# Question: annual demand 2500 holding cost per bracket per year 150...

###### Question details

Annual Demand | 2,500 |

Holding cost per bracket per year | $1.50 |

Order cost per order | $18.75 |

Lead time | 10 days |

Working days per year | 250 |

The Economic Order Quantity is **250 units**.

There are no safety stocks, so the inventory reaches a level of
zero before the new 250-unit order arrives. This means the average
inventory is 250/2 = **125 units**.

The Inventory Holding Cost is **$187.50**.

**10 orders** would be made each year, at an annual
order cost of **$187.50**.

The Total Annual Cost of managing the inventory is
**$375.00 per year**.

The time between orders is **25 days**.

With a lead time of 10 days, the reorder point will be at
**100 units**.

**QUESTIONS:**

1. Joe Henry notices that the demand for the unit he is studying is not constant, but can reasonable be approximated by a normal distribution with average weekly demand of 50 units and a standard deviation of 12 units.

- If the cycle service level is to be set at 95%, find the reorder point as well as the level of the safety stock.
- For this system find the annual ordering cost, the annual cost of holding the cycle inventory. The annual cost of holding the safety stock, the annual cost of goods and the total annual inventory cost.

2. The Accounting department is concerned about Henry’s proposal and favours a periodic review system where orders are placed regularly every four weeks.

- Find the level of the safety stock if the cycle service level is to stay at 98%.
- Find the number of orders per year and the annual ordering cost.
- Find the average order size and the annual cost of holding the cycle inventory (i.e., excluding the safety stock).
- Find the total annual inventory cost of this system, including the cost of the merchandise and the holding cost of the safety stock.
- You are currently at a reorder point and find that there are exactly 130 units left in stock. How many units should you order?
- Determine the probability that you experience a stockout situation before the current order is delivered.