Industry 4.0 · End Term · Jan 2026 · FN

**1. Identify when decisions occur:** Investment allocation is chosen at the start of each of the four years, and the resulting wealth is carried into the following year. **2. Define the DP stage:** Each year is a stage. The available capital is the state at that stage, and the allocation between the two banks is the action. **Answer: A — Year.** A: **Correct:** Each year corresponds to one successive investment-decision stage. B: **Incorrect:** Available capital is the state, not the time stage. C: **Incorrect:** A bank allocation is a decision within a stage. D: **Incorrect:** The allocation pair is the action, not the year index.

**1. Define a feasible allocation:** If \(s_t\) is the investable capital at the start of year \(t\), choose amounts \(x_t\) and \(y_t\) for First Bank and Second Bank satisfying \(x_t+y_t=s_t\), with nonnegative allocations. **2. Interpret the alternatives:** Each feasible allocation pair is an alternative action at that stage. Comparing their returns determines the capital entering the next year. **3. Distinguish representation from meaning:** One amount could mathematically determine the other, but D states the complete economic choice: how much is invested in each bank. **Answer: D — Amounts invested in First Bank and Second Bank in a year.** A: **Incorrect:** The year identifies the stage, not an investment alternative. B: **Incorrect:** Capital is the state available before making the allocation. C: **Incorrect:** One allocation can parameterize a split if the remainder is implicit, but this option alone does not state the complete allocation as clearly as D. D: **Correct:** It explicitly represents the allocation of available capital between both banks.

**1. Identify the information carried forward:** The amount available at the start of a year determines how much can be allocated between the banks. Past choices matter through their effect on this capital. **2. Define the state:** Use the capital available for investment at the start of the year, including that year’s new contribution according to the chosen accounting convention. The year is the stage and the bank split is the action. **Answer: B — Capital available for investment at the start of a year.** A: **Incorrect:** The year is the stage index. B: **Correct:** Available starting capital summarizes the resource available for the current investment decision. C: **Incorrect:** The First Bank allocation is a decision variable. D: **Incorrect:** The allocation pair is the action selected after observing the state.

**1. Read the task durations:** Tasks 1–12 take 5, 4, 12, 9, 10, 8, 7, 6, 9, 3, 5 and 7 minutes, respectively. **2. Apply the indivisible-task lower bound:** A workstation must be able to complete any task assigned to it within one cycle. Therefore \[C_{\min}=\max_i t_i=12\text{ minutes}.\] **3. Check feasibility with enough stations:** Assigning each task to a separate station in a topological order respects precedence and permits this cycle. Precedence affects how tasks may be grouped, not the longest-task bound itself. **Answer: 12.**

**1. Interpret the maximum conventional cycle:** If all tasks are placed at one workstation, one unit requires the entire work content before the next cycle finishes. **2. Sum the durations:** \[C_{\max}=5+4+12+9+10+8+7+6+9+3+5+7=85\text{ minutes}.\] **3. Distinguish this from the critical path:** At one workstation even tasks on different branches are done serially, so all durations are included. The term refers to productive cycle-time bounds, excluding arbitrary extra waiting. **Answer: 85.**

**1. Find the required cycle:** An 8-hour shift provides 480 minutes, so producing 32 units requires \[C_{required}=\frac{480}{32}=15\text{ minutes/unit}.\] **2. Compare task limits:** The longest indivisible task takes 12 minutes, below 15, so it does not prevent the target. Total work is 85 minutes, giving a lower bound of ceiling(85/15)=6 stations. **3. Exhibit a feasible balance:** Seven stations with task groups (1,2), (3), (4), (6,7), (5), (8,9), (10,11,12) have loads 9,12,9,15,10,15,15 minutes. Task 6 precedes task 5, and all other precedence links are also respected, permitting one unit each 15 minutes in steady operation. **Answer: A — Yes — feasible at a 15-minute steady-state cycle.** **Convention note:** The usual daily-output calculation assumes a running/pipelined line and no breaks, breakdowns or other losses. Starting an empty line introduces a separate initial fill time. A: **Correct:** A precedence-feasible seven-station balance achieves a 15-minute cycle. B: **Incorrect:** The longest task is only 12 minutes and a feasible 15-minute assignment exists.

