Safety Stock

If Glare Shade’s managers are uncertain about demand or the purchase-order lead time or if they are uncertain about the quantities of UX1s Rytek can provide, they will hold safety stock. Safety stock is inventory held at all times regardless of the quantity of inventory ordered using the EOQ model. Companies use safety stock as a buffer against unexpected increases in demand, uncertainty about lead time, and unavailability of stock from suppliers. Suppose Glare Shade’s managers are uncertain about demand. They expect the demand for UX1s to be 250 units per week, but it could be as high as 400 units per week or as low as 100 units per week. If stockout costs are very high, the managers will want to hold a safety stock of 300 units and incur higher carrying costs. The 300 units equal the maximum excess demand of 150 400−250 units per week times the 2 weeks of purchase-order lead time. If stockout costs are minimal, no safety stock will be held to avoid incurring the additional carrying costs. But if stockout costs are moderate (neither very high nor very low), managers need to balance the benefits of reducing stockouts with the extra cost of carrying safety-stock inventory.

Managers use a frequency distribution based on prior daily or weekly levels of demand to compute safety-stock levels. Assume that one of the following levels of demand for UX1s will occur over the 2-week purchase-order lead time.

Total Demand for 2 Weeks200 Units300 Units400 Units 500 Units600 Units700 Units800 Units
Probability (sums to 1.00)0.060.090.200.300.200.090.06

We see that 500 units is the most likely level of demand for 2 weeks because it has the highest probability of occurrence. We see also a 0.35 probability that demand will be 600, 700, or 800 units (0.20+0.09+0.06=0.35).

If a customer wants to buy UX1s and the store has none in stock, Glare Shade can “rush” them to the customer at an additional cost to Glare Shade of $4 per unit. The relevant stockout costs in this case are $4 per unit. The optimal safety-stock level is the quantity of safety stock that minimizes the sum of annual relevant stockout and carrying costs. Note that Glare Shade will place 13 orders per year for UX1s and will incur the same ordering costs whatever level of safety stock it chooses. Therefore, ordering costs are irrelevant for the safety-stock decision. Recall that the relevant carrying cost for UX1s is $5.20 per unit per year.

Exhibit 21-3 tabulates the annual relevant total stockout and carrying costs when the reorder point is 500 units. Over the 2-week purchase-order lead time, stockouts can occur if demand is 600, 700, or 800 units because these levels exceed the 500 units in stock at the time Glare Shade places the purchase orders. Consequently, Glare Shade only evaluates safety stock levels of 0, 100, 200, and 300 units of UX1s. If the safety stock is 0 units, Glare Shade will incur stockout costs if demand is 600, 700, or 800 units but will have no additional carrying costs. At the other extreme, if the safety stock is 300 units, Glare Shade will never incur stockout costs but will have higher carrying costs. As Exhibit 21-3 shows, the firm’s annual relevant total stockout and carrying costs are lowest ($1,352) when a safety stock of 200 units of UX1s is maintained. Therefore, 200 units is the optimal safety-stock level. The 200 units of safety stock is the extra stock that Glare Shade always maintains. For example, Glare Shade’s total inventory of UX1s at the time of reordering its EOQ of 1,000 units would be 700 units (the reorder point of 500 units plus safety stock of 200 units).

Exhibit 21-3

Computation of Safety Stock for Glare Shade When Reorder Point Is 500 Units

Spreadsheet screenshot shows computation of safety stock for glare shade when reorder point Is 500 Units.

Details of the table are as follows:

Stockout in Units is calculated by Demand level resulting in stockouts minus Inventory available during lead time (excluding safety stock), 500 units minus Safety stock.

Relevant Stockout Costs is product of Stockout in units and Relevant stockout costs of $4.00 per unit.

Expected stockout costs is product of Probability of stockout and Relevant stockout costs and Number of orders per year.

Relevant Carrying Costs is product of Safety stock, Annual relevant carrying costs of $5.20 per unit (assumes that safety stock is on hand at all times and that there is no overstocking caused by decreases in expected usage).

  1. Safety Stock Level in Units: 0

  2. Demand level resulting in stockouts: 600

  3. Stockout in Units (difference between above 2 minus 500 minus 1): 100

  4. Probability of Stockout: 0.20

  5. Relevant Stockout Costs (product of above 3 and $4): $400

  6. Number Orders per Year: 13

  7. Expected stockout costs (product of above 4, 5 and 6): 1040

  1. Safety Stock Level in Units: 0

  2. Demand level resulting in stockouts: 700

  3. Stockout in Units (difference between above 2 minus 500 minus 1): 200

  4. Probability of Stockout: 0.09

  5. Relevant Stockout Costs (product of above 3 and $4): $800

  6. Number Orders per Year: 13

  7. Expected stockout costs (product of above 4, 5 and 6): 936

  1. Safety Stock Level in Units: 0

  2. Demand level resulting in stockouts: 800

  3. Stockout in Units (difference between above 2 minus 500 minus 1): 300

  4. Probability of Stockout: 0.06

  5. Relevant Stockout Costs (product of above 3 and $4): $1200

  6. Number Orders per Year: 13

  7. Expected stockout costs (product of above 4, 5 and 6): 936

  8. Relevant Carrying Costs (product of above 1 and $5.20): 0

  9. Relevant Total Costs (calculated by sum of above all 7 and 8) for Safety Stock Level in unit 0: $2912

  1. Safety Stock Level in Units: 100

  2. Demand level resulting in stockouts: 700

  3. Stockout in Units (difference of above 2 minus 500 minus 1): 100

  4. Probability of Stockout: 0.09

  5. Relevant Stockout Costs (product of above 3 and $4): $400

  6. Number Orders per Year: 13

  7. Expected stockout costs (product of above 4, 5 and 6): 468

  1. Safety Stock Level in Units: 100

  2. Demand level resulting in stockouts: 800

  3. Stockout in Units (difference between above 2 minus 500 minus 1): 200

  4. Probability of Stockout: 0.06

  5. Relevant Stockout Costs (product of above 3 and $4): $800

  6. Number Orders per Year: 13

  7. Expected stockout costs (product of above 4, 5 and 6): 627

  8. Relevant Carrying Costs (product of above 1 and $5.20): $520

  9. Relevant Total Costs (calculated by sum of above all 7 and 8) for Safety Stock Level in unit 100: $1612

  1. Safety Stock Level in Units: 200

  2. Demand level resulting in stockouts: 800

  3. Stockout in Units (difference between above 2 minus 500 minus 1): 100

  4. Probability of Stockout: 0.06

  5. Relevant Stockout Costs (product of above 3 and $4): $400

  6. Number Orders per Year: 13

  7. Expected stockout costs (product of above 4, 5 and 6): 312

  8. Relevant Carrying Costs (product of above 1 and $5.20): $1040

  9. Relevant Total Costs (calculated by sum of above all 7 and 8) for Safety Stock Level in unit 100: $1352

  1. 1. Safety Stock Level in Units: 300

  2. 7. Expected stockout costs (product of above 4, 5 and 6): 0

  3. 8. Relevant Carrying Costs (product of above 1 and $5.20): $1560

  4. 9. Relevant Total Costs (calculated by sum of above all 7 and 8) for Safety Stock Level in unit 100: $1560.

At a safety stock level of 300 units, no stockout will occur and, hence, expected stockout costs 5 $0.

Companies are getting increasingly sophisticated at understanding customers using techniques such as design thinking and data analytics. This deeper understanding reduces the uncertainties about demand that companies face and the need to hold large quantities of safety stocks.