Planning Under Uncertainty and Risk

Introduction

Aggregate production planning (APP) converts forecasts of demand, available capacity, workforce, inventory, subcontracting and related resources into a medium-term operating plan. In a deterministic setting, planners often assume that demand, supply, processing times and costs are known. In practice, these quantities are uncertain. Customers may order more or less than forecast, suppliers may deliver late, prices may change, labour availability may fluctuate, and production yields may be imperfect.

Uncertainty concerns the lack of knowledge about which future state will occur. Risk is the measurable or assessable consequence of alternative future states. A sound planning system therefore does more than calculate one apparently optimal plan. It evaluates how plans perform across plausible conditions, identifies exposures, establishes trigger points and prepares responses before disruption occurs.

For postgraduate production managers, the central question is not simply “What is the best plan?” It is: “Which plan creates acceptable economic and operational performance across the range of credible futures, and how rapidly can it be adapted as information improves?” This chapter develops scenario analysis, rolling-horizon planning, simulation, stochastic optimization, robust optimization, sensitivity analysis and contingency planning as complementary approaches to that question.

Learning Objectives

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

1. Distinguish uncertainty, variability, risk and ambiguity in aggregate planning.
2. Construct and interpret demand, supply and cost scenarios.
3. Explain how rolling horizons improve plan responsiveness without creating instability.
4. Apply simulation to evaluate aggregate plans under uncertain conditions.
5. Formulate basic stochastic and robust optimization models.
6. Conduct sensitivity and value-of-information analyses.
7. Design practical contingency plans, trigger rules and governance mechanisms.
8. Critically evaluate the limitations, ethical implications and implementation requirements of advanced planning methods.

1. The Nature of Uncertainty in Aggregate Planning

1.1 Sources of uncertainty

Uncertainty enters aggregate planning through several interacting channels:

Demand uncertainty is not limited to total volume. Aggregate volume may be forecast accurately while product mix is highly uncertain. This distinction is important because capacity and materials may be product-specific. A plant can therefore experience shortages even when total demand is close to forecast.

1.2 Risk, uncertainty and ambiguity

Risk is often represented by a probability distribution. If monthly demand D has known probabilities, expected demand is:

Here, D_s is demand in state s, p_s is the probability of state s, and the probabilities sum to 1. The units of E[D] are units of product. This expression is applicable when the states are mutually exclusive and collectively exhaustive and when probabilities are meaningful.

A common measure of dispersion is the standard deviation:

The standard deviation is expressed in the same units as demand. It measures dispersion, not the direction or business consequence of error. Two plans may face the same σ_D but have very different shortage costs.

Ambiguity arises when the set of possible outcomes is known but probabilities are unreliable or contested. For example, a new product may have high, medium and low demand scenarios, but no credible historical basis for assigning probabilities. Robust optimization and scenario planning are particularly useful in such settings.

1.3 Interdependence and correlated uncertainty

Uncertain variables are frequently correlated. A severe storm may simultaneously reduce supplier deliveries, increase freight rates and disrupt internal transportation. Assuming independence when variables are correlated can materially understate risk. If X and Y are uncertain costs, the variance of their sum is:

Cov(X,Y) is covariance. Positive covariance increases total variability; negative covariance reduces it. The formula assumes finite variances and is valid regardless of whether X and Y are independent. Independence is a special case in which Cov(X,Y) = 0.

2. A Decision Architecture for Uncertain Planning

An effective uncertainty-management process links five activities:

1. Sense: collect demand signals, supplier information, capacity data and external indicators.
2. Model: represent possible futures and their operational effects.
3. Evaluate: compare plans using cost, service, resilience and risk measures.
4. Decide: select a plan, policies and contingency actions.
5. Learn and adapt: update assumptions as actual information becomes available.

This architecture prevents a common error: treating a sophisticated mathematical model as a substitute for managerial judgement. Models provide disciplined comparisons, but decisions also depend on contractual commitments, customer relationships, safety, regulation and organizational capability.

A useful planning hierarchy is:

• Strategic layer: capacity investments, supplier qualification and network design.
• Tactical layer: aggregate workforce, inventory, overtime and subcontracting decisions.
• Operational layer: sequencing, dispatching, expediting and daily recovery.

Uncertainty should be managed consistently across the hierarchy. A tactical plan that depends on an unapproved strategic capacity expansion is not implementable.

3. Scenario Analysis

3.1 Purpose and construction

Scenario analysis evaluates a plan against internally consistent descriptions of possible futures. A scenario is not merely a different demand number. It should describe the major drivers of change and their implications for demand, supply, capacity, lead time and cost.

