Exercise set

Operations Resource Loading, Backlog Recovery, and Shutdown Readiness Exercises

Solved operations resource exercises for skill-hour loading, backlog burn-down, overtime recovery, shutdown readiness and release gates.

Branch: Industrial and Management Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises practise resource-loading and recovery decisions: backlog burn-down, overtime capacity, skill-hour fit, resource-constrained shutdown readiness, work-package readiness, contractor support, fatigue limits, scope cuts, restart evidence and release gates.

The goal is to test whether the plan can be staffed, not just whether it fits a dependency network. A schedule can pass the clock while failing because the right skill, permit, tool, material, spare, inspection or release authority is missing.

Assume simplified screening data unless an exercise states otherwise. Real readiness work should also check shift coverage, skill matrices, permit queues, access windows, isolation plans, travel time, craft productivity, supervision, fatigue, abnormal findings, material release and restart validation.

Release Evidence Notes

Resource evidence should be skill-specific. Total headcount can hide a shortage of electrical, controls, inspection, welding, rigging, software, clinical engineering or operator-authority hours.

Backlog evidence should use net burn-down after new arrivals. Reporting gross completion while ignoring incoming demand creates false recovery.

Shutdown readiness evidence should check clock duration and craft-hours separately. A plan can fit a sixteen-hour window and still fail if available craft-hours are too low.

Release evidence should include permits, materials, spares, tools, hold points, test records and owner approval. A ready percentage is weak if any hard-gate item is missing.

Engineering Boundary Notes

This page covers resource loading, backlog recovery and shutdown readiness. Critical path and schedule uncertainty belong in the operations schedule exercise set. Queue waiting time, service-level tails and WIP caps belong in the operations queue exercise set.

If the blocker is spare availability, use the critical spare-parts exercise set for the inventory calculation, then bring the result back here as a shutdown readiness gate.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Backlog recovery	1-4, 10	net burn-down, recovery time and added capacity	Decide whether recovery is credible.
Skill and crew loading	5-8, 12	skill-hour margin, utilization and cross-training	Add labor, resequence or reduce scope.
Shutdown readiness	9, 13-16	work-package readiness, craft-hours, permits, materials and fatigue	Release, delay or restrict the outage.
Release control	11, 17-18	contractor support, scope cut and hard gates	Approve the plan or hold release.

Exercise 1: Backlog Burn-Down with New Arrivals

A team has backlog:

B=240\ \text{work orders}

New arrivals are:

A=35\ \text{work orders/week}

Completions are:

C=55\ \text{work orders/week}

Find weeks to clear the backlog.

Solution

Net burn-down:

R=C-A=55-35=20\ \text{work orders/week}

Time:

T=\dfrac{240}{20}=12\ \text{weeks}

Engineering Comment

Backlog clears only at the rate above new arrivals. If urgent work interrupts the plan, the recovery date slips.

Plausibility Check

Twenty net completions per week clears two hundred forty orders in twelve weeks.

Exercise 2: Backlog Growth When Capacity Is Short

A support team receives:

A=64\ \text{jobs/week}

and completes:

C=58\ \text{jobs/week}

Find backlog growth over eight weeks.

Solution

Weekly growth:

G=A-C=64-58=6\ \text{jobs/week}

Eight-week growth:

B=6(8)=48\ \text{jobs}

Engineering Comment

Small weekly shortfalls become visible backlog. A recovery plan must add net capacity, reduce demand or change priority rules.

Plausibility Check

Six jobs per week for eight weeks gives forty-eight jobs.

Exercise 3: Overtime Recovery Hours

A service operation misses:

B=160\ \text{jobs}

Overtime completes:

r=9\ \text{jobs/h}

but productivity during overtime is $80\%$ of normal. The plan has four days. Estimate overtime hours per day.

Solution

Overtime rate:

r_o=9(0.80)=7.2\ \text{jobs/h}

Total hours:

H=\dfrac{160}{7.2}=22.22\ \text{h}

Per day:

H_d=\dfrac{22.22}{4}=5.56\ \text{h/day}

Engineering Comment

This is aggressive. Fatigue, supervision, material availability and quality review must be checked.

Plausibility Check

At about seven jobs per hour, one hundred sixty jobs take a little over twenty hours.

Exercise 4: Added Crew Recovery Time

Two added technicians each complete:

6\ \text{jobs/day}

The recovery backlog is:

B=96\ \text{jobs}

Find recovery time using only added capacity.

