Question 1

Work/method study tools: applications of a string diagram  A string diagram maps actual movement on a scaled layout for distance/time assessment. Identify valid use cases for a string diagram.

Accepted Answer

ConceptA string diagram uses pinned string/lines over a scale layout to measure routes, distances, and frequencies of movement. It is valuable for: Comparing candidate layouts by travel distance/time. Studying multi-person, multi-machine patterns in one area. Tasks where one operator moves among several stations. Final AnswerAll of the above.

Question 2

Network diagrams (CPM/PERT): basic construction guidelines  Consider standard rules for drawing activity-on-arrow networks. Identify the set of correct guidelines.

Accepted Answer

Guidelines explained• One arrow per activity avoids duplication and ambiguity.• Avoid dangling ends; every activity must start/end at well-defined events.• Dummy activities exist only to maintain logic; they have zero duration and no resource use. Final AnswerAll of the above.

Question 3

Scheduling tools: primary use of a Gantt (bar) chart in production  Identify the most appropriate application area of Gantt charts in operations management. Choose the best option.

Accepted Answer

ConceptGantt (bar) charts provide a time-scaled visual of planned vs. actual start/finish for jobs, machines, or departments. They are widely used for production schedules and progress control. Why others are less appropriateInventory control uses ABC/EOQ etc.; material handling uses different tools. Maintenance can use Gantt, but its primary association in operations is production scheduling. Final AnswerProduction scheduling and tracking.

Question 4

Break-even analysis: components of total cost versus output  In a cost–volume–profit (CVP) framework, total cost (TC) varies with output. Select the correct composition of total cost.

Accepted Answer

DefinitionsTotal cost (TC) = Fixed cost (does not vary with output) + Variable cost (varies with output). Sales revenue and profit are not parts of cost. Break-even conditionAt break-even: Sales revenue = Total cost = Fixed cost + Variable cost. Final AnswerFixed cost + Variable cost.

Question 5

Inventory management: application of A–B–C analysis (Pareto classification)  Identify the function/area where ABC analysis is primarily applied to control items by importance. Choose the correct application.

Accepted Answer

ConceptABC analysis ranks items by annual consumption value (A: vital few, B: moderate, C: trivial many) to focus control where it matters most. It is a core inventory control technique. Final AnswerInventory control (classification of items by value usage).

Question 6

PERT expected time (probabilistic): compute using optimistic, most likely, pessimistic  For an activity with three time estimates: tₒ (optimistic), tₙ (most likely), and tₚ (pessimistic). Choose the correct expression for the PERT expected time.

Accepted Answer

Approach (Beta distribution assumption)PERT models activity time with a (shifted) beta distribution and uses a weighted mean favouring the most likely time. Expected time formulate = (tₒ + 4 tₙ + tₚ) / 6 IllustrationIf tₒ = 4, tₙ = 6, tₚ = 10 (days):te = (4 + 4×6 + 10)/6 = (4 + 24 + 10)/6 = 38/6 ≈ 6.33 days. Common pitfallsDo not average equally; PERT gives 4× weight to the most likely estimate. Final Answer(tₒ + 4 tₙ + tₚ) / 6.

Question 7

PERT time estimates: how many estimates does PERT require for each activity?  According to the PERT (Program Evaluation and Review Technique) approach, identify the number of time estimates used to model activity duration uncertainty. Choose the cor…

Accepted Answer

ConceptPERT models activity duration uncertainty with three estimates: optimistic (a), most likely (m), and pessimistic (b). These combine to give the expected time and variance for network analysis. Why tripleUsing three points better captures uncertainty than a single or double estimate, improving schedule risk analysis. Final Answertriple time estimate

Question 8

Applicability of linear programming (LP) to operations problems  Evaluate the statement: “Linear programming models can be applied to the line balancing problem and the transportation problem.” Mark the statement's correctness.

Accepted Answer

ConceptThe transportation problem is a classic LP. Line balancing can be formulated as an integer/linear program (assigning tasks to stations subject to precedence and cycle-time constraints). ImplicationTherefore, LP-based formulations apply to both problems, although heuristics are often used in practice for line balancing. Final AnswerTrue

Question 9

Project scheduling: interpretation of negative slack/float  When an activity shows negative slack (negative float) in a network schedule, what does it indicate for the overall program status and resources? Choose the most accurate statement.