A practical scenario-development process is:

1. Establish a base case using the current forecast and operating assumptions.
2. Identify critical uncertainties, such as market growth, supplier reliability or energy price.
3. Develop a small number of contrasting but plausible scenarios.
4. Translate each scenario into quantitative planning parameters.
5. Optimize or simulate candidate plans under each scenario.
6. Identify decisions that are robust, scenario-specific or reversible.

Scenarios should be challenging but plausible. Extreme scenarios may be useful for stress testing, but they should be labelled as stress cases rather than forecasts.

3.2 Scenario evaluation

For a plan with cost C_s in scenario s, expected cost is:

If shortage or service performance is important, expected cost alone is insufficient. A risk measure can be added. One common measure is the probability that cost exceeds a threshold C̄:

Another is conditional value-at-risk (CVaR), which represents the average cost in the worst α proportion of cases. In practice, CVaR is useful when managers want protection against severe outcomes rather than only a good average.

Scenario analysis should consider at least four dimensions:

• financial cost;
• customer service and lateness;
• resource and supplier feasibility;
• reversibility and speed of recovery.

A plan with slightly higher expected cost may be preferable if it prevents catastrophic service failures and preserves strategic options.

3.3 Worked scenario example

An appliance manufacturer is evaluating two aggregate plans for the next quarter. Demand scenarios are low, base and high, with probabilities 0.25, 0.50 and 0.25. The estimated quarterly costs, including inventory, overtime, subcontracting and shortage penalties, are:

Cost is measured in thousands of currency units. Expected costs are:

Plan A:

Plan B:

Plan B has the lower expected cost. It also has less exposure to the high-demand case. However, if the organization has poor subcontractor quality or contractual restrictions, the apparent flexibility of Plan B may not be achievable. Scenario analysis therefore supports, but does not replace, feasibility validation.

4. Rolling-Horizon Planning

A fixed annual plan can become obsolete when new information arrives. Rolling-horizon planning maintains a planning window that moves forward through time. At each review date, the organization updates forecasts, actual inventory, capacity and commitments, then extends the plan by adding a new future period.

For example, a twelve-month horizon reviewed monthly always contains the next twelve months. Near-term periods are relatively firm, while distant periods remain flexible. This distinction is often called the planning freeze, slushy zone and liquid zone:

• Frozen zone: changes require formal approval because materials, labour and customer commitments are already arranged.
• Slushy zone: moderate changes are possible with coordination.
• Liquid zone: plans can be revised freely as uncertainty is greatest.

Rolling planning does not mean changing everything every cycle. Excessive replanning creates nervousness, supplier instability and unnecessary cost. Stability rules may limit changes in the frozen zone, impose minimum batch or workforce durations, or require a materiality threshold before replanning.

Let I_t be ending inventory, P_t production, D_t demand and S_t shortage or backorder. A basic inventory balance is:

All terms must be expressed in consistent units for period t. If backorders are not permitted, S_t = 0. In a rolling horizon, the balance is recalculated using actual starting inventory and updated forecasts, not the previous plan’s outdated assumptions.

A useful performance measure is plan nervousness. One simple measure of production nervousness over T periods is:

N has units of production quantity. It is not a universal standard, but it helps reveal instability. It should be interpreted alongside service and cost; a low N is not desirable if it conceals poor responsiveness.

5. Simulation for Aggregate Planning

5.1 Role of simulation

Simulation imitates the operation of a system under specified rules and uncertain inputs. Unlike optimization, simulation does not normally search automatically for the best plan. It estimates how a selected plan or policy performs.

A Monte Carlo simulation repeatedly samples uncertain demand, lead times, failures or yields, applies the planning policy, and records outcomes. For a performance measure Y, the sample mean from R replications is:

If replications are independent and the sample standard deviation is s_Y, an approximate 95% confidence interval for the mean is:

This interval estimates uncertainty in the simulation estimate, not uncertainty in the real-world model assumptions. More replications reduce sampling error, but they cannot correct biased input distributions or an unrealistic operating policy.

5.2 Simulation procedure

A defensible simulation study includes:

1. Scope definition: specify products, resources, time horizon and decisions.
2. Input modelling: estimate distributions for demand, lead times, yields and failures.
3. Policy specification: define reorder rules, overtime rules, subcontracting and allocation priorities.
4. Verification: check that the model follows the intended logic.
5. Validation: compare model behaviour with historical or expert-observed behaviour.
6. Replication design: use enough independent runs and, where relevant, a warm-up period.
7. Output analysis: evaluate mean, variability, percentiles and service measures.
8. Sensitivity testing: examine how results change under alternative assumptions.

