Question

You are the manager at a furniture store. One of your products is a chair. Weekly demand for the chair is normally distributed with mean 40 and standard deviation 20. The lead time from the assembly plant to your store is two weeks and you order inventory replenishments weekly. You use the base-stock level policy to control inventory.

1)Suppose your base-stock level is 220. You are about to place an order and note that your inventory level is 160 and you have 65 chairs on order. How many chairs will you order?

2)What is the optimal base-stock level if you want to target a 98% in-stock probability?

3)What is the optimal base-stock level if you want to target a 98% fill rate?

4)Suppose you decide to maintain a 95% in-stock probability for the chair. What is the expected fill rate in this case?

Answer 1

1)

Using base-stock policy,

order quantity = Basic stock level-Inventory level-units scheduled to receive = 220-160-65 = -5

So no need to order any unit as scheduled receipt will increase the inventory level to more than base stock level

2)

Optimal base-stock level = average weekly demand*(lead time+review period)+z*standard deviation of weekly demand*sqrt(lead time+review period)

= 40*(2+1)+normsinv(0.98)*20*sqrt(2+1)
= 191.1439492 units = 191 units

3)

target backorder level = (average weekly demand/standard deviation of demand over l+p period )*(1-Fill rate)

= (40/(20*sqrt(2+1))*(1-0.98)) = 0.023094011

From standard normal loss table we can see corresponding z = 1.61
Optimal base-stock level = average weekly demand*(lead time+review period)+z*standard deviation of weekly demand*sqrt(lead time+review period)
= 40*(2+1)+1.61*20*sqrt(2+1) = 175.772036 = 176 units

4)
target backorder level = l(z) where z = normsinv(0.95) = 1.65

So, l(1.65) = 0.0206 from standard normal loss table

We know,
target backorder level = (average weekly demand/standard deviation of demand over l+p period )*(1-Fill rate)

or, Fill rate = 1-(target backorder level*standard deviation of demand over l+p period)/average weekly demand

or, Fill rate = 1-(0.0206*20*sqrt(2+1))/40 = 0.982159877 = 98.22%