Optimizing Multi Materials Order
Generally, suppliers provide various goods for your production. Let’s consider that we buy more than one material from a supplier. If we can combine the purchase orders, we can gain some additional benefits from the logistics cost. However, there are some challenges.
First, we have uncertain and different demand patterns for each material. And, they have different opportunity cost parameters (Inventory holding and back-order costs). Is it still possible to combine the orders and optimize the inventory?
Yes, it is possible with the Unified Supply Model. Let’s analyse the method.
As we discussed in Optimizing Single Material Order, each material have a periodic demand (d), and container load (CL). The container utilization (CU) of periodic demand is;
CU = d / CL
Let’s consider that we have (n) different materials from this supplier. If we calculate the container utilization for each material, and sum them up, we reach to the supplier container utilization (SuppCU). The formula is;
SuppCU = CU1 + CU2 + … + CUn
This container (or containers) has the amounts covering the periodic demands. (From Material-1 to Material-n). If we can utilize the container full, each material will have the minimum logistics cost. And according to the structure of the Supply Chain Cost Function, the opportunity cost will be also in minimum.
So, how to increase the order amounts per each material? Let’s first define a correction rate (CR), and figure it out with the formula below;
CR = rndup[ SuppCU ] / SuppCU
The operator rndup[…], rounds the number up to the nearest integer. With this rate, we can increase the order amount of each material (i), to fulfill the container.
OPQ(i) = d(i)* CR
So, for each material, we have the optimum order quantity, with minimum logistics and opportunity costs. In the article Optimizing Single Material Order, I propose a formula for OPQ, as the smallest container amount carrying at least the periodic demand. Here, the gain is on the opportunity cost side, due to lower order quantity. That means, if we compare ordering goods separately vs. an ‘order package’: Opportunity cost of the order package will be lower.
What about the reorder point (R)? The core equation of the Unified Supply Model balances the order quantity with a proper reorder point. The process has three steps;
1) Prepare the leadtime demand function explained in the article Leadtime Demand.
2) Calculate customer service level (CSL) according to the article Customer Service Level.
3) Use the leadtime function, CSL and Q, to calculate R according to the article How to optimize Inventory.
These steps should be completed per each material. At the end, we have the optimized ordering and inventory system.
So, the Unified Supply Model provides a simple algorithm to handle many materials, although each has different demand patterns and cost structures.