Simulation is especially valuable when queues, sequence-dependent setups, supply disruption and nonlinear service penalties make closed-form analysis difficult.

5.3 Simulation limitations

Simulation can produce precise-looking results from poor assumptions. Common weaknesses include arbitrary distributions, ignoring correlation, insufficient replications, coding errors and failure to model managerial response. Simulation should therefore be accompanied by documentation, version control, validation workshops and transparent assumptions.

6. Stochastic Optimization

Stochastic optimization incorporates probability distributions or scenarios directly into the decision model. A two-stage model distinguishes decisions made before uncertainty is realized from recourse decisions made afterward.

A generic two-stage objective is:

Here, x represents first-stage decisions, c is their cost vector, ω is a random scenario, and Q(x,ω) is the minimum second-stage recourse cost after scenario ω occurs. The expectation is taken over the specified probability distribution. The model assumes that the scenarios and probabilities adequately represent relevant uncertainty.

For example, workforce size and supplier reservations may be first-stage decisions. Overtime, temporary labour, expedited freight and subcontracting may be recourse decisions. The model evaluates the cost of committing capacity now while retaining options later.

A simple scenario-based aggregate model may minimize:

where:

• P_ts = regular production in period t and scenario s;
• I_ts = ending inventory;
• B_ts = backorders or shortages;
• O_ts = overtime production;
• Sub_ts = subcontracted quantity;
• F = fixed first-stage capacity or workforce decision;
• c_P, c_I, c_B, c_O and c_Sub = corresponding unit costs;
• c_F = fixed capacity cost.

Non-negativity is normally imposed on physical quantities. Scenario-specific inventory balances must use the demand D_ts for that scenario. Shared first-stage decisions must be identical across scenarios unless the decision is explicitly allowed to wait for information.

6.1 Expected value and the value of stochastic solution

The expected value problem replaces uncertain parameters with their expected values and solves a deterministic model. The wait-and-see solution assumes that uncertainty is known before decisions are made. These are benchmarks, not usually implementable policies.

The expected value of perfect information (EVPI) is:

where z_EEV is the objective value of the expected-value solution evaluated under uncertainty, and z_WSS is the expected objective value of the wait-and-see solutions. For a minimization problem, EVPI is non-negative. It represents the maximum rational value of perfect advance information.

The value of the stochastic solution compares the stochastic model with the expected-value approach. These measures help managers decide whether improved forecasting or data acquisition is worth funding.

7. Robust Optimization

Stochastic models require probabilities. Robust optimization is appropriate when probabilities are unavailable, disputed or strategically unsafe to rely upon. It seeks solutions that remain feasible or perform acceptably for all values within an uncertainty set.

Suppose demand in period t lies within:

D̄_t is nominal demand and Δ_t is the maximum deviation considered credible. A robust plan may impose capacity sufficient for the worst permitted combination of deviations. This can be conservative, especially when all variables are unlikely to reach their extremes simultaneously.

A budgeted uncertainty set controls conservatism. If Γ is an uncertainty budget, no more than Γ units of normalized deviation may occur simultaneously. Conceptually:

where z_t represents the extent of deviation in period t. Γ = 0 gives the nominal plan; larger Γ provides greater protection but generally increases cost. The exact robust counterpart depends on the underlying model and uncertainty structure.

Robustness should be evaluated against the organization’s real risk appetite. A plan that is mathematically robust but requires excessive idle capacity may be economically inferior to a plan supported by credible emergency contracts.

8. Sensitivity Analysis and Stress Testing

Sensitivity analysis changes one or more assumptions and observes the effect on decisions or performance. It answers questions such as:

• At what demand level does overtime become preferable to subcontracting?
• How much can supplier lead time increase before service falls below target?
• Which cost estimate most strongly affects the selected workforce plan?
• Does the solution change when shortage penalties are doubled?

For an objective function Z and parameter θ, a local sensitivity measure is the derivative ∂Z/∂θ when the model is differentiable. Linear programming often provides more useful information through shadow prices. A shadow price estimates the marginal change in the optimal objective value resulting from a small relaxation of a binding constraint, within the range over which the current basis remains valid.

Elasticity expresses proportional responsiveness:

It is dimensionless and useful for comparing parameters measured in different units. Sensitivity results should not be interpreted outside the tested range, particularly when the model contains fixed charges, thresholds or integer decisions.

