Week 5 / Transportation

Question 1

Transportation Problem

Answer 1

The transportation problem involves finding the lowest-cost routes to transport products from sources of production to different destinations.

The transportation problem involves determining a minimum-cost plan for transporting a product from multiple sources to multiple destinations

Question 2

3 Parts to the Transportation Problem

Answer 2

1) List of destinations and their demand
2) Unit cost of transporting items
3) List of sources and their supply quantity

If you have all three of these you have the required information for formulating transportation

Question 3

Traditional Transportation Problems

Answer 3

• Travelling salesman problem (TSP)
• Automated guided vehicle (AGP)
• Vehicle routing problem (VRP)

Question 4

Travelling salesman problem (TSP)

Answer 4

Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?

-One of the hardest problems in the world of commuting
-If there is 10 cities to visit, you have 10 factorial of options
-

Question 5

Automated guided vehicle (AGV)

Answer 5

Using automated vehicles to find the shortest distance for the shortest possible route.

Each block has a connection to the entire loop

Example: Cleveland hospital video

Question 6

Vehicle routing problem (VRP)

Answer 6

Having a primary hub (aka supplier) and having multiple routes

Between each trips the vehicles can refuel

Question 7

Modern Transportation Problems

Answer 7

• Smart City
• Sharing Economy
• Last Mile Delivery

Question 8

Optimization 3 main components

Answer 8

• Minimization of cost/ Maximization of profit
• Based on decisions: developing new product
• Subject to constraints: budget, time, quality

Question 9

Transportation Model

Answer 9

Special case of linear programming

Question 10

Decisions Variables for Transportation Model

Answer 10

= quantities to be transported Xij

i = index for Factory
j = index for demand / customer

Question 11

Objective function for Transportation model

Answer 11

= sum of [cell costs Cij X decision variables xij]

Question 12

Supply constraint for Transportation model

Answer 12

Capacity of each source cannot be exceeded (< greater or equal to)

Question 13

Demand constraint for Transportation model

Answer 13

demand must be met (=)

Question 14

Transportation Model Assumptions

Answer 14

1) Items to be shipped are homogeneous (no difference between items)
2) Transportation cost per unit does not vary by volume (no increases in the cost of transportation)
3) Only one route between each origin and each destination

Question 15

Transportation Types

Answer 15

• 90% of transportation is seas transportation, aka cargo ships, freight transportation
• Then the next is air transportation
• Then by truck

Question 16

Transportation has been studied by who?

Answer 16

Business school
Industrial Engineering
Civil Engineering

It is multidisciplinary

Question 17

Linear programming example

Answer 17

• The number is either 0 or positive (never negative)
• Supply must be greater to or equal to demand
• In an optimal solution, all items in supply will be delivered, so S=D
• SUMPRODUCT (c6:F8, c15:F17)
• The customers multiplied by the factories give you decision variables (4 customers x 3 factories = 12 variables)
• The demands = the constraints
• To solve the supply rows, add up the values of Example: X1a + X1b + X1c + X1d

Question 18

Excel Solver

If you increase Supply

Answer 18

What if I add more 50 units to factory 3’s supply?

The values for the column total role will remain the same.
The row total for factory 3 will remain the same as before and this is imply due to he 50 units not requiring transportation. There is no need to impose additional cost for these units, so we keep these units in factory 3

Question 19

Excel Solver

If you increase Demand

Answer 19

What if increase demand for warehouse B by 50?

The solver will fail and say it cannot find a feasible solution because the demand is larger than the supply (500 vs 450).

Question 20

Optimal decision

Answer 20

There is no solution better than this solution with the total cost as low as that (there can be other solutions, but not where the total cost is less than the lowest amount)

Question 21

If demand is lower than supply,

Answer 21

dont worry about excel solver

Question 22

If supply is more than demand

Answer 22

No need to transport to customers, just keep the extra units in the factories

Question 23

X1a would mean>

Answer 23

From factory one to customer A

Question 24

Constraint =

Answer 24

Number of factories + number of warehouse customers

Question 25

There is no need to have total supply equal

Answer 25

total demand

Question 26

When we see a 0 in a row, there is another solution where the cost is lower

Answer 26

2 options, either transportation costs are heavy, or something about supply.

If there are nothing but 0’s it means the factory is so costly to us that we may as well use the other factories

Question 27

Demand variables

Answer 27

The numbers excel outputs for you

Question 28

So if there are 3 factories and 4 consumers, we have 12 constraints? Or do you add them and it is 7 constraints?

Answer 28

X is the number of variables

Each factory has one constraint, each customers has one constraint