Answer:
a. Units to be ordered to minimize the total cost in the CENTRALIZED system:
= B: 15811 units.
b. Units to be ordered to minimize the total cost in the DECENTRALIZED system:
= E: 5590 units.
Explanation:
a) Data and Calculations:
Demand at each retail outlet = 1,000 per day
Number of days in a typical retail year = 250 days
Total annual demand at each retail outlet = 250,000 (1,000 * 250)
Total annual demand at the distributor = 1,000,000 (250,000 * 4)
Cost of each unit of product = $120
Total cost of product at each retail outlet = $30,000,000 ($250,000 * $120)
Total cost of product at the distributor = $120 million
Holding cost per unit = $14.40 ($120 * 12%)
Ordering cost per order at each retail outlet = $900
Ordering cost per order at the distributor = $1,800 ($900 * 2)
a. Units to be ordered to minimize the total cost in the CENTRALIZED system:
= EOQ = square root of (2 x D x S/H)
where D = annual demand
S = ordering cost
H = Holding cost
= square root of (2 * 1,000,000 * $1,800)/$14.40
= square root of 250,000,000
= 15,811 units
= square root of (2 * 250,000 * $900)/$14.40
= square root of 31,250,000
= 5,590 units
