Question

After graduation, you decide to go into a partnership in an office supply store that has existed for a number of years. Walking through the store and stockrooms, you find a great discrepancy in service levels. Some spaces and bins for items are completely empty; others have supplies that are covered with dust and have obviously been there a long time. You decide to take on the project of establishing consistent levels of inventory to meet customer demands. Most of your supplies are purchased from just a few distributors that call on your store once every two weeks.

You choose, as your first item for study, computer printer paper. You examine the sales records and purchase orders and find that demand for the past 12 months was 5,800 boxes. Using your calculator you sample some days' demands and estimate that the standard deviation of daily demand is 7 boxes. You also search out these figures:

Cost per box of paper: $11.

Desired service probability: 99 percent.

Store is open every day.

Salesperson visits every two weeks.

Delivery time following visit is three days.

Using your procedure, how many boxes of paper would be ordered if, on the day the salesperson calls, 75 boxes are on hand? (Use 365 days a year. 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.)

Answer 1

Given are following data :

Review period ( i.e. frequency of visit of sales person ) = 14 days ( i.e. 2 weeks )

Delivery lead time = 3 days

Therefore , Protection period = Review period + Delivery lead time = 14 + 3 = 17 days

Standard deviation of daily demand = 7 boxes

Therefore ,

Standard deviation of demand during review period

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

= 7 x Square root ( 17 )

= 7 x 4.123

= 28.86

Z value for 99 percent service probability = NORMSINV ( 0.99 ) =2.326

Safety stock

= Z value x Standard deviation of demand during protection period

= 2.326 x 28.86

= 67.128 ( 67 rounded to nearest whole number )

SAFETY STOCK = 67

Average daily demand = Annual demand/ 365 days = 5800/365

Reorder point = Average daily demand x Protection period + safety stock

= ( 5800/365) x 17 + 67 = 270.13 + 67 =337.13 ( 337 rounded to nearest whole number )

Number of boxes on hand =75 boxes

Number of boxes of papers to be ordered = reorder point – Number of boxes on hand = 337 – 75 = 262

NUMBER OF BOXES OF PAPERS TO BE ORDERED = 262