Industry 4.0 · Quiz 2 · Sep 2025

**1. Classify the online/offline journey:** Ordering a phone online and collecting it from a showroom integrates the transaction across channels. This is omni-channel retailing, a.1–b.4. **2. Classify the unplanned belt purchase:** Discovering and buying the belt while shopping for trousers describes impulse buying, a.2–b.1. The belt also complements trousers, but the description emphasizes the unplanned purchasing behavior. **3. Classify the phone and cover:** They are used together, so their relationship is complementary products, a.3–b.3. **Answer: B — a.1–b.4, a.2–b.1, a.3–b.3.** A: **Incorrect:** It confuses the purchase-behavior description with the phone-cover product relationship. B: **Correct:** It correctly maps omni-channel retailing, impulse buying and complementary products. C: **Incorrect:** A phone cover complements rather than substitutes for the phone.

**1. Calculate EOQ using estimated parameters:** The table gives \(D_e=1000,S_e=50,H_e=10\). Thus \[Q_e=\sqrt{\frac{2(1000)(50)}{10}}=100\text{ units}.\] **2. Calculate EOQ using actual parameters:** With \(D_a=2000,S_a=25,H_a=20\), \[Q_a=\sqrt{\frac{2(2000)(25)}{20}}=\sqrt{5000}\approx70.7107.\] **3. Use the actual quantity as the error base:** \[\text{Error}\%=\frac{100-70.7107}{70.7107}\times100=41.42\%.\] Enter 41.42; the estimated optimal lot is larger than the actual optimal lot. **Answer: 41.42.**

**1. Read the axes and component curves:** A is cost and B is quantity. D decreases as \(DS/Q\), so it is ordering cost. E increases as \(HQ/2\), so it is carrying cost. **2. Identify total cost and its minimum:** C is the U-shaped sum of the two component costs. At its minimum, annual ordering and carrying costs are equal, and F marks \(Q^*=\sqrt{2DS/H}\). **3. Match the complete labeling:** A=Cost, B=Quantity, C=Total cost, D=Order cost, E=Carrying cost, F=EOQ. B is the keyed choice; D repeats the same mapping exactly. **Answer: B — B — correct mapping; D is an identical duplicate.** **Convention note:** The export contains two identical correct mappings in B and D, although the source key selects only B. The final_answer retains the keyed canonical choice B; D’s explanation explicitly identifies it as equally correct. A: **Incorrect:** It exchanges the decreasing ordering-cost curve and increasing carrying-cost curve. B: **Correct:** It correctly labels both axes, the component curves, total cost and EOQ. C: **Incorrect:** It reverses the two axes and exchanges the component-cost curves. D: **Correct:** This is identical to B and labels every element correctly. It is a duplicate correct option, although the single-choice source key accepts B only. E: **Incorrect:** The horizontal axis B is general quantity, not the single EOQ point, and F is the optimum quantity. F: **Incorrect:** It confuses the cost axis, total-cost curve, quantity axis and EOQ marker. G: **Incorrect:** A is the cost axis and C is the total-cost curve, not the reverse; D and E are also exchanged.

**1. Classify the product relationship P1:** Tea and coffee can satisfy a similar beverage need, so P1 maps to S2, substitution. **2. Classify P2:** Milk powder can be consumed together with tea, so P2 maps to S1, complementary products. Its unplanned purchase may also involve impulse buying, but the table asks for the product-pair relationship. **3. Explain the biscuit switch P3:** Limited Good-day stock leads Pranjal to buy the available Sun-fist brand. His observed purchase depends on shelf inventory, so P3 maps to S3, inventory-dependent demand. **Answer: B — P1–S2, P2–S1, P3–S3.** A: **Incorrect:** Tea/coffee are not the intended complementary pair, and the other two mappings do not match the scenario. B: **Correct:** It gives P1–S2, P2–S1 and P3–S3. C: **Incorrect:** The biscuit switch is attributed to stock availability rather than an unexplained impulse.

**1. Define a stage and its information:** Let week \(t\) be a stage and \(s_t\) be stock available at the beginning of that week. This stock determines how much new material must be ordered to meet demand \(d_t\). **2. Write the transition:** If \(q_t\) units are ordered, \[s_{t+1}=s_t+q_t-d_t,\qquad 0\le q_t\le5,\quad 0\le s_{t+1}\le4.\] The next week’s initial stock is this week’s ending inventory. **3. Connect to backward recursion:** \[V_t(s_t)=\min_{q_t}\left\{4\mathbf{1}_{\{q_t>0\}}+2q_t+0.5s_{t+1}+V_{t+1}(s_{t+1})\right\}.\] The state passed into the week’s decision is beginning inventory. **Answer: C — Beginning inventory with the warehouse in each week.** A: **Incorrect:** The purchase quantity is the decision/action, not the initial state. B: **Incorrect:** Ending inventory is the result of this week’s action and becomes next week’s state. C: **Correct:** Beginning inventory is the information available when the current decision is made.

