Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each...


Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:

Order Quantity Price/Pair
0-125 $35
126-225 $34
226-350 $33
351+ $32

The optimal order quantity is _____.

Holding Cost:

A holding cost is an important component of the inventory model. It refers to the total cost of the objects that are not sold. It is obtained by dividing the holding sum of inventory by the value of the inventory. It is usually expressed in terms of a percentage.

Answer and Explanation: 1

The given information is as follows:

Annual Demand=500

Ordering cost=$30

Annual holding cost= 20% or 0.20.

The optimal order quantity or {eq}Q* {/eq} can be calculated using the following formula:

{eq}Q*=\sqrt{\dfrac{2\times \text{Annual Demand}\times \text{Ordering cost}}{\text{Annual holding cost per unit}}} {/eq}

Make a table that depicts the order size, pair cost and the corresponding optimal order quantity.

Order Size Pair cost{eq}Q* {/eq}

0 to 125$35{eq}\begin{aligned}Q*(0 \text{ to } 125)&=\sqrt{\dfrac{2\times 500\times 30}{0.20\times 35}}\\&=\sqrt{\dfrac{30000}{7}}\\&=\sqrt{4285.714286}\\&\approx 66\end{aligned} {/eq}

126-22534{eq}\begin{aligned}Q*(126\text{ to } 225)&=\sqrt{\dfrac{2\times 500\times 30}{0.20\times 34}}\\&=\sqrt{\dfrac{30000}{6.8}}\\&=\sqrt{4411.765}\\&\approx 67\end{aligned} {/eq}

226-350 33{eq}\begin{aligned}Q*(226 \text{ to }350)&=\sqrt{\dfrac{2\times 500\times 30}{0.20\times 33}}\\&=\sqrt{\dfrac{30000}{6.6}}\\&=\sqrt{4545.455}\\&\approx 68\end{aligned} {/eq}

351+32{eq}\begin{aligned}Q*(351+)&=\sqrt{\dfrac{2\times 500\times 30}{0.20\times 32}}\\&=\sqrt{\dfrac{30000}{6.6}}\\&=\sqrt{4687.5}\\&\approx 69\end{aligned} {/eq}

Therefore, the order quantity will be 67.

Learn more about this topic:

What Is Inventory Management? - Demand vs. Cost


Chapter 13 / Lesson 3

Inventory management is the system of ordering, storing, and selling of company's inventory or stocks. Learn about the definition of inventory management, the impact of demand, cost, and technology, and the concept of Economic Order Quantity (EOQ).

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