Supermarkets are an effective way to control inventory between two disconnected processes because they’re permitted to hold a maximum quantity of inventory. When the maximum is reached, then production stops at the supplying process. Since the inventory quantity in every supermarket could potentially drop to zero, every supermarket also has a minimum quantity of inventory it can hold. But just how much inventory should a supermarket hold?

Sizing the supermarket can be straightforward in certain situations, such as in a business with steady, repeatable demand. Yet when order quantities vary and fluctuate all the time, it can be challenging for companies, who often increase labor, time at machines and processes and management intervention.

However, if sized correctly supermarkets can buffer operations against variation in customer demand. While there are various parts of a supermarket pull system, three components should be considered for a truly effective system:

- cycle stock
- buffer stock
- safety stock

### Cycle Stock

Cycle stock is the amount of inventory required to cover normal demand. It has two variables: the mathematical mean, or the average rate of customer demand per time period, and the lead time to replenish at the supplying process, which takes into account both how long it takes to actually run the product on the machine or process as well as how long the product will wait until everything else in front of it has been run.

The mathematical mean is calculated as:

To calculate cycle stock, we take the mathematical mean and multiply it by the lead time to replenish at the supplying process^{1 }:

When it comes to sizing supermarkets, the average rate of customer demand, or cycle stock, is part of the total equation, but it is not the only part. If an operation sizes supermarkets based solely on the average rate of customer demand, it will be unable to handle any variation or fluctuation in customer demand, which is why buffer stock is also needed.

### Buffer Stock

Buffer stock is the amount of inventory required to cover customer induced variation. A supermarket with buffer stock is able to continue supplying product even if all the cycle stock is consumed due to larger-than-expected customer orders.

Buffer stock is the mathematical representation of customer induced variation, otherwise known as the standard deviation from the mathematical mean. The standard deviation is calculated as:When sizing buffer stock, two standard deviations are recommended to account for 95.5% of customer induced variation (assuming a normal distribution of demand). So, the equation for buffer stock is:

Because the buffer stock calculation involves standard deviation, a point of caution is necessary. The buffer stock calculation works best if customer demand falls into a normal distribution. As a result, when a company’s demand profile has a great deal of variation, the first step is to try and figure out why (for instance, is it because there’s always an end-of-the-month push to meet sales numbers?), then attempt to reduce the variation before doing buffer stock calculations in order to make them as practical as possible.

Even if the variation in customer demand can’t be reduced, an operation still needs to calculate buffer stock for the supermarket since failing to carry the buffer stock in the quantity dictated by the previous equation will cause the business to end up shorting the customer at some point in the future.

Next, it’s important to understand how to factor internal variation into the size of the supermarket.

### Safety Stock

Safety stock is the amount of inventory required to cover internal losses, which could be scrap, rework, downtime, and other factors. A supermarket with safety stock is able to continue supplying product even if production at the supplying process or other, supporting processes is slowed or halted due to internal causes.

Safety stock is mathematically calculated as a certain percentage of the cycle stock referred to as the safety factor. The size of the safety factor is related to how significant the internal losses are: the higher the internal losses, the higher the safety factor. If, for example, the cycle stock in a supermarket is 1,000 units, and the safety factor is determined to be five percent (5%), then the safety stock carried in that supermarket would be 50 units. So, the equation for safety stock is:

*The total size of the supermarket is the cycle stock, plus the buffer stock, plus the safety stock. However, these basic calculations are not set in stone, nor are they immune to modification. Analysis may reveal reasons to deviate from the calculations. Yet these determinations should be made as a result of an objective process and not because of someone’s personal opinion or what a manager thinks should happen.*

^{1 }We need to make sure our units of measure are consistent here. For example, if we’ve calculated the average customer demand per day, then we also need to measure the lead time to replenish in days.