Engineering Economics and Decision Analysis Exercises

These exercises practise engineering economics and decision analysis for technical alternatives, lifecycle cost, downtime, schedule risk, capacity, uncertainty, staged commitments, and benefit validation. The purpose is not only to compute a financial metric. The purpose is to make engineering assumptions visible before capital, safety, reliability, or operating decisions become difficult to reverse.

Assume the simplified financial treatment stated in each exercise. Real decisions may require inflation, tax treatment, depreciation, financing, contractual penalties, residual value, permitting risk, safety constraints, emissions cost, labor availability, warranty terms, and stakeholder approval.

How to Use These Exercises

For each decision calculation, define:

1. the decision boundary and alternatives;
2. the lifecycle phases included in the cost model;
3. the technical assumptions that drive value;
4. the uncertainty or scenario that could change the recommendation;
5. the validation evidence needed after implementation.

The most common mistake is comparing purchase price while excluding downtime, maintenance, reliability, schedule delay, operator workload, or bottleneck effects. A useful engineering economics model makes those exclusions explicit.

For each result, state whether it supports option screening, capital approval, supplier selection, reliability investment, schedule recovery, staged commitment, or post-audit correction. A financial metric is useful only when the technical assumption that creates the value is visible and testable.

Exercise 1: Lifecycle Cost Comparison

Two pump packages can meet the required duty. Option A has lower purchase cost but higher annual operating cost.

Cost item	Option A	Option B
Installed capital cost	USD 180,000	USD 240,000
Annual energy cost	USD 42,000/year	USD 28,000/year
Annual maintenance cost	USD 12,000/year	USD 8,000/year

Compare six-year lifecycle cost without discounting.

Solution

Option A annual recurring cost:

Six-year lifecycle cost:

Option B annual recurring cost:

Six-year lifecycle cost:

Option B has lower six-year lifecycle cost by:

Engineering Comment

The higher-capital option is economically stronger in this simplified boundary. A final recommendation should still check pump reliability, NPSH margin, maintainability, spare parts, supplier support, energy-price uncertainty, and whether the six-year horizon matches the asset life.

Exercise 2: Present Value and Net Present Value

A retrofit costs:

now. It saves:

for five years and has residual value:

at year 5. Use discount rate:

Calculate net present value.

Solution

Present value of annual savings:

Present value of residual value:

Net present value:

Engineering Comment

The retrofit is positive under these assumptions. The decision is sensitive to savings verification, discount rate, residual value, outage required for installation, and whether the retrofit changes reliability, safety, or maintainability.

Exercise 3: Simple and Discounted Payback

Option B from Exercise 1 requires:

more initial capital than Option A. It saves:

in energy and maintenance. Calculate simple payback. Then estimate discounted payback at 8\% using annual savings.

Solution

Simple payback:

Discounted savings by year:

Cumulative discounted savings through year 4:

Remaining amount after year 4:

Year 5 discounted saving:

Additional fraction of year 5:

Discounted payback is approximately:

Engineering Comment

Simple payback can hide the time value of money and all benefits after the payback point. It is useful as a screening metric, but it should not replace lifecycle value, risk, and technical performance review.

Exercise 4: Expected Annual Downtime Cost

A production asset has annual failure probability:

If the failure occurs, expected outage is:

Lost production is valued at:

Repair cost is:

and restart scrap cost is:

A monitoring upgrade costs USD 9000 per year and reduces annual failure probability to 0.08. Compare expected annual cost before and after the upgrade.

Solution

Consequence per failure:

Expected annual cost before upgrade:

Expected annual cost after upgrade:

Expected annual benefit:

Engineering Comment

The upgrade has positive expected value in this simplified model. The decision should still consider failure consequence distribution, safety exposure, detection effectiveness, false alarms, maintenance response time, and whether the monitoring system detects the failure modes that matter.

Exercise 5: Schedule Delay Cost on the Critical Path

A project has two paths:

Path	Duration
A-B-D	39 days
A-C-D	35 days

Activity B is on the critical path. A supplier delay adds 6 days to activity B. Project overhead is USD 4200/day, and delayed production value is USD 12,000/day. Estimate delay cost.

Solution

The original critical path is A-B-D at 39 days. Since B is on that path, a 6-day B delay increases project duration to:

Delay cost per day:

Total delay cost:

Engineering Comment

Schedule risk is economic risk. A lower-price supplier may be more expensive if it threatens the critical path, commissioning window, permitting sequence, or revenue start date. The schedule model should show float, procurement constraints, and recovery options.

