Question

A computer equipment retailer has four retail locations. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 4,000 units per week. Each unit costs $200; the holding cost is 20% per annum. The fixed cost of each order (administrative plus transportation) is $900. Assume 52 weeks in a year.

1. What are the annual ordering cost, annual holding cost and total cost functions for this company?
2. Given that each outlet orders independently and gets its own delivery, determine the optimal order size at each outlet graphically (find EOQ graphically).
3. Given that each outlet orders independently and gets its own delivery, determine the optimal order size at each outlet mathematically.
4. What is the average inventory for each outlet? Across all outlets?
5. How many orders must be placed annually?
6. How frequently orders must be placed?
7. What is the inventory turnover ratio?

If the purchasing centralizes purchasing (for all four outlets), the retailer will only have to place a single order for all the outlets. The supplier will deliver the order on a common truck to a transit point and individual outlet requirements are identical. The total order is split equally and shipped to the retailers from this transit point. The entire operation has increased the fixed cost of placing an order to $1,800.

A. What is the EOQ under centralization?

B. Compare and discuss the two options. Should the company centralize? Why?

Answer 1

a.

Annual demand, D = 4,000 x 52 = 208,000
Unit cost, C = $200
Unit carrying cost, h = 200 x 20% = $40 per annum
Ordering cost per order, K = $900

Total annual ordering cost = (D/Q) * K = (208,000 / Q)*900 = 187,200,000 / Q
Total annual holding cost = (Q/2)*h = 20 Q

Total cost function, TC(Q) = 187,200,000 / Q + 20 Q

b.

Optimal order size at which Total cost is minimum = 3059.41

c.

EOQ = (2.D.K / h)^1/2 = sqrt(2*208,000*900 / 40) = 3059.41. Round this to the closest integer i.e. 3,059

d.

Average inventory across one location = EOQ/2 = 1,530 and across all stores = 1530 x 4 = 6120

e.

Number of orders = (D/EOQ) = 208,000 / 3,059 = 68 orders

f.

The frequency of orders = EOQ / weekly demand = 3,059 / 4,000 = 0.76 weeks

g.

Inventory turnover ratio = Demand / Average Inventory = 208,000 / 1,530 = 135.9

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Centralization

Annual demand, D = 208,000 x 4 = 832,000
Unit cost, C = $200
Unit carrying cost, h = 200 x 20% = $40 per annum
Ordering cost per order, K = $1,800

A.

EOQ = (2.D.K / h)^1/2 = sqrt(2*832,000*1800 / 40) = 8653.3. Round this to the closest integer i.e. 8,653

B.

Total relevant cost in one location without centralization = (D/EOQ)*K + (EOQ/2)*h = (208000/3059)*900 + (3059/2)*40 = 122376.5

So, total cost across all the 4 locations without centralization = 4 * 122376.5 = $489,505.9

Total relevant cost with centralization = (D/EOQ)*K + (EOQ/2)*h = (832000/8653)*1800 + (8653/2)*40 = $346,132.9

So, centralization yields a savings of 489,505.9 - 346,132.9 = $143,373