Operations Analytics and Decision-Making

Introduction and Context

Operations management increasingly depends on the systematic conversion of operational data into decisions. Firms collect information from enterprise-resource-planning systems, point-of-sale terminals, warehouse scanners, transport platforms, machine sensors, customer-service systems and financial records. Data alone, however, does not improve performance. Value is created when managers define relevant performance measures, analyse evidence appropriately, evaluate alternatives and implement decisions with suitable controls.

Operations analytics is the disciplined use of data, statistical methods, models and managerial judgement to understand operations and select actions. It supports decisions about capacity, inventory, quality, scheduling, sourcing, maintenance, service levels and continuous improvement. Its purpose is not to replace managers but to make assumptions visible, compare alternatives consistently and improve the speed and quality of decisions.

The chapter develops a practical analytics architecture covering key performance indicators (KPIs), dashboards, descriptive and predictive analytics, decision trees, optimization, linear programming, simulation, sensitivity analysis and multicriteria decision methods. It also examines data governance, ethical risks and the limitations of quantitative models.

Learning Objectives

By the end of this chapter, a learner should be able to:

1. Distinguish operational data, information, analytics and managerial decisions.
2. Design meaningful KPIs and dashboards aligned with strategic objectives.
3. Apply descriptive, diagnostic, predictive and prescriptive analytics.
4. Construct and interpret decision trees using expected monetary value.
5. Formulate a basic linear-programming model and interpret its solution.
6. Explain when simulation is preferable to analytical optimization.
7. Perform and interpret sensitivity analysis.
8. Apply multicriteria methods when cost is not the only relevant criterion.
9. Evaluate the governance, ethical and practical limitations of analytics.

1. From Data to Operational Decisions

A useful decision chain is:

data → information → insight → decision → action → feedback

Data are recorded observations, such as delivery times or defect counts. Information is organized data with context, such as the percentage of deliveries arriving late by route. Insight is an interpretation, such as the finding that late deliveries are concentrated on one carrier and one time window. A decision selects an action, while feedback determines whether the action achieved its intended result.

Operations decisions occur at three levels:

Analytics must match the decision horizon. A real-time dashboard may support dispatching but cannot by itself determine whether a factory should be relocated. Conversely, a long-term network model may be too slow and abstract for an urgent production interruption.

A sound analytics question is specific: Which products should receive scarce machine time next week to maximize contribution while meeting contractual demand and labour limits? An unsound question is simply: What can we learn from the data? The first question identifies the decision, constraints and performance criterion.

2. KPIs and Performance Measurement

A key performance indicator is a quantified measure linked to an important objective and used to guide action. A metric becomes a KPI when it has strategic or operational significance, a defined owner, a reliable data source, a reporting frequency and an agreed target.

2.1 Leading and lagging indicators

Lagging indicators measure results after performance occurs. Examples include profit, customer complaints, monthly defect rate and lost-time injury frequency. Leading indicators measure conditions or activities that influence future results, such as preventive-maintenance completion, training hours, schedule adherence and supplier audit closure.

A balanced KPI system combines both types. Relying only on lagging measures can cause managers to react too late. Relying only on leading measures can reward activity without proving outcomes.

2.2 Common operations formulas

The following measures are widely used. Definitions must be standardized because apparently similar measures can be calculated differently across departments.

Throughput rate is the number of completed units per unit of time:

Throughput has units such as units/hour. It should be calculated over a period in which output and operating time are measured consistently.

Capacity utilization compares actual output with effective capacity:

Effective capacity is achievable capacity under normal conditions, not necessarily theoretical design capacity. Utilization above 100% indicates inconsistent definitions or unsustainable overtime and should be investigated.

First-pass yield (FPY) is the proportion of units completing a process without rework:

Scrap and rework conventions must be stated. FPY is different from final yield, which may count units after rework.

On-time-in-full (OTIF) measures deliveries that meet both timing and quantity requirements:

An order delivered early but short is not OTIF unless the organization explicitly defines its policy otherwise.

Inventory turnover is commonly expressed as:

Both numerator and denominator must use the same valuation basis and period. Average inventory is often calculated as opening plus closing inventory divided by two, although more frequent averages are preferable when inventory fluctuates substantially.

Mean absolute deviation (MAD) measures average forecast error magnitude:

Here, A_t is actual demand in period t, F_t is forecast demand, and n is the number of periods. MAD has the same units as demand.

