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# Inventory problems

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Inventory Control Models

1. Rascal's Inc. stocks beef jerky, an item that has a normally distributed demand during the reorder period with a mean of 7 dozen boxes and a standard deviation of three dozen boxes. If it is desirable to experience a stockout only 10 percent of the time, what is the appropriate safety stock?

2. Art Organ, Ltd. distributes mechanical replacements for human mitral heart valves. Their artificial valve has a demand of 12,765 units per year and sells for \$7,900 per unit. The cost of ordering is \$75 per order and the average carrying cost per unit per year is \$150. Determine the economic order quantity.

3. Art Organ, Ltd. distributes porcine replacements for human mitral heart valves. Their replacement valve has a demand of 12,765 units per year and sells for \$7,900 per unit. The cost of ordering is \$75 per order and the average carrying cost per unit per year works out to be about 5% of the cost of the valve. Lead time is 4 working days. Determine (assume 250 working days):

(a) The economic order quantity
(b) The reorder point
(c) The optimal number of orders per year
(d) The optimal number of days between any two orders

4. We use 2,750 per year of a certain subassembly that has a purchase cost of \$450, and an annual holding cost of \$500 per unit. Each order placed costs us \$150. We operate 300 days per year and have found that an order must be placed with our supplier 6 working days before we can expect to receive that order. For this subassembly, find:

(a) economic order quantity
(b) annual holding cost (using EOQ)
(c) annual ordering cost (using EOQ)
(d) reorder point

5. We use 1,300 of a certain spare part that costs \$35 for each order and has a \$32 annual holding cost. Calculate the total cost for order sizes of: 25, 40, 50, 60, and 100. Identify the economic order quantity and consider the implications for making an error in calculating the economic order quantity.

6. The H.A.L. Computer Store sells a printer for \$400. Demand for this is constant during the year, and annual demand is forecasted to be 1100 units. The holding cost is \$20 per unit per year, while the cost of ordering is \$90 per order. Currently, the company is ordering 12 times per year (92 units each time). There are 250 working days per year and the lead time is 8 days.

(a) Given the current policy of ordering 92 units at a time, what is the total of the annual ordering cost and the annual holding cost?
(b) If the company used the absolute best inventory policy, what would the total of the ordering and holding cost be?
(c) What is the reorder point?
(d)How many days between orders with 12 orders