Question

An health center uses 1000 splints per year, with a uniform demand rate. The workers estimate that to place each order from a local supplier the health center has to spend about $5.00 for the call and paperwork. The ankle splints cost $12.00 each and holding costs are based on a 20% annual rate.

Determine:

1) The economic order quantity and frequency of orders.

2) The total annual fixed order cost, total annual holding cost, and the total overall annual cost.

3) A network of health centers is considering centralizing their purchasing function (for four health centers). In this situation, a single order (for all health centers) is placed with the supplier. The supplier delivers the orders to each location individually. This approach will reduce the cost per splint to $11.00, but will increase the fixed cost of placing an order to $100. What is the total annual cost for this case?

Is this a desirable situation compared to the independent approach taken in part A? What other issues should they consider with respect to this possible operating change?

Answer 1

(1)

Annual Demand = D = 1000/year

Ordering Cost = C_o = $5

Holding Cost = C_c = 20% of 12 = $2.40/year

Economic Order Quantity Q* = √(2DC_o/C_c) = √(2*1000*5/2.40) = 64.54

(2)

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*C_c = (64.54/2)*2.40 = $77.45

Annual Order cost = Number of orders * cost/order = (D/Q*) C_o = (1000/64.54)*5 = $77.47

Total Annual Cost = Annual Inventory Holding Cost + Annual Order Cost = 77.45 + 77.47 = $154.92

(3)

Annual Demand = D = 1000/year

Ordering Cost = C_o = $100

Holding Cost = C_c = 20% of 11 = $2.20/year

Economic Order Quantity Q* = √(2DC_o/C_c) = √(2*1000*100/2.20) = 301.51

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*C_c = (301.51/2)*2.20 = $331.66

Annual Order cost = Number of orders * cost/order = (D/Q*) C_o = (1000/301.51)*100 = $331.66

Total Annual Cost = Annual Inventory Holding Cost + Annual Order Cost = 331.66 + 331.66 = $663.32

No, this is not a desirable situation since the annual cost is increasing