Capacity Planning Under Variability and UncertaintyIntroductionCapacity requirement planning (CRP) is often introduced as a comparison between required workload and available productive hours. That comparison is necessary, but it is not sufficient when production systems operate under uncertainty. Demand fluctuates, processing times differ between jobs, machines fail, employees are absent, materials arrive late, and output may be rejected because of quality losses. A plan that is feasible under average conditions may fail repeatedly in actual operation. Capacity planning under variability therefore concerns not only how much capacity is required, but also how much capacity must be protected against uncertainty, where that protection should be located, and how much risk management is economically justified. The central managerial problem is to balance utilization, responsiveness, cost, reliability and resilience. This chapter develops a risk-based approach to capacity planning. It combines deterministic workload calculations with probability distributions, scenario analysis, sensitivity analysis, safety capacity, queuing concepts, simulation and supply-disruption analysis. The emphasis is on postgraduate-level interpretation: managers must understand not only the calculations, but also the assumptions, model limitations and organizational consequences of capacity decisions. Learning ObjectivesAfter studying this chapter, the reader should be able to: - distinguish variability, uncertainty, risk and ambiguity in capacity planning;
- calculate effective capacity after considering availability, performance, quality, absenteeism and yield loss;
- evaluate demand, processing-time, downtime and supply-disruption scenarios;
- explain why high utilization increases waiting time and reduces operational responsiveness;
- determine safety capacity using service-level and risk-based reasoning;
- apply sensitivity analysis and basic simulation logic to capacity decisions;
- formulate an integrated capacity plan and assess its managerial, ethical and governance implications.
1. The Nature of Variability and UncertaintyVariability refers to observable differences in events or operating conditions. Examples include different processing times for different products, daily fluctuations in demand and variation in machine repair duration. Variability may be represented statistically when historical data are available. Uncertainty refers to incomplete knowledge about future conditions. A new product may have no reliable demand history, or the probability of a geopolitical supply interruption may be difficult to estimate. Risk exists when uncertain outcomes and their probabilities can be described sufficiently to support decisions. Ambiguity exists when alternative interpretations, models or probability estimates are plausible. Capacity decisions are affected by several interacting sources: | Source | Typical manifestation | Capacity consequence |
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| Demand variation | Peaks, seasonality, forecast error | Required output changes over time | | Processing-time variation | Product mix, learning, rework | Workload becomes uncertain | | Downtime | Failure, setup, maintenance, utilities | Available hours decline | | Absenteeism | Illness, turnover, leave | Labor hours and skills decline | | Yield loss | Scrap, defects, rework | More input is required for good output | | Supply disruption | Late or defective materials | Capacity becomes unusable or unbalanced | | Policy variation | Overtime rules, batch sizes, priorities | Nominal capacity differs from practical capacity |
A key insight is that sources of uncertainty do not simply add independently. For example, a material shortage can create idle labor, while an urgent demand peak can increase overtime, fatigue and quality losses. Consequently, capacity should be modeled as a system rather than as a single number. 2. From Rated Capacity to Effective and Risk-Adjusted Capacity2.1 Basic capacity definitionsDesign capacity is the theoretical maximum output under ideal conditions. Effective capacity is the maximum output under stated operating conditions, including planned breaks, setups, maintenance and normal organizational constraints. Actual output is the output achieved in a particular period. If a resource has N identical machines, H scheduled hours per machine, and r units per hour, its theoretical time capacity is: Cd = N × H × r where Cd is design capacity in units per planning period. This equation assumes that all machines are available, product mix is constant, quality is perfect and the rate is stable. These assumptions are rarely realistic. A time-based representation is usually safer for mixed products. If job type i requires standard time ti and planned quantity Qi, total workload is: W = ∑(i=1 to m) Qi × ti + S where W is required workload in labor-hours or machine-hours, m is the number of job types and S is setup and other planned time in the same units. Capacity is feasible only when available productive hours are at least equal to workload, subject to timing and skill constraints. 