In real life situations one rarely comes across inventory lead times and usage rates that are known with certainty. When usage rate and/or lead time vary, then the reorder level should naturally be at a level high enough to cater to the production needs during the procurement period and also to provide some measures of safety for at least partially neutralizing the degree of uncertainty.

The question will naturally arise as to the magnitude of **safety stock**. There is no specific answer to this question. However, it depends, *inter alia, *upon the degree of uncertainty surrounding the usage rate and lead time. It is possible to a certain extent to quantify the values that usage rate and lead time can take along with the corresponding chances of occurrence, known as probabilities. These probabilities can be ascertained based on previous experiences and/or the judgemental ability of astute executives. Based on the above values and estimates of stock-out costs and carrying costs of inventory, it is possible to work out the total cost associated with different **levels of safety stock**.

Once we realize that higher the quantity of **safety stock**, lower will be the stock-out cost and higher will be the incidence of carrying costs, the formula for estimating the reorder level will call for a trade-off between stock-out costs and carrying costs. The reorder level will then become one at which the total stock-out costs (to be more precise, the expected stock-out costs) and the carrying costs will be at their its minimum. We consider below through an illustration the way of arriving at the reorder level in a situation where both usage rate and lead time are subject to variation.

**Illustration:**

Below are presented the daily usage rate of a material and the lead time required to procure the material along with their respective probabilities (which are independent) for ABC Ltd. The probabilities and the values of usage rate and lead time are based on optimistic, realistic and pessimistic perceptions of the executives concerned.

Average Daily Usage Rate (units) |
Probability of Occurrence |
Lead Time (No. of days) |
Probability of Occurrence |

200 |
0.25 |
12 |
0.25 |

500 |
0,50 |
16 |
0.50 |

800 |
0.25 |
20 |
0.25 |

From the data contained in the table we can calculate the expected usage rate and expected lead time.

The expected usage rate is nothing but the weighted average daily usage rate, where the weights are taken to be the corresponding probability values. Thus, expected daily usage rate is 200 x 0.25 + 500 x 0.5 + 800 x 0.25 = 500 units

Similarly expected lead time is 12 x 0.25 + 16 x 0.5 + 20 x 0.25 = 16 days

Normal consumption during lead time can be obtained by multiplying the above two values.

i.e., Normal consumption during lead time = 500 units per day x 16 days = 8,000 units

Since normal consumption during lead time has been obtained as 8000 units, stock-outs can occur only if the consumption during lead time is more than 8,000 units.

Let us enumerate the situations with lead time consumption of more than 8,000 units, along with their respective probabilities of occurrence. This can be achieved by considering the possible levels of usage.

The possible levels of usage are:

Daily usage rate |
Lead time in days |
Possible levels of usage |
|||

Units |
Probability |
Units |
Probability |
Units |
Probability |

12 |
0.25 |
2400 |
0.0625 |
||

200 |
0.25 |
16 |
0.50 |
3200 |
0.1250 |

20 |
0.25 |
4000 |
0.0625 |
||

12 |
0.25 |
6000 |
0,1250 |
||

500 |
0.5 |
16 |
0.50 |
8000 |
0.250 |

20 |
0.25 |
10000 |
0.1250 |
||

12 |
0.25 |
9600 |
0.0625 |
||

800 |
0.25 |
16 |
0.50 |
12800 |
0.1250 |

20 |
0.25 |
16000 |
0.0625 |

From the above table it is clear that the situations with the lead time consumption of more than 8,000 units (normal usage) are 10,000 units with a probability of 0.1250, 9,600 units with 0.0625, 12,800 units with 0.1250 and 16,000 units with 0.0625 probability. And the levels of stock-out are 2,000 units, 1,600 units, 4,800 units and 8,000 units respectively. Thus, safety stock level can be maintained at any of the above levels.