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.

4. Compute the total ordering and carrying costs of ALL warehouses in the CENTRALIZED system.

The potential answers are:

A: 339411 dollars.

B: 451796 dollars.

C: 623538 dol- lars.

D: 831384 dollars.

E: 876356 dollars.

5. Compute the flow time in the DECENTRALIZED system. The potential answers are:

A: 3.23 days.

B: 1.71 days.

C: 2.8 days.

D: 2.15 days.

E: 1.91 days.

6. Compute the flow time in the CENTRALIZED system.

The potential answers are:

A: 0.72 days.

B: 1.02 days.

C: 0.86 days.

D: 1.98 days.

E: 1.52 days.

please Help Thank you!

Answer 1

4.

Centralized system,

EOQ = sqrt((2DS)/h) Where D = annual demand = 8*2000*250 = 4000000, S = ordering cost = 3000, h = 16%*200 = 32

EOQ = sqrt((2*4000000*3000)/32) = 27386.12788

total ordering and carrying cost = (4000000/27386.12788)*3000+(27386.12788/2)*32 = 876356.092

Correct answer is E. 876356 dollars

5.

Decentralized system

EOQ = sqrt((2DS)/h) Where D = annual demand =2000*250 = 500000, S = ordering cost = 1500, h = 16%*200 = 32

EOQ = sqrt((2*500000*1500)/32) = 6846.531969

According to little's law,
Number of items in the system = flow time*Annual demand
Flow time for centralized system,
flow time = Number of items in the system /Annual demand = (Average inventory/annual demand) = (6846.531969/2)/500000 = 0.006846532 year = 0.006846532*250 = 1.711633 days = 1.71 days (Approximately)
So correct answer is B. 1.71 days
6.
Centralized system
According to little's law,
Number of items in the system = flow time*Annual demand
Flow time for centralized system,
flow time = Number of items in the system /Annual demand = (Average inventory/annual demand) = (27386.12788/2)/4000000 = 0.003423266 year = 0.003423266*250 = 0.8558165
days = 0.86 days (Approximately)
So correct answer is C. 0.86 days