2.2 Effective capacity with lossesLet scheduled hours be Hs. If planned availability is A, performance relative to standard rate is P, and first-pass yield is Y, then effective productive hours expressed as good-output-equivalent hours are: He = Hs × A × P × Y Here, A, P and Y are proportions between 0 and 1. Availability excludes planned or unplanned time during which the resource cannot run; performance captures speed losses; yield captures the proportion of output accepted without requiring replacement or rework. The formulation is conceptually related to overall equipment effectiveness, although exact definitions must be aligned with the organization’s measurement system. If the standard output rate is r, good output capacity is: Ce = Hs × A × P × Y × r Units are consistent: hours × units/hour × dimensionless factors = good units. The equation assumes that losses are multiplicative and sufficiently separable. If downtime, speed and quality are statistically dependent, direct multiplication may misstate capacity. Worked Example 1: Effective machine capacityA machine is scheduled for 2 shifts of 8 hours on 20 days, giving Hs = 320 hours per month. Planned and unplanned availability is 0.90, performance is 0.95 and first-pass yield is 0.98. The standard rate is 10 units per hour. Ce = 320 × 0.90 × 0.95 × 0.98 × 10 Ce = 2,679.84 good units per month Thus, practical good-output capacity is approximately 2,680 units, not the design value of 3,200 units. The combined loss is approximately 16.3% of theoretical output. A plan based on 3,200 units would therefore contain a substantial hidden shortfall. 2.3 Labor capacity and absenteeismFor a labor group with Ne employees, scheduled hours per employee h, attendance rate a, and skill qualification factor q, available qualified hours are: HL = Ne × h × a × q The qualification factor is useful when not every employee can perform every task. It should not be used to conceal poor cross-training; its definition must be documented. If absenteeism differs by day or skill, an average attendance rate may be inadequate, and scenario or distribution-based analysis is preferable. 2.4 Yield loss and input requirementsIf the required saleable quantity is Qg and yield is Y, the required input quantity is: Qi = Qg ÷ Y This applies when yield is expressed as the proportion of input becoming acceptable output and when rework is not already included in the processing-time standard. For example, producing 1,000 good units at a yield of 0.95 requires approximately 1,052.6 input units. If rework consumes capacity, both additional material and additional processing time must be modeled. 3. Modeling Demand and Workload Uncertainty3.1 Demand distributions and forecast errorA forecast is not a commitment that demand will equal one number. It is an estimate with an error distribution. If demand in period t is Dt and the forecast is Ft, forecast error may be defined as: et = Dt − Ft The mean absolute deviation is: MAD = (1/n) × ∑(t=1 to n) |et| The root mean square error is: RMSE = √[(1/n) × ∑(t=1 to n) et²] MAD is less sensitive to extreme errors than RMSE. Neither metric alone proves that future errors will follow the historical pattern. Structural changes, promotions and new competitors can invalidate historical estimates. When demand is approximately normal with mean μD and standard deviation σD, a capacity level covering probability α may be estimated as: C_α = μD + z_α × σD where z_α is the standard-normal quantile satisfying P(D ≤ C_α) = α. This approximation is inappropriate for highly skewed, intermittent or bounded demand unless a suitable transformation or empirical distribution is used. 3.2 Workload rather than unit demandCapacity risk depends on workload, not merely units. With several products, workload is: W = ∑(i=1 to m) Di × ti If demand quantities are random, workload is random as well. Under independence between product demands, its variance is: Var(W) = ∑(i=1 to m) ti² × Var(Di) If demands are correlated, covariance terms must be included: Var(W) = ∑(i=1 to m) ti² Var(Di) + 2∑(i<j) ti tj Cov(Di,Dj) Ignoring positive correlation understates capacity risk. For example, several products may peak simultaneously during the same market event. 4. Downtime, Absenteeism, Yield and Supply Disruption4.1 Downtime and reliabilityFor a repairable machine, availability can be approximated by: A = MTBF ÷ (MTBF + MTTR) where MTBF is mean time between failures and MTTR is mean time to repair. This steady-state relationship assumes stable failure and repair behavior, a consistent definition of failure, and no major effects from preventive maintenance or spare-part shortages. If planned downtime is included, the numerator and denominator must be defined consistently. Reliability analysis should distinguish random failure from common-cause failure. Ten machines may appear to provide redundancy, but a shared electrical system or common supplier can cause simultaneous loss of capacity. 4.2 Absenteeism and skill bottlenecksAverage labor capacity can be misleading when absenteeism affects a scarce skill. A 5% overall absence rate may be manageable, while a 5% absence rate among certified welders may stop an entire production cell. Capacity plans should therefore model skill pools, cross-training and substitution rules. A practical approach is to create scenarios such as: - normal attendance: 95%;
- adverse attendance: 88%;
- critical-skill absence: one or more key qualifications unavailable;
- recovery condition: overtime or temporary labor available with stated lead time.
