6. (12 points) A company currently maintains 3 warehouses across the nation. Eac
ID: 350246 • Letter: 6
Question
6. (12 points) A company currently maintains 3 warehouses across the nation. Each warehouse is essentially identical. The demand at each is the same: 100,000 units per year. The cost to hold a unit of inventory for one year is the same: $12.50. Likewise the cost to place an order is the same at all 3: $250. The company is considering switching to a single warehouse that would service the entire demand. Holding and ordering costs would remain the same: $12.50 per unit per year and $250 per order. How much would the company expect to save in holding and ordering expenses over the course of a year?Explanation / Answer
First let’s calculate the Economic order quantity and total cost for one warehouse
Annual demand for one warehouse, D1 = 100,000 units
Ordering cost S = $250 per order
Annual Inventory holding cost, H = $12.50 per unit per year
Formula of economic order quantity (EOQ)
EOQ = Q = (2 * Annual Demand * Ordering cost/ Inventory holding cost)
Therefore
EOQ = Q = (2 * 100,000 *$250 / $12.50)
EOQ = Q = (4,000,000) = 2,000 unit
Total Cost = Annual ordering cost + Annual inventory holding cost
= (D/Q)* S + (H*Q)/2
= (100,000 / 2000) *$250 + ($12.50*2000)/2
= $12,500 +$12,500
= $25,000
Therefore total cost for three identical warehouses = 3* $25,000 = $75,000
Now assume that there is one centralized warehouse with Annual demand, D = 300,000 units
Ordering cost S = $250 per order
Annual Inventory holding cost, H = $12.50 per unit per year
Formula of economic order quantity (EOQ)
EOQ = Q = (2 * Annual Demand * Ordering cost/ Inventory holding cost)
Therefore
EOQ = Q = (2 * 300,000 *$250 / $12.50)
EOQ = Q = (12,000,000) = 3,464.10 unit
Total Cost = Annual ordering cost + Annual inventory holding cost
= (D/Q)* S + (H*Q)/2
= (300,000 / 3,464.10) *$250 + ($12.50*3,464.10)/2
= $21,650.64 + $21,650.64
= $43,301.27
Total cost for a centralized warehouse = $43,301.27
Therefore saving in total cost (Annual ordering cost + annual inventory holding cost) = $75,000 - $43,301.27 = $31,698.73
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