A firm stocks n different items in the same warehouse.
Item i requires a(i) square feet of warehouse
space per unit. The total warehouse space available is A
square feet. All n items are replenished independently
in batches of size Q(i). Holding costs assessed on the
average inventory level amount to h dollars per dollar
invested per year. The value of item i is v(i)
dollars per unit. The fixed ordering cost for item i
is K(i) per batch, and the annual demand is d(i).
a. Develop a mathematical program to minimize the annual total
inventory holding and ordering costs for all n items
subject to warehouse availability. Assume that each item is
allotted a space in the warehouse required to store Q(i).
b. Given that the warehouse space available is A and
all will be used, form the Lagrangian function and determine
expressions to find the optimal order quantities Q*(i)
(i.e., set partial derivatives to zero).
c. Use A = 2000 sq ft, h = 0.2, and the following
data to find the optimal Q*(i) and the minimum cost.
How much of the total cost can be attributed to the warehouse
restriction?
Parameter

1

2

3

d(i) (units)

12,000

5,000

2,000

v(i) ($/unit)

$20

$40

$50

K(i) ($/order)

$160

$200

$50

a(i) (sq ft)

1

2

4

