## 3 Inventory Management: NeuralCore's AI Chip Decisions (45 points) NeuralCore designs AI accelerator chips and, like NVIDIA, depends entirely on TSMC for manufacturing. They face two distinct inventory decisions: **Decision 1 - Special Production Run (Newsvendor):** For a new customer (Tesla), NeuralCore must decide how many chips to produce in a one-time run. These chips are custom-designed and become obsolete after Tesla's model year ends. **Decision 2 - Regular Operations ((R,Q) Policy):** For standard AI chips sold to multiple customers, NeuralCore maintains ongoing inventory. They order in batches of Q = 50,000 chips and reorder when inventory hits level R. **Why This Matters:** Single-source dependency on TSMC means any disruption affects both decisions differently. **Current Operating Parameters:** - Daily demand: μ = 1,000 chips, σ = 1,000 chips (high uncertainty due to AI market volatility) - Selling price: $1,000/chip - Manufacturing cost: $200/chip - End-of-life value: $0 (obsolete chips cannot be resold) - TSMC lead time: 10 days currently - Required service level: 97.7% (k = 2.0) due to customer contracts ### Part A: Understanding Both Models (15 points) 1. **(3 points)** For the Tesla one-time run, calculate the critical ratio α. What does this ratio represent in business terms? 2. **(3 points)** Using k = 2.0, how many chips should NeuralCore produce for Tesla? (newsvendor q*) 3. **(3 points)** For regular operations with Q = 50,000, what is the expected demand during TSMC's lead time? 4. **(3 points)** Calculate the reorder point R* for regular operations. 5. **(3 points)** Of the inventory at the reorder point, how much is buffer stock versus expected demand? ### Part B: Supply Chain Disruptions (20 points) _Each scenario below affects NeuralCore's decisions differently:_ 6. **(4 points)** **AI Boom Scenario:** ChatGPT-5 launch quadruples daily demand (μ = 4,000, σ = 1,000). - Calculate new quantities for both Tesla run (q*) and regular operations (R*) - Explain why the impacts differ 7. **(4 points)** **Market Chaos:** Crypto mining demand creates volatility (μ = 1,000, σ = 2,500). - How does this change the Tesla one-time production quantity? 8. **(4 points)** **Premium Pricing:** Chip shortage allows $2,000/chip pricing. - Does this affect the one-time run quantity? The reorder point? Explain. 9. **(4 points)** **Taiwan Tensions:** Shipping disruptions extend TSMC lead time to 27 days. - Which decision model is affected and by how much? 10. **(4 points)** Based on your calculations: "To double inventory levels requires: mean demand to increase __×, OR volatility to increase __×, OR lead time to increase __×" ### Part C: Product Mix Strategy (9 points) NeuralCore sells two products with identical demand patterns (μ = 1,000, σ = 1,000): - **AI Accelerator:** Price $1,000, Cost $200, Obsolete value $0 - **Basic GPU:** Price $100, Cost $80, Obsolete value $0 11. **(3 points)** Calculate the service level (α) each product should target. 12. **(3 points)** Which product justifies carrying more safety stock? Show calculations. 13. **(3 points)** A manager suggests: "Since Basic GPU has lower margins, we should set a lower reorder point." Is this correct for (R,Q) policy? Explain. ### Part D: Strategic Implementation (8 points) 14. **(5 points)** Your CFO asks: "Why does doubling volatility have more impact than doubling average demand?" Write a 100-word explanation using your calculations from Part B. 15. **(3 points)** **Nightmare Scenario:** AI demand doubles AND Taiwan blockade doubles lead time. Calculate the combined impact on reorder point. ### Bonus: Breaking TSMC Dependency (10 points) 16. **(10 points)** NeuralCore evaluates Intel Foundry as a second source: **Proposed Split:** - TSMC: 70% of volume, 10-day lead time, reliable - Intel: 30% of volume, 20-day lead time, new partner a) Calculate separate reorder points for each supplier b) Compare total safety stock to current single-source approach c) Beyond the math: What risk