a Poisson model (Figure 2-6), there is no explicit service factor and the risk element is accounted for in the probability part of the model. Here’s how that works. The Poisson function calculates the probability of a certain level of demand over a period of time. If you set that quantity as your ROP, then the probability can be treated as your service factor. Your risk of a stockout is 100 minus the probability of that level of demand.
So, if you look at Figure 2-6, the probability of 7 or fewer demands is 96.4%. Therefore, the risk of a stockout, if you have a reorder point of 7, that is — the risk that there will be more than 7 demands during the lead time for restocking — is:
100 − 94.9 = 5.1%.
The major issue though with the probability/impact decision is the Service Factor Trap. The service factor is the percent of time that the storeroom can supply the required item when it is needed. So a theoretical service factor of, say, 97% sounds high, but in reality for engineering materials and spares, this may not be acceptable.
First, if measured across the entire inventory, no one will care about the 97% figure if the 3% includes critical parts and your plant is shut for a week while they get air-freighted in!
Second, you can have a high overall service level and still be significantly overstocked in individual items, meaning that you have still spent money on items that are not needed.
This is the Service Factor Trap. It can be misleading in terms of the inventory being able to fulfill its actual requirements and in terms of how efficiently money has been invested in inventory. Sweeping statements relating to service factors are convenient and reassuring, but add no real value to the practice of materials and inventory management.
The impact characteristic also depends upon where are you located. Consider a situation where a machine will not run without a specific part. Without doubt, this part would be considered critical and the impact of a stockout significant. However, if you are in an urban center with lots of suppliers close by you, may be able to convince one to hold the part for you and then get the required part delivered within an acceptable time frame – for instance while you remove the failed part. However, if you are located in a remote area where delivery takes days, then the stockout has more significant implications. Both situations have the same probability of failure and at one level the same impact — that level is the plant stops. However, the real impact is different if the full materials management cycle is taken into account. The one size fits all solutions that get rolled out to every situation do not bring the required results.
Location, culture, operating mode, financial status, reliability, and risk tolerance are all things that need to be taken into consideration when determining the ROP.
Figure 2-4: The Normal or Gaussian Distribution
Notes:
1. This calculation uses a Mean Average Deviation (MAD) rather than a Standard Deviation. MAD is a simplified way of determining the deviation and is calculated by determining the average value by which demand deviates from the mean, in absolute terms.
2. The Customer Service Factor is based on a MAD scale, not the Standard Deviation of a Normal curve.
Figure 2-5: Example ROP Calculation
Figure 2-6: The Poisson Distribution
Determining the Re-Order Quantity (ROQ)
The other key decision for materials and spares inventory management is to calculate the Reorder Quantity (ROQ). The ROQ is usually not so highly discussed as the ROP but it has as much, if not more, impact on the quantity of inventory that is held. This is because the point at which a company actually commits to holding inventory and tying up working capital is when the items are ordered. The classic formula for calculating the ‘economic’ ROQ is as follows:
Where:
Order Cost = the company internal cost for processing requisitions, issuing purchase orders and receiving deliveries.
Demand Rate = the expected demand over a year.
Item Cost = the purchase cost of the item, including delivery costs.
Holding Cost = the financial charge for holding inventory (see Chapter 3: The Financial Impact of Inventory).
Although simple in concept, there are some complications in practice.
1.The order cost is crucial to the calculation.
Of the four variables in the calculation, this is the least simple to determine because there is no set rate. The actual order cost will be different for every company and is dependent upon internal company efficiency, local pay rates, and so on. To calculate the order cost, some companies use an Activity Based Costing approach; some just use an estimate such as $100 per order. Note that it is a mistake to use a simplistic calculation such as the total cost of the purchasing and stores departments divided by the number of orders placed because this assumes 100% capacity utilization. No matter which approach you choose, the key is to understand the impact of an error in this value. From the formula you can see that the ROQ varies directly with the square root of the order cost. So, if your estimate of order cost is two times the actual order cost, you will be ordering 41% too much stock and that could be a lot of money. (Recall that the square root of 2 is 1.41.) This estimation error is simple to make. Let’s say the real order cost is $50 per order, but you decide to use $100, just to be sure that everything is covered. This doesn’t seem like much, but will add 41% to the quantity of inventory purchased.
2.The formula assumes that the order cost is fixed.
Your actual order cost may vary due to efficiencies related to the supplier. This could include extra costs at your end due to the supplier being inefficient, losing paperwork, hard to contact, requiring follow up, and order expediting. Or the costs could be less due to acceptance of blanket orders, use of electronic methods, and so on. A blanket approach could result in significant overstocking and the calculated ROQ should be reviewed for any orders of a significant value.
3.The formula assumes that the demand is constant.
We have already seen an example where the demand varies significantly over time. If the calculation is performed when the demand is high, the calculated ROQ value will be high and you will be overstocked.
4.The formula assumes one delivery per order, no allowance for scheduling or batching.
Not all orders are delivered in one delivery and each delivery costs you money in terms of workload.
When faced with determining the factors used to calculate the ROQ, it is suggested that values are used that minimize the order quantity rather than maximize the order quantity as this is the lesser of two evils.
If you overestimate, you will
