Industry 4.0 · Quiz 1 · May 2024

**1. Distinguish alignment scope:** Global alignment compares both complete sequences, allowing gaps but not discarding prefixes or suffixes. Local alignment selects the highest-scoring pair of substrings. **2. Identify the optimization method:** A locally best match or gap need not belong to a globally best alignment. Standard exact alignment uses dynamic programming rather than a generally valid greedy choice. **3. Interpret the free edges:** Source-to-any-node and any-node-to-sink free edges allow irrelevant beginnings and endings to be skipped. Under the usual maximum-score alignment-graph convention, this is a local-alignment construction, not global alignment. **4. Check the space claim:** Scores can be calculated using rolling rows. Hirschberg’s divide-and-conquer method can reconstruct an optimal global alignment in \(O(mn)\) time and \(O(m+n)\) space, so linear-space alignment is possible. **Answer: A, D — A and D.** **Convention note:** This sequence-alignment question is an extra entry carried into the Industry 4.0 export from the preceding subject section. It is solved as exported; the section metadata accidentally appended to option D is not part of the mathematical statement. A: **Correct:** It correctly distinguishes whole-sequence alignment from substring alignment. B: **Incorrect:** Greedy choices do not generally guarantee an optimal alignment for arbitrary sequences and scoring schemes. C: **Incorrect:** Free rides that skip prefixes and suffixes correspond to local rather than global alignment in the usual scoring graph. D: **Correct:** Linear-space score computation and divide-and-conquer alignment reconstruction are possible.

**1. Map the first two eras:** Industry 1.0 is associated with mechanization and steam power. Industry 2.0 is associated with electrical power, assembly lines and mass production. **2. Map the later eras:** Industry 3.0 uses electronics and computer-controlled automation, including CNC. Industry 4.0 extends this toward connected digital systems and data integration. **3. Read the complete mapping:** 1.0–Steam Engine, 2.0–Mass production, 3.0–CNC, 4.0–Digitization is the intended pairing. **Answer: D — 1.0: Steam Engine; 2.0: Mass production; 3.0: CNC; 4.0: Digitization.** **Convention note:** Digitization began before Industry 4.0. Here the fourth-era label is shorthand for broader digital connectivity and integration, rather than the claim that digital technology first appeared then. A: **Incorrect:** It places steam power in the fourth era and CNC in the first. B: **Incorrect:** It reverses the intended third- and fourth-era outcomes. C: **Incorrect:** It reverses the early eras and places CNC in the fourth instead of the third. D: **Correct:** It follows the intended historical sequence across all four eras.

**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. Identify the intended production setting:** Aircraft assembly involves a large, heavy product for which moving every partially assembled unit through small functional departments can be impractical. **2. Apply the fixed-position principle:** The aircraft stays at its assembly position while workers, tools and components are brought to it. This is the fixed-position layout intended by the question. **Answer: D — Fixed position layout..** **Convention note:** The campus-style image labels functional buildings and does not itself prove that every aircraft operation is stationary. Real aircraft plants can combine layouts; D is the intended final-assembly classification. A: **Incorrect:** A product layout moves work through a fixed sequence of stations; it is not the intended stationary-aircraft arrangement. B: **Incorrect:** A process layout groups similar functions and routes jobs between them. C: **Incorrect:** A group layout organizes resources into cells for product families. D: **Correct:** The large aircraft remains in place while resources come to the assembly location.

**1. Read the axes:** Variety rises upward and volume rises to the right. Thus A is high-variety/low-volume, B is high-variety/high-volume, and D is low-variety/high-volume. **2. Match the layout choices:** A needs process-layout flexibility. B uses the question’s group/cellular compromise, organizing related product families. D favors a dedicated product flow line. **Answer: C — A: Process; B: Group; D: Product.** **Convention note:** The diagram is a simplified classification. Cellular/group layouts usually serve product families at intermediate variety and volume; the quadrant labels are interpreted within this figure. A: **Incorrect:** It places a product line in the high-variety quadrant and a process layout in the low-variety/high-volume quadrant. B: **Incorrect:** It assigns a product line to low volume/high variety and misses the high-volume/low-variety product quadrant. C: **Correct:** It gives A=Process, B=Group and D=Product, matching the displayed framework.

