How to calculate Total Supply Chain Cost

In order to understand the supply chain, we need to form a precise cost function. That cost function should represent the uncertainty in demand & supply, and several cost items like production setup, logistics etc.

Let’s focus on the certain issues first, like the production setup cost. It’s a result of order quantity (Q). During leadtime demand (D), we will have some amount of production quantity (Q) and each of them has a setup cost (K). Total setup cost can be formulated as;

TC1 = KD/Q

What about the other ones, like logistics? We will analyse them in another article.

When we switch to uncertainty side, we will observe two different issues; expected inventory holding and backorder (lost sales) costs. They are uncertain because they are linked with the demand occurrence.

Firstly, we need to define leadtime demand function, which is discussed in Why need for Leadtime Demand. We may use any type of possibility function in order to represent the leadtime demand, but the analysis and application might be complex. The Unified Supply Model may have a proper solution for any possibility function, but I will not discuss this case here. Therefore, we assume the normal distribution for the demand.

Let’s focus on the inventory holding cost, which is analysed in How to define Customer Service Level. We have the holding cost per unit as (hT). Consider that we want to calculate the expected inventory holding cost of our inventory amount (A).

With the parameter definitions, mean (D) and standard deviation (DSd), our cost function will be;

TC2(A) = (hT) Pst[(A-D)F(A) – (DSd)f(A)]

First, we reach to the expected stock amount left, after the leadtime demand occurs. The operation Pst[..] will consider only the positive results within parenthesis. If the result of this calculation is negative, there’s no need to consider an inventory holding cost.

Because we’ll hold the stock during leadtime period, we multiply the result of Pst[..]  with (hT) to reach the expected inventory holding cost.

Next, let’s check the backorder side. We defined the backorder cost (b) in How to define Customer Service Level. Again for the stock amount (A), our formula is;

TC3(A) = (b) Pst[(D-A)(1-F(A)) + (DSd)f(A)]

First, we calculate what should be the back ordered (or lost sales) amount when our stock is A. Then, we just take the positive ones with the function Pst[..]. Finally, we multiply it with the backorder cost (b)

The sum of TC2 & TC3 is the Opportunity Cost of stock amount (A). Let’s say;

OppCost(A) = TC2(A) + TC3(A)

What about our R & Q cases? As I explained in How to optimize Inventory, the inventory position moves between R and R+Q. In order to calculate whole system’s opportunity cost, we need to apply the formula above for each possible position between R & R+Q, and take the average of them. The simplified version is below.

OppCost = Avg[ OppCost(R) + OppCost(R+Q/2) + OppCost(R+Q) ]

It averages the opportunity cost of the min, middle and max point of the inventory position.

So, the total supply chain cost is;

TC = TC1 + OppCost

Please notice that this calculation is just for a leadtime period. Also, please notice that this is a simplified version, and it can be far away from the real life. Because at start, we assumed normal distribution...

If you want to make it precise, please check the Advanced Version of the Unified Supply Model.

This calculation is for the production environment. We need to establish it for the material ordering. More precisely, the supply chain systems where the logistics is a priority…

Although the opportunity side is same, there are some significant changes on TC1. Before analyzing them, we will optimize the order quantity, in the next article.