The classic sawtooth model is a really a good inventory model.

However, the classic model uses quantities instead of inventory days.

How the sawtooth model works:

1. When inventory level reaches the order point, start a purchase/production order.
2. The amount to order or produce is called the order quantity. 
3. The order quantity complete the gap to the target max inventory.

Explanations:

Inventory day = the amount of material we use on average every day (if it is a finished product, use 1 sale day).

Reorder point = the inventory level that triggers replenishment of stock. When reaching that point we will open a purchase order or a production order.

Safety stock = the shield that protects us from reaching zero inventory due to unknown increase in the demand or a purchase order that arrives late.

Target max inventory = the largest amount of inventory days we plan to have when the purchase/production order arrives.

Time between purchase orders (or production orders) – the time we wish to have between 2 orders. Some organization would wish to have a purchase order every week, another every 6 month. It depends on the cost of the inventory and the cost of creating, following, and accepting purchase orders.

Calculation:

Reorder point* = Safety stock (inventory days) + Lead time (days)

Lead time = Average actual lead time** +  (Actual lead time standard deviation**  X (1 or 2))

Safety stock = depends on the fluctuation of the demand and the lead time. Remember that you will usually not use this stock, so make sure it is not too large.

Time Between Purchase Orders (or production orders)  = TBPO

Order quantity = reorder point (days) + TBPO

if TBPO > Lead time, then we better use X times of lead times (if the lead time is a week, we can use 4 weeks as the TBPO.

If TBPO < Lead time, then this is a more complicated model that I will address in future if there is demand.

Target max inventory*** = Safety stock + Order quantity or

Target max inventory*** = Safety stock + TBPO

***Note: We need to assume that either the TBPO or the Target max inventory is predefined. The second value will be calculated using the equation above.

Inventory day =  Take (30*4)=120 days of past consumption and divide it by 120. If you have a forecast of X days ahead then divide the sum of all forecast by this X .If you are looking for a finished goods inventory model, then use 1 sales day (30*4)=120 days of sales divided by 120.

*Note: If the time between 2 purchase orders is longer than the Lead time, then use the formula above. If not then the calculation are different and i will address it in the future.

**Note: When calculating the average and STD, make sure you eliminate the outliers.

If it hasn’t been clear until now, each value here is in inventory days.

The only value you keep updating is the “inventory day” that can be recalculated every month/quarter.

Example:

Let’s assume that we make chocolate bars.

Every chocolate bar uses 50 grams of cocoa. We make 1,000 bars a day.

The average lead time for new cocoa is 40 days. But sometimes the shipment arrives after 45 or even 50 days. The standard deviation for the lead time is 5 days.

Suppose we want to order only once every 2 months.

So let’s calculate the model:

Every day we use 1,000×50 grams of cocoa, which is 50kg a day.

 

1 inventory day = 50kg

Lead time = 30 days (average) + 2xStandard deviation of lead time = 30+2×5=40

Since the demand is almost constant (50kg a day) and the lead time takes 2 standard deviations in its calculation, we can use a small safety stock. The safety stock will be 7 days just in case we have an extraordinary lead time or sudden high demand.

Safety stock = 7days

Reorder point = Safety stock (7) + Lead time (40) = 47

TBPO = 60 days (2 months)

Order quantity =  Reorder point (47) + TBPO(60)  = 107

Target max inventory = Safety stock + Order quantity = 7 + 107= 114

 

 

The example solution in a story:

When we arrive at 47 days of inventory, we will order 107 inventory days. 1 inventory day = 50kg

Our stock should not be more than 114 days .

Our stock should not be less than 7 days (unless we have a purchase order that is over 7 days late)

Once a month/quarter/year we will check again how much is 1 inventory day.

I will be happy if you leave a comment or send me a note to theplanningmaster@gmail.com

You can read the same article in hebrew here.