Stress testing examines deliberately severe conditions, such as a 30% demand surge, a major supplier loss or a two-week transport disruption. It is not a forecast. Its purpose is to reveal failure modes and test whether contingency actions are sufficient.

9. Contingency Planning and Real Options

A contingency plan specifies what will be done if a defined event occurs. It should identify:

• the trigger condition;
• the responsible decision owner;
• the action and required lead time;
• capacity, materials and information needed;
• customer and supplier communication;
• the point at which the response is terminated or escalated.

Examples include prequalified alternate suppliers, reserved subcontracting capacity, cross-trained labour, postponement of final customization, strategic safety stock and transportation alternatives.

Contingency planning is closely related to real-options thinking. A flexible contract, modular product design or postponable process may cost more initially but preserve the right—not the obligation—to respond later. The value of flexibility increases when uncertainty, irreversibility and potential downside are high.

A decision-trigger matrix may be structured as follows:

Thresholds must be calibrated to product criticality, contractual service levels and financial consequences. Arbitrary thresholds can either trigger expensive action too early or delay intervention until recovery is impossible.

10. Integrated Applied Case: Meridian Medical Devices

The following is an illustrative case constructed for educational purposes.

Background

Meridian Medical Devices manufactures a diagnostic cartridge using a specialized membrane purchased from one primary supplier. Monthly demand is forecast at 20,000 units, but demand can vary significantly because hospital tenders are uncertain. The membrane supplier has a nominal lead time of four weeks, with occasional delays of up to three weeks. A second supplier can provide a partial quantity at a 12% higher purchase cost after qualification.

Meridian currently uses a level production plan and maintains two weeks of membrane inventory. Management is concerned that the plan performs well on average but fails during demand surges or supplier delays.

Problem

The planning team must decide whether to:

1. retain the level plan;
2. increase membrane inventory;
3. qualify the second supplier and reserve emergency capacity;
4. use a flexible workforce and overtime policy.

The objective is not to minimize expected manufacturing cost alone. Medical customers impose high penalties for late delivery, and product substitution is subject to regulatory approval.

Analysis

The team identifies two major uncertainties: demand and membrane lead time. It develops three scenarios:

Because probabilities are based on limited history, the team also conducts a robust stress test in which demand reaches 24,000 and lead time is seven weeks simultaneously. It simulates twelve months under candidate policies, including random monthly demand and lead-time draws, a two-week initial inventory position and an emergency-supplier rule.

The simulation measures total cost, fill rate, emergency purchases and months below the regulatory service target. The level plan has the lowest cost in the low-demand case but produces unacceptable shortages in the high-demand/delayed-supply case. Increasing inventory improves service but ties up working capital and does not fully protect against a seven-week lead time. The second-supplier option has a higher expected cost but substantially reduces the probability of a severe shortage.

Approach and solution

Meridian adopts a layered policy:

• retain a moderate increase in membrane inventory rather than the maximum stock level;
• qualify the second supplier and reserve a defined emergency quantity;
• use a rolling three-month detailed horizon within a twelve-month aggregate horizon;
• freeze production and material commitments for four weeks except for executive-approved changes;
• trigger alternate sourcing when supplier on-time performance falls below 90% for two consecutive deliveries or projected cover falls below three weeks;
• conduct a monthly scenario review and a quarterly stress test.

The policy is implemented as a stochastic simulation-supported rolling plan rather than as a single static optimum. The organization also records supplier qualification lead time and regulatory approval time, because an alternate source that cannot be activated quickly has limited practical value.

Outcome

In the illustrative evaluation, the flexible policy has a slightly higher expected cost than the original level plan but produces a materially higher service level and lower worst-case shortage exposure. Management accepts the additional expected cost because the avoided shortage penalty, reputational damage and risk to hospital supply are disproportionate. The decision is reviewed after six months using actual demand, supplier reliability and emergency-use frequency.

Learning points

1. Demand and lead-time uncertainty should be modelled jointly when they can interact.
2. A contingency resource is valuable only if it is qualified, available and contractually executable.
3. Rolling horizons preserve adaptability, but freeze rules prevent destructive nervousness.
4. Expected cost should be supplemented by tail-risk and service measures.
5. Regulatory and ethical requirements can make apparently attractive substitutions infeasible.