does this strategy NOT address? ----- ## Model Answer - NeuralCore's AI Chip Decisions ### Part A: Understanding Both Models (15 points) **1. (3 points)** - Critical ratio α = (r-c)/(r-c+c-s) = (1000-200)/(1000-200+200-0) = 800/1000 = **0.8** - Business meaning: NeuralCore should produce enough chips to meet demand 80% of the time. The 20% stockout risk is economically optimal given the high margins. **2. (3 points)** - Newsvendor q* = μ + k·σ = 1,000 + 2(1,000) = **3,000 chips** **3. (3 points)** - E[DDLT] = μ × LT = 1,000 × 10 = **10,000 chips** **4. (3 points)** - σ[DDLT] = σ × √LT = 1,000 × √10 = 3,162 chips - R* = E[DDLT] + k·σ[DDLT] = 10,000 + 2(3,162) = **16,324 chips** **5. (3 points)** - Buffer stock = k·σ[DDLT] = 6,324 chips - Expected demand = 10,000 chips - Buffer stock percentage = 6,324/16,324 = **38.7%** ### Part B: Supply Chain Disruptions (20 points) **6. (4 points)** - Tesla run: q* = 4,000 + 2(1,000) = **6,000 chips** (2× increase) - Regular ops: R* = 40,000 + 2(3,162) = **46,324 chips** (2.84× increase) - **Why different:** Newsvendor doubles because both mean and safety stock terms scale with demand. R* doesn't double because safety stock (k·σ·√LT) remains unchanged when only μ increases. **7. (4 points)** - New q* = 1,000 + 2(2,500) = **6,000 chips** - This doubles the original quantity (3,000 → 6,000) **8. (4 points)** - New α = (2000-200)/(2000-200+200-0) = 1800/2000 = 0.9 - For α = 0.9, k ≈ 1.28 (not 2.0) - **One-time run:** Affected but doesn't double (need k ≈ 4 to double) - **Reorder point:** Unaffected - R* stays at 16,324 because (R,Q) doesn't depend on prices **9. (4 points)** - Only affects (R,Q) model - New R* = 1,000(27) + 2(1,000√27) = 27,000 + 10,392 = **37,392 chips** - Factor increase = 37,392/16,324 = **2.29×** **10. (4 points)** - Mean demand: **4×** - Volatility: **2.5×** - Lead time: **2.7×** ### Part C: Product Mix Strategy (9 points) **11. (3 points)** - AI Accelerator: α = 800/1000 = **0.8** - Basic GPU: α = 20/100 = **0.2** **12. (3 points)** - AI Accelerator: k = 0.84, safety stock = 0.84(3,162) = **2,656 chips** - Basic GPU: k = -0.84, safety stock = **-2,656 chips** - **AI Accelerator needs more** - high margins justify holding safety stock **13. (3 points)** - **Manager is incorrect.** R* = μ·LT + k·σ·√LT doesn't include price/cost terms. Both products have R* = 16,324 if using same service level (k = 2.0). The (R,Q) model separates inventory decisions from economics. ### Part D: Strategic Implementation (8 points) **14. (5 points)** _Sample answer:_ "Volatility has more leverage because it enters inventory formulas directly through safety stock (k·σ), while mean demand is 'diluted' by the constant safety stock term. In newsvendor: q* = μ + k·σ, doubling σ adds 2,000 units, but doubling μ only adds 1,000. With k=2, volatility has twice the marginal impact. In (R,Q), the √LT factor further amplifies volatility's effect while mean scales linearly." **15. (3 points)** - New R* = 2,000(20) + 2(1,000√20) = 40,000 + 8,944 = **48,944 chips** - Factor increase = 48,944/16,324 = **3.0×** (multiplicative risk) ### Bonus: Breaking TSMC Dependency (10 points) **16a. (4 points)** - TSMC (70%): R* = 700(10) + 2(√700√10) = 7,000 + 1,674 = **8,674 chips** - Intel (30%): R* = 300(20) + 2(√300√20) = 6,000 + 1,342 = **7,342 chips** **16b. (3 points)** - Dual-source safety stock: 1,674 + 1,342 = 3,016 chips - Single-source safety stock: 6,324 chips - **Reduction: 52%** due to risk pooling **16c. (3 points)** Risks NOT addressed: - **Correlated failures:** Both suppliers could face simultaneous disruptions (e.g., global chip shortage) - **Quality risk:** Intel's new process might have yield issues - **Capacity risk:** If TSMC fails completely, Intel can't handle 100% volume --- **Grading Notes:** - Full credit for correct formulas even with minor calculation errors - Partial credit for right approach with wrong numbers - Emphasis on explaining intuition, not just calculations - Bonus requires understanding beyond formulas