Exercise set

Supply Chain Inventory Policy EOQ, Reorder Point, and Safety Stock Exercises

Solved inventory-policy exercises for EOQ, reorder points, safety stock, service level, MOQ exposure, inventory turns and release gates.

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

These exercises practise inventory-policy decisions for engineered supply chains: economic order quantity, reorder point, safety stock, lead-time demand, service level, minimum order quantity, cycle stock, days of supply, inventory turns, stockout exposure and policy release gates.

The goal is to decide whether inventory rules protect production without hiding cost, obsolescence, shelf-life or shortage risk. Gross stock is not enough; the policy must specify which units are quality-cleared, unallocated, revision-correct and usable inside the planning horizon.

Assume simplified planning models unless an exercise states otherwise. Real inventory release should also check BOM revision, demand phase, forecast bias, allocation conflicts, shelf life, storage limits, ERP accuracy, quality holds, supplier lead-time distribution and shortage consequence.

Release Evidence Notes

Inventory evidence should state item number, planning horizon, demand basis, lead-time boundary and inventory state. On-hand stock, available-to-promise stock, quality-cleared stock and allocated stock are different numbers.

EOQ evidence should be treated as a cost screen. Final policy may be governed by MOQ, shelf life, supplier lot size, price breaks, packaging multiple, storage capacity or shortage criticality.

Safety-stock evidence should state whether demand variability, lead-time variability or both are included. If lead time has heavy tails or intermittent demand, a normal approximation may be weak.

Release evidence should check that the chosen policy is executable in the ERP and visible to planners, purchasing, receiving, inspection and production release.

Engineering Boundary Notes

This page covers inventory policy and stock protection. Kanban cards, unit loads, line-side replenishment and inspection release belong in the material replenishment exercise set. Supplier lead-time service, disruption recovery and supplier release gates belong in the supplier performance exercise set.

Critical maintenance spares have additional asset-criticality, repairability and shelf-life concerns; use the critical spare-parts exercise set for that narrower reliability-spares decision.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Order quantity and cost	1-4	EOQ, annual cost, cycle stock and MOQ exposure	Set economic but feasible order rules.
Reorder and safety stock	5-10	lead-time demand, demand variation, z margin and service level	Set reorder points and stock buffers.
Inventory health	11-15	days of supply, turns, allocation, stockout cost and obsolescence	Decide whether policy is usable.
Policy release	16-18	forecast bias, shelf-life exposure and hard gates	Release, restrict or revise the inventory policy.

Exercise 1: Economic Order Quantity

Annual demand is:

D=24000\ \text{units/year}

Order cost is:

S=85

Annual holding cost is:

H=2.40\ \text{per unit-year}

Calculate EOQ.

Solution

Use:

Q^*=\sqrt{\dfrac{2DS}{H}}

Substitute:

Q^*=\sqrt{\dfrac{2(24000)(85)}{2.40}}=\sqrt{1700000}=1303.84

Round:

Q^*=1304\ \text{units}

Engineering Comment

EOQ minimizes a simplified ordering and holding-cost model. It does not check shelf life, MOQ, packaging multiple or supplier capacity.

Plausibility Check

Demand is high and holding cost is modest, so an order above one thousand units is plausible.

Exercise 2: Annual Ordering Cost at EOQ

Using:

D=24000,\quad Q=1304,\quad S=85

estimate annual ordering cost.

Solution

Number of orders per year:

N=\dfrac{D}{Q}=\dfrac{24000}{1304}=18.40

Ordering cost:

C_o=NS=18.40(85)=1564

Engineering Comment

Fractional orders are acceptable in annual cost screening. Actual execution must use whole orders and approved lot sizes.

Plausibility Check

About eighteen orders per year at $85$ each gives a cost a little above $1500$ .

Exercise 3: Annual Holding Cost at EOQ

Using:

Q=1304,\quad H=2.40

estimate annual cycle-stock holding cost.

Solution

Average cycle stock:

I_c=\dfrac{Q}{2}=\dfrac{1304}{2}=652

Holding cost:

C_h=I_cH=652(2.40)=1565

Engineering Comment

At EOQ, ordering and holding costs should be similar. If not, check units, annualization and cost assumptions.

Plausibility Check

The holding cost is nearly equal to Exercise 2 ordering cost, which is expected at EOQ.

Exercise 4: MOQ Exposure

Monthly demand is:

D_m=600\ \text{units/month}

Supplier minimum order quantity is:

MOQ=2400\ \text{units}

Find months of supply and average cycle stock.