**1. Identify the controllable choice:** At the beginning of week \(t\), the firm chooses order quantity \(q_t\). Beginning inventory \(s_t\) and demand \(d_t\) constrain that choice. **2. State the feasible action set:** Orders must meet demand and leave feasible inventory: \[\mathcal A_t(s_t)=\{q\in\{0,1,\ldots,5\}:0\le s_t+q-d_t\le4\}.\] **3. Distinguish state and consequence:** \(s_t\) is the state; \(q_t\) is the action; \(s_t+q_t-d_t\) is ending stock. Backward recursion compares the feasible order quantities. **Answer: A — How many units of the raw material needs to be purchased in a week.** A: **Correct:** The action is how many units to purchase in the current week. B: **Incorrect:** Ending inventory follows from beginning stock, the order and demand. C: **Incorrect:** Beginning inventory is the state entering the decision.

**1. Recognize the smoothing update:** Simple exponential smoothing uses \[F_{t+1}=\alpha D_t+(1-\alpha)F_t,\qquad0\le\alpha\le1.\] It combines the latest actual observation with the previous forecast. **2. Interpret the weighting:** Expanding the recurrence gives past observations weights proportional to \(\alpha(1-\alpha)^k\), decreasing geometrically with age. This explains the term “exponential smoothing.” **Answer: A — F(t+1)=αD(t)+(1−α)F(t).** A: **Correct:** It is the standard weighted update using the latest observation and prior forecast. B: **Incorrect:** The displayed mean-minus-lagged-error form is an MA-type error model, not this simple exponential-smoothing update.

**1. Distinguish cycles from seasons:** Cyclical fluctuations follow expansions and contractions whose duration need not be a fixed calendar interval. Seasonal fluctuations repeat with a known calendar frequency. **2. Classify the examples:** A recession is part of the business cycle. A recurring winter sales effect or year-end tourist peak is seasonal, regardless of whether that particular seasonal direction is typical. **Answer: A — Economic recission.** A: **Correct:** An economic recession is associated with the non-fixed-length business cycle. B: **Incorrect:** A recurring winter pattern is seasonal rather than cyclical; increased fan sales in winter is unusual but the calendar classification is unchanged. C: **Incorrect:** A recurring end-of-year tourist peak has a fixed annual seasonal timing.

**1. Identify the modeling task:** Forecasting first looks for systematic structure such as level, trend, seasonality, cycles and dependence over time. **2. Identify useful relationships:** Relationships between the target and its own past values, seasonal positions or other available predictors can be used to form forecasts. This is the intended meaning of discovering relationships. **3. Separate setup from analysis:** Choosing which business quantity to forecast is necessary problem formulation. The question’s intended pair concerns the subsequent analytical work: identifying patterns and discovering useful relationships. **Answer: A, C — A and C.** **Convention note:** Pure univariate time-series forecasting does not require discovering relationships among multiple distinct external variables. C is interpreted broadly to include dependence on past observations; otherwise its wording would describe a broader predictive-modeling task. A: **Correct:** Recognizing systematic temporal structure is a core forecasting task. B: **Incorrect:** Selecting the target is an initial setup task, rather than one of the intended two modeling tasks. C: **Correct:** Modeling temporal dependence or predictive relationships helps translate patterns into forecasts.

**1. Define a shortage cost:** A shortage occurs when inventory cannot satisfy demand. Its cost includes immediate lost margin and longer-term losses caused by disappointing customers. **2. Identify the relevant losses:** Damaged goodwill, losing a customer and missing the profit on an unfulfilled sale all arise directly from a stockout. Returns of already supplied products normally belong to return/quality costs instead. **Answer: A, C, D — A, C and D.** A: **Correct:** Unavailability can damage the seller’s reputation and customer goodwill. B: **Incorrect:** A product return is normally a reverse-logistics or quality cost, not itself a stockout cost. C: **Correct:** A stockout can cause the customer to leave permanently. D: **Correct:** A sale not fulfilled can lose its associated contribution or profit.

