(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) Let μ be the mean annual income of all workers. Since it is suspected that local workers have higher than average income, the test is right-tailed: H₀: μ = ₹5,000 H₁: μ > ₹5,000 Use the one-sample Z-test for mean, because σ is known and n = 144 is large. Standard error: SE = σ/√n = 1200/√144 = 1200/12 = ₹100. Test statistic: Z = (x̄ − μ)/SE = (5500 − 5000)/100 = 500/100 = 5. At α = 0.05, the one-tailed critical value is z₀.₀₅ = 1.645. Since Z = 5 > 1.645, reject H₀. Equivalently, p-value = P(Z ≥ 5) ≈ 2.87 × 10⁻⁷ < 0.05. Therefore, there is significant evidence that local workers have higher mean annual income than the total population. Conditions: random and independent sample, known population standard deviation, and normal population or large sample by the Central Limit Theorem. Final: Yes, local workers have significantly higher income than the total population (Z = 5, p < 0.05).

(b) During the Covid-19 lockdowns, e-commerce supply chains shifted from efficiency-first to resilience-and-essentials-first. Amazon, Flipkart and similar firms adopted these SCM strategies:

• Demand prioritisation and assortment rationalisation: focused on groceries, medicines, health, hygiene and household essentials; paused non-essential categories; used AI/ML for surge demand forecasting and stock allocation.
• Supplier and sourcing resilience: diversified vendors, onboarded local kirana stores, farmers, MSMEs and regional sellers; adopted direct farm sourcing; maintained buffer stocks for critical SKUs; developed alternative suppliers.
• Inventory and network redesign: expanded dark stores, micro-fulfilment centres, hyperlocal hubs and forward stocking near demand; repositioned inventory across fulfilment centres; added temporary fulfilment nodes.
• Logistics and last-mile: adopted contactless delivery, sanitised packaging, QR/OTP verification, route optimisation, Amazon Flex and Flipkart eKart, gig workforce, and partnerships with local transporters; used air/rail/road priority for essentials.
• Technology and visibility: used control towers, real-time tracking, demand sensing, digital payments, virtual customer support and data analytics to reduce stockouts and improve delivery ETAs.
• Safety and workforce: implemented PPE, thermal screening, social distancing, staggered shifts, paid leave, hiring of additional workers and safety audits.
• Collaboration: worked with governments for movement passes, health/pharma supply, NGOs and local authorities. Amazon prioritised Amazon Fresh and Prime Now, household and health products, hired workers, raised wages, expanded Flex and fulfilment capacity, and used technology for demand forecasting. Flipkart prioritised essentials, medicines and groceries; expanded Flipkart Quick, hyperlocal delivery, kirana partnerships and Flipkart Wholesale; used eKart for contactless delivery and direct sourcing from farmers. Final: The key SCM strategies were essentials prioritisation, local sourcing, hyperlocal fulfilment, resilient logistics, digital visibility, safety protocols and government collaboration.

(c) Information systems bring competitive advantage by improving the speed, quality and scope of managerial decisions. They collect, process, store, retrieve and distribute data; convert it into information and knowledge for planning, organising, controlling and leading. At the operational level, TPS and real-time inventory/POS systems automate transactions and trigger reorders. At the tactical level, MIS, DSS, ERP, SCM and CRM support budgeting, forecasting, scheduling, procurement, pricing and resource allocation. At the strategic level, EIS, BI, data mining and AI/ML support scenario analysis, what-if modelling, market intelligence and strategy formulation. Competitive advantage arises through:

• Cost leadership: JIT, inventory reduction, automation, efficient logistics and lower transaction costs.
• Differentiation: customisation, faster delivery, better after-sales service and superior customer experience.
• Focus: customer segmentation and personalised offerings for niche markets.
• Innovation: new business models such as e-commerce, fintech and platform ecosystems.
• Decision quality: accurate, timely, relevant and complete information reduces uncertainty and improves responsiveness.
• Coordination and control: ERP/SCM integrate suppliers, factories, warehouses and customers; KPIs and dashboards enable corrective action. Examples include Amazon’s recommendation and fulfilment systems, Walmart’s replenishment, Flipkart’s logistics analytics, banks’ credit scoring and airlines’ yield management. Conditions for success include top-management support, strategic alignment, data quality, cyber security, user training and continuous upgrading. Final: IS supports managerial decision-making at all levels and creates competitive advantage mainly through lower cost, differentiation, speed, innovation and better customer responsiveness.