Solution

Added daily capacity:

C_a=2(6)=12\ \text{jobs/day}

Recovery time:

T=\dfrac{96}{12}=8\ \text{days}

Engineering Comment

Added people help only if they have the right skills, access and authority. Shadowing or training time reduces effective capacity.

Plausibility Check

Twelve jobs per day clears ninety-six jobs in eight days.

Exercise 5: Skill-Hour Loading

A shutdown task list needs:

Skill	Required hours	Available protected hours
mechanical	$92$	$104$
electrical	$64$	$58$
controls	$36$	$44$

Find the limiting skill.

Solution

Margins:

M_{mech}=104-92=12\ \text{h}

M_{elec}=58-64=-6\ \text{h}

M_{ctrl}=44-36=8\ \text{h}

Electrical is limiting with a:

6\ \text{h}

shortfall.

Engineering Comment

Total labor can look adequate while one critical skill blocks release.

Plausibility Check

Only electrical has fewer available than required hours.

Exercise 6: Crew Utilization after Added Demand

A field crew can complete:

C=72\ \text{jobs/week}

Current demand is:

54\ \text{jobs/week}

A program adds:

10\ \text{jobs/week}

The utilization rule is at most $85\%$ . Check release.

Solution

New demand:

D=54+10=64\ \text{jobs/week}

Utilization:

U=\dfrac{64}{72}=0.889=88.9\%

The rule fails.

Engineering Comment

Absolute capacity remains above demand, but reserve is too small for rework, travel and urgent jobs.

Plausibility Check

Demand is close to capacity, so utilization near ninety percent is expected.

Exercise 7: Protected Craft-Hour Reserve

A task requires:

H_r=118\ \text{craft-h}

Available crew provides:

7

people for:

16\ \text{h}

Find craft-hour margin.

Solution

Available hours:

H_a=7(16)=112\ \text{craft-h}

Margin:

M=H_a-H_r=112-118=-6\ \text{craft-h}

Engineering Comment

The work should not be released unless labor is added, scope is reduced or duration changes.

Plausibility Check

Seven people for sixteen hours cannot cover one hundred eighteen craft-hours.

Exercise 8: Cross-Trained Crew Credit

Controls work has a shortfall:

S=10\ \text{h}

Two cross-trained technicians can each contribute:

4\ \text{h}

Find remaining shortfall.

Solution

Cross-trained contribution:

H_c=2(4)=8\ \text{h}

Remaining shortfall:

S_r=10-8=2\ \text{h}

Engineering Comment

Cross-training helps only when authorization and supervision are valid for the task. Partial credit should be explicit.

Plausibility Check

Eight hours of credit against a ten-hour gap leaves two hours.

Exercise 9: Resource-Constrained Shutdown Readiness

A shutdown has critical-path duration:

13.5\ \text{h}

inside a:

16\ \text{h}

window. Required craft-hours are:

118

Available craft-hours are:

112

Check readiness.

Solution

Duration margin:

M_t=16-13.5=2.5\ \text{h}

Craft-hour margin:

M_h=112-118=-6\ \text{craft-h}

Duration passes, craft-hours fail.

Engineering Comment

Clock time and labor loading are different gates. The outage should not be released on schedule margin alone.

Plausibility Check

The plan fits the window but lacks craft-hours, so the mixed result is plausible.

Exercise 10: Recovery Capacity after Routine Load

A crew has weekly capacity:

C=80\ \text{h/week}

Routine committed work uses:

R=58\ \text{h/week}

Find recovery capacity for backlog.

Solution

Available recovery capacity:

C_r=C-R=80-58=22\ \text{h/week}

Engineering Comment

Recovery planning should use capacity left after routine and urgent commitments, not total crew capacity.

Plausibility Check

Eighty total hours minus fifty-eight committed hours leaves twenty-two.

Exercise 11: Contractor Support Margin

A shutdown requires:

H_r=140\ \text{h}

Internal crew can provide:

H_i=104\ \text{h}

A contractor can provide:

H_c=42\ \text{h}

Find final margin.

Solution

Total hours:

H_t=104+42=146\ \text{h}

Margin:

M=146-140=6\ \text{h}

Engineering Comment

The margin passes, but contractor mobilization, induction, permits and supervision must be confirmed.

Plausibility Check

The contractor covers the internal shortfall and leaves six hours.

Exercise 12: Shift Coverage Ratio

A restart requires:

N_r=5

qualified operators per shift. Available qualified operators:

N_a=6

Find coverage ratio.

