 How does customer order lead time affect inventory management and safety stock calculations?
To discuss how customer order lead time affects your inventory safety stock calculation, let’s first look at the formula for calculating safety stock: The first term deals with the variability of demand and the second term deals with the variability in the lead time.  Today I want to focus on the lead time.

The lead time in this equation specifically refers to the supply lead time.  Let us look at this through some examples. Say, in a fictitious company, it takes:

• 3 days to procure the raw materials
• 2 days of wait time for unpacking etc.
• 1 day to produce
• 4 more days of wait time for ‘curing of the finished good’
• 5 days to transfer to the demand time

Then, the total lead time to create the supply is 3+2+1+4+5 = 15 days.

Let us now look at some variations of the above.

1. Say, the same company likes to keep inventory of the Raw material on hand. 50% of the time, inventory is available to proceed with the production. The other 50% of the time, it is not available. In this case, the lead time is effectively a max of 15 days (when inventory of the raw material is not available) and 10 days (when the inventory of the raw material is available as the first two steps (= 3+2 days) are done beforehand).

The average lead time would be 10+5*0.5 = 12.5 days.

1. Say, the same company likes to keep even more inventory of the Raw material on hand, such that, 90% of the time, inventory is available to proceed with the production. The other 10% of the time, it is not available. In this case, the average lead time would be 10+5*0.1 = 10.5 days.
2. Alternately, assuming the raw material needs to be shipped on a barge. And the barge runs once a week. Now this will effectively lengthen the supply lead time. Instead of the original 15 days, now it will be 15+7 (when you order a second after this week’s barge departs) days on the high side, and 15+0 (when you order a second before this week’s barge departs) days on the low side.

On average the lead time will be 15+7*0.5=18.5 days.

1. If 1 and 3 were both true, the average lead time would be: 10+5*0.5+7*0.5 =16 days
2. If 2 and 3 were both true, the average lead time would be: 10+5*0.1+7*0.5 =14 days

Likewise, one can consider the cases where the company keeps a lot of inventory of the finished product in hand.

## Factoring in Customer Order Lead Time When Calculating Safety Stocks

Let us now consider the base case (lead time = 15 days) and add the following twist: What if the customer orders this product with some lead time say 7 days of order lead time on average.

The customer order lead time effectively gives a business more time to make the material available. So, the lead time to be considered for safety stock calculations would be reduced by 7 days, resulting in lower safety stock. An extreme case of this would be when the customer order lead time is more than the supply lead time. In this case, there is no need to carry safety stock. In fact, this product then becomes a make-to-order product.

So, in this example, the supply lead time to consider would be 15-7 = 8 days.

### Calculating Safety Stocks for a Product with Different Order Lead Times

What if there are two customers ordering this product, and both provide different order lead times? In this case, there are several approaches to consider.

Approach A: Safety Stock = Overall supply lead time – Shorter lead time

One approach is to subtract the shorter of the two lead times from the overall supply lead time to calculate the Safety stock. This the conservative approach.

Approach B: Safety Stock = Overall supply lead time – Longer lead time

The more aggressive approach would be to subtract the longer of the two order lead times from the overall supply lead time. This approach is not recommended.

Calculating Virtual Safety Stocks for the Same Product

If the two customers with the differing lead times are equally important and for instance each account for one-half of the demand for a particular product, then neither of the approaches above represent a good idea. A better approach in that case is to consider two virtual safety stocks for the same product.

As an example, let’s assume that “customer-1” has 3-day order lead time, and “customer-2” has 7-day order lead time.

Then:

• Use a lead time of 15-3=12 days and calculate Safety stock using the demand for the customer 1.
• Use a lead time of 15-7=8 days and calculate Safety stock using the demand for the customer 2.
• Add the two numbers to get the total safety stock for the product in question.

It’s evident that the approach with the lead times when calculating safety stocks are very pragmatic and common sense oriented. Adjustments based on business knowledge are highly recommended.

1. Sometimes adding the lead time variability has the adverse effect because practitioners draw statistical conclusions from very few data points.
• Very true and simple remedy: Ensure there is enough data before calculating things like standard deviation and variance.
2. Wouldn’t splitting the calculation by customer increase variability and therefore increase the safety stock?
• Again very true. The way I see it:
1. One can ignore customer order lead time altogether; this will lead to high SS. I like this option the least, but it seems to be the most commonplace.
2. One can deduct average order lead time from the total supply lead time.
3. One can do what I have suggested, which is to calculate SS differently by treating the demand streams separately, calculating the SS and summing it up. A way to think of this is that I am supplying these two customers from different warehouses (albeit located in the same building). This could also be done after grouping the customers with lead times close to each other to increase statistical significance.

I would do 2 if all customers were either similar in order lead time, or at least were low in volume. I would do 3 if the volumes were significant.