3.(a) A company has an annual demand of 1600 units for an item, whose unit cost is ₹70/-. The annual holding cost comprises 18% for interest charges, 1% for insurance, 1·5% allowances for obsolescence of unit cost and ₹2·50 for building overheads, ₹3

Question

3.(a) A company has an annual demand of 1600 units for an item, whose unit cost is ₹70/-. The annual holding cost comprises 18% for interest charges, 1% for insurance, 1·5% allowances for obsolescence of unit cost and ₹2·50 for building overheads, ₹3·40 for damage loss, and ₹7·0 miscellaneous costs. Placing each order costs the company ₹100/-.

(i) Calculate Economic Order Quantity (EOQ) and the total costs of stocking the units.

(ii) If the supplier of the items will only deliver batches of 250 units, how is the total variable cost influenced ?

(iii) If the supplier relaxes their order size requirements, as the company has limited storage space it can stock a maximum of 100 units at any time. What would be the optimal ordering policy and associated costs ? 15

(b) Consider the following aggregate planning problem for four months :

|  | Regular time | Overtime | Subcontracting |
|---|---|---|---|
| Production capacity/month | 900 units | 300 units | 200 units |
| Production cost/unit | ₹6/- | ₹8/- | ₹9/- |

The forecasted demand for the next four months is 1300, 1400, 1225 and 1475 units respectively. Shortages are not permitted. The initial inventory is 50 units, and the carrying cost is ₹1·60 per unit per month.

Provide the aggregate plan for this problem. 15

(c) The warehouse owner of Quick Industries is considering a new computer system for accounting and inventory control. A computer vendor sent the following information about the system installation :

| Activity Identification | Activity description | Immediate Predecessor | Time (Days) Most optimistic | Time (Days) Most likely | Time (Days) Most pessimistic |
|---|---|---|---|---|---|
| A | Selection of Computer Model | – | 5 | 7 | 9 |
| B | Input/output System Design | A | 6 | 8 | 16 |
| C | Monitoring System Design | A | 5 | 9 | 13 |
| D | Computer Hardware Assembly | B | 16 | 21 | 26 |
| E | Development of main Programs | B | 11 | 19 | 27 |
| F | Input/output routines development | C | 9 | 10 | 17 |
| G | Database Creation | E | 5 | 9 | 13 |
| H | Installation of the system | D, F | 2 | 3 | 4 |
| I | Testing and Implementation | G, H | 7 | 8 | 9 |

(i) Draw the network diagram for this information. Identify the Critical Path and expected project completion time.

(ii) Calculate the probability that the project will be completed in 61 days.

(iii) When the company wants to be 95% sure that the system will be installed by a certain date, how many days prior to that should it start the work ? 20

UPSC Answer Check · Accepted Answer

This numerical question demands precise calculations across five sub-parts: allocate ~30% time to 3(a) EOQ with holding cost breakdown (15 marks), ~25% to 3(b) aggregate planning with transportation method (15 marks), and ~45% to 3(c) PERT network with probability analysis (20 marks). Structure as: clear formula statement → step-wise computation → final answer with units → brief interpretation where asked.
- 3(a)(i): Correct EOQ formula application with total holding cost = 18%+1%+1.5% of ₹70 + ₹2.50+₹3.40+₹7.0 = ₹12.60+₹12.90 = ₹25.50/unit/year; EOQ = √(2×1600×100/25.50) ≈ 112 units; total cost calculation
- 3(a)(ii): Total variable cost at Q=250 vs EOQ, showing cost penalty for batch constraint; compare ordering + holding costs
- 3(a)(iii): Modified EOQ under storage constraint (max 100 units); optimal policy becomes ordering at capacity limit with adjusted cost analysis
- 3(b): Transportation method/linear programming formulation for aggregate planning; month-wise production allocation across regular, overtime, subcontracting minimizing total cost (production + inventory carrying); show inventory balance constraints
- 3(c): PERT network construction with AOA or AON; ES/EF/LS/LF calculations; critical path identification; variance and Z-score for probability; 95% confidence time calculation using normal distribution

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	25%	12.5	All formulas correctly stated (EOQ, total inventory cost, PERT time estimates te=(a+4m+b)/6, variance σ²=((b-a)/6)², Z-score); arithmetic accurate to 2 decimal places; critical path correctly identified; aggregate plan satisfies all constraints with minimum cost	Correct formulas but minor calculation errors; critical path identified with minor timing errors; aggregate plan feasible but not optimal	Wrong formulas (e.g., omitting 4 in PERT, wrong holding cost components); major calculation errors; incorrect critical path; infeasible aggregate plan
Framework citation	15%	7.5	Explicitly cites Harris EOQ model (1913), Wilson formula; PERT developed by US Navy (1958) for Polaris project; mentions transportation method for aggregate planning; distinguishes PERT (probabilistic) vs CPM (deterministic)	Implicit use of correct frameworks without attribution; mentions EOQ or PERT without historical/theoretical context	No framework identification; confuses EOQ with EPQ or PERT with CPM; wrong theoretical basis
Case / Indian example	10%	5	Cites Indian application: ISRO's use of PERT/CPM for Chandrayaan missions; Indian Railways inventory management; or HAL/DRDO project scheduling; connects to Make in India operational efficiency	Generic mention of Indian manufacturing or public sector without specific case	No Indian context; only Western examples (Ford, NASA) or no examples at all
Multi-perspective analysis	25%	12.5	For 3(a): compares unconstrained vs constrained EOQ, analyzes cost trade-offs; for 3(b): evaluates chase vs level strategy implications; for 3(c): interprets probability meaningfully, discusses crashing possibilities, sensitivity of critical path	Calculates all parts correctly but limited interpretation; no comparison across scenarios	Mechanical calculations only; no understanding of why constraints matter; no sensitivity or scenario analysis
Conclusion & recommendation	25%	12.5	Summarizes key findings: optimal order policy under each constraint, minimum cost aggregate plan with month-wise schedule, project completion time with confidence intervals; practical recommendations for supplier negotiation, capacity expansion, or buffer time; clear actionable insights	Brief restatement of answers without synthesis; generic recommendations	No conclusion; incomplete answers; missing final recommendations; no units in final answers

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