A company stocks replacements for water purification filters. Annual demand for

Question

A company stocks replacements for water purification filters. Annual demand for these filters is 5000 units. The cost of each filter is$5.33. Annual holding cost is 15% of the cost of the filter, Each time the company orders it has to pay an ordering fee of $20. Assume 250 working days in a year. What is the economic order quantity for this product? (Round to closest whole number). (5 pts) a. b. What is the optimal number of orders per year? (3 pts) c. What is the average inventory carried if the optimal order quantity is used? (2 pts) If the lead time is 4 days how many units should the company have in stock when it places an order? (2 pts) d. Its current order quantity is 2500 units. How much money willit save by switching to the quantity you calculated in (a)? (8 pts) e.

Explanation / Answer

Annual Demand = 5000 filters, Cost per Filter = $ 5.33 and Holding Cost per Filter = 15% of Filter Cost = 0.15 x 5.33 = $ 0.7995. Ordering Cost per Order = $20

Let number of filters in each order be K

(a) Then Total ordering costs = [Annual Demand / Number of Filters per Order] x Ordering Cost per Order = [5000 / K] x 20 $

Total Holding Cost = Holding Cost per Unit x Average Inventory Level = 0.7995 x [Annual Demand / 2] = 0.7995 x 2500 = $ 1998.75

Therefore, Total Cost = Total Holding Cost + Total Ordering Cost . The optimal or economic order quantity is the number of filters per order which minimizes the total cost (or the sum of the two types of costs). The sum of the two types of costs (or any two expressions for that matter) is minimum only when they are equal to each other(The minimum cost value expression can also be calculated using differentiation and setting the resulting expression equal to zero).

Let the economic order quantity be Q

Therefore, Total Holding Cost = Total Ordering Cost

[Q/2] x 0.7995 = [5000 /Q] x 20

Solving the above equation we get Q = 500.15 which can be rounded off to 500

Therefore, the economic or optimal order quantity per order is 500 filters

(b) The optimal number of orders per year = [Annual Demand / Economic Order Quantity] = 5000 / 500 = 10

(c) Average Inventory Carried = Annual Demand / 2 = 5000 / 2 = 2500

(d) Lead time is the period between order placement and order delivery. If the lead time is 4 days then one should place order when inventory level equals 4 days demand.

Daily Demand = [ Annual Demand / Number of Annual Working Days] = 5000 / 250 = 20 filters

Therefore, Number of Units Required when placing order = Lead Time X Daily Demand = 4 x 20 = 80 filters

This is also known as the reorder point in the inventory

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