Mean absolute percentage error (MAPE) is:

It is unsuitable when actual demand is zero and can exaggerate errors for small denominators. Weighted or scale-dependent measures may be more appropriate.

2.3 KPI design principles

A strong KPI is relevant, clearly defined, controllable or influenceable by its owner, timely, comparable and resistant to manipulation. Managers should document the formula, numerator, denominator, exclusions, data source, owner, target, tolerance and escalation rule.

KPI conflicts are common. Maximizing machine utilization may increase inventory and reduce responsiveness. Minimizing purchasing price may increase defects, transport costs or disruption risk. A balanced scorecard or KPI hierarchy can connect financial, customer, process, people and sustainability outcomes.

Targets should be challenging but credible. If a target is impossible, employees may conceal problems or abandon the measure. If it is too easy, improvement stops. Incentive systems require special care because people often optimize what is rewarded rather than what the organization truly values—a phenomenon associated with Goodhart’s law.

3. Dashboards and Operational Visibility

A dashboard is a visual interface that presents selected information for a defined audience and decision purpose. It is not merely a collection of charts. Effective dashboards answer three questions: What is happening? Why does it matter? What action is required?

A useful dashboard architecture has three layers:

1. Strategic layer: a small number of outcome measures such as operating margin, OTIF, safety and carbon intensity.
2. Tactical layer: trends, comparisons, capacity gaps, supplier performance and forecast accuracy.
3. Operational layer: exceptions requiring immediate action, such as machine stoppages, overdue orders or stock-outs.

Design principles include displaying trends rather than isolated values, using consistent definitions, showing targets and tolerances, enabling drill-down from aggregate to root cause, and distinguishing missing data from zero performance. Colour should not be the only means of communication, because accessibility and printing may be affected.

Dashboards can create false confidence. A visually precise chart does not compensate for biased data, delayed updates or an inappropriate KPI. Managers should record data refresh time, quality status and the responsible data owner. Alerts should be exception-based; excessive alerts cause alarm fatigue.

4. The Analytics Hierarchy

4.1 Descriptive and diagnostic analytics

Descriptive analytics summarizes what has happened through totals, averages, distributions, control charts and trend analysis. Diagnostic analytics investigates why it happened using segmentation, drill-down, correlation analysis, process mapping and cause-and-effect analysis.

Averages require caution. If five processing times are 4, 4, 5, 5 and 22 minutes, the mean is 8 minutes but the median is 5 minutes. The mean is affected by the extreme observation; the median better represents a typical case. Managers should inspect variation, percentiles and outliers rather than relying on a single average.

Correlation does not establish causation. A relationship between overtime and defects may reflect a third factor, such as demand surges. Before acting, analysts should examine process knowledge, timing, alternative explanations and, where feasible, controlled tests.

4.2 Predictive analytics

Predictive analytics estimates future outcomes from historical and current data. Applications include demand forecasting, failure prediction, late-delivery prediction, staffing requirements and credit or supplier-risk assessment.

A forecast should be evaluated on data not used to fit the model. Time-series data require chronological validation; randomly mixing future observations into training data creates leakage. Accuracy should be compared with a simple baseline, such as a naive forecast equal to the previous period.

For a simple moving-average forecast with window size k:

This method assumes that recent observations are informative and that no strong trend or seasonal pattern is being ignored. Increasing k smooths noise but may make the forecast less responsive.

For a weighted moving average:

The weights w_i reflect the relative importance assigned to past observations. Forecast performance must be assessed using an appropriate loss measure, not selected solely because the forecast appears smooth.

4.3 Prescriptive analytics

Prescriptive analytics recommends actions under objectives and constraints. Optimization, simulation, decision analysis and multicriteria methods are prescriptive tools. Their output is conditional: a recommendation is valid only under the model’s data, assumptions and constraints.

5. Decision Trees and Expected Monetary Value

A decision tree represents sequential decisions and uncertain events. Squares denote decision nodes, circles denote chance nodes and branches represent alternatives or outcomes. Probabilities at each chance node must be mutually exclusive and collectively exhaustive.

For alternatives with uncertain payoffs, expected monetary value (EMV) is:

where a is an alternative, s is a state of nature, P(s|a) is its probability and V(a,s) is the payoff. This calculation assumes risk neutrality, reliable probabilities and payoffs expressed on a comparable basis. A risk-averse manager may prefer a lower-EMV alternative with less downside exposure.

