In: Operations Management
Ergonomics Inc. sells ergonomically designed office chairs. The company has the following information: Average demand = 30 units per day Average lead time = 37 days Item unit cost = $57 for orders of less than 270 units Item unit cost = $56 for orders of 270 units or more Ordering cost = $32 Inventory carrying cost = 20% The business year is 250 days Assume there is no uncertainty at all about the demand or the lead time.
a. Calculate EOQ if unit cost is $57 and $56. (Note: These EOQs do not need to be feasible in their price range.)
b. Calculate annual ordering costs for each alternative?
c. Calculate annual inventory carrying costs for each alternative?
d. Calculate annual product costs for each alternative?
e. What will be the total costs for each alternative? (Round your answers to 2 decimal places.)
f. Based on your analysis, how many chairs should they order at a time?
g. How much the firm can save annually by using the order quantity in Part f. instead of the first EOQ shown in Part a?
Average demand per day = 30 units
The business year = 250 days
Annual Demand, D = 250 *30 = 7500 units
Average lead time = 37 days
Unit cost = $57 for orders of less than 270 units
unit cost = $56 for orders of 270 units or more
Ordering cost, S = $32
Inventory carrying cost = 20%
For orders of less than 270 units, Holding Cost per unit, H = 20% *57
For orders of 270 units or more, Holding Cost per unit, H = 20% *56
@56 unit price, EOQ = 207.0197
@57 unit priceEOQ = 205.1956
|No.of Orders = 7500/EOQ||27.77778||36.55048|
|Order Cost = No.of orders*32||888.8889||1169.615|
|Purchase cost = 7500*unit price||420000||427500|
|Annual Holding Cost = (EOQ/2)*H||1512||1169.615|
Annual Ordering Cost @ 56 = $ 888.88
Annual Ordering Cost @ 57 = $ 1169.615
Annual inventory carrying cost @ 56 = $ 1512
Annual inventory carrying cost @ 57 = $ 1169.615
Annual product cost @ 56 = 420000
Annual product cost @ 57 = 427500
Total costs @56 = 422400.9
Total costs @57 = 429839.2
Ordering the chair at the discount price has less total cost. Hence 270 units should be ordered.
|EOQ||270.000||205.196||207.020||Initial EOQ Quantity|
|No.of Orders = 7500/EOQ||27.77778||36.55048||36.22844|
|Order Cost = No.of orders*32||888.8889||1169.615||1159.31|
|Purchase cost = 7500*unit price||420000||427500||420000|
|Annual Holding Cost = (EOQ/2)*H||1512||1169.615||1159.31|
Saved at discount by ordering 270 units = 429839.2-422400.9 = 7438.342
The EOQ for 56 unit price is 207.02.
By ordering 270 units to avail discount, 429839.2-422318.6 = 82.26 is lost when compared with part a.