The analysis should report both total lost hours and the number of orders affected by skill-specific shortages. 4.3 Yield loss and quality capacityQuality losses reduce capacity in two ways. Scrap requires replacement production, while rework consumes time that could have been used for new orders. If s is scrap proportion and rw is the additional rework time per defective unit, the expected workload may be represented as: Wtotal = Q × t × (1 + s × rw/t) where Q is planned saleable output and t is standard processing time per unit. This expression assumes a stable defect rate and one defined rework path. If rework has a different routing or queue, it should be modeled as a separate workload stream. 4.4 Supply disruption and effective capacityA machine’s nominal capacity has little value when required materials are unavailable. Supply disruption should be represented through at least three dimensions: probability, duration and consequence. A simple expected-loss measure is: Expected capacity loss = ∑(k=1 to K) pk × Lk where pk is the probability of disruption scenario k and Lk is the capacity loss under that scenario. Expected loss alone is insufficient for low-probability catastrophic events; tail consequences and recovery time must also be considered. Useful mitigations include dual sourcing, strategic inventory, substitute materials, supplier capacity reservations, postponement, design standardization and contractual recovery provisions. Each mitigation creates cost and sometimes new risk, such as quality variation from an unqualified second source. 5. Scenario Planning and Sensitivity AnalysisScenario planning evaluates coherent combinations of assumptions rather than changing one variable in isolation. A capacity scenario may specify demand, mix, uptime, attendance, yield, material availability, overtime and recovery policy. | Scenario | Demand | Availability | Attendance | Yield | Management interpretation |
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| Base | 100% | 90% | 95% | 98% | Operating plan | | Upside | 115% | 90% | 95% | 98% | Growth response required | | Adverse operations | 100% | 82% | 88% | 94% | Stress test | | Combined stress | 115% | 82% | 88% | 94% | Resilience threshold |
Sensitivity analysis changes one assumption while holding others constant, or uses a structured design to identify interactions. If required capacity is R and effective capacity is C, utilization is: u = R ÷ C A sensitivity table can show how utilization changes as demand or availability changes. The most influential variables deserve improved measurement, preventive action or explicit management reserves. Sensitivity is not the same as probability: a variable can have a large effect but low likelihood, or a small effect but high likelihood. 6. Safety Capacity and Service-Level PlanningSafety capacity is capacity deliberately retained to absorb uncertainty. It may take the form of spare machines, flexible labor, overtime rights, cross-training, reserved supplier capacity, time buffers or modular equipment. If required workload is approximately normal with mean μW and standard deviation σW, and effective capacity is treated as a fixed level, a capacity target with service probability α is: C_α = μW + z_α × σW The safety capacity above the mean is: SC = z_α × σW This calculation assumes a stable distribution and a clearly defined service event, such as “total workload does not exceed capacity in the planning period.” It does not automatically guarantee on-time delivery because timing, sequencing and bottleneck location also matter. A risk-based decision compares the cost of additional capacity with the cost of shortage. If the marginal cost of one unit of safety capacity is cC and the expected shortage cost avoided is cS, additional capacity is economically justified when the expected avoided shortage cost exceeds its cost. In practice, shortage cost may include lost contribution, expediting, penalties, reputational damage and safety consequences, not merely overtime. 7. Queuing Concepts and the Utilization ParadoxA resource can have average capacity greater than average demand and still create unacceptable waiting. Queuing theory explains why. As utilization approaches 100%, waiting time can increase sharply because arriving jobs encounter work already in process and because variability accumulates. For a simple single-server M/M/1 queue, arrivals are Poisson with rate λ, service times are exponential with rate μ, and λ < μ. Utilization is: ρ = λ ÷ μ The expected time in the system is: W = 1 ÷ (μ − λ) and expected number in the system is: L = λ × W These results rely on the stated queue assumptions and should not be applied literally to every manufacturing system. They nevertheless demonstrate the utilization effect. In a more general queue, the Kingman approximation for a single-server, first-come-first-served process is: Wq ≈ [ρ ÷ (1 − ρ)] × [(ca² + cs²) ÷ 2] × E[S] where Wq is approximate mean waiting time, ca is the coefficient of variation of interarrival times, cs is the coefficient of variation of service times, and E[S] is mean service time. The coefficient of variation is standard deviation divided by mean. The approximation assumes a stable queue and is most useful for managerial insight rather than exact scheduling. The implication is important: reducing variability can be as valuable as adding nominal capacity. Smaller batches, reliable material supply, preventive maintenance, standardized work and better sequencing may reduce waiting without purchasing another machine. 