The annual demand for an item is 20,000 units. The cost to process an order is $

Question

The annual demand for an item is 20,000 units. The cost to process an order is $80 and the annual inventory holding cost is $3 per item per year. What is the optimal order quantity, given the following price breaks for purchasing the item? a. What is the economic order quantity? b. What is the optimal order quantity (taking into account the quantity discount) and total cost (purchase cost, holding cost and ordering cost)? c. Will the firm take advantage of the lowest price available ($2.25/unit)? Explain.

Explanation / Answer

Annual Demand 20000 Ordering Cost $       80.00 Carrying Cost $         3.00 a. EOQ = 2AO / C where A = Annual Demand O = Ordering Cost per order C = Carrying Cost per unit per annum Initial EOQ at base price EOQ = 2AO / C = (2 * 20000 * 800) / 3 = 1032.796 units or, 1033 units Since supplier gives discount when qty ordered is more than 199, hence optimal order qty needs to ascertained at each price breaks Since EOQ is 1033, optimal order qty at each price break would be the qty at lower range Optimal Order Quanity 1 - 1499: EOQ 1033 units 1500 - 4999: 1500 500 or more: 5000 Optimal Order Quantity Calculation Inventory Order Size (A) 1033 1500 5000 Price (B) $2.50 $2.30 $2.25 Direct Cost (Price * Annual Demand = B* 20000) (C) $50,000.00 $46,000.00 $45,000.00 No of orders (Annual Demand/Order Quantity per order = 20000 / A) (D) 19 13 4 Ordering Cost (No orders * $80 = D *$80) ( E) $1,548.89 $1,066.67 $320.00 Carrying Cost per unit - $3 (F) $3.00 $3.00 $3.00 Carrying Cost (Order Size / 2 * Carrying Cost per unit per annum = A/2 * F) (G) $1,549.50 $2,250.00 $7,500.00 Total Cost (B+E+G) $53,098.39 $49,316.67 $52,820.00 Since the total cost is lowest at 1500 units, this is the optimal order quantity. Total Cost of Ordering Optimal Order quanity = $49,316.67 c No the firm will not take advantage of price break of $2.25 as carrying cost increase manifold, which offsets the reduction is price from $2.30 or $2.25. Rather, it makes inventory expensive.

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