The toilet paper crisis of 2020: why this hoarding behavior is mathematically sound

The recent behavior of buying up toilet paper as a result of the COVID-19 pandemic can be explained as logical behavior using everyday inventory mathematics.  I am not advocating for hoarding toilet paper, but I do understand why it happened / is happening. 

As our environment changes, our purchasing decisions change.  I noticed recently that I have been buying more milk than normal.  I am doing this because recently a few times when I have needed to purchase milk the store was out.  This is a key item for my family, so I am now not letting my inventory of milk drop to as low of a level (MIN) and I am buying more than I normally do (MAX).   This is the same thing that is happening with toilet paper – but with toilet paper it is happening in a more drastic way. 

Every household purchases things they need to function – this is inventory.  These purchasing decisions can be compared to business inventory management.  We help organization optimize their inventory with goals to reduce overall inventory cost while ensuring materials are available when needed.  We use math to determine when (MIN) and how much (MAX) of each material should be purchased. 

One methodology for inventory management is MIN / MAX levels.  A MIN is the minimum amount that an organization wants to have on hand.  Once the inventory level falls below the MIN, the purchasing team will be triggered to purchase more.  The MAX is the maximum amount that an organization wants to have on hand.  When the inventory level falls below the MIN, the purchasing team will submit an order to bring the inventory level back to the MAX. 

When calculating the appropriate MIN / MAX levels, we incorporate the following variables:

• Forecast & Forecast Variation

  • The expected usage and the standard deviation of the forecast.

• SKU classification (A, B, C, F) & Service Level

  • Classification of your materials.  ‘A’ items are the most important and have the highest target service level. 

  • Service level indicates the acceptable level of stock outs.  A service level of 95% means the organization requires this item to be in stock 95% of the time and 5% of the time the item will be out of stock. 

• Lead Time

  • The standard lead time for receiving this product; how long it takes to receive the item once you have ordered it.

• Shelf Life

  • Length of time the product will remain viable before spoiling.

• Storage Cost

  • The cost of storing or holding the good.  This includes the cost of capital.

I do the grocery shopping for my family.  While I enjoy math and inventory, I have not calculated MIN / MAX levels for my household goods.  I typically review what I have on hand, review of what I plan to cook for the week and create a list of what I need to purchase.   While we do not run inventory algorithms to decide what to buy for our households, our behavior does loosely follow inventory theory. 

Why Toilet Paper?  What happened?

Let’s look at how the COVID-19 pandemic impacted the inventory variables:

Forecast: No change or slight increase.  As people stay home more there could be a slight increase in toilet paper needs, but I believe this is minimal in driving behavior change.

Service Level: Toilet paper is a unique item in that it is a key item in nearly EVERY household.  This is an item that we NEVER want to run out of -- a service level of 99.9%. 

Lead Time: Typical lead time for toilet paper is just the time it takes you to go to the store.  Once the store ran out of toilet paper, the lead time for customers increased.  We no longer know the lead time – this unknown is the largest factor driving our behavior change.

Shelf Lie: No change.  Note: toilet paper has a very long shelf life.  People are confident that if they buy extra it will be good when they are ready to use it.

Storage / Capital Cost: No change: Note: the cost of toilet paper is relatively low, and most people have space to store extra toilet paper.  Interestingly, most people actually buy way more toilet paper than even they want to due to large package sizes and price discounts.

Why are we buying more & why it is mathematically logical

The formula for calculating the MIN – the amount that triggers consumers to purchase more is:

MIN = Safety Stock + Lead Time Demand

Safety stock is the amount of inventory held to ensure service levels (in-stock %) are maintained despite fluctuations in demand.  The usage of toilet paper in our households is not changing… well maybe a little because we are all working from home and the kids are home from school.   

Lead Time Demand is the amount of toilet paper needed once the order has been placed.  A typical lead time for toilet paper is the amount of time needed to get to the store.  In my house, we go to Costco every week or two, so our lead time demand is the amount of toilet paper needed over the course of a week. 

As a result of this pandemic and toilet paper not being consistently available at the store when needed, our lead time has increased and, in fact, we don’t know when we will be able to purchase toilet paper, so our lead time is unknown.  Since shelf life and storage costs are not issues with toilet paper, mathematically we should be increasing our families MIN / MAX levels on toilet paper.  Hoard away! 

(A future article on The Bullwhip Effect will explain, however, why this behavior is terrible for the supply chain.)