# Safety Stock

A safety stock refers to inventories held by a company as a buffer/reserve against any increase is demand during the work-order lead time and/or delay in receipt/production of inventories.

A safety stock is a rainy-day stock held by a company to guard against stock-out costs. Stock out costs are costs that result from non-availability of raw materials and/or finished goods. Availability of adequate raw materials is important for production to continue smoothly. If there is any disruption in supply of raw materials, the production process would stop, and the company must incur significant setup costs to restart it. Similarly, availability of sufficient finished goods inventory is also critical because if there is no finished goods inventory on hand, the company will lose sales and it would hurt its reputation.

## Formula

Estimation of appropriate level of safety stock depends on the nature and extent of stock-out costs and carrying costs. A company should select its safety stock such that the sum of its stock-out costs and carrying costs is minimized.

If the stock-out costs are very high, maintaining maximum safety stock might make sense. The maximum safety stock level can be worked out using the following formula:

Maximum Safety Stock
= (Maximum Weekly Demand – Average Weekly Demand) × Maximum Lead Time (in Weeks)

But this approach is not optimal in all cases. It is because when safety stock is high, carrying costs are high too. In practice, companies identify their optimal safety cost by conducting a scenario analysis based on the probability of different demand levels. Identifying the safety stock under this method involves the following steps:

STEP 1: Find out carrying cost per unit, stock-out cost per unit, economic order quantity (EOQ) and reorder level.

STEP 2: Using historical data, assign different probabilities to occurrence of difference demand levels.

STEP 3: Select a safety stock level and find out expected stock out costs and carrying costs using the following formulas:

Expected Stock Out Costs = Σ (SO × P × O × SOC)

Where SO is the shortage of unit i.e. the volume of stock-out, P is the associated probability the stock-out, O stands for number of orders and SOC is the stock-out cost per unit.

Expected Carrying Costs = S × CC

Where S is the safety stock level and CC is the carrying cost per unit per annum.

STEP 4: Select another safety stock level and calculate expected stock-out costs and carrying costs.

STEP 5: Identify the safety stock level which minimizes the sum of stock-out costs and carrying costs.

## Example

You work as Management Accountant at Merin Inc., is a company which provides consumables used in diesel generators. Your average weekly consumption is 1,250 units and maximum consumption is 1,500. The average lead time and maximum lead time for the order that you place are 2 weeks and 3 weeks respectively. Further, stock-out cost is \$4 per unit, carrying costs are \$2 per unit per annum and you place 12 orders per annum.

If you are the most risk-averse when it comes to your reputation, you may build a safety stock based on worst-case scenario

Maximum Safety Stock = (1,500 – 1,250) × 3 = 750

Your reorder level at the safety stock level of 750 units would be 3,250.

Reorder Level
= Average Weekly Demand × Average Lead Time + Safety Stock
= 1,250 × 2 + 750
= 3,250 units.

Your CFO suspects that the safety stock is too high. He provided you the following table of expected demand and associated probabilities and asked you to carry out a scenario analysis at safety stock of 250, 500 and 750 and see which level is optimal.

 Demand 2,200 2,400 2,500 3,000 3,500 Probability 0.15 0.20 0.40 0.15 0.10

The following table works out the sum of stock-out costs and carrying costs at the aforementioned safety stock levels:

Safety Stock Demand Stock Out in Units Probability Stock Out Costs Orders Annual Stock-Out Costs Annual Carrying Costs Total Costs
250 2,200 - 0.15 - 12 -
2,400 - 0.20 - 12 -
2,500 - 0.40 - 12 -
3,000 250 0.15 150 12 1,800
3,500 750 0.10 300 12 3,600
5,400 1,500 6,900
500 2,200 - 0.15 - 12 -
2,400 - 0.20 - 12 -
2,500 - 0.40 - 12 -
3,000 - 0.15 - 12 -
3,500 500 0.10 200 12 2,400
2,400 3,000 5,400
750 2,200 - 0.15 - 12 -
2,400 - 0.20 - 12 -
2,500 - 0.40 - 12 -
3,000 - 0.15 - 12 -
3,500 250 0.10 100 12 1,200
1,200 4,500 5,700

In the table above, stock-out in units is calculated using the following formula:

Stock-out = Demand - Reorder Level - Safety Stock

Since the total cost is minimum when safety stock is 500, it is the optimal safety stock.

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