**1. Identify the three unit values:** Selling price p=₹2, purchase/production cost c=₹1 and salvage value v=₹0.50. The ₹2 is treated as sales revenue per sold diya, not additional net profit. **2. Compute mismatch costs:** \(C_u=p-c=1\) and \(C_o=c-v=0.5\). **3. Calculate the critical ratio:** \[CR=\frac{C_u}{C_u+C_o}=\frac{1}{1+0.5}=\frac23\approx0.67.\] Retain the exact fraction when calculating the optimal quantity. **Answer: 0.67.**

**1. Compute the exact critical ratio:** \(C_u=2-1=1\), \(C_o=1-0.5=0.5\), so \(CR=2/3\). Do not substitute the rounded 0.67 prematurely. **2. Invert the uniform CDF:** For \(D\sim U[800,1000]\), \(F(Q)=(Q-800)/200\). Therefore \[Q^*=800+200\left(\frac23\right)=933.333\ldots.\] **3. Interpret the quantity:** The continuous-model answer is 933.33 units. If only whole diyas may be made, compare the neighboring integers; 933 is optimal under this continuous uniform expected-cost model. **Answer: 933.33.**

**1. Compare mismatch penalties:** If \(C_o<C_u\), then \(CR=C_u/(C_u+C_o)>0.5\). Avoiding an expensive shortage merits stocking above the median. **2. Locate the uniform quantile:** The uniform mean and median are both \((800+1000)/2=900\). A quantile above 0.5 lies to the right of 900; here the ratio 2/3 gives about 933.33. **Answer: C — Towards the right of the mean.** A: **Incorrect:** Below the mean corresponds to a critical ratio below 0.5, when overage is more costly. B: **Incorrect:** The mean is optimal when the two mismatch costs are equal. C: **Correct:** A higher underage cost produces a quantile above the mean/median.

**1. Put all inputs on an annual basis:** \(D=1500(12)=18{,}000\) units/year; ordering cost \(S=150\) rupees/order; holding cost \(H=0.20(27)=5.40\) rupees/unit/year. **2. Apply EOQ:** \[Q^*=\sqrt{\frac{2DS}{H}}=\sqrt{\frac{2(18{,}000)(150)}{5.4}}=\sqrt{1{,}000{,}000}=1000.\] **3. Interpret the minimization:** This balances annual ordering and holding costs. With a fixed unit purchase price and fixed annual demand, purchase expenditure does not vary with lot size. **Answer: 1000.**

**1. Find annual demand and EOQ:** \(D=1500(12)=18{,}000\), \(H=0.20(27)=5.4\), and \(Q^*=\sqrt{2(18{,}000)(150)/5.4}=1000\) units. **2. Divide demand into lots:** \[n=\frac{D}{Q^*}=\frac{18{,}000}{1000}=18\text{ orders/year}.\] Each order supplies the next 1000 units of demand. **Answer: 18.**

**1. Find optimal order frequency:** Annual demand is \(18{,}000\), annual holding cost per unit is \(5.4\), and EOQ is \(\sqrt{2(18{,}000)(150)/5.4}=1000\). Thus the firm places \(18{,}000/1000=18\) orders/year. **2. Multiply by the cost per order:** \[C_{order}=\frac{D}{Q^*}S=18(150)=2700\text{ rupees/year}.\] This excludes material purchase expenditure. **Answer: 2700.**

**1. Determine the replenishment lot:** \(D=18{,}000\) per year and \(H=5.4\) give \(Q^*=\sqrt{2(18{,}000)(150)/5.4}=1000\) units. **2. Describe the EOQ inventory cycle:** Under constant demand and instantaneous replenishment without safety stock, on-hand inventory decreases uniformly from 1000 just after delivery to 0 before the next delivery. **3. Take the average:** \[\bar I=\frac{Q^*+0}{2}=\frac{1000}{2}=500\text{ units}.\] **Answer: 500.**

**1. Compute unit holding cost:** \(H=0.20(27)=5.40\) rupees/unit/year. Annual demand is \(18{,}000\), so \(Q^*=\sqrt{2(18{,}000)(150)/5.4}=1000\). **2. Use average inventory:** With no safety stock, \(\bar I=Q^*/2=500\) units. **3. Calculate annual carrying cost:** \[C_{hold}=H\bar I=5.4(500)=2700\text{ rupees/year}.\] It equals annual ordering cost at the unconstrained EOQ. **Answer: 2700.**