An item experiences an annual demand of 3,600 units. It costs $10 to hold an item in inventory for one year and $20 to place an order. If the EOQ model is used, what is the time between orders? Assume that there are 52 business weeks in a year.

Question

BlackTom AI · Accepted Answer

We’re given: annual demand D = 3,600 units/year, ordering cost S = $20 per order, holding cost H = $10 per unit-year, and 52 weeks per year. To find the EOQ, use EOQ = sqrt(2DS/H).

Compute EOQ step by step:
- 2 * D * S = 2 * 3,600 * 20 = 144,000
- Divide by H: 144,000 / 10 = 14,400
- Take the square root: sqrt(14,400) = 120 units per order.

Next, determine how many orders occur per year:
- Orders per year = D / EOQ = 3,600 / 120 = 30 orders/year.

Time between orders is the reciprocal of orders per year, expressed in years:
- Time between orders (years) = 1 / 30 ≈ 0.0333 years.
- Convert to weeks using 52 weeks per year: 0.0333 * 52 ≈ 1.733 weeks.

Now evaluate each option against the computed interval (in weeks):
- Option: less than 1 week. This would require a time between orders < 1 week, but the calculated value is about 1.73 weeks, so this option is inconsistent with the calculation.
- Option: greater than 3 weeks. Our value 1.73 weeks is clearly not greater than 3 weeks, so this is incorrect.
- Option: greater than 2 weeks but less than or equal to 3 weeks. Our value falls below 2 weeks, so this option does not fit.
- Option: greater than 1 week but less than or equal to 2 weeks. This aligns with the computed 1.733 weeks, which sits between 1 and 2 weeks.

In short, the EOQ calculation leads to a periodic ordering schedule of roughly 1.73 weeks between orders, which places the result in the last option category. The other options either overstate or understate the interval when compared to the calculated 1.73 weeks, reflecting common misconceptions such as misapplying EOQ formula or miscounting the unit handling costs.

An item experiences an annual demand of 3,600 units. It costs $10 to hold an item in inventory for one year and $20 to place an order. If the EOQ model is used, what is the time between orders? Assume that there are 52 business weeks in a year. 单项选择题

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EOQ should be used if you use a make-to-order strategy and the customer specifies that the entire order be delivered in one shipment.

Considering the EOQ model, larger lots are justified with higher holding costs.

The EOQ is the smallest lot size that a supplier will allow a customer to order.

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