Worked example: capacity expansion

An operations manager can install a small line or a large line. Demand may be high with probability 0.6 or low with probability 0.4. Payoffs, already expressed as incremental contribution after relevant costs, are:

Small-line EMV:

0.6 × 140,000 + 0.4 × 90,000 = 120,000

Large-line EMV:

0.6 × 220,000 + 0.4 × (−20,000) = 124,000

The large line has the higher EMV by $4,000. However, its low-demand loss is significant. The decision should therefore include risk appetite, financial resilience and the possibility of staged expansion. EMV is an aid to judgement, not an automatic instruction.

If perfect information about demand could be obtained before choosing, the expected value with perfect information would be:

0.6 × 220,000 + 0.4 × 90,000 = 168,000

The expected value of perfect information is $168,000 − $124,000 = $44,000. This is the maximum rational amount to pay for perfect information under the stated assumptions.

6. Optimization and Linear Programming

Optimization selects the best feasible solution according to an objective. Linear programming (LP) applies when the objective and constraints are linear and decision variables are continuous, or when integer restrictions are explicitly added through mixed-integer programming.

A general maximization LP is:

Here, x_j is the quantity of activity j, c_j is its contribution per unit, a_ij is resource usage, b_i is available resource i, and Z is total contribution. Units must be consistent: if c_j is dollars per unit, Z is dollars; each constraint must compare the same resource units.

An LP assumes proportionality, additivity, divisibility, certainty of coefficients and non-negativity unless otherwise stated. These assumptions may be unsuitable where setup costs, economies of scale, indivisible projects or uncertain demand are important.

Worked example: product mix

A workshop makes products A and B. Each A contributes $40 and uses 2 labour hours and 1 machine hour. Each B contributes $30 and uses 1 labour hour and 2 machine hours. Weekly resources are 100 labour hours and 80 machine hours.

Let x be units of A and y be units of B.

At the intersection of the two resource constraints:

2x + y = 100 and x + 2y = 80.

From the first equation, y = 100 − 2x. Substitution gives x + 2(100 − 2x) = 80, so −3x = −120, x = 40, and y = 20. The contribution is 40(40) + 30(20) = 2,200.

The feasible corner points include (0,0), (50,0), (0,40) and (40,20). Their contributions are $0, $2,000, $1,200 and $2,200 respectively. Therefore, the optimal continuous product mix is 40 units of A and 20 units of B, assuming all stated conditions hold.

The solution uses all labour and machine capacity. This does not prove that expanding either resource is worthwhile; the marginal value of extra capacity and the feasibility of market demand must also be examined. Solver software can find larger solutions, but managers must validate the model and interpret its output.

7. Simulation for Complex Operations

Simulation imitates the behaviour of a system over time or across repeated trials. It is valuable when queues, variability, feedback, probabilistic failures or nonlinear rules make exact optimization difficult.

A discrete-event simulation represents events such as arrivals, service completion, machine failure and replenishment. A Monte Carlo simulation repeatedly samples uncertain inputs to estimate a distribution of outcomes, such as total cost, waiting time or service level.

A basic simulation workflow is:

1. Define the decision problem, system boundary and performance measures.
2. Map entities, resources, states, events and rules.
3. Collect and validate input distributions.
4. Build and verify the model.
5. Validate results against observed system behaviour.
6. Run a warm-up period where initial conditions would distort results.
7. Use multiple replications and report confidence intervals.
8. Compare scenarios using common random numbers where appropriate.
9. Conduct sensitivity analysis and communicate assumptions.

For independent replication results Y₁,…,Y_R, the sample mean is:

The estimated standard error is s ÷ √R, where s is the sample standard deviation. An approximate 95% confidence interval for the mean is:

This interval relies on appropriate independent replications and the usual assumptions supporting the t-based estimate. It describes uncertainty in the estimated mean, not necessarily the entire range of individual outcomes.

Simulation does not find an optimum automatically. It evaluates specified policies. Optimization-simulation combines an optimizer with simulation but can be computationally expensive and vulnerable to noisy performance estimates.

8. Sensitivity and Scenario Analysis

Sensitivity analysis asks how a recommendation changes when an input or assumption changes. It identifies critical assumptions, fragile solutions and information priorities.

For the product-mix example, suppose the contribution of A changes from $40 to $c_A while the same solution remains feasible. The contribution at (40,20) is:

Z = 40c_A + 20(30) = 40c_A + 600.

The competing corner (50,0) gives 50c_A. The current solution is preferred when:

40c_A + 600 ≥ 50c_A,

which implies c_A ≤ 60. Thus, if A’s contribution rises above $60, the comparison with the all-A corner changes, subject to all other assumptions. This is a simple break-even sensitivity calculation, not a complete re-optimization under every possible change.