Accepted Answer

ConceptSlack (float) is the allowable delay of an activity without affecting project dates. Negative slack means the required finish date is earlier than the earliest achievable finish—indicating the schedule is already behind. ImplicationsNegative float typically requires acceleration measures (e.g., crashing, fast-tracking, or allocating more resources) to meet deadlines. Final AnswerThe programme is behind schedule and additional resources are required to finish on time

Question 10

Cost-volume-profit (CVP): For fixed cost F, variable cost per unit V, and selling price per unit P, the break-even point in units equals…

Accepted Answer

Introduction / Context:Break-even analysis is a foundation of operations and manufacturing economics. It determines the output level where total revenue equals total cost, i.e., neither profit nor loss. The relationship among fixed cost, variable cost per unit, and selling price per unit leads directly to a simple formula for break-even units. Given Data / Assumptions: Fixed cost F is independent of volume within the relevant range. Variable cost per unit V and selling price per unit P are constant over the range considered. No inventory change; units produced = units sold. Concept / Approach:Total cost = F + V * Q. Total revenue = P * Q. At break-even, P * Q = F + V * Q. Solve for Q to obtain the units required to cover fixed cost given the contribution margin (P − V) per unit. Step-by-Step Solution: Set P * Q = F + V * Q.Rearrange → (P − V) * Q = F.Solve → Q = F / (P − V). Verification / Alternative check:Check units: numerator is currency, denominator is currency per unit; result is in units. Test a quick example: F = 10,000; P = 100; V = 60 → Q = 10,000 / 40 = 250 units; revenue 25,000, total cost 10,000 + 60250 = 25,000 → balanced. Why Other Options Are Wrong:F/(P+V) ignores contribution margin; P/(P−V) lacks fixed cost; (FP)/(P−V) overstates units; F*(P−V) is dimensionally incorrect (currency squared). Common Pitfalls:Using total variable cost instead of per-unit variables without consistent units; forgetting price or variable cost changes at different volumes; ignoring capacity constraints. Final Answer:F / (P - V)

Question 11

Project management (CPM/PERT): What is the slack (float) of a critical activity on the critical path?

Accepted Answer

Introduction / Context:Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are used to plan, schedule, and control projects. Activities on the critical path determine the project duration. Understanding slack (float) clarifies which activities have scheduling flexibility and which do not. Given Data / Assumptions: Well-defined network with activity durations and precedence relationships. Earliest and latest start/finish times computed by forward/backward passes. Critical path identified as the longest-duration path through the network. Concept / Approach:Total slack (float) = Latest Start − Earliest Start = Latest Finish − Earliest Finish. For activities on the critical path, earliest and latest times coincide because any delay directly delays project completion. Hence, slack equals zero for all critical activities. Step-by-Step Solution: Perform forward pass → compute earliest event/finish times.Perform backward pass → compute latest allowable times without delaying completion.For critical activities → ES = LS and EF = LF → Slack = 0. Verification / Alternative check:Move a critical activity by even one time unit; the project finish moves by the same amount, confirming zero float. Noncritical activities can shift within their float without affecting completion date. Why Other Options Are Wrong:Maximum or average slack applies to noncritical activities; negative slack refers to imposed deadlines tighter than calculated schedule and indicates schedule compression needs, not a property of critical activities. Common Pitfalls:Confusing free float with total float; assuming multiple critical paths cannot exist— they can, and all critical activities still have zero slack. Final Answer:Zero slack

Question 12

Network planning (PERT/CPM): understanding a dummy activity In a project network diagram, what is a “dummy activity” used for, and how is it represented visually?

Accepted Answer

Introduction / Context:Project scheduling with PERT/CPM frequently requires representing logical precedence accurately. A special construct called a dummy activity is introduced to maintain correct relationships among real activities without implying extra work. This question checks recognition of the purpose, properties, and standard drawing convention of dummy activities. Given Data / Assumptions: We are working with classic arrow-on-activity (AOA) networks. The network must reflect correct precedence and avoid false parallelism. Dummy activities serve only for logic, not for work execution. Concept / Approach:In AOA networks, each activity is an arrow and each event is a node. Sometimes two different activities share the same start and end events, or a particular sequencing must be distinguished. A dummy activity (a dotted arrow) is inserted to preserve uniqueness of activity representation and to encode correct precedence when required by the logic but without adding work. Step-by-Step Solution:Identify the role: logic maintenance only, no physical work.Recognize standard notation: drawn as a dotted/broken arrow between events.Attribute durations/resources: set to zero; it consumes no time, manpower, or cost.Conclude: all listed statements (dotted line, artificial, no time/resources) are true. Verification / Alternative check:Compare early/late times: introducing a dummy does not change the critical path or total duration; it merely ensures correct dependency representation. Why Other Options Are Wrong:Any option implying a real duration or resource load contradicts the definition of a dummy activity. Common Pitfalls:Confusing a dummy with a milestone; a milestone is an event (node), whereas a dummy is a zero-duration arrow used to model logic. Final Answer:All of these

