a qualified worker to perform a task at a defined performance level, including allowances. Motion study analyses movements to eliminate unnecessary motion and design the best method. Together they improve productivity and set time standards.
(b)(ii) Work study and method study
Work study is the systematic examination of work methods and time to improve productivity and establish standards; it comprises method study and work measurement. Method study is the systematic recording and critical examination of existing or proposed methods of doing work, to develop easier, safer, cheaper and more effective methods and reduce waste.
(b)(iii) Steps in work study and method study
Steps in work study: select the job/process; record facts; examine critically; develop improved method; measure work to set standard time; install the method; maintain through audit and revision. Steps in method study: select; record using charts/diagrams; examine by questioning purpose, place, sequence, person and means; develop the best method; define and install it; maintain it. Method study supplies the improved method, while work measurement supplies the standard time within overall work study.
(c)(i) Characteristics of control charts
Control charts have a central line showing process average and upper/lower control limits, usually at ±3σ. They separate common-cause and special-cause variation. Control limits are based on process variation, not specification limits. Points are plotted over time; an in-control process shows random variation within limits. Out-of-control signals include points outside limits, runs, trends, cycles or unusual patterns near limits.
(c)(ii) The P-chart
A P-chart is an attributes control chart for the proportion defective, i.e. nonconforming. Centre line p̄ = total defectives/total inspected. For constant sample size n, limits are p̄ ± 3√(p̄(1−p̄)/n). For variable n, limits are computed for each nᵢ. If LCL is below zero, it is taken as zero. It assumes independent binomial samples.
(c)(iii) P-chart for the ten lots
Total defectives = 25 + 30 + 35 + 40 + 45 + 35 + 40 + 30 + 20 + 50 = 350 defective pieces. Number of lots = 10; sample size n = 300 pieces per lot. Total inspected = 10 × 300 = 3000 pieces. Average fraction defective: p̄ = 350/3000 = 7/60 = 0.116667. Standard deviation of proportion: σₚ = √(p̄(1−p̄)/n) = √((7/60)(53/60)/300) = √(371/1,080,000) = 0.0185343. Three-sigma limits: UCL = p̄ + 3σₚ = 7/60 + 3√(371/1,080,000) = 0.172269 ≈ 0.1723. LCL = p̄ − 3σₚ = 7/60 − 3√(371/1,080,000) = 0.061064 ≈ 0.0611. Since LCL > 0, no truncation is needed. Lot fractions defective: 25/300 = 0.0833, 30/300 = 0.1000, 35/300 = 0.1167, 40/300 = 0.1333, 45/300 = 0.1500, 35/300 = 0.1167, 40/300 = 0.1333, 30/300 = 0.1000, 20/300 = 0.0667, 50/300 = 0.1667. All lie between 0.0611 and 0.1723, and no run signal is evident. Average fraction defective p̄ = 7/60 = 0.1167; three-sigma limits are UCL = 0.1723 and LCL = 0.0611; hence the process is in control. Validity: independent random lots, constant n = 300 pieces, binomial conditions, np̄ = 35 and n(1−p̄) = 265, both ≥ 5.
How this answer will be evaluated
Framework: Aggregate Planning Strategies (Chase vs Level) and Statistical Process Control (P-Chart)
What earns full marks: Precise definitions, clear distinction between strategies, and flawless calculation of P-chart limits with a correct control conclusion.
Evaluation rubric
Each sub-part is marked on its own, against the marks and word limit printed on the paper.
