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Take-home quiz: Inventory management - Solutions

Due: Monday, March 7th at the beginning of class.

Please show all the work for partial credit.

Also, this is an individual assignment. Please turn in your own work.

1. The local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previous day is sold to a dealer that resells it to farmers, who uses it to feed their animals. This week the supermarket can buy fresh lettuce for $4 a box. The lettuce is sold for $10 a box and the dealer that sells old lettuce pays $1.5 a box. Past history says that tomorrow’s demand for lettuce averages 250 boxes with a standard deviation of 34 boxes. How many boxes of lettuce should the supermarket purchase?

Solution:

Cu = $10 - $4 = $6
Co = $4 - $1.50 = $2.50

[pic 1]→  Corresponding z value=0.54

Should purchase 250 + .541446 (34) = 268.4 or 268 boxes of lettuce.

1. Daily demand for a product is 120 units, with a standard deviation of 30 units. The review period is 14 days and the lead time is 7 days. At the time of the review, 130 units are in stock. If only a 1% risk of stocking out is acceptable, how many units should be ordered?

Solution:

Service level P = .99, [pic 2] = 120, RP = 14 days, L = 7days, [pic 3]d = 30 per day, and I =130.

[pic 4]

[pic 5]

 =137.5

From Standard normal distribution, z = 2.33

[pic 6]

1. A company currently has 200 units of a product on hand that it orders every two weeks when the salesperson visits the premises. Demand for the product averages 20 units per day with a standard deviation of 5 units. Lead time for the product to arrive is seven days. Management has a goal of 95% probability of not stocking out for this product. Salesperson is due to come in late this afternoon when 180 units are left in stock (assuming 20 are sold today). How many units should be ordered?

Solution:

Service level P = .95, [pic 7] = 20, T = 14 days, L = 7days, [pic 8]d = 5 per week, and I =180.

[pic 9]

 =23[pic 10]

From Standard normal distribution, z = 1.64

[pic 11]

1. A distributor of large appliances needs to determine the order quantities and reorder points for its products. The following data refers to a specific refrigerator in its product line.

Order cost:                                $100

Holding cost:                                20% of product cost (per year)

Refrigerator cost:                        $500

Monthly demand:                        42 units

Std. dev of demand during lead time:        10 refrigerators

Lead time:                                 7 days

The firm operates 365 days