Exercise 6: Capacity Value at the Real Bottleneck

A production line has three stations:

Station	Cycle time before upgrade	Cycle time after upgrade
A	3.6 min/unit	3.6 min/unit
B	4.8 min/unit	3.2 min/unit
C	4.0 min/unit	4.0 min/unit

The upgrade affects only station B. Contribution margin is USD 38/unit and annual available time is 1600 h. Estimate annual value from increased throughput.

Solution

Before the upgrade, the bottleneck is station B:

After the upgrade, station C becomes the bottleneck:

Throughput increase:

Annual value:

Engineering Comment

The value is limited by the new bottleneck, not by the upgraded station’s standalone capacity. A decision model that values station B as if the whole line could run at 60/3.2=18.75 units/h would overstate the benefit.

Exercise 7: Energy Price Threshold for a More Efficient Option

An efficient motor package costs:

more than the standard package. It saves:

and reduces maintenance cost by:

Find the electricity price threshold in $/MWh needed to reach a four-year simple payback.

Solution

Required annual savings for four-year simple payback:

Required annual energy savings after maintenance savings:

Electricity price threshold:

Engineering Comment

This threshold is useful because it turns a debate about energy price into a testable condition. The final decision should also check motor loading, duty cycle, power quality, drive losses, installation cost, spare compatibility, and whether maintenance savings are supported by evidence.

Exercise 8: Expected Value of a Staged Expansion Option

A modular design costs:

more now but preserves an expansion option. Scenario outcomes for the preserved option are:

Scenario	Probability	Future value of option
High demand	0.35	USD 190,000
Medium demand	0.45	USD 80,000
Low demand	0.20	-USD 20,000

Calculate expected net value of choosing the modular design.

Solution

Expected future value:

Expected net value after extra cost:

Engineering Comment

The expected value is positive but small relative to the uncertainty. The decision may still be justified if the high-demand scenario is strategically important or if the modular option reduces schedule risk. It may be weak if the low-demand downside is underestimated.

Exercise 9: Pareto Dominance in a Trade-Off Table

Four alternatives are compared using lower-is-better metrics:

Alternative	Capital cost	Technical risk score	Annual emissions
A	100	8	30
B	120	5	25
C	130	7	35
D	150	4	18

Identify any dominated alternatives.

Solution

Alternative C is dominated by B because B has:

• lower capital cost: 120<130;
• lower technical risk score: 5<7;
• lower annual emissions: 25<35.

Alternatives A, B, and D are not dominated by another listed option. A is cheapest, D has lowest risk and emissions, and B is intermediate.

Engineering Comment

Removing dominated options simplifies the decision without hiding trade-offs. The remaining alternatives still require stakeholder judgment: how much extra capital is justified for lower risk or emissions, and which constraints are hard limits rather than preferences.

Exercise 10: Post-Audit Benefit Tracking

A reliability project was predicted to reduce downtime cost by USD 140,000/month net. Actual data show baseline downtime was:

and post-implementation downtime is:

Downtime is valued at:

The new maintenance program adds:

Calculate actual net monthly benefit and realization versus the predicted net benefit.

Solution

Downtime reduction:

Gross benefit:

Net benefit:

Realization versus predicted net benefit:

Engineering Comment

The project delivered value but less than predicted. The post-audit should identify whether the gap came from optimistic baseline assumptions, weak implementation, new operating conditions, measurement error, or failure modes not addressed by the project.

Review Checklist

A strong decision-analysis solution should check:

• whether the decision boundary and alternatives are explicitly defined;
• whether lifecycle cost includes downtime, maintenance, energy, training, spares, warranty, and end-of-life effects;
• whether the time basis, discount rate, residual value, and payback rule match the decision context;
• whether schedule, reliability, capacity, safety, emissions, and human-operation assumptions are included when they drive value;
• whether sensitivity thresholds identify the assumption that would change the recommendation;
• whether Pareto trade-offs distinguish hard constraints from preferences;
• whether staged decisions preserve real options without hiding downside exposure;
• whether post-implementation data can verify realized benefit, not only project completion.

The final answer should not only name the cheapest option. It should explain why the recommendation remains credible under realistic lifecycle, reliability, schedule, capacity, and operating conditions.