Dunstreet\'s Department Store would like to develop an inventory ordering policy

Question

Dunstreet's Department Store would like to develop an inventory ordering policy of a 98 percent probability of not stocking out. To illustrate your recommended procedure, use as an example the ordering policy for white percale sheets.

     Demand for white percale sheets is 4,700 per year. The store is open 365 days per year. Every two weeks (14 days) inventory is counted and a new order is placed. It takes 13 days for the sheets to be delivered. Standard deviation of demand for the sheets is five per day. There are currently 110 sheets on hand.

How many sheets should you order? (Use Excel's NORMSINV() function to find the correct critical value for the given -level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

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Dunstreet's Department Store would like to develop an inventory ordering policy of a 98 percent probability of not stocking out. To illustrate your recommended procedure, use as an example the ordering policy for white percale sheets.

     Demand for white percale sheets is 4,700 per year. The store is open 365 days per year. Every two weeks (14 days) inventory is counted and a new order is placed. It takes 13 days for the sheets to be delivered. Standard deviation of demand for the sheets is five per day. There are currently 110 sheets on hand.

Explanation / Answer

Given:

Ordering frequency = T = 14 days ( 2 weeks )

Lead time = L = 13 days

Therefore ,

Protection Period , P = T + L = 14 + 13 = 27 days

Standard deviation of daily demand for the sheets = 5 / day

Hence, Standard deviation of demand during the Protection period

= Standard deviation of daily demand x Square root ( Protection Period )

= 5 x Square root ( 27)

= 25.98

Z value corresponding to in stock probability of 0.98

= NORMSINV (0.98)

= 2.053

Therefore Safety stock requirement during protection period

= Z value x Standard deviation of demand during Protection period

= 2.053 x 25.98

= 53.33

Hence,

Reorder point

= Average daily demand x Protection period ( days) + Safety stock

= (Annual demand / 365)   x 27 + 25.98

= ( 4700 x 27/ 365) + 25.98

= 347.67 +25.98

= 373.65

However , number of sheets already in hand = 110

Therefore , Number of sheets should be ordered

= Reorder point – number of sheets already in hand

= 373.65 – 110

= 263.65 ( 264 rounding to next higher whole number )

NUMBER OF SHEETS TO BE ORDERED = 264

NUMBER OF SHEETS TO BE ORDERED = 264

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