Question

In response to the pressures of a weak economy, a firm that has been achieving a 95% service level is considering reducing its inventory levels. (Assume there will be no change in demand.)

a) What service level can they expect to achieve if they reduce their safety stock by 10%?

b) What service level can they expect to achieve if they reduce their safety stock by 30%?

Answer 1

We know that Safety Stock = Z × σ_LT × D avg

where Z = Service factor for desired service level, σ_LT is the standard deviation of lead time, and D avg is average demand during a particular period.

As per question, there is no change in demand and we assume that lead time is constant

Hence, Safety stock is directly proportional to Service factor Z

a) Let initial safety stock = S1, New safety stock = S2

Let initial service factor be Z1 and new service factor be Z2

Hence, Safety Stock = k*Z where k is constant (σ_LT × D avg)

We know, for Service level = 95%, Z1 = 1.64

Hence, S1 = k*1.64

S2 = 0.9*S1

Hence, S2 = 0.9*(k*1.64)

S2 = k* (0.9*1.64) = k* 1.476

From above, we get Z2 = 1.476 = 1.48

For this service factor we find service level

For Z = 1.48, service level = 93%

Hence, 93% service level can they expect to achieve if they reduce their safety stock by 10%

b) Similarly, for S3 = 0.7*S1 (Safety stock reduced by 30% = 1-0.3 = 0.7)

S3 = 0.7*(k*1.64) = k*(0.7*1.64) = k*1.148 = k*1.15

From above, we get Z3 = 1.15

For Z = 1.15, service level = 87.5%

Hence, 87.5% service level can they expect to achieve if they reduce their safety stock by 30%