safety stock levelthe simple economic order

Question

Safety Stock Level

The simple Economic Order Quantity (EOQ) model used in inventory management assumes that the reorder point  will be at a level equal to (Lead time in number of days x usage in units per day). In other words, EOQ assumes that the usage is uniform and that the lead time can be predetermined and does not tend to vary. If both these assumptions hold good, the economic quantity ordered will just reach the stores when all the existing units in stock have been consumed in production. Hence there cannot be a situation of 'stock-out', that is, a situation where customers are denied goods or when the production line is stopped for want of input materials.

In reality, the usage in units per day may not be predictable and may move in a random manner and similarly the lead time could also be a random variable. Instead of being able to define these two parameters exactly, the organization may be in a position only to gain an idea of the probability distribution of the usage and the lead time. In addition, when both usage and lead time tend to vary, situations of stock-out could easily arise. A stock-out could lead to losses on account of,

1. Loss of potential customers.

2. Loss of goodwill among existing customers.

3. The need to make emergency purchases at a high cost either to satisfy the demand or keep the production line moving.

4. Idle time costs when the production has to be temporarily halted till the quantity ordered is received in stores.

Any organization must view a stock-out with sufficient concern and one way to avoid stock-outs is to maintain a safety stock. The safety stock acts as a buffer which can be drawn in periods when the usage tends to be higher than the usual or when the lead time tends to be longer than normal or both such adverse conditions co-exist. The safety stock acts as a cushion against the time required for placing an order and receiving the material.

While deciding on the level of safety stock, the organization must try to choose the optimum quantity at which the stock-out costs and carrying costs are minimized. Determination of safety stock is illustrated with the help of the following example.

 

Example

 

Maruti Components Limited has determined that the EOQ of material P23 is 250 units. The normal lead time is 20 days and normal usage is 5 units per day. The company orders P23, six times a year. The probability  distribution of usage during reorder period is given below:

Usage During Reorder Period (Units)	Probability
90	0.17
95	0.20
100	0.45
105	0.10
110	0.05
115	0.03

The cost of a stock-out is estimated to be Rs.30 per unit and the annual carrying cost is Rs.6 per unit.

Required

1. Determine the reorder point when no safety stock is maintained.

2. Also, determine the optimum  safety stock and the reorder point when it is decided to carry a safety stock.

Solution

          1. In this example, the normal lead time is given as 20 days and the normal usage as 5 units per day.

If no safety stock were maintained, when the stock falls to 100 units, that is (20 x 5), the company should order the EOQ.

Hence, the reorder point when no safety stock is maintained is 100 units.

2. Safety stock is required as a buffer during those periods when the usage is more than 100 units. While carrying a high level of safety stock would decrease the stock-out costs, the corresponding inventory carrying costs would be very high. On the other hand, while carrying a low level of safety stock would decrease the carrying costs, the stock-out costs would be high. The optimal safety stock should be fixed at that level where the total cost of carrying and stock-out is the minimum. This optimal level can be determined by considering the total costs at various safety stock units.

From the pattern of usage given, the possible safety stock levels are, zero units, 5 units, 10 units and 15 units only (since the usages equal to and higher than 100 are 100, 105, 110 and 115).

The stock-out costs at various safety stock levels are computed as below:

Safety Stock	Probability of being out of Stock	Number of Stock- out Units	Expected Stock-out Costs (Shortage x Prob. of Shortage x Stock-out Cost x No. of orders per year)  Rs.	Total Annual Stock-out Costs  Rs.
0	0.10 when usage is 105	5	5 x 0.10 x 30 x 6    = 90	261
	0.05 when usage is 110	10	10 x 0.05 x 30 x 6 = 90
	0.03 when usage is 115	15	15 x 0.03 x 30 x 6= 81
5	0.05 when usage is 110	5	5 x 0.05 x 30 x 6    = 45	99
	0.03 when usage is 115	10	10 x 0.03 x 30 x 6= 54
10	0.03 when usage is 115	5	5 x 0.03 x 30 x 6    = 27	27
15	Nil	Nil	Nil	Nil

The carrying costs and total of stock-out and carrying costs for various safety stock levels is tabulated below:

Safety Stock	Carrying Cost Rs.	Stock-out Cost Rs.	Total Cost Rs.
0	0	261	261
5	30	99	129
10	60	27	87
15	90	-	90

Since the total cost is minimum when the safety stock level is 10 units, we may conclude that the optimum safety level is 10 units.

The reorder point with the safety stock being maintained is 110 units. In the above example, a probability distribution for various levels of usage had been given. In reality there could be a probability distribution for usage per day and another probability distribution for the lead time. Determining the optimum safety stock when both usage and lead time behave randomly can be quite complex.