Weekly demand for gaming consoles at Liverpool, a Mexican department store chain

Question

Weekly demand for gaming consoles at Liverpool, a Mexican department store chain, is normally distributed with a mean of 1, 000 and a standard deviation of 400. The replenishment lead time from the supplier is four weeks. Liverpool is targeting a CSL of 95 percent and uses a periodic review policy under which it reorders consoles every eight weeks. What is the average order size? How much safety inventory of consoles should Liverpool carry? What should its order up to level be? How much safety inventory would be required if Liverpool switched to a continuous review policy?

Explanation / Answer

Given is the following in the problem

Weekly Demand d = 1,000

Standard deviation Sd = 4,00

Lead time L = 4 weeks

z = 95% , using NORMSINV in excel to find z value

z = 1.64

Review period Rp = 8 weeks

1. Average order size = (d x Rp) / 2

= (1000 x 8)/2

= 4,000

The average order size is 4,000

2. Safety Stock = z x Sd x sqroot (L)

= 1.64 x 400 x sqroot (4)

= 1.64 x 400 x 2

= 1312

Liverpool should carry the safety stock of 1,312 gaming consoles

3. Reorder level = d x L

= 1,000 x 4

= 4,000

The reorder level should be 4,000

4. Reorder point = d x L + Safety stock

= 1,000 x 4 + 1312

= 4000 + 1312

= 5312

The reorder point is 5,312

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