Scenario analysis changes several coherent assumptions together, such as a high-demand, constrained-supply scenario. Stress testing examines adverse but plausible conditions, such as a major supplier failure or a 30% demand decline. Sensitivity results should be presented with units, ranges and operational meaning rather than as unexplained percentages.

9. Multicriteria Decision-Making

Many operations decisions involve cost, quality, delivery, safety, flexibility, sustainability and risk. A single monetary objective may omit important consequences. Multicriteria decision-making (MCDM) makes trade-offs explicit.

A simple weighted-sum model is:

where a is an alternative, w_j is the weight for criterion j, r_aj is the normalized rating of alternative a, and ∑w_j = 1. Ratings must be oriented consistently: a higher score should always mean better performance. Cost and defect rate may therefore require reverse scaling.

One min–max normalization for a beneficial criterion is:

For a cost criterion, a reversed form is:

These formulas require a nonzero range and are sensitive to the alternatives included. Thresholds should be applied before scoring when a minimum safety or regulatory standard is mandatory. An unsafe supplier should not win because of a low price.

Methods such as the analytic hierarchy process, TOPSIS and outranking methods provide more elaborate structures, but they do not eliminate judgement. Weight selection, criterion independence, scale choice and stakeholder bias must be documented. A good practice is to conduct a rank-reversal and weight-sensitivity check.

10. Integrated Illustrative Case: Northstar Foods

The following is a fictional illustrative case.

Background

Northstar Foods produces chilled ready meals. OTIF has fallen from 96% to 88% over six months, while overtime and expedited freight have increased. Management has data from production, demand planning, suppliers and transport providers, but departments use different definitions of “on time” and “available capacity.”

Problem

The operations director must decide whether to add a weekend shift, outsource part of production or improve scheduling. The decision must consider cost, service, quality and food-safety risk.

Analysis

The analytics team first standardizes data definitions and builds a dashboard showing OTIF, schedule adherence, FPY, changeover time, forecast MAD, overtime, stock-outs and supplier fill rate. Drill-down reveals that 70% of late orders are associated with two high-variance products and a production sequence that creates long changeovers.

A descriptive analysis shows that average daily demand has not risen substantially, but its variance has increased. A predictive model identifies a high probability of late completion when demand exceeds the 80th percentile and a particular packaging line is scheduled after a long changeover. The model is validated on later weeks and compared with a simple rule-based baseline.

The team formulates an LP for the next planning week. Variables represent quantities by product and shift. Constraints include labour hours, line hours, ingredient availability, minimum contractual quantities and a food-safety restriction. Because overtime and outsourcing have fixed activation costs, a mixed-integer model is considered rather than a basic continuous LP.

A discrete-event simulation then evaluates candidate schedules because queueing and changeover variability make average-time assumptions unreliable. Ten or more scenario replications are run for each policy, with common random inputs to improve comparison. Results indicate that a modest weekend shift reduces the probability of missing OTIF targets more reliably than outsourcing, while a scheduling rule that groups compatible products further reduces changeover losses.

MCDM is used for the final recommendation. Cost receives a 30% weight, OTIF 30%, quality 20%, flexibility 10% and food-safety risk 10%. Food safety is treated as a threshold: any option failing the required standard is rejected before weighted scoring. A sensitivity test shows that outsourcing becomes preferred only under an extreme labour shortage and remains inferior on quality risk.

Outcome and control plan

Northstar implements the weekend shift as a four-week pilot, introduces the compatible-product sequencing rule and retains outsourcing as a contingency. The dashboard reports weekly results with data-quality flags. The pilot is evaluated against a baseline period using OTIF, overtime cost, FPY, employee fatigue indicators and customer complaints. The decision is revisited if demand, labour availability or supplier reliability changes materially.

Learning points

The case demonstrates that no single method is sufficient. Dashboards establish visibility; predictive analysis identifies risk; optimization allocates resources; simulation captures variability; MCDM incorporates nonfinancial criteria; and governance ensures that the recommendation remains safe, auditable and aligned with strategy.

11. Governance, Ethics and Technology

Analytics requires data governance: ownership, definitions, access controls, retention rules, lineage, quality checks and version control. Personal data should be collected only for legitimate purposes, protected against unauthorized access and used consistently with applicable privacy law. Employee monitoring requires transparency, proportionality and attention to power imbalances.

