## Problem Description:

CoLinx, a manufacturing company, is faced with the task of optimizing its inventory management for three different types of bearings: Standard, Light, and Precision. The company wants to determine the most cost-effective approach for ordering these bearings. Two methods are considered: individual ordering for each type of bearing and combined ordering for all three types. The goal is to minimize the total inventory-related costs while maintaining the required inventory levels.

## Solution:

To address CoLinx's inventory management challenge, we will first calculate the Economic Order Quantity (EOQ) for each bearing type and then compare the total costs for both individual and joint ordering approaches.

### Given Data:

- Demand per month for Standard Bearing: 15,000
- Demand per month for Light Bearing: 5,500
- Demand per month for Precision Bearing: 2,500
- Production-Specific Order Cost for Standard Bearing: $600
- Production-Specific Order Cost for Light Bearing: $2,000
- Production-Specific Order Cost for Precision Bearing: $3,500
- Unit Cost for Standard Bearing: $500
- Unit Cost for Light Bearing: $1,500
- Unit Cost for Precision Bearing: $5,500
- Per Unit Inventory Holding Cost for Standard Bearing: $75
- Per Unit Inventory Holding Cost for Light Bearing: $225
- Per Unit Inventory Holding Cost for Precision Bearing: $825

### Individual Ordering Approach:

For each type of bearing, we calculate the EOQ, order frequency, annual ordering cost, and annual inventory holding cost.

**Standard Bearing:**- EOQ1 = 1697
- Order Frequency (per year) for Standard Bearing = 106.07
- Annual Ordering Cost for Standard Bearing = $63,639.61
- Annual Inventory Holding Cost for Standard Bearing = $63,639.61
**Light Bearing:**- EOQ2 = 1083
- Order Frequency (per year) for Light Bearing = 60.93
- Annual Ordering Cost for Light Bearing = $121,860.6
- Annual Inventory Holding Cost for Light Bearing = $121,860.6
**Precision Bearing:**- EOQ3 = 505
- Order Frequency (per year) for Precision Bearing = 59.46
- Annual Ordering Cost for Precision Bearing = $208,116.6
- Annual Inventory Holding Cost for Precision Bearing = $208,116.6

The total cost of individual ordering is $787,233.5.

### Combined Ordering Approach:

For the combined ordering approach, we calculate the total ordering cost (S) and the combined order frequency (n*).

- Total Ordering Cost (S) = $6,100
- Combined Order Frequency (n*) = 65.97/year

**The optimal lot sizes for all three bearings under combined ordering are as follows:
**

- EOQ1 for Standard Bearing = 2,728
- EOQ2 for Light Bearing = 1,000
- EOQ3 for Precision Bearing = 455

Total annual ordering costs = n* * S = $402,417 Total annual inventory holding cost = $402,487.5

The total cost of joint ordering is $804,904.5.

## Conclusion:

The results indicate that CoLinx should adopt the use of individual ordering, as it is more economical in terms of cost. The total cost of individual ordering is $787,233.5, which is $17,671 cheaper than joint ordering, which costs $804,904.5. By using the EOQ analysis, CoLinx can make informed decisions to optimize its inventory management and reduce costs.