8. Simulation for Capacity RiskSimulation is appropriate when interactions, distributions and operating rules are too complex for closed-form equations. A discrete-event simulation may represent arrivals, routing, setup, machine failures, repairs, labor calendars, quality checks, queues and dispatching priorities. A basic Monte Carlo procedure is: - define the planning horizon and performance measures;
- assign probability distributions or empirical samples to uncertain inputs;
- generate random observations for demand, processing time, downtime and yield;
- execute the production logic for one replication;
- record output, utilization, queue time, shortages and service performance;
- repeat for many replications;
- summarize the distribution of outcomes and compare alternatives.
Simulation outputs should include confidence intervals, not just one average. Initial transient conditions should be handled through a warm-up period where appropriate. Random-number seeds, input data, validation tests and model version control are governance requirements. Simulation is not a substitute for knowledge. A highly detailed model with poor assumptions can produce precise but misleading results. Validation should include face validation by operational experts, comparison with historical performance and sensitivity tests for key assumptions. 9. Integrated Capacity-Planning FrameworkA robust planning process can be organized into eight stages: Stage 1: Define the decision and service promiseSpecify the horizon, products, customer service requirement, bottleneck resources and consequences of failure. “Enough capacity” is meaningless unless the required service level is defined. Stage 2: Build the workload modelTranslate demand and product mix into processing, setup, inspection, material-handling and rework requirements. Use standard times that are current and traceable. Stage 3: Estimate effective capacityAdjust scheduled hours for availability, performance, quality, attendance, skills, planned maintenance and calendar restrictions. Identify bottlenecks by period, not only in aggregate. Stage 4: Characterize uncertaintyUse historical distributions, forecast-error analysis, supplier evidence, engineering judgment and scenario workshops. Document assumptions and distinguish measured data from subjective estimates. Stage 5: Test scenarios and sensitivitiesEvaluate base, upside, downside and combined-stress conditions. Identify threshold points at which overtime, subcontracting, rescheduling or capital investment becomes necessary. Stage 6: Select capacity protectionOptions include flexible shifts, overtime, cross-training, temporary labor, preventive maintenance, spare parts, subcontracting, dual sourcing, finished-goods inventory and modular capital. The choice should consider reversibility and lead time. Stage 7: Simulate or pilot critical decisionsUse discrete-event simulation for complex networks and pilot tests for new work methods. Compare not only average output but also tail risk, queue time and recovery performance. Stage 8: Monitor and updateTrack leading indicators such as forecast bias, processing-time dispersion, absenteeism by skill, failure intensity, supplier confirmation reliability, queue length and first-pass yield. Capacity planning is a control process, not a once-a-year calculation. 10. Illustrative Case: Northstar ComponentsThe following case is fictional and is intended for analytical instruction. BackgroundNorthstar Components produces precision pump housings on a machining cell. Monthly customer demand is forecast at 4,800 good units. Each unit requires 0.50 machine-hours. The cell has three machines, each scheduled for 176 hours per month. Historical availability is 0.88, performance is 0.94 and first-pass yield is 0.97. Demand standard deviation is 420 units. The operations director is considering whether to accept a new contract that would add 12% to demand. ProblemThe average calculation suggests that three machines may be adequate, but the plant has experienced late deliveries during demand peaks and material shortages. Management needs to evaluate average feasibility, service-level capacity and practical risk. Analysis of current demandScheduled machine-hours are: Hs = 3 × 176 = 528 hours Effective good-output-equivalent hours are: He = 528 × 0.88 × 0.94 × 0.97 = 423.0 