Clement Bait and Tackle has been buying a chemical water conditioner for its bait (to help keep its baitfish alive) in an optimal fashion using EOQ analysis
The supplier has now offered Clement a discount of $0.50 off all units if the firm will make its purchases monthly or $1.00 off if the firm will make its purchases quarterly. Current data for the problem are: D = 720 units per year; S = $6.00, I = 20% per year; P = $25.
(a) What is the EOQ at the current behavior?
(b) What is the annual total cost, including product cost, of continuing their current behavior?
(c) What are the annual total costs, if they accept either of the proposed discounts?
(d) At the cheapest of the total costs, are carrying costs equal to ordering costs? Explain.
(a) Q* = = 41.57 or 42 units at a time.
(b) TC = 720($25 ) + ($6 ) + (.2 )($25 ) = $18,000 + $103.92 = $103.93 + $18,207.85
(c) Placing orders on a monthly basis implies twelve orders per year where Q = 720 / 12 = 60. Placing orders on a quarterly basis implies four orders per year where Q = 720/4 = 180.
The following table shows the total costs.
Range 1 Range 2 Range 3
Quantity 1-59 60-179 ≥180
Unit Price, P $25 $24.5 $24
Q* (Square root formula) 41.57 41.99 42.43
Order Quantity 41.57 60 180
Setup cost 103.92 72 24
Holding cost 103.93 147 432
Product cost 18,000.00 17,640 17,280
Total cost, TC $18,207.85 $17,859 $17,736
(d) They are not. Accepting the discount requires an order quantity that is not EOQ. With the more favorable discount, setup costs are $24 while holding costs are $432. The trade-off is worth it due to the $720 in annual product cost savings.
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