You have been hired as the Operations Manager at one of Apex Shoe’s factories. While trying to 
understand the annual Economic Order Quantity for ordering gum for your factory, what 
assumptions would make? 
Data table: 
Annual demand (units) 14400
Per order cost (Tk) 200
Holding rate 20%
Unit cost (Tk) 20
Order Lead Time in days 6
Days in a year 360
Based on the above data, calculate: 
i. EOQ & Annual purchase cost 
ii. Annual holding cost 
iii. Annual order cost 
iv. Orders to be placed per year along with the duration between two orders. 


To calculate the Economic Order Quantity (EOQ) and other associated costs for the factory, I'll start by outlining the assumptions typically made in such EOQ models and then proceed with the calculations based on the provided data.

### Assumptions of the EOQ Model:
1. **Constant Demand:** The annual demand is known and remains constant throughout the year.
2. **Constant Lead Time:** The lead time, or time between placing an order and receiving it, is constant.
3. **No Stockouts:** The model assumes no stockouts or shortages.
4. **Instantaneous Replenishment:** When an order is placed, the items arrive in full at the same time.
5. **No Quantity Discounts:** The unit price remains constant regardless of the order size.
6. **Constant Holding and Ordering Costs:** The holding cost per unit and the ordering cost per order are constant over the year.

### Provided Data:
- **Annual demand (D):** 14,400 units
- **Per order cost (S):** 200 Tk
- **Holding rate (h):** 20% of the unit cost
- **Unit cost (C):** 20 Tk
- **Order lead time:** 6 days
- **Days in a year:** 360 days

#### Calculations:

### 1. **EOQ (Economic Order Quantity)**:
The EOQ formula is:

\[
\text{EOQ} = \sqrt{\frac{2DS}{H}}
\]

Where:
- \( D \) is the annual demand (14,400 units),
- \( S \) is the ordering cost per order (200 Tk),
- \( H \) is the holding cost per unit per year, which is the unit cost multiplied by the holding rate:
\[
H = C \times \text{Holding rate} = 20 \times 0.20 = 4 \text{ Tk per unit per year}
\]

Now substituting the values into the EOQ formula:

\[
\text{EOQ} = \sqrt{\frac{2 \times 14,400 \times 200}{4}} = \sqrt{\frac{5,760,000}{4}} = \sqrt{1,440,000} = 1,200 \text{ units}
\]

So, the Economic Order Quantity (EOQ) is **1,200 units**.

### 2. **Annual Purchase Cost**:
The annual purchase cost is simply the cost to purchase the total annual demand:

\[
\text{Annual Purchase Cost} = D \times C = 14,400 \times 20 = 288,000 \text{ Tk}
\]

### 3. **Annual Holding Cost**:
The annual holding cost is calculated as:

\[
\text{Annual Holding Cost} = \frac{\text{EOQ}}{2} \times H
\]

Substituting the values:

\[
\text{Annual Holding Cost} = \frac{1,200}{2} \times 4 = 600 \times 4 = 2,400 \text{ Tk}
\]

### 4. **Annual Ordering Cost**:
The annual ordering cost is calculated as:

\[
\text{Annual Ordering Cost} = \frac{D}{\text{EOQ}} \times S
\]

Substituting the values:

\[
\text{Annual Ordering Cost} = \frac{14,400}{1,200} \times 200 = 12 \times 200 = 2,400 \text{ Tk}
\]

### 5. **Number of Orders per Year and Duration Between Orders**:
- **Orders per year:**

\[
\text{Orders per year} = \frac{D}{\text{EOQ}} = \frac{14,400}{1,200} = 12 \text{ orders}
\]

- **Duration between two orders:** Since there are 360 days in a year:

\[
\text{Duration between two orders} = \frac{360}{\text{Orders per year}} = \frac{360}{12} = 30 \text{ days}
\]

### Summary of Results:
1. **EOQ:** 1,200 units
2. **Annual Purchase Cost:** 288,000 Tk
3. **Annual Holding Cost:** 2,400 Tk
4. **Annual Ordering Cost:** 2,400 Tk
5. **Orders per year:** 12 orders
6. **Duration between two orders:** 30 days

---

Do you want further details on any calculation? Here are 5 related questions to expand the topic:

1. How would a change in the holding rate affect the EOQ?
2. What happens to the EOQ if the unit cost decreases due to discounts?
3. How would you account for stockouts in the EOQ model?
4. What if demand fluctuates seasonally—how would you adjust your order strategy?
5. How would lead time uncertainty affect your order quantities?

**Tip:** Regularly reviewing demand forecasts and adjusting your EOQ can help reduce unnecessary costs if demand patterns change.

You have been hired as the Operations Manager at one of Apex Shoe’s factories. While trying to understand the annual Economic Order Quantity for ordering gum for your factory, what assumptions would make? Data table: Annual demand (units) 14400 Per order cost (Tk) 200 Holding rate 20% Unit cost (Tk) 20 Order Lead Time in days 6 Days in a year 360 Based on the above data, calculate: i. EOQ & Annual purchase cost ii. Annual holding cost iii. Annual order cost iv. Orders to be placed per year along with the duration between two orders.

Calculate the Economic Order Quantity (EOQ) and associated costs for ordering gum at Apex Shoe's factory. This problem involves analyzing demand, order costs, holding rates, and lead time using key inventory management formulas. Suitable for business students studying operations management.

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