Question 13

Thermal power plant logistics From the coal handling plant to the boiler bunkers, which material handling equipment is most commonly used to transport coal continuously?

Accepted Answer

Introduction / Context:Efficient fuel handling is essential in thermal power stations. Coal must be moved reliably from unloading points to stockyards and onward to boiler bunkers. The choice of equipment balances capacity, continuity, safety, and operating cost. Given Data / Assumptions: Large, continuous throughput is required (hundreds of tonnes per hour). The path from coal handling to bunkers is generally fixed and long. Equipment must operate continuously with minimal manual intervention. Concept / Approach:Belt conveyors provide steady, continuous transport over long distances with gentle handling and high capacity. They integrate well with crusher houses, transfer towers, and tripper systems that distribute coal into multiple bunkers. Alternative equipment like bucket conveyors or cranes is typically used for intermittent or vertical lifts, not for long continuous runs. Step-by-Step Solution:Assess need: continuous, high-capacity movement.Match technology: belt conveyor best fits long, fixed routes and high tonnage.Confirm plant practice: tripper or shuttle conveyors commonly feed multiple bunkers. Verification / Alternative check:Typical plant layouts show conveyor galleries bridging CHP to boiler house bunkers, confirming industry standard practice. Why Other Options Are Wrong:Bucket conveyors are for short vertical transfers; cranes and forklifts are intermittent and labor-intensive; pneumatic tubes are unsuitable for coarse bulk solids like coal. Common Pitfalls:Underestimating dust control, belt cleaning, and fire detection requirements along the conveyor route. Final Answer:Belt conveyor

Question 14

Value engineering focus In value engineering (VE), which guiding idea receives the most important consideration when analyzing and improving a product or process?

Accepted Answer

Introduction / Context:Value engineering is a systematic method to improve the “value” of goods or services by examining function. Value is often expressed as Value = Function / Cost. Rather than cutting cost indiscriminately, VE seeks to deliver the required functions at the lowest life-cycle cost consistent with performance, quality, and safety. Given Data / Assumptions: Project team applies VE during design or process planning. Customer-required functions are documented and prioritized. Life-cycle cost is considered, not just initial price. Concept / Approach:The heart of VE is the function concept: clearly define what the product must do, in verb–noun format (e.g., “support load,” “prevent leakage”). Once essential and secondary functions are understood, alternatives are generated to achieve them more economically without degrading performance. This prevents “penny wise, pound foolish” cost cuts that harm function or quality. Step-by-Step Solution:Define essential functions using FAST or similar tools.Evaluate alternative materials, processes, or configurations.Select the option that meets function at the lowest justified life-cycle cost. Verification / Alternative check:Successful VE cases show equal or improved performance with reduced cost because the function was preserved while waste was eliminated. Why Other Options Are Wrong:Cost or profit objectives alone can compromise function. Customer satisfaction is crucial but must be achieved through reliably delivering required functions. Aesthetics may be a secondary function, not the sole focus. Common Pitfalls:Confusing VE with cost cutting; skipping function analysis; ignoring user needs and life-cycle impacts. Final Answer:Function concept (what it must do)

Question 15

Interpreting positive slack (float) in project scheduling When an activity in a CPM/PERT schedule has positive slack, what does it indicate for the project and resources?