hours approximately Good-output capacity is therefore: Ce = 423.0 ÷ 0.50 = 846 units? The preceding expression exposes a unit mistake: 423 hours divided by 0.50 hours per unit equals 846 units, which is inconsistent with the likely output from three machines. The correct interpretation is that 0.50 hours per unit applies to one machine, so 423 effective machine-hours produce: Ce = 423.0 ÷ 0.50 = 846 units per machine-equivalent? This reveals that the stated standard is incompatible with the demand and asset count if interpreted literally: three machines at 176 hours and 0.50 hours per unit have design capacity 3,168 units, not 4,800. The data must therefore be clarified before a decision. If the intended processing time is 0.10 machine-hours per unit, effective capacity becomes approximately 4,230 units, still below the 4,800-unit forecast. This diagnostic is itself a major CRP finding: inconsistent master data can invalidate sophisticated analysis. Northstar’s engineering review confirms that the correct standard is 0.10 machine-hours per unit, and that the forecast includes 12% subcontracted output not requiring the cell. Internal demand is therefore 4,224 units. Effective capacity of approximately 4,230 units leaves almost no average margin. Risk analysisAssuming internal demand is approximately normal, a 95% period service target requires: C95 = 4,224 + 1.645 × 420 = 4,915 units approximately The current effective capacity of 4,230 units is far below this risk-adjusted requirement. The contract would increase internal demand by 12%: Rcontract = 4,224 × 1.12 = 4,731 units That level is above average capacity and close to, but still below, the estimated 95% requirement before considering supply disruption. Approach and solutionNorthstar evaluates four alternatives: - add a fourth machine, with a six-month acquisition lead time;
- authorize weekend overtime equivalent to 60 machine-hours monthly;
- qualify a second supplier for a critical casting;
- reduce performance losses through tool-condition monitoring and standardized setup.
The recommended immediate plan combines supplier qualification, 40 machine-hours of flexible overtime and setup reduction. The fourth machine is approved conditionally, triggered if rolling three-month demand exceeds 4,600 units or if the 90th-percentile queue-time target is missed for two consecutive months. This staged decision avoids treating a forecast as certainty while preserving a path to expansion. Outcome and learning pointsThe case demonstrates that capacity analysis begins with data validation. It also shows that average capacity can conceal service failure, that subcontracted demand must be separated from internal workload, and that a portfolio of flexible and structural responses is often superior to a single large investment. Finally, risk-adjusted capacity should include supply and quality conditions, not just machine hours. 11. Technology, AI and Contemporary PracticeModern manufacturing execution systems, industrial internet platforms and advanced planning systems can provide near-real-time data on cycle time, downtime, queue length and quality. Digital twins can test alternative routings, maintenance policies and staffing plans before implementation. Machine-learning models may improve demand forecasts, failure prediction and processing-time estimation. However, predictive accuracy does not guarantee decision quality. Models can fail when operating conditions change, when data omit unplanned work, or when historical schedules encode unfair labor assumptions. AI-supported capacity planning should therefore include human review, data lineage, uncertainty intervals, drift monitoring and override authority. A useful governance principle is to separate prediction from policy. An algorithm may estimate a high probability of absenteeism, but management must still decide whether the response is cross-training, temporary labor, overtime or schedule redesign. Decisions affecting employee workload, safety or employment conditions require transparency and compliance with labor law and organizational policy. 12. Limitations, Ethics and GovernanceCapacity models can encourage managers to maximize utilization at the expense of safety, maintenance and employee well-being. Persistent overtime may appear to solve a capacity gap while increasing fatigue, defects and injury risk. Ethical capacity planning treats legal working-time limits, safe staffing and humane scheduling as constraints, not optional costs. Other governance concerns include: - misrepresenting effective capacity by excluding rework or unpaid labor;
- using optimistic supplier probabilities without evidence;
- hiding uncertainty through a single deterministic number;
- allocating scarce capacity in ways that unfairly discriminate among customers or workers;
- allowing AI systems to make unreviewed employment or safety decisions;
- failing to document assumptions used in investment approvals.