- (a)(i) Enumerate the strategic objectives of aggregate planning. 5 marks
enumerate— list the items in order → one line each → no commentary
Must cover
- Minimizing total system costs
- Maintaining a responsive level of customer service
- Keeping workforce size and utilization stable
- Minimizing inventory and backorder levels
Loses marks
- Listing operational rather than strategic goals
- Vague statements without specific planning metrics
Earns more
- Balancing production capacity with demand
- Reducing overtime and temporary labor usage
Extra mark
- Reference to specific cost components (holding, shortage, labor)
- (a)(ii) Explain chase and level strategies and recommend a preferred one. 5 marks
describe— define → structure or process in order → labelled diagram → significance
Must cover
- Definition of Chase strategy (varying workforce/output)
- Definition of Level strategy (constant workforce/output)
- Comparison of cost implications (labor vs inventory)
- A clear verdict on which is preferred
Loses marks
- Describing strategies without a comparative verdict
- Confusing aggregate planning with master production scheduling
Earns more
- Mention of hybrid strategies
- Contextual factors for preference (e.g., labor market)
Extra mark
- Example of a company using a specific strategy
- (a)(iii) Differentiate aggregate planning in services from manufacturing. 5 marks
compare— paired headings or point-wise contrast → key differences → significance → conclusion
Must cover
- Inability to inventory services (perishability)
- Variability in service demand (seasonality)
- Role of demand management (pricing, scheduling)
- Focus on workforce flexibility over inventory buffers
Loses marks
- Treating services as if they can be stocked
- Ignoring the demand-side levers in service planning
Earns more
- Mention of simultaneous production and consumption
- Impact of customer participation on capacity
Extra mark
- Specific service industry example (e.g., airlines, hospitals)
- (b)(i) Define 'time and motion study'. 4 marks
define— precise definition → the distinguishing feature → one example
Must cover
- Definition of Time Study (measuring time for standard work)
- Definition of Motion Study (analyzing body movements)
- Linking both to efficiency and standardization
Loses marks
- Defining only one of the two components
- Confusing time study with general time management
Earns more
- Mention of stop-watch or video recording methods
- Reference to Gilbreth or Taylor
Extra mark
- Specific example of a motion principle (e.g., use of both hands)
- (b)(ii) Define 'work study' and 'method study'. 5 marks
define— precise definition → the distinguishing feature → one example
Must cover
- Work Study as the combination of Method Study and Time Study
- Method Study as the systematic examination of methods
- Goal of Work Study: improving efficiency and reducing cost
- Goal of Method Study: finding the 'best way' to do a job
Loses marks
- Treating Method Study and Work Study as identical
- Omitting the relationship between the two terms
Earns more
- Mention of standardization of methods
- Reference to ILO or standard industrial engineering definitions
Extra mark
- Diagram showing Work Study = Method Study + Time Study
- (b)(iii) Outline the steps involved in work study and method study. 6 marks
describe— define → structure or process in order → labelled diagram → significance
Must cover
- Steps for Method Study (Record, Examine, Develop, Install)
- Steps for Time Study (Select job, Measure time, Determine rating, Apply allowances)
- Logical sequence of operations
- Final output: Standard Time or Standard Method
Loses marks
- Listing steps out of logical order
- Mixing up steps for method study and time study
Earns more
- Mention of flow process charts or stratum charts
- Explanation of performance rating factors
Extra mark
- Specific chart type used in the 'Record' step
- (c)(i) List the characteristics of control charts. 4 marks
highlight— name the salient points → one line of substance each → close
Must cover
- Graphical tool for monitoring process variation
- Use of Upper and Lower Control Limits (UCL/LCL)
- Distinction between common cause and special cause variation
- Used for process stability and capability assessment
Loses marks
- Confusing control limits with specification limits
- Describing it as a quality inspection tool only
Earns more
- Mention of Central Line (CL) or Mean
- Reference to statistical process control (SPC)
Extra mark
- Mention of specific chart types (X-bar, R, p, c)
- (c)(ii) Define what a P-chart is. 4 marks
define— precise definition → the distinguishing feature → one example
Must cover
- Attribute control chart for fraction defective
- Used when sample size is constant or variable
- Based on Binomial distribution
- Monitors the proportion of non-conforming items
Loses marks
- Defining it as a chart for continuous data
- Confusing it with a Pareto chart
Earns more
- Contrast with C-chart (count vs proportion)
- Mention of 'p' as the variable plotted
Extra mark
- Formula for standard deviation of p
- (c)(iii) Calculate average fraction defective, 3-sigma limits, and determine control status. 12 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Calculation of p-bar (Total Defectives / Total Inspected)
- Calculation of Standard Error (Sqrt(p-bar(1-p-bar)/n))
- Calculation of UCL and LCL (p-bar +/- 3*SE)
- Comparison of individual p-values against limits to conclude control status
Loses marks
- Using 'n' as total inspected instead of sample size per lot
- Failing to check if LCL is negative (should be 0)
- Arithmetic errors in the square root or fraction calculation
Earns more
- Correct check of every lot against the limits (all ten lots lie within them)
- Clear presentation of the formula used
- Correct arithmetic for the final limits
Extra mark
- Suggestion for corrective action based on the out-of-control point
What "Calculate" is asking you to do
Apply the standard formula or schedule to data the question has already supplied — a table of readings, cost records, a balance sheet — and produce the number. The method is rarely in doubt; the marks sit in the named intermediate quantities, each of which has to appear as a labelled line.
Structure that answers it
Data as given → formula or standard treatment, named → substitution → each intermediate, labelled → result with units
Where marks are lost
Omitting an intermediate the marking scheme pays for separately, or rounding at an intermediate line so the final figure drifts. In commerce and accountancy, any figure in a statement that no numbered working note supports is treated as unearned.
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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