The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost.

Quantity Price
1 - 9 $2.95 per unit
10 - 999 $2.50 per unit
1,000 - 4,999 $2.30 per unit
5,000 or more $1.85 per unit

What is the correct ordering policy (give optimal order quantity), given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior?

or ordering quantity 1-9,

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*2.95)) = 1594.48201

Optimal ordering quantity will not be in this range as calculated EOQ is beyond the range

For ordering quantity 10-999,

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*2.5)) = 1732.050808

Optimal ordering quantity will not be in this range as calculated EOQ is beyond the range

For ordering quantity 1000-4999,

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*2.3)) = 1805.787796

Total annual cost = ordering cost + holding cost + purchase cost = (10000/1805.787796)*75+(1805.787796/2)*(20%*2.3)+10000*2.3 = 23830.66239

For ordering quantity 5000 or more,

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*10000*75)/(20%*1.85)) = 2013.468166

EOQ is adjusted upwards to 5000 to avail the discount

Total annual cost = ordering cost + holding cost + purchase cost = (10000/5000)*75+(5000/2)*(20%*1.85)+10000*1.85 = 19575

So, optimal ordering quantity = 5000

Firm should pay $1.85 per unit

Annual cost at the optimal behavior = 19575

Explanation:

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