Solution

Months of supply:

MOS=\dfrac{2400}{600}=4\ \text{months}

Average cycle stock:

I_c=\dfrac{2400}{2}=1200\ \text{units}

Engineering Comment

Four months of supply may create engineering-change, shelf-life and cash exposure even when unit price looks favorable.

Plausibility Check

At six hundred units per month, twenty-four hundred units last four months.

Exercise 5: Reorder Point with Safety Stock

Average demand is:

d=240\ \text{units/day}

Average lead time is:

L=5\ \text{days}

Safety stock is:

SS=280\ \text{units}

Find reorder point.

Solution

Lead-time demand:

dL=240(5)=1200\ \text{units}

Reorder point:

ROP=dL+SS=1200+280=1480\ \text{units}

Engineering Comment

The calculation should use usable inventory, not gross stock. Inspection holds and allocations can invalidate the trigger.

Plausibility Check

Five days of demand is twelve hundred units; adding safety stock gives fourteen eighty.

Exercise 6: Lead-Time Demand Variation

Daily demand standard deviation is:

\sigma_d=35\ \text{units/day}

Lead time is:

L=6\ \text{days}

Assuming constant lead time, estimate lead-time demand standard deviation.

Solution

For independent daily demand:

\sigma_{LTD}=\sigma_d\sqrt{L}

So:

\sigma_{LTD}=35\sqrt{6}=85.7\ \text{units}

Engineering Comment

This excludes lead-time variability. If supplier lead time varies, safety stock can be much larger.

Plausibility Check

Six independent days increase standard deviation by $\sqrt{6}$ , not by six.

Exercise 7: Safety Stock from Demand Variation

Use:

\sigma_{LTD}=85.7\ \text{units},\qquad z=1.65

Find safety stock.

Solution

Safety stock:

SS=z\sigma_{LTD}=1.65(85.7)=141.4

Round up:

SS=142\ \text{units}

Engineering Comment

Rounding up is appropriate for release screening. Rounding down creates a small but avoidable service-level loss.

Plausibility Check

One and two thirds times eighty-six is a little above one hundred forty.

Exercise 8: Safety Stock with Lead-Time Variation

Daily demand is:

d=180\ \text{units/day}

Demand standard deviation:

\sigma_d=35

Average lead time:

L=6

Lead-time standard deviation:

\sigma_L=1.2\ \text{days}

Use $z=1.65$ .

Solution

Combined standard deviation:

\sigma_{LTD}=\sqrt{L\sigma_d^2+d^2\sigma_L^2}

\sigma_{LTD}=\sqrt{6(35^2)+180^2(1.2^2)}=232.39

Safety stock:

SS=1.65(232.39)=383.44

Round:

SS=384\ \text{units}

Engineering Comment

Lead-time variability dominates. The corrective action may be supplier stabilization rather than more inventory.

Plausibility Check

Including lead-time variation raises safety stock far above the demand-only case.

Exercise 9: Service-Level Z Margin

Lead-time demand has:

\mu=1450,\qquad \sigma=210

Reorder point is:

ROP=1800

Find z margin.

Solution

Use:

z=\dfrac{ROP-\mu}{\sigma}

Substitute:

z=\dfrac{1800-1450}{210}=1.67

Engineering Comment

Z margin is a service-level screen. It should not be used blindly for intermittent or heavy-tail demand.

Plausibility Check

The buffer is $350$ units, or a little more than one and a half standard deviations.

Exercise 10: Stockout Probability from Z

For:

z=1.67

use a one-sided normal tail of:

4.8\%

Find coverage probability.

Solution

Coverage is:

C=1-0.048=0.952

So:

C=95.2\%

Engineering Comment

Coverage should be compared with shortage consequence. A ninety-five percent rule may be weak for a line-stopping engineered component.

Plausibility Check

A z value near $1.65$ normally corresponds to about ninety-five percent one-sided coverage.

Exercise 11: Days of Supply

Usable inventory is:

I=3600\ \text{units}

Average demand is:

d=450\ \text{units/day}

Find days of supply.

Solution

Days of supply:

DOS=\dfrac{I}{d}=\dfrac{3600}{450}=8\ \text{days}

Engineering Comment

Days of supply should use usable inventory and a current demand rate. Old averages can hide launch or shutdown changes.

Plausibility Check

Four hundred fifty units per day consumes thirty-six hundred units in eight days.

Exercise 12: Inventory Turns

Annual demand value is:

V_d=960000

Average inventory value is:

V_i=120000

Find annual inventory turns.

