If the lead-time is, say, 5 days, an order has to be placed before stocks have been exhausted. Specifically, the order should be placed when there is still sufficient stock to last 5 days, i.e:

Re-order level (ROL) = Demand in lead-time

So, if lead-time for a particular stock item is 5 days and daily demand is 30 units, the re-order level would be 5 days at 30 units per day, 150 units.

### Variable demand in the lead-time

If demand in lead-time varied, it could be described by means of some form of probability distribution. Taking the previous example of the demand in lead-time being 150 units, we’re considering the possibility of demand being more than 150 or less than that. See Figure 5.

Note: This aspect of stock control produces a few problems. The EOQ formula requires that demand (and lead-time) for a stock item be constant. Here the possibility of demand varying or lead-time varying or both varying is introduced. Setting that problem aside, most ACCA syllabuses at the lower levels avoid any discussion of uncertainty or probability distributions. However, uncertainty in lead-time demand in stock control has featured in exams.

In these circumstances, a firm could place an order with a supplier when the stock fell to 150 units (the average demand in the lead-time). However, there’s a 33% chance (0.23 + 0.08 + 0.02 = 0.33) that demand would exceed this re-order level, and the organisation would be left with a problem. It is therefore advisable to increase the re-order level by an amount of ‘buffer stock’ (safety stock).

### Buffer stock

Buffer stock is simply the amount by which ROL exceeds average demand in lead-time. It is needed when there is uncertainty in lead-time demand to reduce the chance of running out of stock and reduce the cost of such shortages.

If a ROL of 160 units was adopted, this would correspond to a buffer stock of 10 units (and reduce the chance of running out of stock to 0.08 + 0.02 = 0.1, or 10%). A ROL of 170 is equivalent to a buffer stock of 20 and reduces the chance of running out to 2%, and a ROL of 180 implies 30 units of buffer stock (and no chance of running short).

### Optimal Re-order Levels

This leaves the problem of how to calculate the optimal ROL. There are two common ways in which one could determine a suitable re-order level (if the information was available):

- A tabular approach – Calculate, for each possible ROL (each level of buffer stock) the cost of holding different levels of buffer stock and the cost incurred if the buffer is inadequate (‘stock-out’ costs). The optimal re-order level is that level at which the total of holding and stock-out costs are a minimum.
- A ‘service level’ approach – An organisation has to determine a suitable level of service (an acceptably small probability that it would run out of stock), and would need to know the nature of the probability distribution for lead-time demand. These two would be used to find a suitable ROL.

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**Tony Mock is a freelance lecturer and writer and an ACCA subject coordinator**