11. Governance, Ethics and Technology

Uncertainty models influence workforce levels, supplier allocation and customer priority. Governance is therefore essential. Decision rights should be clear, assumptions documented and material model changes approved. Scenario probabilities should not be manipulated to justify a preferred plan. When probabilities are weak, the organization should disclose that limitation and use robust or sensitivity analysis.

Ethical issues arise when scarce capacity must be allocated among customers. Priority rules should be transparent and consistent with contractual, safety and public-interest obligations. In healthcare, food, energy and other critical sectors, a purely financial objective may be inadequate.

Artificial intelligence and machine learning can improve demand sensing, anomaly detection and lead-time prediction. However, historical data may contain bias, structural breaks and censored demand caused by previous stockouts. AI-generated forecasts should therefore be monitored for drift, explainability and stability. Human planners remain responsible for interpreting exceptional events and approving high-consequence actions.

Digital twins can combine real-time inventory, supplier, capacity and transportation data with simulation. Their value depends on data quality, integration and disciplined process ownership. Technology does not eliminate uncertainty; it can improve detection, response speed and scenario evaluation.

12. Best Practices and Limitations

Best practices include:

• distinguish forecast uncertainty from controllable variability;
• model product mix, not only aggregate volume;
• represent correlation where operationally credible;
• use scenarios to communicate assumptions across functions;
• combine expected performance with tail-risk measures;
• maintain a rolling horizon with explicit freeze boundaries;
• validate simulation models against actual behaviour;
• use stochastic optimization when probabilities are credible;
• use robust optimization when probabilities are weak or ambiguity is high;
• conduct sensitivity analysis before approving major commitments;
• predefine triggers, owners and response times;
• evaluate flexibility as an economic option;
• review forecasts, scenarios and policies after disruptions.

No method is universally superior. Scenario analysis is accessible but may be subjective. Simulation represents operational detail but can be computationally demanding and assumption-sensitive. Stochastic optimization is theoretically elegant but depends on probability quality and may become large and difficult to explain. Robust optimization protects against specified deviations but can be overly conservative. Rolling horizons improve adaptation but may create instability if governance is weak.

The appropriate design is usually hybrid: scenario thinking for strategic understanding, optimization for structured decisions, simulation for operational validation, sensitivity analysis for critical assumptions and contingency planning for execution.

Chapter Summary

Planning under uncertainty recognizes that demand, supply, lead times, capacity and costs are not known with certainty. Effective aggregate planning therefore evaluates alternative futures rather than relying on one forecast. Scenario analysis provides a structured view of plausible states; rolling horizons update plans as information improves while freeze rules control nervousness. Simulation estimates the distribution of outcomes under realistic operating policies. Stochastic optimization incorporates probability-weighted scenarios and recourse decisions, whereas robust optimization seeks acceptable performance across an uncertainty set when probabilities are unreliable. Sensitivity analysis identifies influential assumptions, and stress testing exposes failure modes. Contingency planning converts analysis into executable actions through triggers, owners, reserved resources and communication protocols. Good governance, ethical allocation, data quality and human oversight are essential, particularly when AI and digital systems support planning. The strongest managerial approach combines these methods according to the decision context, risk appetite and quality of available information.

Key Terms

Uncertainty: Lack of complete knowledge about future conditions.

Risk: The measurable or assessable consequence of uncertain outcomes.

Ambiguity: Uncertainty about the appropriate probabilities, models or interpretations.

Scenario analysis: Evaluation of plans under several internally consistent future conditions.

Rolling horizon: A planning window that is periodically updated and extended forward.

Planning freeze: A period in which changes require special authorization.

Plan nervousness: Instability caused by repeated changes to previously published plans.

Monte Carlo simulation: Repeated sampling of uncertain inputs to estimate outcome distributions.

Replication: One independent run of a simulation model.

Stochastic optimization: Optimization using probabilistic parameters or scenarios.

Recourse: A decision made after uncertain information is revealed.

Expected value: Probability-weighted average of possible outcomes.

EVPI: Expected value of perfect information.

Robust optimization: Optimization designed to perform acceptably over a defined uncertainty set.

Uncertainty set: The range or structure of parameter values considered plausible.

Sensitivity analysis: Examination of how results change when assumptions vary.

Stress test: Evaluation under deliberately severe but relevant conditions.

Contingency plan: Predefined response to a specified disruption or trigger.

Real option: The value of preserving flexibility to act later.

Model validation: Assessment of whether a model adequately represents the real system.