Solution

Turns:

T=\dfrac{V_d}{V_i}=\dfrac{960000}{120000}=8

Engineering Comment

High turns can be good, but not if they create repeated shortage risk on constrained engineered parts.

Plausibility Check

Inventory value is one eighth of annual demand value, so turns are eight.

Exercise 13: Available Inventory after Allocations

Gross on-hand stock is:

S_g=2200

Inspection hold is:

S_q=500

Allocated stock is:

S_a=180

Find usable inventory.

Solution

Usable inventory:

S_u=S_g-S_q-S_a=2200-500-180=1520

Engineering Comment

Inventory policy must act on usable inventory. Gross stock can make a shortage invisible until release.

Plausibility Check

Blocked and allocated stock total $680$ , leaving $1520$ .

Exercise 14: Expected Stockout Cost

Stockout probability during lead time is:

p=0.048

Cost of a stockout is:

C_s=18000

Find expected stockout exposure.

Solution

Expected exposure:

E=pC_s=0.048(18000)=864

Engineering Comment

Expected cost may understate safety or contractual consequences. Some stockouts require hard maximum risk.

Plausibility Check

About five percent of eighteen thousand is just under nine hundred.

Exercise 15: Periodic Review Order-Up-To Level

Average demand is:

d=200\ \text{units/day}

Review period is:

P=7\ \text{days}

Lead time is:

L=5\ \text{days}

Safety stock is:

SS=320

Find order-up-to level.

Solution

Protection period:

P+L=12\ \text{days}

Order-up-to level:

S=d(P+L)+SS=200(12)+320=2720

Engineering Comment

Periodic review needs more stock than continuous review because it protects through the review period plus lead time.

Plausibility Check

Twelve days of demand is $2400$ units; adding $320$ gives $2720$ .

Exercise 16: Forecast Bias Impact on Inventory

Forecast demand is:

F=1000\ \text{units/week}

Actual demand is consistently:

A=1080\ \text{units/week}

For a four-week policy horizon, find hidden shortage from bias.

Solution

Weekly bias:

b=A-F=1080-1000=80

Four-week shortage:

S=4b=4(80)=320\ \text{units}

Engineering Comment

Safety stock can be consumed by bias before random variation occurs. Correct the forecast before increasing buffers blindly.

Plausibility Check

Eighty units per week for four weeks gives three hundred twenty units.

Exercise 17: Shelf-Life Exposure from Policy

Order quantity is:

Q=2400

Monthly demand is:

600

Shelf life is:

3\ \text{months}

Check whether the order is fully consumed before expiry.

Solution

Months of supply:

MOS=\dfrac{2400}{600}=4\ \text{months}

Since:

4>3

the order quantity exceeds shelf-life coverage.

Engineering Comment

MOQ or EOQ can conflict with shelf life. A smaller lot, supplier concession or demand-sharing plan may be needed.

Plausibility Check

The lot lasts four months, but shelf life is only three months.

Exercise 18: Inventory Policy Release Gate

An inventory policy has:

Gate	Requirement	Current result
service coverage	at least $95\%$	$95.2\%$
usable stock basis	required	pass
shelf-life exposure	no expiry before use	fail
forecast bias action	closed	open

Decide whether to release.

Solution

Service coverage and stock basis pass:

95.2\%\geq95\%

Shelf-life and forecast-bias gates fail. The policy is not releasable.

Engineering Comment

Inventory release is not only a service-level calculation. Shelf life and forecast bias can invalidate an otherwise acceptable reorder rule.

Plausibility Check

Two hard gates fail, so release should be held or restricted.

Validation Package Checklist

A strong inventory-policy solution should check:

whether inventory state is usable, quality-cleared and unallocated;
whether EOQ is reconciled with MOQ, packaging and shelf life;
whether reorder point includes lead-time demand and approved safety stock;
whether demand and lead-time variability are both considered when relevant;
whether service level is appropriate for shortage consequence;
whether forecast bias is corrected before adding buffer;
whether ERP triggers match the approved policy;
whether release gates include shelf life, allocation and evidence closure.

Common Release Mistakes

Common mistakes include using gross stock as usable stock, treating EOQ as a release rule, ignoring MOQ exposure, excluding lead-time variation from safety stock, applying a normal service level to intermittent demand, using forecast MAPE while ignoring bias, accepting high inventory turns while stockouts increase, and releasing a policy that passes service level but fails shelf-life or evidence gates.

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