(d)(i) Annual demand: D = annual purchase value ÷ unit purchase cost = ₹2,20,000 ÷ ₹22 = 10,000 parts per year. Ordering cost: S = ₹350 per order. Unit cost: C = ₹22 per part. Carrying cost rate: i = 15% = 0.15. Carrying cost per unit per year: H = iC = 0.15 × 22 = ₹3.30 per part per year. Use the Economic Order Quantity formula: EOQ = √(2DS/H). Substitute: EOQ = √(2 × 10,000 × 350 / 3.30) = √(7,000,000 / 3.30) = √(2,121,212.1212) ≈ 1,456.44 parts. Final: EOQ ≈ 1,456 parts per order.

(d)(ii) Assuming 365 days per year: Daily demand = D/365 = 10,000/365 = 27.3973 parts per day. Number of days supply per optimum order: = EOQ / daily demand = 1,456.44 / 27.3973 = 53.16 days. Equivalently, number of orders per year = D/EOQ = 10,000/1,456.44 = 6.866; days supply = 365/6.866 = 53.16 days. If a 360-day commercial year is assumed, days supply = 1,456.44 / (10,000/360) = 52.43 days. Final: Optimum days supply per optimum order ≈ 53.16 days, about 53 days, assuming a 365-day operating year.

(e) Fisher’s ideal index is a weighted price or quantity index that is the geometric mean of the Laspeyres and Paasche indices. For price index, let p₀ and q₀ be base-period prices and quantities, and p₁ and q₁ be current-period prices and quantities. Laspeyres price index: L_p = (Σp₁q₀ / Σp₀q₀) × 100. Paasche price index: P_p = (Σp₁q₁ / Σp₀q₁) × 100. Fisher’s ideal price index: F_p = √(L_p × P_p) = √[(Σp₁q₀ / Σp₀q₀) × (Σp₁q₁ / Σp₀q₁)] × 100. For a quantity index, replace p by q in the corresponding positions: L_q = (Σq₁p₀ / Σq₀p₀) × 100, P_q = (Σq₁p₁ / Σq₀p₁) × 100, F_q = √(L_q × P_q). It is called ideal because it satisfies the two important consistency tests: the time reversal test and the factor reversal test. In ratio form, F₀₁ × F₁₀ = 1; when base 100 is used, the product is 10,000. Also, in ratio form, Fisher’s price index × Fisher’s quantity index = value index; with base 100, (F_p × F_q)/100 = value index. It uses both base-period and current-period quantities, so it balances the upward bias of Laspeyres and the downward bias of Paasche. It is symmetric and uses all relevant price and quantity data. It does not generally satisfy the circular test, so “ideal” here means ideal with respect to reversal tests and balanced weighting. Computation steps:

1. Identify the base year and current year, and list commodities with p₀, q₀, p₁, q₁.
2. Compute p₀q₀, p₁q₀, p₀q₁ and p₁q₁ for each commodity.
3. Sum each column: Σp₀q₀, Σp₁q₀, Σp₀q₁ and Σp₁q₁.
4. Compute Laspeyres index L_p = (Σp₁q₀ / Σp₀q₀) × 100.
5. Compute Paasche index P_p = (Σp₁q₁ / Σp₀q₁) × 100.
6. Compute Fisher’s index F_p = √(L_p × P_p), or directly by the formula above.
7. Interpret: F_p > 100 means net price rise; F_p < 100 means net price fall; F_p = 100 means no net change. For quantity index, use the analogous q ratios with p weights. Final: Fisher’s ideal index is F = √(Laspeyres × Paasche); it is ideal because it satisfies time and factor reversal tests and balances Laspeyres-Paasche bias.