Ordering Help EOQ Quantity Discounts Space-Man orders parking tickets from a loc
ID: 433506 • Letter: O
Question
Ordering Help EOQ Quantity Discounts Space-Man orders parking tickets from a local paper company: The Paper Cut. The parking lot expects to use 400,000 tickets this year. The cost to order and have the tickets delivered each time is $300 (order cost). The annual carrying cost is $1.90 per ticket. The Paper Cut offers the following quantity discount pricing schedule. Number of Pounds 0-999 10,000- 19,999 20,000- 29,999 30,000 39,999 40,000 49,999 0,000-49,999 Price Per Pound $3.40 $3.20 $3.00 $2.80 $2.60 $2.40 A new local mill, The Pulpinator, has just opened and would like to start selling to Space-man. They offer the following quantity discount price schedule, with no order cost or delivery fee (providing a 0 for order cost will not solve this problem, you will need to think about it mathematically). The carrying cost will remain the same Number of Pounds 0-999 10,000-19,999 20,000-29,999 30,000 39,999 40,000 49,999 50,000- 49,999 Price Per Pound $4.00 $3.90 $3.00 $2.60 $2.30 $2.10Explanation / Answer
Demand (D) = 400,000
Ordering cost (S) = 300
Holding cost (H) = 1.9
EOQ = sqrt(2*D*S/H) = sqrt(2*400000*300/1.9) = 11239 (Round off)
Total cost = D/EOQ*S + EOQ/2*H + Price*D = 400000/EOQ*300 + EOQ/2*1.9 + Price*400000 = 120,000,000/EOQ + EOQ*0.95 + Price*400,000
Cases:
1) Existing Vendor, Price = 3.2, EOQ = 11239
Total cost = 120,000,000/11239 + 11239*0.95 + 3.2*400,000 = 1,301,354
2) Existing Vendor, Price = 3, EOQ = 20000
Total cost = 120,000,000/20000 + 20000*0.95 + 3*400,000 = 1,225,000
3) Existing Vendor, Price = 2.8, EOQ = 30000
Total cost = 120,000,000/30000 + 30000*0.95 + 2.8*400,000 = 1,152,500
4) Existing Vendor, Price = 2.6, EOQ = 40000
Total cost = 120,000,000/40000 + 40000*0.95 + 2.6*400,000 = 1,081,000
5) Existing Vendor, Price = 2.4, EOQ = 50000
Total cost = 120,000,000/50000 + 50000*0.95 + 2.4*400,000 = 1,009,900
1) New Vendor, Price = 3.9, EOQ = 11239
Total cost = 120,000,000/11239 + 11239*0.95 + 3.9*400,000 = 1,581,354
2) New Vendor, Price = 3, EOQ = 20000
Total cost = 120,000,000/20000 + 20000*0.95 + 3*400,000 = 1,225,000
3) New Vendor, Price = 2.6, EOQ = 30000
Total cost = 120,000,000/30000 + 30000*0.95 + 3*400,000 = 1,232,500
4) New Vendor, Price = 2.3, EOQ = 40000
Total cost = 120,000,000/40000 + 40000*0.95 + 2.3*400,000 = 961,000
5) New Vendor, Price = 2.1, EOQ = 50000
Total cost = 120,000,000/50000 + 50000*0.95 + 2.1*400,000 = 889,900
Ans: Order from New Vendor, 50,000 units at 2.1$ per unit
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