Question

A manufacturer keeps a continuous inventory review system on the key component, part X. The annual demand on part X is 12,000 units and the demand rate is constant. The supplier charges $50 for each unit of part X. Each order costs $150 to process and annual holding cost per unit is 20% of the purchase price.

(a) What is the economic order quantity? How many orders will be placed each year (365 days)? If the lead time is 3 days, what is the reorder point? (5 points)

(b) The supplier plans to offer discount on large orders in the following way:

Find out the optimal order quantity. (10 points)

Order quantity (units)	Price per unit
0 to 800	$50
800 or more	$45

Answer 1

The data of the component X in a continuous review system is given below: Annual demand, D=12,000 units Ordering cost per order, S = $150 Purchase cost, p = $50 Annual holding cost per unit, H = 20% of $50 100*50 = $10 Lead time, 1 = 3 days Calculate the Economic order quantity using the following formula: E00 = 2xDxs 9VH 2x(12,000)>(150) 10 36,00,000 V 10 = 13,60,000 = 600 Therefore, the EOQ of component X is (600 units).

Calculate the orders that will be placed each year as follows: Annual Demand Number of total orders = Number of units 12,000 Reorder point, ROP = 600 = 20 Therefore, the number of orders required is 20 Orders PerYear. Calculate the daily demand, d as shown below: Annual demand Daily demand, d = Number of days 12,000 365 = 32.87 – 33 units Calculate the reorder point as shown below: Reorder point, ROP = Daily demand Lead time = 33x3 = 99 units Therefore, the reorder point is 99 units

b. Calculate economic order quantity (EOQ) in excel, using the following formula as shown below: 2DS Optimal lot size, 2 * = V hp A B C D E 1 Order quantity Price per unit Demand Ordering cost Canying cost EOQ 0 to 800 50 12000 150 =20%*B2 =SQRT((2*C2*D2)/E2) 3 800 or more 45 12000 150 =20%*B3 =SQRT(2*C3*D3)/E3) The results are as follows: A B C D E F 1 Order quantity Price per unit Demand Ordering cost Carrying cost EOQ 2 0 to 800 50 12,000 150 10 600 3 800 or more 45 12,000 150 9 632.46 From the above calculation, the EOQ of quantity 800 and more are outside the price range. The optimal order quantity is 600 units for quantity 0-800. As lower cost exists beside the EOQ's total cost, each must be checked against the minimum cost generated. Determine the best ordering quantity by determining the cost of each policy in excel, using the following equation as shown below:

Total cost = = S+ hp + (pxD) C D 1 Order quantity Price per unit Demand Ordering cost Carrying cost Unit purchase cost Total cost 2 600 12000 =(C2/A2)*B2 =(A2/2)*(20%*B2) =B2*C2 =D2+E2+F2 3 800 45 12000 =(C3/A3)*B3 =(A3/2)*(20%*B3) (=B3*C3 =D3+E3+F3 50 The results are as follows: A B C D E F 1 Order quantity Price per unit Demand Ordering cost Carrying cost Unit purchase cost Total cost 12,000 1000 3000 600000 604000 3 800 4 5 12,000 675 3600 540000 544275 600 50 From the above calculation, the company should produce 800 units, as it is the least costly than the other. Therefore, the optimal order quantit 800 units