**1. Identify the unit economics:** Treat ₹5 as the selling price, ₹3 as cost and ₹1 as salvage value. **2. Calculate underage and overage costs:** \(C_u=5-3=2\) and \(C_o=3-1=2\) rupees per unit. **3. Form the critical ratio:** \[CR=\frac{C_u}{C_u+C_o}=\frac{2}{2+2}=0.5.\] Equal mismatch penalties place the optimal continuous order at the median demand. **Answer: 0.5.**

**1. Compute the mismatch ratio:** \(C_u=5-3=2\) and \(C_o=3-1=2\), so \(CR=2/(2+2)=0.5\). **2. Invert the uniform demand distribution:** For \(D\sim U[800,1000]\), \[Q^*=800+(1000-800)(0.5)=900\text{ diyas}.\] **3. Interpret the result:** The symmetric uniform distribution has mean and median 900; equal underage and overage costs make that central quantity optimal. **Answer: 900.**

**1. Identify the price, cost and recovery:** p=₹3,000, c=₹1,500 and v=₹1,200 per returned jacket. **2. Find marginal mismatch costs:** \(C_u=p-c=1500\), while \(C_o=c-v=300\). The return recovery makes overstocking relatively inexpensive. **3. Calculate and round:** \[CR=\frac{1500}{1500+300}=\frac56=0.833333\ldots\approx0.83.\] The mean and standard deviation are needed for quantity, not for this ratio. **Answer: 0.83.**

**1. Choose the appropriate normal quantile:** \(CR=(3000-1500)/[(3000-1500)+(1500-1200)]=5/6\). The question supplies \(z=0.97\) for this quantile. **2. Convert from standard-normal units:** \[Q^*=\mu+z\sigma=300+0.97(50)=348.5\text{ jackets}.\] **3. Interpret the numerical answer:** 348.5 is the continuous approximation requested using the given z-value. If a whole-jacket decision is required, compare 348 and 349 using the unrounded distribution rather than assuming every quantile must be rounded upward. **Answer: 348.5.**

**1. Standardize the stocked quantity:** With \(Q=350,\mu=300,\sigma=50\), \[z=\frac{350-300}{50}=1.\] **2. Use the upper tail:** A stockout means \(D>350\), not \(D\le350\). The supplied CDF gives \[\Pr(D>350)=1-\Phi(1)=1-0.8413=0.1587.\] **3. Round to the requested format:** Three decimals gives 0.159. Do not enter 15.9, since the question asks for a probability rather than a percentage. **Answer: 0.159.**

**1. Form the coordinate differences:** From P to Q the changes are \(-3-2=-5\), \(4-(-1)=5\), and \(2-5=-3\). **2. Apply three-dimensional Euclidean distance:** \[d=\sqrt{(-5)^2+5^2+(-3)^2}=\sqrt{25+25+9}=\sqrt{59}\approx7.6811.\] **3. Report the distance:** Approximately 7.68 coordinate units. Adding absolute differences would calculate rectilinear distance instead. **Answer: 7.68.**

**1. Identify physical-layout objectives:** Layout planning arranges resources and movement paths to support safe, efficient operations and access. **2. Apply the objectives:** Shorter, better-organized routes reduce handling delay; appropriate customer-facing arrangements can support sales; access around equipment enables maintenance. Project financing is a funding decision rather than a physical-layout objective. **Answer: A, B, C — A, B and C.** A: **Correct:** Reducing unnecessary movement and handling delay is a direct layout objective. B: **Correct:** An appropriate retail or service arrangement can improve visibility, access and customer experience, supporting sales. C: **Correct:** Maintenance needs safe access and adequate space around equipment. D: **Incorrect:** Obtaining funds concerns financing rather than resource placement.

**1. Identify the distance objective:** The usual Euclidean location problem minimizes weighted straight-line distances: \[\min_{x,y}\sum_i w_i\sqrt{(x-x_i)^2+(y-y_i)^2}.\] Its solution is a weighted geometric median. **2. Distinguish the center of gravity:** A weighted coordinate mean minimizes the sum of squared distances, a different objective. It can coincide with a geometric median in symmetric cases, but equality is not guaranteed. **3. Interpret the standard result:** A nondegenerate Euclidean problem generally identifies a particular optimal point, rather than the median interval/rectangle possible with rectilinear distance. **Answer: B, C — B and C — generally a point, not generally the center of gravity.** **Convention note:** The question uses “rarely” informally. Coincidence depends on the data, and special collinear configurations can have an interval of minimizers. The answer assumes the usual unsquared Euclidean objective and a nondegenerate instance. A: **Incorrect:** A region is not the usual nondegenerate Euclidean-location result, though special collinear cases can have multiple optimal points. B: **Correct:** Read as “does not generally coincide”: a geometric median is not generally the weighted coordinate mean. C: **Correct:** A point is the standard nondegenerate result; this is not a uniqueness theorem for every possible dataset. D: **Incorrect:** If the malformed phrase means “none,” it is false because symmetry can produce coincidence; if it means “most,” that is not generally guaranteed.