Review Questions

Short Answer Questions

1. Distinguish risk from ambiguity in aggregate production planning.
2. What is the purpose of a planning freeze in a rolling-horizon system?
3. State two limitations of Monte Carlo simulation.
4. Explain the meaning of recourse in a two-stage stochastic model.
5. Why might robust optimization be preferred when probabilities are unreliable?

Long Answer Questions

1. Explain how scenario analysis should be designed and evaluated for uncertain demand, supply and costs.
2. Discuss the relationship between rolling-horizon planning, plan nervousness and organizational governance.
3. Compare stochastic optimization and robust optimization, including their assumptions, advantages and limitations.
4. Describe a complete simulation study for an aggregate production plan, from input modelling through validation and output analysis.
5. Explain how contingency planning and real-options thinking improve resilience in aggregate production systems.

Analytical / Application Questions

1. A manufacturer has three demand scenarios with probabilities 0.20, 0.50 and 0.30. Two plans have costs of (300, 340, 500) and (360, 370, 420), respectively. Calculate expected cost for each plan and discuss why expected cost alone may not determine the decision.
2. Design a trigger matrix for a firm whose main supplier has uncertain lead time, including at least three indicators, threshold levels and responsible responses.
3. A company’s aggregate plan is feasible under nominal demand but fails when demand and supplier delay are both high. Recommend a combined use of rolling horizons, simulation, robust optimization and contingency planning, explaining the role of each method.

Multiple Choice Questions with Answers

Question 1

Which statement best distinguishes stochastic optimization from robust optimization?

A. Stochastic optimization ignores uncertainty, while robust optimization uses historical averages.

B. Stochastic optimization uses probabilities or scenarios, while robust optimization protects against values within an uncertainty set.

C. Stochastic optimization is used only for scheduling, while robust optimization is used only for inventory.

D. Stochastic optimization always produces a higher-cost plan than robust optimization.

Correct Answer: B. Stochastic optimization uses probabilities or scenarios, while robust optimization protects against values within an uncertainty set.

Question 2

A twelve-month planning window is updated every month and extended by one month. This is an example of:

A. Fixed-period planning

B. Backward scheduling

C. Rolling-horizon planning

D. Wait-and-see optimization

Correct Answer: C. Rolling-horizon planning

Question 3

If demand scenarios have probabilities p_s and values D_s, which expression represents expected demand?

A. ∑_s D_s/p_s

B. ∑_s p_sD_s

C. ∑_s (D_s−p_s)²

D. max(D_s)−min(D_s)

Correct Answer: B. ∑_s p_sD_s

Question 4

In a two-stage stochastic production model, which is most likely a first-stage decision?

A. Emergency overtime after demand is observed

B. Expedited freight after a supplier delay

C. Workforce or capacity reservation made before uncertainty is resolved

D. Final allocation of inventory after customer orders arrive

Correct Answer: C. Workforce or capacity reservation made before uncertainty is resolved

Question 5

What is the primary purpose of a simulation replication?

A. To change the optimization objective

B. To produce an independent estimate of system performance under sampled uncertainty

C. To eliminate all model assumptions

D. To guarantee the globally optimal plan

Correct Answer: B. To produce an independent estimate of system performance under sampled uncertainty

Question 6

A planning freeze is mainly intended to:

A. Prevent all future forecasts from being updated

B. Reduce destructive short-term changes to committed plans

C. Increase the number of emergency changes

D. Replace capacity planning with inventory planning

Correct Answer: B. Reduce destructive short-term changes to committed plans

Question 7

If two uncertain costs have positive covariance, the variance of their sum is generally:

A. Lower because the costs move together

B. Unaffected by covariance

C. Higher than the sum of their individual variances alone

D. Always zero

Correct Answer: C. Higher than the sum of their individual variances alone

Question 8

Which item is essential in an executable contingency plan?

A. An undefined aspiration to respond quickly

B. A trigger condition, responsible owner and specified action

C. Only the worst-case demand forecast

D. A guarantee that disruption will not occur

Correct Answer: B. A trigger condition, responsible owner and specified action

Question 9

A stress test differs from a normal forecast because it:

A. Uses only the most probable outcome

B. Examines deliberately severe but relevant conditions

C. Cannot include supply disruptions

D. Always assigns equal probability to all outcomes

Correct Answer: B. Examines deliberately severe but relevant conditions

Question 10

For a minimization problem, the expected value of perfect information represents:

A. The cost of ignoring all scenarios

B. The maximum value attributable to knowing the future state before deciding

C. The standard deviation of demand

D. The cost of a rolling horizon

Correct Answer: B. The maximum value attributable to knowing the future state before deciding