If the lead-time is, say, five days, an order has to be placed before inventories have been exhausted. Specifically, the order should be placed when there is still sufficient inventory to last five days, ie:

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

So, if lead-time for a particular inventory item is five days and daily demand is 30 units, the re-order level would be five 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.

Note: This aspect of inventory control produces a few problems. The EOQ formula requires that demand (and lead-time) for a inventory 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 inventory control has featured in exams.

In these circumstances, a firm could place an order with a supplier when the inventory 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 inventory’ (safety inventory).

### Buffer inventory

Buffer inventory 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 inventory and reduce the cost of such shortages.

If a ROL of 160 units was adopted, this would correspond to a buffer inventory of 10 units (and reduce the chance of running out of inventory to 0.08 + 0.02 = 0.1, or 10%). A ROL of 170 is equivalent to a buffer inventory of 20 and reduces the chance of running out to 2%, and a ROL of 180 implies 30 units of buffer inventory (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 inventory) the cost of holding different levels of buffer inventory 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 inventory), 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.

Written by a member of the Paper F2/FMA examining team