**1. Identify a seasonal pattern:** Seasonality repeats at fixed calendar intervals, such as month, quarter, winter or the end of each year. **2. Classify the examples:** A recurring winter fan-sales effect and recurring year-end tourist traffic are seasonal. A recession is cyclical because business cycles do not have a fixed calendar frequency. **Answer: B, C — B and C.** **Convention note:** The winter increase is accepted as the hypothetical pattern stated in the option. Its economic plausibility in a particular region is separate from whether its timing is seasonal. A: **Incorrect:** Recessions are business-cycle fluctuations, not a fixed calendar season. B: **Correct:** A recurring winter-related sales increase is seasonal, even though fans more typically sell strongly in hot weather. C: **Correct:** A recurring year-end tourist peak is an annual seasonal pattern.

**1. Apply the ownership test:** Outsourcing assigns an activity to an external organization rather than performing it through the organization’s own employees or units. **2. Classify the arrangements:** Concentrix handling Amazon customer service and TCS operating IIT Madras’s exam portal involve external providers. Mastercard and Micron establishing their own teams describe internal operations, even if those teams are overseas. **Answer: A, C — A and C.** A: **Correct:** Amazon delegates a function to a separate service provider. B: **Incorrect:** Setting up Mastercard’s own team does not establish external outsourcing. C: **Correct:** IIT Madras delegates portal operation and evaluation services to TCS. D: **Incorrect:** Micron’s own team in India is captive offshoring, not outsourcing as described.

**1. Identify what network structure determines:** The number and location of distribution facilities affect how goods are stored, moved, handled and coordinated. **2. Trace the affected cost categories:** Inventory depends on stock placement and risk pooling; transport depends on route lengths and shipment consolidation; facilities/handling depend on sites and flows; information costs depend on tracking and coordination systems. **3. Distinguish the offered non-cost category:** Selling price is a commercial decision rather than one of these standard distribution-network cost components. **Answer: A, B, C, D — A, B, C and D.** A: **Correct:** Stock placement and pooling change inventory-related costs. B: **Correct:** Routes, shipment sizes and distance change transportation costs. C: **Correct:** The number and operation of facilities determine site and handling costs. D: **Correct:** Network coordination requires information systems and communication. E: **Incorrect:** Price is not itself a distribution-network operating-cost category, although costs can influence pricing decisions.

**1. Locate the initial inbound movement:** In the vendor–distribution-centre–store–customer chain used here, the first movement takes products from the vendor into the distribution network. **2. Distinguish later legs:** Distribution-centre to store is an intermediate leg; store to customer is the last-mile leg. **Answer: A — Movements from Vendor to Distribution centres.** **Convention note:** “First mile” can be defined relative to the logistics network, such as seller pickup to a sorting hub in parcel delivery. A matches the stages offered in this question. A: **Correct:** It describes the initial supplier-to-distribution-centre movement in the stated chain. B: **Incorrect:** This is the next distribution stage after goods enter the network. C: **Incorrect:** This is the final customer-delivery leg.

**1. Identify the course’s advanced-transport example:** Hyperloop proposes high-speed movement of pods through low-pressure tubes, combining advanced propulsion, controls and infrastructure. **2. Match the offered choices:** Within this course’s historical examples, Hyperloop is the intended Industry 4.0 transport concept. An internal-combustion engine and an electric drivetrain alone do not define digitally connected transport. **Answer: C — Hyperloop.** **Convention note:** This is a course-specific example, not a universal technical definition of Industry 4.0. Connected, data-driven and autonomous systems can also be Industry 4.0 transport applications; an electric vehicle can incorporate them. A: **Incorrect:** The internal-combustion engine is an earlier industrial transport technology. B: **Incorrect:** Electric propulsion alone is not the course’s intended marker for Industry 4.0. C: **Correct:** Hyperloop is the advanced transport concept intended in this question.

**1. Match the earlier revolutions:** The first is conventionally associated with England and steam-powered mechanization. The second is associated here with US mass-production development. **2. Match the later revolutions:** The course groups electronics/computer automation under USA/Japan for the third, and the Industry 4.0 initiative under Germany for the fourth. **3. Read the table labels:** England=B1, USA=B2, USA/Japan=B3 and Germany=B4. Therefore A1–B1, A2–B2, A3–B3, A4–B4. **Answer: A — A1–B1, A2–B2, A3–B3, A4–B4.** **Convention note:** These are simplified course associations, not claims that each technological revolution developed in only one country. The second industrial revolution also had major European contributions. A: **Correct:** It matches all four country labels as intended by the table. B: **Incorrect:** It reverses the first and second associations. C: **Incorrect:** It assigns the early steam revolution and later Industry 4.0 label to inappropriate entries. D: **Incorrect:** It misassigns the first three entries even though the Germany pairing is retained.

