Question

A large distributor has 8 retail outlets. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 2000 per day. Assume there are 250 days per year. Each unit of product costs 200 dollars, and holding cost per unit of product per year is 16% of the product cost. The fixed cost of each order (administrative plus transportation) is 1500 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.

1. How much does EACH warehouse need to order individually to minimize the total cost in the DECENTRALIZED system?

The potential answers are:

A: 8660 units.

B: 5657 units.

C: 5590 units.

D: 6847 units.

E: 6124 units.

2. How much should ALL the warehouses order together to minimize the total cost in the CENTRALIZED system?

The potential answers are:

A: 20785 units.

B: 36742 units.

C: 21909 units.

D: 16000 units.

E: 27386 units.

3. Compute the total ordering and carrying costs of ALL warehouses in the DECENTRALIZED system.

he potential answers are:

A: 1752712 dollars.

B: 958405 dollars.

C: 1322724 dollars.

D: 1763633 dollars.

E: 1558846 dollars.

Answer 1

1

D

Working note:

EOQ for the each warehouse = (2*annual demand*ordering cost/holding cost per unit per year)^.5

EOQ for the each warehouse = (2*250*2000*1500/(16%*200))^.5

EOQ for the each warehouse = 6846.53 or 6847 units

-------------

2.

E

Working note:

EOQ ( when ordered together) = (2* total annual demand*ordering cost/holding cost per unit per year)^.5

EOQ ( when ordered together) = (2*8*250*2000*3000/(16%*200))^.5

EOQ ( when ordered together) = 27386.13 or 27386 units

---------------

3.

A

Working note:

Total ordering and carrying cost in decentralized system = 8*((250*2000/6847)*1500 + (6847/2)*(16%*200))

Total ordering and carrying cost in decentralized system = $1752712.2 or $1752712