A defensible capacity plan should preserve an audit trail: data sources, definitions, formulas, scenario assumptions, model validation results, decision thresholds and approval responsibilities. Best-Practice ChecklistA professional capacity plan should: - calculate workload in time units as well as product units;
- distinguish design, effective, actual and risk-adjusted capacity;
- model bottleneck skills and materials explicitly;
- include downtime, attendance, yield, setup and rework;
- use distributions or scenarios rather than relying only on averages;
- test correlated and common-cause disruptions;
- examine queue time and service performance, not only utilization;
- compare flexible, structural and supply-side responses;
- validate data and simulation logic with operational experts;
- define trigger points for escalation and capacity expansion;
- report uncertainty and tail outcomes to decision makers;
- protect safety, legal compliance, fairness and employee well-being.
Chapter SummaryCapacity planning under variability and uncertainty extends conventional CRP by recognizing that demand, processing time, availability, attendance, yield and supply are not fixed. Design capacity must be converted into effective capacity through explicit loss factors, while mixed-product requirements should be expressed as workload hours. Demand and workload distributions support service-level planning, but correlation and distributional assumptions must be examined carefully. Scenario planning reveals how coherent combinations of adverse conditions affect feasibility. Sensitivity analysis identifies influential variables, while safety capacity provides protection against specified levels of uncertainty. Queuing theory explains why high utilization can produce disproportionate waiting, making variability reduction an important alternative to adding assets. Simulation is valuable when routing, failures, priorities and recovery rules interact, provided that the model is validated and its uncertainty is reported. The professional capacity planner integrates quantitative analysis with staged decisions, operational judgment, data governance, supply resilience and ethical responsibility. The objective is not maximum utilization; it is reliable, safe and economically sustainable performance under plausible future conditions. Key TermsVariability: Observable differences in demand, time, quality or operating conditions. Uncertainty: Incomplete knowledge about future events or their outcomes. Risk: Uncertainty whose possible outcomes and probabilities are sufficiently characterized for decision analysis. Design capacity: Theoretical maximum output under ideal conditions. Effective capacity: Practical capacity after planned and normal operating losses. Actual output: Output achieved during a specified period. Workload: Required processing and related time expressed in labor-hours or machine-hours. Availability: Proportion of scheduled time during which a resource is operational. Performance: Actual operating speed relative to the applicable standard speed. First-pass yield: Proportion of input producing acceptable output without rework. Safety capacity: Deliberately retained capacity used to absorb uncertainty. Service level: Probability or proportion of demand fulfilled within a specified requirement. Sensitivity analysis: Examination of how an output changes when an input assumption changes. Scenario analysis: Evaluation of coherent combinations of assumptions about future conditions. Utilization: Required workload divided by available capacity. Queuing: Waiting and service behavior arising when work arrives at constrained resources. Coefficient of variation: Standard deviation divided by the mean. Monte Carlo simulation: Repeated random sampling used to estimate a distribution of outcomes. Common-cause failure: A disruption that affects multiple resources because they share a cause. Resilience: The ability of a production system to absorb disruption and recover acceptable performance. Review QuestionsShort Answer Questions- Distinguish design capacity, effective capacity and actual output.