Algorithmic decisions may reproduce historical discrimination. A model trained on past supplier awards may encode previous bias. Predictive maintenance can allocate attention unevenly if sensor coverage differs by machine age or location. Managers should test performance across relevant groups, document variables, provide human review for high-impact decisions and establish appeal or correction channels.

AI and machine learning can improve forecasting, anomaly detection, computer vision and natural-language analysis of maintenance records. However, explainability, data drift, cybersecurity, hallucinated recommendations and automation bias remain concerns. Generative AI should not be allowed to invent operational facts or override safety controls. Model outputs require validation, access governance and clearly assigned accountability.

Sustainability analytics should include life-cycle consequences where relevant. A transport decision that minimizes immediate cost may increase emissions or create resilience risk. Carbon, water, waste and social indicators should be measured with clear boundaries and avoid double counting.

12. Best-Practice Implementation

An effective implementation sequence is:

1. Start with a decision and process owner, not with a software purchase.
2. Define the objective, constraints, decision horizon and acceptable risk.
3. Establish a data dictionary and assess data quality.
4. Build a transparent baseline before introducing complex models.
5. Select the least complex method that answers the question adequately.
6. Validate calculations, assumptions and model outputs with operational experts.
7. Separate training, validation and test data where prediction is involved.
8. Use scenarios, sensitivity analysis and stress tests.
9. Pilot recommendations and define rollback conditions.
10. Monitor outcomes, drift, unintended consequences and data changes.
11. Document decisions so that results are reproducible and auditable.

The central professional skill is model judgment: knowing what a model represents, what it omits and when its result should be challenged.

Challenges and Limitations

Analytics can fail because data are incomplete, inconsistent, delayed or measured after the decision has already been made. Models may confuse correlation with causation, assume stable relationships, ignore rare events or optimize a proxy rather than the true objective. Optimization can produce mathematically feasible but operationally unacceptable plans. Simulation can create false precision when input distributions are poorly estimated. MCDM can conceal subjective preferences behind numerical scores.

Organizational barriers include low trust, weak process ownership, fragmented systems, inadequate analytical capability and incentives that encourage local optimization. Managers should combine quantitative evidence with process observation, expert knowledge and consultation with affected employees. Uncertainty should be communicated explicitly rather than hidden behind decimal places.

Chapter Summary

Operations analytics converts operational data into evidence for decisions. KPIs must be aligned with objectives, clearly defined and balanced between leading and lagging measures. Dashboards support visibility and exception management but cannot correct poor data or weak definitions. Descriptive analytics explains what happened, diagnostic analysis investigates causes, predictive analytics estimates future outcomes and prescriptive analytics evaluates actions.

Decision trees and expected monetary value support choices under uncertainty, while risk attitudes and information value must be considered. Linear programming allocates scarce resources when objective functions and constraints are appropriately linear. Simulation is useful for variable, dynamic and queueing systems, but requires verification, validation, replications and uncertainty reporting. Sensitivity and scenario analysis reveal fragile assumptions and decision boundaries. Multicriteria methods make trade-offs explicit when cost, service, quality, risk and sustainability all matter.

Responsible analytics requires data governance, privacy protection, fairness assessment, cybersecurity, human accountability and continuous monitoring. The best operational decisions combine models with managerial judgement, transparent assumptions and controlled implementation.

Key Terms

Operations analytics: Use of data, models and analysis to improve operational decisions.

KPI: A quantified measure linked to an important objective and decision.

Leading indicator: A measure of conditions or activities that influence future results.

Lagging indicator: A measure of an outcome after performance has occurred.

Dashboard: A visual interface presenting decision-relevant operational information.

Descriptive analytics: Analysis of what has happened.

Diagnostic analytics: Analysis of why an outcome occurred.

Predictive analytics: Estimation of future outcomes.

Prescriptive analytics: Evaluation or recommendation of actions under constraints.

Expected monetary value: Probability-weighted average payoff of an alternative.

Decision tree: A representation of sequential choices and uncertain events.

Linear programming: Optimization using linear objectives and constraints.

Decision variable: A controllable quantity determined by an optimization model.

Constraint: A limitation or requirement restricting feasible decisions.

Simulation: Imitation of system behaviour under specified rules and uncertainty.

Sensitivity analysis: Examination of how outputs change when inputs change.

Scenario analysis: Evaluation of coherent alternative assumptions about the future.

Multicriteria decision-making: Structured evaluation of alternatives across several criteria.

