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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.

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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 × [tex]\sqrt{L}[/tex])

= (152 × 4) + (1.6 × 33 × [tex]\sqrt{4}[/tex])

= (152 × 4) + (1.6 × 33 × 2)

= 608 + 105.6

= 713.6

The value of the target inventory position will be 713.6 gallons.

The following can be illustrated from the information given:

  • Average demand per day, D = 152
  • Standard deviation of demand, σ = 33
  • Lead time for delivery, L = 4
  • Z value for 94.5% service level = 1.6

Therefore, the target inventory position will be:

= (Average demand x Lead time) + Safety stock

= (D × L) + (Z× σ × ✓L )

= (152 × 4) + (1.6 × 33 × ✓4 )

= (152 × 4) + (1.6 × 33 × 2)

= 608 + 105.6

= 713.6

Therefore, the target inventory position will be 713.6 gallons.

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