**1. Find the bottleneck:** Each unit must pass through the required stations. The station with the longest effective processing time cannot supply units as quickly as the others. **2. Convert its time into a rate:** For a simple serial line without parallel capacity, \(\text{maximum rate}=1/\max_i t_i\). Faster stations cannot remove that bottleneck merely by working faster. **Answer: A — Slowest station.** A: **Correct:** Its effective capacity limits the serial line’s sustainable throughput. B: **Incorrect:** A fast station can finish early but must wait for the bottleneck. C: **Incorrect:** An idle station is not the normal capacity-setting rule. D: **Incorrect:** The bottleneck station is already identified by A.

**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 a process layout:** Similar equipment or functions are grouped together, and each job follows the departments needed for its own processing requirements. **2. Identify the principal advantage:** Different products can follow different routes, giving flexibility for high variety and lower-volume production. This flexibility typically brings more handling, scheduling and operator-skill requirements. **Answer: D — It can accommodate high variety of products.** A: **Incorrect:** Variable routing generally increases material movement relative to a dedicated flow line. B: **Incorrect:** Queues, moves and different routes can lengthen throughput time. C: **Incorrect:** General-purpose equipment and varied jobs usually require skilled operators and substantial training. D: **Correct:** Flexible routing can accommodate many different product types.

**1. Identify a product layout:** Workstations follow the fixed processing sequence for a standardized product. **2. Explain the inventory benefit:** A balanced, repetitive flow reduces movement and waiting between operations, helping keep work in process small. It does not guarantee low investment or high utilization under every demand level. **Answer: A — Small in-process inventory.** A: **Correct:** Continuous, coordinated flow can reduce intermediate queues and work in process. B: **Incorrect:** High variety generally favors a flexible process layout rather than a dedicated line. C: **Incorrect:** Utilization depends on demand and line balance; it is not guaranteed for all dedicated machines. D: **Incorrect:** Dedicated lines can require substantial initial investment.

**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 “in neither cases” means never, the statement is false: a symmetric demand configuration can make the geometric median and weighted center of gravity coincide.

**1. Convert daily operating time:** Two 8-hour shifts provide \(T=2(8)(3600)=57{,}600\) seconds per day. **2. Divide time by required output:** \[C=\frac{T}{Q}=\frac{57{,}600}{30{,}000}=1.92\text{ seconds/unit}.\] **3. Apply the requested rounding:** The required line cycle time is 1.9 seconds to one decimal. This is the permitted interval between completed bulbs, not the sum of all task times. **Answer: 1.9.**

**1. Compute the unrounded cycle time:** \(C=57{,}600/30{,}000=1.92\) seconds per bulb. Retain this value while calculating the station requirement. **2. Divide total work by cycle time:** \[N_{\min}=\left\lceil\frac{\sum t_i}{C}\right\rceil=\left\lceil\frac{12}{1.92}\right\rceil=\lceil6.25\rceil=7.\] **3. Interpret the bound:** A fraction of a workstation is not allowed, so round upward. Seven is a theoretical lower bound; individual task times and precedence can require more stations. **Answer: 7.**

**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. Calculate the station loads:** For the groups (1,2), (3), (4), (5), (6,7), (8,9), (10,11,12), the times are 5+4=9, 12, 9, 10, 8+7=15, 6+9=15 and 3+5+7=15 minutes. **2. Find available station time and idle time:** There are \(N=7\) stations and the cycle is the largest load, \(C=15\). Total available station time is \(NC=105\) minutes per cycle; total task work is 85, leaving \(105-85=20\) idle station-minutes. **3. Compute balance delay:** \[BD=\frac{NC-\sum t_i}{NC}\times100=\frac{20}{105}\times100=19.05\%.\] This is the percentage of available station time that is idle. **Answer: 19.05.** **Convention note:** The printed station order puts task 6 after task 5 even though the diagram has 6→5. The percentage is nominal arithmetic for the stated loads, not proof that the order is feasible. Swapping stations (5) and (6,7) repairs the precedence violation while preserving the 15-minute cycle, efficiency and delay.