Optimizing Material Order under Logistics Constraints

In the field of material planning, we observe some critical differences compared to the production planning. In this article, I will try to analyse these differences and propose an optimum material order function.

Let’s first try to adapt the improved EOQ discussed in How to optimize Production Order. The formula is;

EOQ = Sqrt[ 2Kd / (hCSL)]

If we want to apply it to the material supply, we need to change (K). Instead of applying a setup cost, we need to put the transportation cost per load.

Here, the container load is (CL). And, we need a number (m) of the containers to carry a periodic demand (d). Then;

m= Rndup[d/CL]

Rndup[…] is the operator, rounding up the division to the nearest integer. So if the transportation cost per CL is (G), then the total transportation cost (K) to carry load (d) is;

K = mG

After we calculate EOQ with this K, we need to compare it with mCL. mCL is the number of container that should carry the periodic demand (d).

We need to choose the minimum of EOQ and mCL, because of the behavior of the total supply chain cost function. First, the logistics cost per unit is at minimum level, when we order container multiples. So, the logistics cost of EOQ can’t lower than mCL. Second, if the order quantity increases, the opportunity cost increases.

Therefore, the optimum purchase quantity (OPQ) formula is as below;

OPQ = min[EOQ, mCL]

The operator min[…] takes the minimum of these two options. If the demand function is not exotic, (a bell shaped or decreasing trend after mean), we can apply easily this formula to our material orders.

It proposes small amounts but frequent shipments. That reduces the total inventory and the logistics cost, significantly.

After the calculation of OPQ, we can find the reorder point (R). The method is discussed in the article How to optimize inventory. 

You may check Unified Supply Model, for more details.

In the next article, we’ll enter to the special cases like minimum order quantity.