Solution

Coverage ratio:

C=\dfrac{N_a}{N_r}=\dfrac{6}{5}=1.20

Engineering Comment

One spare qualified operator gives resilience for breaks or minor absence, but not for extended illness or parallel troubleshooting.

Plausibility Check

Six available against five required is twenty percent reserve.

Exercise 13: Work-Package Readiness

A shutdown requires:

N=36

work packages ready. Fully ready:

N_r=29

The release rule requires at least $90\%$ ready. Check readiness.

Solution

Readiness:

R=\dfrac{29}{36}=0.806=80.6\%

The rule fails:

80.6\%<90\%

Engineering Comment

Readiness is not only a schedule percentage. Missing permits, tools or materials can stop work even if the network logic passes.

Plausibility Check

Seven of thirty-six packages are not ready, so readiness is clearly below ninety percent.

Exercise 14: Permit Closure Gate

Required permits:

N=18

Approved permits:

N_a=17

The rule requires all permits approved. Check release.

Solution

Closure:

C=\dfrac{17}{18}=94.4\%

But the hard gate requires:

100\%

The gate fails.

Engineering Comment

A single missing permit can block a workface. Percent complete is not enough when the rule is all-or-nothing.

Plausibility Check

Seventeen of eighteen looks high, but one missing permit violates the hard gate.

Exercise 15: Overtime Fatigue Limit

A recovery plan requires:

H_d=5.56\ \text{overtime h/day}

The fatigue rule allows at most:

H_{max}=4.0\ \text{overtime h/day}

Find excess overtime.

Solution

Excess:

E=H_d-H_{max}=5.56-4.0=1.56\ \text{h/day}

Engineering Comment

The recovery plan must be extended, staffed differently or reduced. Excess overtime can damage quality and safety.

Plausibility Check

The plan is more than one and a half hours per day above the limit.

Exercise 16: Restart Evidence Completion

Restart release requires:

N=25

evidence items. Closed and reviewed:

N_c=24

The rule requires $100\%$ closure for restart. Check release.

Solution

Closure:

C=\dfrac{24}{25}=96\%

Because the requirement is $100\%$ , the restart fails.

Engineering Comment

Restart evidence often covers safety, isolation removal, function tests and owner handover. One missing item can be material.

Plausibility Check

Ninety-six percent is high, but one missing hard-gate item still blocks release.

Exercise 17: Scope Cut to Fit Craft-Hours

A shutdown has craft-hour shortfall:

S=6\ \text{h}

One optional work package requires:

H_o=8\ \text{h}

If it is removed, find new margin.

Solution

Removing the optional package reduces required hours by $8$ :

M=-6+8=2\ \text{h}

The craft-hour gate now passes with two hours margin.

Engineering Comment

Scope cuts should remove genuinely deferrable work, not hidden critical tasks. Deferred risk must be documented.

Plausibility Check

Removing eight hours from a six-hour shortfall leaves two hours positive.

Exercise 18: Resource Readiness Release Gate

A restart plan has:

Gate	Requirement	Current result
craft-hour margin	nonnegative	$+2$ h
work-package readiness	at least $90\%$	$80.6\%$
permit closure	$100\%$	$94.4\%$
overtime limit	at most $4$ h/day	$5.56$ h/day

Decide whether to release.

Solution

Craft-hour margin passes:

+2\ \text{h}\geq0

Readiness, permits and overtime fail:

80.6\%<90\%,\quad 94.4\%<100\%,\quad 5.56>4

The restart is not releasable.

Engineering Comment

Resource readiness requires all hard gates. A positive craft-hour margin does not compensate for missing packages, missing permits or fatigue exposure.

Plausibility Check

Three gates fail, so release should be held or scope should be changed.

Validation Package Checklist

A strong resource-loading and shutdown-readiness solution should check:

whether capacity is skill-specific and protected for the relevant window;
whether backlog recovery uses net burn-down after new arrivals;
whether overtime productivity and fatigue limits are realistic;
whether contractor hours include mobilization, permits and supervision;
whether shutdown duration and craft-hours are checked separately;
whether work-package readiness includes permits, tools, materials and hold points;
whether optional scope cuts are truly deferrable and documented;
whether restart evidence is complete before release authority signs off.

Common Release Mistakes

Common mistakes include counting total headcount instead of required skills, using gross backlog completion instead of net burn-down, planning overtime without fatigue limits, assuming contractors are immediately productive, releasing a shutdown because the critical path fits while craft-hours fail, treating one missing permit as a minor percentage gap, cutting scope without recording deferred risk, and restarting with incomplete evidence because most items are closed.

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