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# Optimal Storage Space

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A tire manufacturer is planning to introduce a new type of tire that is specifically designed to have anti-skid properties. The manufacturer should increase the storage space by building a new high-bay warehousing system. The forecasted demand for the new tire is 10,000 units per year and is expected to be stable for several years ahead. The cost of the raw material, utilities and labor is \$40 per tire.

The company estimates that it will require \$200 per production setup and the current capacity is 50,000 tires/year. Assuming a) an inventory carrying cost of 20% of the cost of the tire per year, b) a tire requiring 2 cu. ft of space, and c) an average annual cost of \$1 per year per cu.ft, determine the optimal storage space that should be built.

#### Solution Preview

Dear Student:

This problem is an optimal order quantity problem, most easily solved by the production order quantity model formula

Q_p^*=square root (2DS/H[1-d/p] )

Where D = 50000 (annual demand in units), S = \$200 (production set up cost), H = (20%)(\$42) = \$8.40 (carrying cost per unit per year equals 20% of cost of a tire), d = 10000/365 = 27.3973 ...

#### Solution Summary

This solution calculates the optimal size of storage space to be built to store tires, using the economic production quantity formula. An Excel solution is included.

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