Question: Sam Dudnick is the purchasing manager for Koller Enterprises, which produces PVC pipe. The machinery requires 16,000 cases per year of a special catalyst from Beck Chemical Company. Beck charges $4,000 to Koller Enterprises every time they send in an order (hazardous chemicals have certain procedures) on any of the 320 days per year they do business and charges for the catalyst on the following basis.

Order Size Price per Case

Fewer than 1000 Cases $ 125

1,000 to 4,999 Cases 120

5,000 to 9,999 Cases 117

10,000 or More Cases 116

Dudnick figures his inventory holding costs at about 10% on average inventory value, due to interest, insurance, pilferage, and miscellaneous stock problems.

1. If KE merely assumes that it faces a $125 per case cost (doesn't know about discounts), how large should each order be so as to minimize the sum of ordering and holding costs for the catalyst? (EOQ)
2. Calculate what would be the EOQ for KE if Koller Enterprises decided to make their own catalyst for the same $125 per case cost. Their startup cost each time they needed more would be the same amount Beck charges as an order charge, and they could, when they need more, turn out 90 cases per day while they are producing the catalyst. The adjustment would be that Koller would not have to store as many cases on average because some would be consumed concurrent with their arrival.
3. If Beck wanted Koller to order quarterly instead of at the rate you determined in part a, to what level should they change their order charge (S) to induce such a change (assuming we still have a $125 per case price and Beck expects KE simply to react as an EOQ decision maker)? [Hint: The EOQ model is fairly insensitive to changes in inputs. Use the sensitivity relationship or solve for S in the EOQ formula, knowing the order quantity]
4. Drop propositions b and c, and view the discounting scheme shown above. What size order would be best for KE every time they order catalyst? Make certain that your method takes into account the annual cost of ordering, holding and purchasing the goods. (Remember that they will be ordering continually for many years, so the number of orders per year does not have to be a whole number.) The four step process (and chart) for this is included with the in-class exercise. Follow it to the letter and the analysis will be easy.

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