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F&R Stockroom

Cycle stock · Lead time · Safety stock under random demand

Designed by Daniela Hurtado-Lange, based on Fritz & Roscoe case by Martin Lariviere and Achal Bassamboo. Operations Department, Kellogg School of Management.

Fritz & Roscoe’s Pet Food Store

Turn both switches off for the perfect textbook sawtooth, then add one complication at a time.

Costs

Cost per order S

$/truck

Holding cost H

$/bag·yr

Demand

Average weekly demand R

bags/wk

🎲 Randomness dial

Std. dev. of weekly demand σ_R

Lead time

Order → delivery L

weeks

Policy — how much to order?

Order quantity Q

Policy — when to order?

Reorder point ROP

bags

⇄

Service level CSL

Inventory over time

🏪

Week 0 — customers so far

0 —

⚡ Speed 2 wk/s

🔍 Window 16 wk

Demand during the lead time

theory: Normal(L·R, σ_R√L) what actually happened stock-out (demand > ROP)

Show the common mistake: σ_R × L instead of σ_R × √L

Scoreboard — does the simulation agree with the formula?

Cycles run

order → delivery

Stock-outs

—

CSL simulated

—

what happened

CSL formula

—

NORM.DIST

Fill rate

—

% of bags served

Safety stock

—

I_s = ROP − L·R

Cycle service level counts cycles without a stock-out. Fill rate counts bags served on time — it is always the friendlier number, which is why the two are so easy to confuse.

What it costs — the financial tree, per store per year

Adding lead time costs nothing — we just order earlier, and the average inventory is unchanged. Adding variability costs real money, because the safety stock sits in the warehouse all year long.

How to read this

The people strip above the chart is one mark per customer walking into the store. A week with more people makes the inventory line fall faster — the slope is the demand rate.
Each little step down in the inventory line is one customer buying. Zoom in (small window) to see the steps; zoom out and they blur into the straight diagonal from the slides.
The amber band is a lead time: the stretch between placing an order and the truck arriving. The only thing that decides a stock-out is how far inventory falls inside that band.
Every band produces one dot on the right panel. That is where the bell curve comes from — it is not an assumption, it is the pile of realised lead-time demands.
The ROP line is the cut. Everything to its right in the right panel is a stock-out. Drag ROP and watch the histogram stay exactly where it is while only the cut moves.
Turn the randomness dial to 0 to get the perfect textbook sawtooth, then turn it up slowly.