Accepted Answer

Introduction / Context:Sensitivity to float (slack) values helps project managers prioritize activities. Slack indicates how much an activity can slip without affecting key dates or overall completion, guiding resource leveling and sequencing decisions. Given Data / Assumptions: Deterministic CPM network with calculated early/late dates. Positive slack means Late Start > Early Start or Late Finish > Early Finish. Critical path activities have zero total float. Concept / Approach:Total float for an activity is TF = LF − EF or LS − ES. If TF > 0, the activity can be delayed by TF units without delaying the project finish. This flexibility may be used to reallocate crews, reduce peaks in resource demand, or resolve conflicts, while preserving the planned completion date. Step-by-Step Solution:Compute early and late event times by forward and backward pass.Find float: TF = LS − ES = LF − EF.Interpret TF > 0: the activity has schedule leeway; project finish remains unchanged. Verification / Alternative check:Resource leveling often delays noncritical tasks within their float; when done properly, the project completion date does not slip, confirming the meaning of positive slack. Why Other Options Are Wrong:“Behind schedule” implies negative float. “On the critical path” implies zero float. “Any one of the above” is not possible because positive slack has a specific meaning. Common Pitfalls:Misusing float of a near-critical path; repeated consumption of float can make a path critical. Final Answer:Extra scheduling flexibility is available without delaying project completion

Question 16

Project time–cost trade-off terminology What is the essential condition for “decompression” of an activity (i.e., relaxing a previously crashed activity) in time–cost analysis?

Accepted Answer

Introduction / Context:Time–cost trade-off (crashing) shortens project duration by increasing activity direct costs. When schedule pressure eases, managers may “decompress” activities—reversing some crashing to reduce costs. Understanding the boundary conditions prevents invalid changes to baseline logic and durations. Given Data / Assumptions: Each activity has a normal time and a crash time with corresponding costs. Crashing reduces duration toward crash time at higher cost; decompression is the reverse movement toward normal time. Network logic and precedence are unchanged. Concept / Approach:Normal time is the standard (uncrashed) duration. Decompression can only restore duration back toward this normal point; it cannot increase duration beyond normal without redefining scope or logic. Thus, the essential condition is that decompression is bounded by the normal time of the activity. Project duration may or may not change depending on whether the decompressed activity lies on the current critical path. Step-by-Step Solution:Identify crashed activities and their current durations.Move duration back toward normal to reduce direct cost.Ensure duration after decompression ≤ normal time limit (i.e., not exceeding normal time).Recalculate floats and critical path to see if project duration changes. Verification / Alternative check:Cost–slope tables show valid duration range: crash time ≤ allowed ≤ normal time. Any value beyond normal time is outside the defined envelope. Why Other Options Are Wrong:Project duration need not change (option a). Exceeding normal time (option b) contradicts the defined range. Option e suggests going below crash time, which is not allowed. Common Pitfalls:Forgetting that decompression on a noncritical activity will not affect project duration, but may improve resource leveling and reduce direct costs. Final Answer:An activity can be decompressed only up to its normal (unchanged) time, not beyond

Question 17

Cost comparison across production types For batch production versus jobbing (one-off) production, how does the unit cost typically compare, assuming similar quality and technology?

Accepted Answer

Introduction / Context:Manufacturing economics differ by production system choice: jobbing (one-of-a-kind), batch, and mass production. Understanding how unit cost trends change with volume guides quoting, process planning, and capacity investment decisions. Given Data / Assumptions: Product design and quality requirements are comparable. Learning effects and setup amortization apply with repeated batches. Overheads and tooling are allocated appropriately. Concept / Approach:Batch production runs groups of identical items, distributing setup time and tooling cost over multiple units, improving labor learning, and enhancing material utilization. Jobbing production lacks repetition; unique setups dominate each unit, raising unit cost. Therefore, unit cost in batch production is typically lower than in jobbing as economies of repetition are realized. Step-by-Step Solution:Identify cost contributors: setup, direct labor, materials, overheads.Recognize repetition in batches reduces setup per unit and increases operator learning.Infer: total cost per unit in batch < jobbing, all else equal. Verification / Alternative check:Cost-versus-volume curves show declining average cost with increasing lot size up to a practical minimum, before inventory and changeover costs dominate. Why Other Options Are Wrong:“Same” or “independent” contradict economic principles; “higher in batch” is unusual unless batch sizes are extremely small or changeover costs are mismanaged. Common Pitfalls:Ignoring inventory carrying cost and obsolescence; excessively large batches can raise total system cost even if unit conversion cost is low. Final Answer:Lower unit cost in batch production

Question 18

Work measurement technique suitability The statement “Sampling (work sampling) method of determining standard time is profitable for long-cycle operations.” Evaluate its correctness.

