A terminal has four customers that need delivery by truck. The customers have the following demand:

Customer        Demand

1          5 tonnes

2          8 tonnes

3          7 tonnes

4          6 tonnes

The truck load capacity is 15 tones. The distances (km) between the customers and the terminal are:
 
 
Terminal         Customer 1     Customer 2     Customer 3     Customer 4

Terminal         -                                              

Customer 1     100      -                                  

Customer 2     100      20        -                      

Customer 3     120      40        30        -          

Customer 4     130      60        10        10        -

3a. Calculate the driving distance savings matrix.

1. How much is saved if Customer 1 and 2 are served in one route?

2. How much is saved if Customer 1 and 3 are served in one route?

3. How much is saved if Customer 1 and 4 are served in one route?

4. How much is saved if Customer 2 and 3 are served in one route?

5. How much is saved if Customer 2 and 4 are served in one route?

6. How much is saved if Customer 3 and 4 are served in one route?

### Part 3a: Driving Distance Savings Matrix

To calculate the savings matrix, we first need to understand how much distance would be saved if two customers are served on the same route. The savings can be calculated using the formula:

\[
\text{Savings} = \text{Distance from Terminal to Customer A} + \text{Distance from Terminal to Customer B} - \text{Distance between Customer A and Customer B}
\]

Let's calculate the savings for each pair of customers.

### Savings Calculation

#### 1. Savings if Customer 1 and 2 are served in one route:

\[
\text{Savings} = \text{Distance from Terminal to Customer 1} + \text{Distance from Terminal to Customer 2} - \text{Distance between Customer 1 and 2}
\]
\[
\text{Savings} = 100 + 100 - 20 = 200 - 20 = 180 \text{ km}
\]

#### 2. Savings if Customer 1 and 3 are served in one route:

\[
\text{Savings} = \text{Distance from Terminal to Customer 1} + \text{Distance from Terminal to Customer 3} - \text{Distance between Customer 1 and 3}
\]
\[
\text{Savings} = 100 + 120 - 40 = 220 - 40 = 180 \text{ km}
\]

#### 3. Savings if Customer 1 and 4 are served in one route:

\[
\text{Savings} = \text{Distance from Terminal to Customer 1} + \text{Distance from Terminal to Customer 4} - \text{Distance between Customer 1 and 4}
\]
\[
\text{Savings} = 100 + 130 - 60 = 230 - 60 = 170 \text{ km}
\]

#### 4. Savings if Customer 2 and 3 are served in one route:

\[
\text{Savings} = \text{Distance from Terminal to Customer 2} + \text{Distance from Terminal to Customer 3} - \text{Distance between Customer 2 and 3}
\]
\[
\text{Savings} = 100 + 120 - 30 = 220 - 30 = 190 \text{ km}
\]

#### 5. Savings if Customer 2 and 4 are served in one route:

\[
\text{Savings} = \text{Distance from Terminal to Customer 2} + \text{Distance from Terminal to Customer 4} - \text{Distance between Customer 2 and 4}
\]
\[
\text{Savings} = 100 + 130 - 10 = 230 - 10 = 220 \text{ km}
\]

#### 6. Savings if Customer 3 and 4 are served in one route:

\[
\text{Savings} = \text{Distance from Terminal to Customer 3} + \text{Distance from Terminal to Customer 4} - \text{Distance between Customer 3 and 4}
\]
\[
\text{Savings} = 120 + 130 - 10 = 250 - 10 = 240 \text{ km}
\]

### Summary of Savings:

1. **Customer 1 and 2**: 180 km
2. **Customer 1 and 3**: 180 km
3. **Customer 1 and 4**: 170 km
4. **Customer 2 and 3**: 190 km
5. **Customer 2 and 4**: 220 km
6. **Customer 3 and 4**: 240 km

These values represent the driving distance savings if the respective pairs of customers are served in one route instead of separate routes.

Do you want more details on any of these steps or have any other questions?

---

**Related Questions:**
1. How would the savings change if the truck capacity was increased?
2. What would the savings be if a different distance matrix was used?
3. Can you explain how to optimize the delivery routes for maximum savings?
4. What if the demand for each customer changed—how would it affect the routing?
5. How would you account for road conditions or traffic in this analysis?
6. What other factors could affect the driving distance savings?
7. How would adding a fifth customer change the savings matrix?
8. How can you use this matrix to minimize overall transportation costs?

**Tip:** When calculating route savings, consider not only the distance but also the capacity and demand constraints to ensure feasible and efficient routes.

Learn how to calculate driving distance savings matrix for delivery routes with a detailed step-by-step solution. This problem involves optimizing delivery routes based on customer demand and truck load capacity constraints. Suitable for advanced learners interested in logistics and optimization.

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