Exercise set

Material Replenishment Kanban, Unit Load, and Line-Side Release Exercises

Solved replenishment exercises for Kanban cards, unit loads, line-side stock, frozen windows, inspection delay, kitting and transport release.

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

These exercises practise operational replenishment decisions: Kanban card count, container sizing, unit loads, line-side stock, route frequency, frozen-window material coverage, incoming inspection delay, available material, kit completeness, transport capacity and replenishment release gates.

The goal is to decide whether material can physically and administratively reach the point of use before work starts. Inventory policy may be correct while line-side release fails because stock is under inspection, in the wrong container, missing a kit item, blocked by transport capacity or not synchronized with the frozen schedule.

Assume simplified screening data unless an exercise states otherwise. Real replenishment release should also check point-of-use location, scan discipline, packaging, ergonomics, handling damage, route timing, staging space, lot traceability, quality status, permit or access windows and shortage escalation.

Release Evidence Notes

Replenishment evidence should state the material state and location: supplier, receiving, inspection, supermarket, line-side, kit, tote, pallet, truck, workface or released order.

Kanban evidence should include demand rate, replenishment lead time, safety factor, container size and route discipline. A card count is weak if the route cannot complete on time or line-side space cannot hold containers.

Unit-load evidence should connect physical handling with planning units. A pallet, tote or kit may contain many components, but release fails if one required item, label or quality document is missing.

Line-side release evidence should be checked against the frozen schedule and the exact BOM revision. Available material must be quality-cleared, unallocated and at the correct point of use.

Engineering Boundary Notes

This page covers execution of material flow to production or field work. Inventory policy and safety stock belong in the inventory-policy exercise set. Supplier capacity, lead-time performance and disruption recovery belong in the supplier-performance exercise set.

If the problem is an internal station bottleneck rather than material movement, use production-flow or queue-capacity exercises instead.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Kanban and containers	1-5	card count, container demand, route frequency and line-side space	Set pull-loop size and route rules.
Frozen schedule and material release	6-10	BOM coverage, usable inventory, inspection delay and kit completeness	Release, hold or reallocate material.
Transport and point-of-use flow	11-15	truck capacity, pallets, route time and staging limits	Decide whether replenishment can execute.
Replenishment release	16-18	scan accuracy, shortage exposure and hard gates	Release, restrict or correct the loop.

Exercise 1: Kanban Card Count

A line consumes:

d=32\ \text{containers/day}

Replenishment lead time is:

L=0.75\ \text{day}

Safety factor is:

15\%

Find required cards.

Solution

Base cards:

N_0=dL=32(0.75)=24

With safety factor:

N=24(1.15)=27.6

Round up:

N=28\ \text{cards}

Engineering Comment

Kanban cards authorize physical containers. The loop also needs route discipline, container return and line-side space.

Plausibility Check

Three quarters of a day at thirty-two containers per day is twenty-four; safety allowance brings it near twenty-eight.

Exercise 2: Line-Side Container Space

Each Kanban container occupies:

0.18\ \text{m}^2

The loop needs:

28

containers. Available line-side footprint is:

4.5\ \text{m}^2

Check space.

Solution

Required footprint:

A=28(0.18)=5.04\ \text{m}^2

Since:

5.04>4.5

the layout fails.

Engineering Comment

Kanban sizing must be compatible with safe point-of-use storage. A mathematically correct loop can create congestion or handling risk.

Plausibility Check

Twenty-eight containers at almost one fifth of a square meter each need a little above five square meters.

Exercise 3: Unit Load Totes per Day

Each assembly consumes:

q=3\ \text{brackets}

Daily production is:

D=420\ \text{assemblies/day}

Each tote holds:

C=70\ \text{brackets}

Find totes per day.

Solution

Bracket demand:

B=qD=3(420)=1260

Totes:

N=\dfrac{1260}{70}=18

Engineering Comment

Unit-load sizing affects route frequency, ergonomic handling and line-side stock visibility.

Plausibility Check

Eighteen totes at seventy brackets each deliver $1260$ brackets.

Exercise 4: Milk-Run Frequency

Daily container demand is:

32\ \text{containers/day}

The route carries:

8\ \text{containers/trip}

The plant runs:

16\ \text{h/day}

Find trips per day and average interval.

Solution

Trips:

N=\dfrac{32}{8}=4\ \text{trips/day}

Interval:

I=\dfrac{16}{4}=4\ \text{h}

Engineering Comment

The interval must be shorter than the depletion time at point of use. Otherwise the route arrives too late.

Plausibility Check

Four trips spread over sixteen hours gives one trip every four hours.

Exercise 5: Container Depletion Time

Line-side stock is:

S=8\ \text{containers}

Consumption is:

r=2.5\ \text{containers/h}

Find depletion time.

Solution

Depletion time:

T=\dfrac{S}{r}=\dfrac{8}{2.5}=3.2\ \text{h}

Engineering Comment

If the milk run interval is four hours, this stock will deplete before the next route unless safety stock or route timing changes.

Plausibility Check

At two and a half containers per hour, eight containers last a little over three hours.

Exercise 6: Frozen-Window BOM Coverage

A frozen two-week schedule requires:

1840\ \text{finished units}

Each unit consumes one controller and two brackets. Available stock is:

Item	Available
controller	$1900$
bracket	$3500$

Check material coverage.

Solution

Controller demand:

D_c=1840

Bracket demand:

D_b=2(1840)=3680

Margins:

M_c=1900-1840=60

M_b=3500-3680=-180

The release fails because brackets are short by $180$ .

Engineering Comment

Every constrained BOM item must clear. The headline component passing does not release the schedule.

Plausibility Check

Bracket demand is twice finished-unit demand, so the $3500$ bracket stock is not enough.

Exercise 7: Incoming Inspection Delay

Gross stock is:

S_g=2200

Incoming inspection hold is:

500

Allocated stock is:

180

Production need is:

D=1650

Find release margin.

Solution

Available material:

S_a=2200-500-180=1520

Margin:

M=1520-1650=-130

Engineering Comment

Quality hold changes material state. A production order should not be released from gross inventory.

Plausibility Check

Blocked and allocated stock remove $680$ units, leaving less than the need.

Exercise 8: Inspection Acceleration Requirement

The shortage from Exercise 7 is:

130\ \text{units}

Inspection can clear:

80\ \text{units/h}

Find hours required to remove the shortage.

Solution

Hours:

H=\dfrac{130}{80}=1.625\ \text{h}

Round planning time:

H=1.7\ \text{h}

Engineering Comment

Inspection acceleration is useful only if the inspected stock is the correct revision and can physically reach line-side before release.

Plausibility Check

At eighty units per hour, clearing one hundred thirty units takes less than two hours.

Exercise 9: Kit Completeness

A field kit requires:

N=16

items. Released and verified items:

N_c=15

The work rule requires complete kits. Check release.

Solution

Completeness:

C=\dfrac{15}{16}=93.75\%

But the rule requires:

100\%

The kit fails.

Engineering Comment

A single missing seal, fastener, cable or label can stop work. Kit release is often all-or-nothing.

Plausibility Check

Fifteen of sixteen is high percentage completion but not complete.

Exercise 10: Two-Bin Replenishment Signal

Each bin holds:

120\ \text{units}

Consumption is:

30\ \text{units/h}

Replenishment lead time is:

3\ \text{h}

Check whether one bin covers lead time.

Solution

Lead-time demand:

D_L=30(3)=90\ \text{units}

One bin coverage:

120\geq90

The two-bin rule passes on quantity.

Engineering Comment

The rule still needs reliable bin signaling and route response. If the empty-bin signal is delayed, coverage shrinks.

Plausibility Check

One bin covers four hours of demand, more than the three-hour lead time.

Exercise 11: Transport Pallet Capacity

Inbound material needs:

P=26\ \text{pallets}

One truck carries:

10\ \text{pallets}

Find trucks required.

Solution

Trucks:

N=\dfrac{26}{10}=2.6

Round up:

N=3\ \text{trucks}

Engineering Comment

Transport capacity should be scheduled before release. A partial truck count does not move the last pallets.

Plausibility Check

Two trucks carry only twenty pallets; three are needed for twenty-six.

Exercise 12: Staging Area Limit

Each pallet occupies:

1.1\ \text{m}^2

Staging area allows:

24\ \text{m}^2

Can $26$ pallets be staged?