Model validation: Assessment of whether a model represents the real system adequately for its intended use.

Data governance: Policies and controls for data quality, ownership, access, security and use.

Review Questions

Short Answer Questions

1. Distinguish a KPI from a general operational metric.
2. Why should a dashboard display data-refresh time and data-quality status?
3. State one limitation of MAPE.
4. What is the difference between an LP constraint and an objective function?
5. Why are simulation replications used?

Long Answer Questions

1. Explain how descriptive, diagnostic, predictive and prescriptive analytics can be integrated in a capacity decision.
2. Discuss the assumptions of linear programming and situations in which they may be inappropriate.
3. Explain how a decision tree and expected monetary value can support a capacity-expansion decision.
4. Compare dashboards and analytical models as tools for operational control.
5. Discuss ethical and governance requirements for using AI in workforce or supplier decisions.

Analytical / Application Questions

1. A service centre has actual demand of 100, 120 and 80 units in three successive periods. Calculate the two-period moving-average forecast for period four and explain one limitation of the result.
2. A firm has two projects with uncertain payoffs. Project X returns $100,000 with probability 0.7 and −$20,000 with probability 0.3. Project Y returns $70,000 with probability 0.9 and $10,000 with probability 0.1. Calculate both EMVs and recommend an option, while identifying one non-EMV factor that should be considered.
3. Design a multicriteria supplier-selection model using cost, quality, delivery reliability and sustainability. Specify weights, rating direction, one mandatory threshold and one sensitivity test.

Multiple Choice Questions with Answers

Question 1

Which statement best describes prescriptive analytics?

A. It reports historical totals without interpretation.

B. It recommends or evaluates actions subject to objectives and constraints.

C. It records raw observations from operational systems.

D. It replaces all managerial judgement with automation.

Correct Answer: B. It recommends or evaluates actions subject to objectives and constraints.

Question 2

A delivery is counted as OTIF when it is:

A. Delivered early, regardless of quantity.

B. Delivered on time and in the promised quantity.

C. Delivered late but with no defects.

D. Dispatched on time, regardless of receipt.

Correct Answer: B. Delivered on time and in the promised quantity.

Question 3

If actual demand is 100 units and the forecast is 90 units, what is the absolute forecast error?

A. −10 units

B. 9 units

C. 10 units

D. 190 units

Correct Answer: C. 10 units

Question 4

In a linear-programming model, decision variables represent:

A. The quantities or choices controlled by the decision-maker.

B. Only unavoidable external events.

C. The historical accuracy of the data.

D. The graphical design of a dashboard.

Correct Answer: A. The quantities or choices controlled by the decision-maker.

Question 5

An alternative has payoffs of $100,000 with probability 0.6 and $40,000 with probability 0.4. What is its EMV?

A. $60,000

B. $64,000

C. $76,000

D. $140,000

Correct Answer: C. $76,000

Question 6

Which condition is especially important when calculating EMV at a chance node?

A. Probabilities must be mutually exclusive and collectively exhaustive.

B. All outcomes must have identical payoffs.

C. The decision-maker must be risk seeking.

D. All probabilities must be zero.

Correct Answer: A. Probabilities must be mutually exclusive and collectively exhaustive.

Question 7

Why is simulation particularly useful in many operations problems?

A. It guarantees an optimal solution without assumptions.

B. It can represent variability, queues and dynamic system behaviour.

C. It eliminates the need for validation.

D. It is limited to deterministic data.

Correct Answer: B. It can represent variability, queues and dynamic system behaviour.

Question 8

In a weighted-sum multicriteria model, the weights should normally:

A. Sum to one and reflect criterion importance.

B. All be negative.

C. Be assigned only after seeing the preferred result.

D. Represent measurement units rather than preferences.

Correct Answer: A. Sum to one and reflect criterion importance.

Question 9

What is a major risk of using MAPE when actual demand can be zero or very small?

A. It always produces a value of zero.

B. It becomes undefined at zero and can exaggerate small-denominator errors.

C. It measures only financial performance.

D. It cannot compare forecasts in any circumstances.

Correct Answer: B. It becomes undefined at zero and can exaggerate small-denominator errors.

Question 10

What is the primary purpose of sensitivity analysis?

A. To hide uncertainty from decision-makers.

B. To determine how recommendations change when assumptions or inputs change.

C. To convert all qualitative criteria into costs.

D. To guarantee that a model is causally correct.

Correct Answer: B. To determine how recommendations change when assumptions or inputs change.