Question

A large distributor has 4 retail outlets. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 1000 per day. Assume there are 250 days per year. Each unit of product costs 120 dollars, and holding cost per unit of product per year is 12% of the product cost. The fixed cost of each order (administrative plus transportation) is 900 dollars in the decentralized system. The fixed cost of each order in the centralized system is twice of the decentralized system. Holding cost per unit are the same in the two systems.
3a. How much should ALL the warehouses order together to minimize the total cost in the CENTRALIZED system?The potential answers are:_______.A: 14606 units.
B: 15811 units.C: 19365 units.D: 12344 units.E: 12500 units.3B. How much does EACH warehouse need to order individually to minimize the total cost in the DECENTRALIZED system?The potential answers are:_______.A: 5164 units.B: 6124 units.C: 3904 units.D: 3953 units.E: 5590 units.

Answer 1

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