Question

A supermarket uses a periodic review system to manage inventory of gallons of drinking water. Average demand is 152 gallons of water per day with standard deviation of 33 gallons per day. It costs ​$57 to order water from the​ supplier, and orders are delivered after 4 days. The holding cost for a gallon of water is ​$0.11 per year. The supermarket is open 360 days per year. If the supermarket aims for a 94.5% service level for gallons of drinking water (z = 1.6), what value should be used for T, the target inventory position at the time of ordering?
The target inventory position is T= ______ gallons.

Answer 1

Answer:

The target inventory position is T= 713.6 gallons.

Explanation:

Given:

Average demand =per day = D = 152 Gallons

Standard deviation of demand = σ = 33 Gallons per day

Lead time for delivery = L = 4 days

Z value for 94.5% service level = 1.6

The target inventory position  = (Average demand x Lead time) + Safety stock

= (D × L) + (Z× σ × $\sqrt{L}$)

= (152 × 4) + (1.6 × 33 × $\sqrt{4}$)

= (152 × 4) + (1.6 × 33 × 2)

= 608 + 105.6

= 713.6