**1. Interpret the supervision distinction:** A process layout groups similar machines or operations into functional departments. Each department can be supervised by a specialist in that process. **2. Identify the intended answer:** This enables specialized/functional supervision rather than relying only on one general supervisor across unlike operations. It does not eliminate supervision. **Answer: B — Process layout.** **Convention note:** Read “do not require general supervision” as “permit specialized functional supervision.” A process layout still requires supervision and can be demanding to schedule. A: **Incorrect:** A flow line still needs line coordination and supervision; it is not the functional-supervision answer sought. B: **Correct:** Grouping like processes supports specialized departmental supervision. C: **Incorrect:** Cells may support team supervision, but this is not the course’s intended functional-layout distinction. D: **Incorrect:** A stationary-product project still requires coordination of multiple specialties.

**1. Identify the components:** The equations maintain a level a(t) and a trend b(t), then forecast the next observation as their sum. Two smoothing coefficients update these two components. **2. Distinguish the methods:** Holt’s linear method explicitly models trend. Simple exponential smoothing has only a level; Holt–Winters adds a seasonal component as well. **3. Correct the printed level equation:** Standard Holt smoothing uses \[a_t=\alpha D_t+(1-\alpha)(a_{t-1}+b_{t-1}),\qquad F_{t+1}=a_t+b_t.\] The figure’s minus sign before the previous trend is inconsistent with this standard form. **Answer: C — Holt’s method for trend.** **Convention note:** The source prints a(t−1)−b(t−1) in the level update. With a positive trend convention and F(t+1)=a(t)+b(t), this should be a plus sign. The literal printed equations are not exactly standard Holt equations. A: **Incorrect:** Holt’s method belongs to the exponential-smoothing family, but A is less specific than the named trend model. B: **Incorrect:** No seasonal component or seasonal smoothing equation is present. C: **Correct:** The level-and-trend structure identifies Holt’s method, with the stated sign correction. D: **Incorrect:** C identifies the intended method; the sign typo should be corrected rather than hiding its structure.

**1. Define digitization:** Digitization converts information from a physical or analog form into a digital representation. **2. Distinguish process automation:** Generating an automatic daily report uses digital systems to perform a business process; it is an example of automation/digitalization rather than merely converting a physical record to a digital one. **3. Apply the negative wording:** The question asks which is not an example of digitization, so select the automated-report option. **Answer: B — Generating an automated daily sales report.** A: **Incorrect:** Converting a physical book into an electronic copy is digitization; do not select it. B: **Correct:** Select this: automatically generating reports changes how the reporting process is performed. C: **Incorrect:** Converting a physical drawing into CAD creates a digital representation; do not select it. D: **Incorrect:** Converting a paper invoice into an electronic copy is digitization; do not select it.

**1. Define logistics scope:** Logistics coordinates movement and storage of materials and products, including inbound supply flows, materials handling and outbound distribution. **2. Distinguish broader customer relationships:** Customer relationship management covers acquisition, retention and relationship strategy. It is not the core material-flow function asked for here, although logistics delivery and service performance affect customers. **Answer: C — Customer Management.** **Convention note:** Logistics does include customer-service activities connected with orders and delivery. The answer interprets “Customer Management” as broader CRM, not a claim that logistics has no customer-facing responsibilities. A: **Incorrect:** Inbound procurement-related flows are included in the course’s broad logistics scope. B: **Incorrect:** Managing material storage and movement is a core logistics activity. C: **Correct:** Select this: broad customer relationship management is outside the intended logistics-function list. D: **Incorrect:** Outbound distribution is a core logistics activity.

**1. Interpret the course’s categories:** Industrial internet connects operational assets and processes; commercial/business internet supports enterprise transactions; consumer internet serves individual communication and services. **2. Identify the unmatched label:** “Philanthropic” describes a charitable purpose, rather than one of the sector/application categories used in this classification. **Answer: C — Philanthropic.** **Convention note:** This is a teaching taxonomy rather than a universal formal list of internet types. Charities can, of course, use internet technologies. A: **Incorrect:** Industrial internet is a recognized application category for connected industrial systems. B: **Incorrect:** Commercial internet describes business-facing applications in the course classification. C: **Correct:** Select this: philanthropic is not a category in the listed taxonomy. D: **Incorrect:** Consumer internet describes user-facing digital services and connected consumer applications.