- Why should mixed-product capacity requirements be expressed in workload hours?
- State two limitations of using average demand in capacity planning.
- What is the utilization effect described by queuing theory?
- Identify three forms of safety capacity.
Long Answer Questions- Explain how availability, performance, yield, absenteeism and rework jointly influence effective capacity.
- Compare scenario analysis, sensitivity analysis and simulation as capacity-planning methods.
- Discuss the assumptions and managerial usefulness of the M/M/1 queue model.
- Develop a risk-based framework for responding to supply disruption.
- Critically evaluate the use of AI and digital twins in capacity requirement planning.
Analytical / Application Questions- A cell has 2,400 scheduled hours, availability of 0.86, performance of 0.93, yield of 0.96 and a standard rate of 2 units per hour. Calculate effective good-output capacity and explain the assumptions.
- Forecast workload is normally distributed with mean 10,000 hours and standard deviation 700 hours. Estimate capacity for a 90% service probability using z = 1.282, and calculate safety capacity above the mean.
- A plant is below average capacity but experiences long queues. Propose a diagnostic using variability, bottleneck, quality and dispatching data, and recommend two interventions other than purchasing a new machine.
Multiple Choice Questions with AnswersQuestion 1Which expression best represents effective good-output capacity when losses are modeled as separable factors? A. Ce = Hs × A × P × Y × r B. Ce = Hs + A + P + Y + r C. Ce = Hs × (A + P + Y) ÷ r D. Ce = Hs ÷ A × P × Y × r Correct Answer: A. Ce = Hs × A × P × Y × r Question 2A process has 1,000 scheduled hours, availability 0.90, performance 0.80, yield 0.95 and a rate of 5 units per hour. What is its effective good-output capacity? A. 3,420 units B. 3,600 units C. 3,420? D. 3,420 units after rounding Correct Answer: D. 3,420 units after rounding Question 3If demand is normally distributed with mean μ and standard deviation σ, which expression estimates capacity at service probability α? A. μ − z_α σ B. μ + z_α σ C. z_α ÷ (μ + σ) D. μ × z_α ÷ σ Correct Answer: B. μ + z_α σ Question 4What is the principal implication of utilization approaching 100% in a variable production system? A. Waiting time generally rises sharply B. Quality losses necessarily become zero C. Demand variation disappears D. Required capacity becomes independent of processing time Correct Answer: A. Waiting time generally rises sharply Question 5In the availability relationship A = MTBF ÷ (MTBF + MTTR), MTTR denotes: A. Mean time between requirements B. Mean total resource rate C. Mean time to repair D. Maximum time to recover demand Correct Answer: C. Mean time to repair Question 6Which issue is most likely to be missed by using only an overall absenteeism percentage? A. The effect of absence on scarce skills B. The existence of scheduled hours C. The definition of product demand D. The standard unit of currency Correct Answer: A. The effect of absence on scarce skills Question 7What is the main purpose of sensitivity analysis in capacity planning? A. To prove that one forecast is correct B. To identify how changes in assumptions affect decisions C. To eliminate all uncertainty from the model D. To replace operational data with intuition Correct Answer: B. To identify how changes in assumptions affect decisions Question 8A simulation replication in a capacity model should normally record which type of result? A. Only the most favorable output B. Output, queues, utilization and shortages C. Only the random-number seed D. Only the purchased-equipment cost Correct Answer: B. Output, queues, utilization and shortages Question 9If saleable output required is 1,000 units and yield is 0.80, how many input units are required, ignoring other constraints? A. 800 B. 1,000 C. 1,250 D. 1,800 Correct Answer: C. 1,250 Question 10Which is an example of safety capacity? A. Removing preventive maintenance B. Eliminating all cross-training C. Retaining flexible overtime or qualified backup labor D. Planning exactly at average demand with no reserve Correct Answer: C. Retaining flexible overtime or qualified backup labor
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