Question

Drugs Online (DO) is an online retailer of prescription drugs and health supplements. Vitamins represent a significant percentage of its sales. Demand for vitamins is 9,000 bottles per month. DO incurs a fixed order placement and receiving cost of $100 each time an order for vitamins is placed with the manufacturer. The purchase price is $3.00 per bottle. DO incurs a holding cost of 20 percent per year. (Assume 30 days a month.) a and b: Retailer Part a) Assume that DO places an order for 4,500 bottles every 15 days. Compute the annual ordering and holding cost for the current ordering policy. Part b) What is the optimal order quantity to minimize the annual ordering and holding cost? Part (c) The manufacturer: Now consider the manufacturer of vitamins who supplies DO. The manufacturer has a production line dedicated for producing vitamins supplied to DO. This line produces 9,000 bottles per month at a daily constant rate of 300 per day. The variable manufacturing cost is $2 per bottle. Manufacturer incurs a fixed cost of $250 to process, pack, and ship an order to DO. The holding cost is 20% year. Compute the following if DO’s order size is 4,500 bottles. Assume that the manufacturer’s inventory falls to zero when a batch of 4,500 bottles is shipped to DO. (i) Manufacturer’s average inventory: (ii) Number of orders manufacturer fills per year (iii) Manufacturer’s annual cost of holding inventory and filling orders: Part (d) for the supply chain: Now consider the supply chain that consists of both the manufacturer and DO. (i) For order sizes of 4,500 by the DO to the manufacturer, write the annual inventory holding and order cost for the supply chain. [Hint: It is sum of cost in part a and c(iii).] (ii) Find the optimal order size by DO to the manufacturer in order to minimize the annual inventory holding and order cost for the supply chain

Answer 1

Solution and Explanation:

a) Number of orders per year, N = $30 / 15 * 12=24$

Annual Ordering cost = 24*100 = $ 2400

Annual Holding cost = $4500 / 2 * 3 * 20 \%=\ 1350$

Total cost = $ 3750

b)  Annual Demand, D = 9000*12 = 108000

Holding cost, H = $3 * 20 \%=0.6$

Ordering Cost, S = 100

Optimal order quantity = $\mathrm{EOQ}=\sqrt{(} 2 \mathrm{SD} / \mathrm{H})=\underbrace{\sqrt{(} 2 * 100 * 108000 / 0.6)}=6000$

Annual Ordering cost = $108000 / 6000 * 100=\ 1800$

Annual Holding cost = $6000 / 2 * 0.6=\ 1800$

Total cost = $ 3600  

c)  (i) Manufacturer's Average Inventory = Average of minimum and maximum inventory = $(0+4500) / 2=2250$

(ii) Number of orders manufacturer fills per year = 24

(iii) Cost of holding inventory = $2250 * 2 * 20 \%=\ 900$

Cost of filling orders = 24*250 = $ 6000

Total cost = $ 6900

d)  (i) Total holding and ordering cost of supply chain = 3750 + 6900 = $ 10650

(ii) To find the optimal order size to minimize the total supply chain cost, we need to calculate the ordering cost and holding cost of supply chain.

Ordering cost of supply chain, S = 100 + 250 = 350,

Holding cost of supply chain = $3^{*} \cdot 2+2^{*} \cdot 2=1$

Optimal order qty = $\mathrm{EOQ}=\sqrt{(} 2 \mathrm{SD} / \mathrm{H})=\underline{\sqrt{(} 2 * 350 * 108000 / 1)}=8695$

Annual Ordering cost of Supply chain = $108000 / 8695 * 350=4347.4$

Annual Holding cost of Supply chain =$8695 / 2^{*} 1=4347.4$

Total cost of supply chain = 8695