Solution

Required area:

A=26(1.1)=28.6\ \text{m}^2

Since:

28.6>24

the staging plan fails.

Engineering Comment

Material release should check physical staging capacity, not only truck capacity.

Plausibility Check

Twenty-six pallets at slightly more than one square meter each exceed twenty-four square meters.

Exercise 13: Route Time Capacity

A replenishment route has:

8

stops. Average stop time is:

6\ \text{min}

Travel time per loop is:

22\ \text{min}

Find loop time.

Solution

Stop time:

T_s=8(6)=48\ \text{min}

Loop time:

T=48+22=70\ \text{min}

Engineering Comment

Loop time must fit the replenishment interval. Adding stops without route redesign can starve points of use.

Plausibility Check

The stops dominate the loop; total time just over an hour is expected.

Exercise 14: Route Loops per Shift

A shift has:

480\ \text{min}

Available route time after breaks and checks is:

420\ \text{min}

Loop time is:

70\ \text{min}

Find loops per shift.

Solution

Loops:

N=\dfrac{420}{70}=6

Engineering Comment

The route has no spare loop capacity if six loops are fully consumed. Expedites may require reserve or a second route.

Plausibility Check

Six seventy-minute loops take exactly four hundred twenty minutes.

Exercise 15: Line-Stop Exposure from Late Replenishment

A line consumes:

2.5\ \text{containers/h}

The route is late by:

1.2\ \text{h}

Find extra containers needed to avoid starvation.

Solution

Extra containers:

N=2.5(1.2)=3.0

So:

3\ \text{containers}

are needed.

Engineering Comment

Late-route exposure can be controlled by route reliability, emergency stock or shorter intervals. Adding containers may create space and inventory problems.

Plausibility Check

At two and a half containers per hour, a little over one hour requires about three containers.

Exercise 16: Scan Accuracy

In a cycle audit:

N=120

line-side scans are checked. Errors found:

e=5

Find scan accuracy.

Solution

Accuracy:

A=1-\dfrac{e}{N}=1-\dfrac{5}{120}=0.958

So:

A=95.8\%

Engineering Comment

Poor scan accuracy weakens replenishment signals. Physical stock may be correct while system stock drives wrong releases.

Plausibility Check

Five errors in one hundred twenty checks is a little over four percent error.

Exercise 17: Replenishment Shortage Exposure

A frozen schedule needs:

3680

brackets. Available brackets:

3500

Line output is:

230\ \text{units/h}

Each unit needs two brackets. Estimate lost output hours if no brackets arrive.

Solution

Bracket shortage:

S=3680-3500=180

Finished units short:

U=\dfrac{180}{2}=90

Lost hours:

H=\dfrac{90}{230}=0.391\ \text{h}

Engineering Comment

Small component shortages can stop high-rate production. The response may be inspection acceleration, reallocation or schedule resequencing.

Plausibility Check

Ninety finished units at two hundred thirty units per hour is less than half an hour.

Exercise 18: Line-Side Release Gate

A material release package has:

Gate	Requirement	Current result
Kanban space	sufficient	fail
BOM coverage	no shortages	fail
kit completeness	$100\%$	$93.75\%$
scan accuracy	at least $98\%$	$95.8\%$

Decide whether to release.

Solution

All listed gates fail. The material release is not releasable.

Engineering Comment

Line-side release needs physical space, complete material and trustworthy signals. A good inventory policy cannot overcome failed execution gates.

Plausibility Check

Multiple hard gates fail, so the only defensible decision is hold or restrict release.

Validation Package Checklist

A strong material replenishment solution should check:

whether material location and quality state are explicit;
whether Kanban cards match lead time, demand and route reliability;
whether line-side space can safely hold the required containers;
whether unit loads match handling, ergonomics and point-of-use needs;
whether frozen-window demand is checked for every constrained BOM item;
whether inspection-hold material is excluded until released;
whether kits are complete, labeled and revision-correct;
whether transport, staging, scan accuracy and route timing are verified.

Common Release Mistakes

Common mistakes include sizing Kanban without checking space, counting gross stock as line-side available, releasing a frozen schedule while one BOM item is short, ignoring inspection delay, treating ninety-percent kit completion as enough, adding transport capacity without staging space, trusting scan data without audit evidence, and releasing material flow because inventory policy passes while point-of-use gates fail.

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