Week 5 / Transportation Flashcards
Transportation Problem
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
3 Parts to the Transportation Problem
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
Traditional Transportation Problems
- Travelling salesman problem (TSP)
- Automated guided vehicle (AGP)
- Vehicle routing problem (VRP)
Travelling salesman problem (TSP)
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
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Automated guided vehicle (AGV)
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
Vehicle routing problem (VRP)
Having a primary hub (aka supplier) and having multiple routes
Between each trips the vehicles can refuel
Modern Transportation Problems
- Smart City
- Sharing Economy
- Last Mile Delivery
Optimization 3 main components
- Minimization of cost/ Maximization of profit
- Based on decisions: developing new product
- Subject to constraints: budget, time, quality
Transportation Model
Special case of linear programming
Decisions Variables for Transportation Model
= quantities to be transported Xij
i = index for Factory j = index for demand / customer
Objective function for Transportation model
= sum of [cell costs Cij X decision variables xij]
Supply constraint for Transportation model
Capacity of each source cannot be exceeded (< greater or equal to)
Demand constraint for Transportation model
demand must be met (=)
Transportation Model Assumptions
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
Transportation Types
- 90% of transportation is seas transportation, aka cargo ships, freight transportation
- Then the next is air transportation
- Then by truck
Transportation has been studied by who?
Business school
Industrial Engineering
Civil Engineering
It is multidisciplinary
Linear programming example
- 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
Excel Solver
If you increase Supply
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
Excel Solver
If you increase Demand
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).
Optimal decision
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)
If demand is lower than supply,
dont worry about excel solver
If supply is more than demand
No need to transport to customers, just keep the extra units in the factories
X1a would mean>
From factory one to customer A
Constraint =
Number of factories + number of warehouse customers
There is no need to have total supply equal
total demand
When we see a 0 in a row, there is another solution where the cost is lower
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
Demand variables
The numbers excel outputs for you
So if there are 3 factories and 4 consumers, we have 12 constraints? Or do you add them and it is 7 constraints?
X is the number of variables
Each factory has one constraint, each customers has one constraint
