Operations and Supply Chain Management The Core

INVENTORY MANAGEMENT chapter 11 381
b. The total ordering cost for a year is
​ __ D Q ​ S = ​ _____ 1,000 ​($5) = $100​
50
c. The storage cost for a year is
​ __ Q 2 ​ H = ​ ___ 50 ​($4) = $100​
2
SOLVED PROBLEM 3
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 review, 130 units are in stock. If only a 1 percent
risk of stocking out is acceptable, how many units should be ordered?
Solution
​σ​ T + L ​=
​
___________
​√ (14 + 7) ​(30)​ 2 ​ = ​√ ______
18,900 ​ = 137.5
z = 2.33
q​ ​
=​ ¯ ​d ​(T + ​ L) + z​σ​ T + L ​ − I​
​=
120(14 + 7) + 2.33(137.5) − 130
​=
2,710 units
​
​
SOLVED PROBLEM 4
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 a
95 percent probability of not stocking out for this product.
The salesperson is due to come in late this afternoon when 180 units are left in stock
(assuming that 20 are sold today). How many units should be ordered?
Solution
Give I = 180, T = 14, L = 7, d = 20
______
​σ​ T + L ​=
​√ 21 ​(5)​ 2 ​ = 23
​
z = 1.64 ​ ​
​
q ​
= ​
¯ ​d ​(T + L) + z​σ​ T + L ​ − I ​
​
​=
20(14 + 7) + 1.64(23) − 180
q = 278 units
SOLVED PROBLEM 5
Sheet Metal Industries Inc. (SMI) is a Tier 1 supplier to various industries that use components
made from sheet metal in their final products. Manufacturers of desktop computers and electronic
devices are its primary customers. SMI orders a relatively small number of different raw sheet
metal products in very large quantities. The purchasing department is trying to establish an ordering
policy that will minimize total costs while meeting the needs of the firm. One of the highest volume
items it purchases comes in precut sheets direct from the steel processor. Forecasts based on historical
data indicate that SMI will need to purchase 200,000 sheets of this product on an annual basis.