Accepted Answer

Introduction / Context:Work measurement establishes standard times for planning and control. Two common techniques are direct time study (stopwatch) and work sampling. Selecting the appropriate method depends on cycle length, repetition, and variability of tasks. Given Data / Assumptions: Operations considered have long or irregular cycles, possibly with significant nonproductive elements. We seek reliable estimates of utilization and time standards. Statistical sampling with confidence bounds is acceptable. Concept / Approach:Work sampling observes activities at random intervals and estimates the proportion of time spent on defined categories. It is effective when cycles are long, irregular, or a mixture of tasks makes continuous timing impractical. Stopwatch time study excels for short, repetitive, well-defined cycles. Therefore, for long-cycle operations, work sampling is an efficient and “profitable” (cost-effective) approach to obtain standards and utilization data. Step-by-Step Solution:Define activity categories (productive, setup, delay, etc.).Plan a statistically valid sample size for desired confidence.Conduct random observations; compute proportions and standard times where applicable. Verification / Alternative check:Confidence intervals narrow as observations grow; when long cycles prevent many continuous timings, sampling yields robust estimates faster. Why Other Options Are Wrong:Restricting work sampling only to machine-paced or micro-cycles misunderstands its strength; direct time study suits micro-cycles better. Common Pitfalls:Nonrandom observation schedules bias results; unclear category definitions reduce usefulness. Final Answer:Correct

Question 19

Nature of break-even analysis Break-even analysis (cost–volume–profit) is most appropriately considered a:

Accepted Answer

Introduction / Context:Break-even analysis determines the output level where total revenue equals total cost. It guides pricing, volume targets, and feasibility for new products or capacity decisions. Given Data / Assumptions: Fixed costs are constant over the relevant range. Variable cost per unit and selling price per unit are constant. Sales mix and efficiency remain stable. Concept / Approach:These assumptions usually hold only in the short run over a limited range of output. In the long run, fixed costs may step up, variable costs and prices change, and scale effects alter cost behavior. Hence, break-even is a short-term, within-range decision tool to test sensitivity of profit to volume. Step-by-Step Solution:Define contribution: contribution per unit = price − variable cost.Compute break-even units: fixed cost / contribution.Use for short-run planning under stable assumptions. Verification / Alternative check:When price or variable cost changes with volume, the linear break-even line loses validity—confirming its short-run applicability. Why Other Options Are Wrong:Long-term analysis requires dynamic costs and investments; “timing-independent” and “purely qualitative” mischaracterize a quantitative tool. Common Pitfalls:Using break-even outside the relevant range; ignoring capacity constraints or multi-product complexities. Final Answer:Short term analysis

Question 20

Break-even computation – small scale unit A small-scale unit has fixed cost Rs. 5,000 per month. Variable cost is Rs. 20 per piece and selling price is Rs. 30 per piece. What is the monthly break-even production (in pieces)?

Accepted Answer

Introduction / Context:Break-even analysis helps determine the output where total revenue equals total cost, resulting in zero profit and zero loss. It is widely used for pricing and production planning in small enterprises. Given Data / Assumptions: Fixed cost per month = Rs. 5,000. Selling price per unit = Rs. 30 per piece. Variable cost per unit = Rs. 20 per piece. Linear cost and price behavior within the relevant range. Concept / Approach:Break-even units (Q_BE) are computed from the contribution per unit. Contribution per unit = Price − Variable cost. Break-even occurs when Fixed cost = Contribution per unit * Q_BE, so Q_BE = Fixed cost / Contribution per unit. Step-by-Step Solution:Compute contribution per unit: 30 − 20 = 10 Rs/piece.Set equation: 5,000 = 10 * Q_BE.Solve for Q_BE: Q_BE = 5,000 / 10 = 500 pieces per month. Verification / Alternative check:Check totals at 500 pieces: Total revenue = 500 * 30 = Rs. 15,000; Total variable cost = 500 * 20 = Rs. 10,000; Add fixed cost 5,000 → Total cost = Rs. 15,000. Revenue equals cost, confirming break-even. Why Other Options Are Wrong:300 and 460 understate output; revenue would be less than total cost. 1000 overstates output; revenue would exceed cost, yielding profit. Common Pitfalls:Forgetting to use contribution (price − variable cost) instead of price alone; ignoring fixed cost changes at different capacity levels. Final Answer:500

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