Question

(20pts) A pharmacy sells three types of syrups. Demand and cost data are summarized as: Syrup-2 Syrup-3 Syrup-1 110 2.0 2.4 Order cost (liras per order) Purchasing cost (liras per bottle) Holding cost (liras per bottle per year) Annual demand (bottles per year) 65 4.0 2.6 900 3.0 2.5 800 600 What should be the optimal order quantities for each type of syrup if there is a budget limitation of 1400 liras which can be used for inventory-on-hand at any given time. What will be the annual cost for this optimal solution. (20pts) Reconsider the problem in Q.2. Suppose that there is no budget limitation for the inventory, but the storage space can take at most 400 bottles at any time (assuming that all bottles for different syrups are identical). What will be the optimal order quantities in this case.

Answer 1

While making decisions regarding order quantity to be placed by a company for its products, it has to consider two costs namely

1. Ordering cost : Total Cost incurred by a company for making one order which may include loading, unloading and freight charges.
2. Carrying cost ( Holding cost) : Total cost incurred by a company with respect to carrying and storing the inventory in the ware house/ Storage godown etc. It may include insurance cost, finance cost, obsolescence cost etc.

The company should choose that order quantity at which total ordering and total carrying cost gets minimized. Such ideal ordering quantity is known as Economic order quantity.

In the given problem, the company has a budget constraint of 1400 liras which can be used for the purpose of inventory on hand i.e., at the chosen ordering quantity, the carrying cost of all the three syrups shall not exceed 1400 liras.

The simplest procedure for finding Economic order quantity is by using formula method (Besides other methods of trial and error method and Graphical method).

Formula for finding Economic order quantity Economic order quantity (EOQ) =
V2A0/C

Where A = Annual demand of the product

            O = Ordering cost per order

            C = Carrying cost per unit per annum

Carrying cost (Holding cost) = 1/2 (Ordering quantity*carrying cost per unit per annum)

Particulars	Syrup-1	Syrup-2	Syrup-3
EOQ	(2+ 600 + 110/2.4	2 * 900 * 80/2.6	2 * 800 * 65/2.5
EOQ	= 235 bottles	= 235 bottles	= 204 bottles
Carrying cost at EOQ	=1/2(235*2.4)	= 1/2(235*2.6)	=1/1(204*2.5)
	=282 liras	= 306 liras	=255 liras

Total carrying cost will be incurred by the company at EOQ level = 282+306+255 = 842 liras. which is within the budget limit of 1400 liras.

Hence the optimal ordering quantities to be adopted by the company with respect to each type of syrup are

1. Syrup-1 : 235 bottles
2. Syrup-2 : 235 bottles
3. Syrup-3 : 204 bottles

Answer to question 2: In this case, it is not possible to use formula method. So we have to opt Trial and Error method for finding the optimal order quantities for each type of syrup. In trial and error method, there are a number of altrernatives and it is not possible to find out the ordering cost and carrying cost for each alternative, we are randomly considering a few order quantities.

Ordering cost = Total orders to be placed*ordering cost per order

Carrying cost = Order quantity/2*carrying cost per unit per annum

Particulars	Total ordering cost and carrying cost(TOCC) Syrup-1	TOCC syrup-2	TOCC syrup-3	Total
illustration1: 160,140,100	600/160*110+160/2*2.4 =412.5+192 = 604.5	900/140*80+140/2*2.6 = 514+182=696	800/100*65+100/2*2.5 =520+125=645	1945
illustration2: 140,160,100	600/140*110+140/2*2.4 =471+168=639	900/160*80+160/2*2.6 = 450+208=658	800/100*65+100/2*2.5 =520+125=645	1942
illustration3: 100,140,160	600/100*110+100/2*2.4 = 660+120=780	900/140*80+140/2*2.6 = 514+182=696	800/160*65+160/2*2.5 = 325+200=525	2001

In our example the optimum quantity that can be used by the company for minimizing the ordering cost and carrying cost

1. Syrup 1 = 140
2. Syrup 2 = 160
3. Syrup 3 = 100