Part 2

0.0/1.0 point (graded)

The manager at GetFit notices that the suppliers have different levels of service. The levels of service of the companies are listed in Table 2a. The costs per % level of service depends on the SKU, and are listed in Table 2b. The costs and maximum total number of units that can be supplied by each supplier remain the same as in Part 1.

Please normalize the costs to Supplier A's level of service (92%) to get the answer.

Table 2a. Level of service (%)

Supplier A

Supplier B

Supplier C

Supplier D

92

98

97

96

Table 2b. Cost per % level of service

Parts

Cost per %

W32A

10

Y33A

2

W32B

1

X33B

3

Z32A

8

Considering the levels of service of the suppliers, what is the minimum total procurement cost for GetFit?

To adjust the costs based on the levels of service, we'll normalize the costs to Supplier A's level of service (92%) and then recalculate the total procurement cost. The cost normalization adjusts the costs from other suppliers to reflect the differences in their service levels compared to Supplier A.

### Steps to Normalize Costs
1. **Determine the normalization factor** for each supplier by comparing their service level to Supplier A's service level:
   \[
   \text{Normalization Factor} = \frac{\text{Service Level of Supplier}}{\text{Service Level of Supplier A}} = \frac{\text{Service Level}}{92}
   \]

2. **Adjust the cost** for each SKU based on this normalization factor:
   \[
   \text{Normalized Cost} = \text{Original Cost} + \text{Cost per %} \times (\text{Normalization Factor} - 1) \times 92
   \]

3. **Recalculate the total cost** using the normalized costs and then minimize it using linear programming.

### Normalization Factors
- Supplier A: \( \frac{92}{92} = 1.0 \)
- Supplier B: \( \frac{98}{92} = 1.0652 \)
- Supplier C: \( \frac{97}{92} = 1.0543 \)
- Supplier D: \( \frac{96}{92} = 1.0435 \)

Now, we'll normalize the costs for each SKU from each supplier and solve the optimization problem again.After normalizing the costs to Supplier A's level of service (92%), the minimum total procurement cost for GetFit is **11,965,783** dollars (rounded to the nearest integer).

Would you like to explore this further or need additional details?

Here are some follow-up questions:

1. How would the procurement cost change if Supplier B's service level dropped to 95%?
2. What if Supplier C's service level improved to match Supplier B's at 98%?
3. How does normalizing for service levels impact the distribution of purchases among suppliers?
4. What would be the impact on costs if the demand for SKU W32A increased by 20%?
5. How sensitive is the total cost to changes in service levels across different suppliers?
6. Could you calculate the normalized cost if Supplier D had a service level of 94% instead of 96%?
7. What is the normalized cost per unit for SKU X33B from Supplier D?
8. How would the total procurement cost change if the cost per % level of service for SKU Z32A doubled?

**Tip:** Service level adjustments often reveal hidden costs in procurement decisions, making normalization crucial in supplier evaluation.

Learn how to minimize procurement costs by normalizing supplier service levels. Understand the process of adjusting costs based on different service levels and calculate the minimum total procurement cost. Suitable for advanced college-level students and professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation