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# Economic Order Quantity and Inventory Costs

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13-25. The office manager for the Metro Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6500 boxes per year. Annual carrying costs are \$3 per box, and ordering costs are \$28. The following discount price schedule is provided by the office supply company:
Order Quantity (boxes) Price per Box
200-999 \$16
1000-2999 14
3000-5999 13
6000+ 12
Determine the optimal order quantity and the total annual inventory cost. (Russell 585)

Reference:
Russell, Roberta S. Operations Management: Creating Value Along the Supply Chain, 7th Edition. John Wiley & Sons,

#### Solution Preview

The problem is a specialized case of incremental quantity discount case where the purchase price per unit declines as per increasing order quantity.
As per the graph shown below, with the total cost represented on the y-axis and the order quantity (no. of boxes) represented on the x-axis, the total cost, given an order size of Q boxes per order is represented by
TC = 6,500 * C + (6500/ Q) * 28 + 3 * (Q/2), where C is the purchase price per box
For 200 <= Q <= 999; C = \$16 hence TC = 104,000 + (6500/ Q) * 28 + 3 * (Q/2)
For 1000 <= Q <= 2999; C = \$14 hence TC = 91,000 + (6500/ ...

#### Solution Summary

This solution provides calculations of economic order quantity as well as total inventory costs in case of discount on unit purchase price as per increasing volume

\$2.19