(a) The mean annual income of workers in a company is ₹ 5,000 with a standard deviation of ₹ 1,200. It is suspected that local…

(a) Test of local workers' income

H₀: μ = ₹5,000; H₁: μ > ₹5,000 (right-tailed, since local income is suspected to be higher).

σ is known and n = 144 is large, so use the Z-test.

Standard error = σ/√n = 1,200/12 = ₹100.

Z = (5,500 − 5,000)/100 = 5.

At α = 0.05 the one-tailed critical value is 1.645 (the table gives 0.4500 between 0 and Z, i.e. Z ≈ 1.645). Since 5 > 1.645, H₀ is rejected; the p-value is almost zero, far below 0.05.

Conclusion: local workers' mean income is significantly higher than ₹5,000, assuming a random sample.

(b) SCM strategies of Amazon and Flipkart in the lockdown

The lockdown turned supply chains from efficiency-first to resilience-first. Both firms used these strategies:

Prioritising essentials: operations were limited to groceries, medicines and hygiene products, with non-essential categories paused and demand forecasts and stock allocation reworked for the surge.

Sourcing resilience: wider seller and supplier bases, including local kirana stores, farmers and MSMEs, and buffer stock of critical items.

Network redesign: stock placed closer to demand through hyperlocal hubs and additional fulfilment nodes.

Last-mile innovation: contactless delivery, sanitised packaging, OTP and digital payments, delivery fleets (Amazon Flex, Flipkart's eKart) and gig workers.

Visibility and safety: real-time tracking and analytics to cut stock-outs, thermal screening, masks and staggered shifts, plus coordination with authorities for movement passes.

These measures kept supply chains functioning and strengthened resilience against disruption.

(c) Information systems and competitive advantage

Information systems support managers at three levels. Operationally, transaction processing and point-of-sale systems automate routine work and trigger reorders. Tactically, MIS, DSS, ERP and CRM support budgeting, forecasting, scheduling and pricing. Strategically, executive information systems and business intelligence support scenario analysis and market intelligence.

Better decisions create advantage through:

1. Speed and accuracy: real-time data cuts uncertainty and response time.
2. Cost leadership: tighter inventory, automation and lower transaction costs.
3. Differentiation: personalisation, faster delivery and better service from customer data.
4. Coordination: ERP and SCM link suppliers, plants and customers.

Illustration: Walmart's data-driven replenishment keeps shelves stocked at low cost; Amazon's recommendation engine lifts sales. Success needs data quality, user training, security and alignment with strategy.

(d)(i) Economic order quantity

Annual demand D = 2,20,000 ÷ 22 = 10,000 parts. Ordering cost S = ₹350; carrying cost H = 15% of 22 = ₹3.30 per part per year.

EOQ = √(2DS/H) = √(2 × 10,000 × 350 ÷ 3.30) = √2,121,212 ≈ 1,456 parts.

The EOQ assumes constant demand, constant cost and instant replenishment.

(d)(ii) Days' supply per order

Daily demand = 10,000/365 = 27.4 parts.

Days' supply = 1,456.4 ÷ 27.4 ≈ 53 days (about 6.87 orders a year; about 52 days on a 360-day year).

(e) Fisher's ideal index

Fisher's index is the geometric mean of the Laspeyres and Paasche indices: F = √(L × P) × 100 in ratio form, where L = Σp₁q₀/Σp₀q₀ and P = Σp₁q₁/Σp₀q₁.

It is called ideal because it satisfies both the time reversal test (F₀₁ × F₁₀ = 1) and the factor reversal test (price index × quantity index = value index), and it balances the upward bias of Laspeyres against the downward bias of Paasche. It does not satisfy the circular test.

Steps:

1. Fix base and current years; list p₀, q₀, p₁, q₁ for each item.
2. Compute p₀q₀, p₁q₀, p₀q₁ and p₁q₁.
3. Sum each column.
4. Compute Laspeyres L = Σp₁q₀/Σp₀q₀ × 100.
5. Compute Paasche P = Σp₁q₁/Σp₀q₁ × 100.
6. Take the square root of L × P.
7. Read above 100 as a net rise, below 100 as a net fall.