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Review. Transportation problems are a special type of LP.We use a streamlined version of the simplex method to solve.Classic problem involves transporting items from one set of nodes to another.But other problems can be modeled as transportation problems and solved more easily.. Review. Basicall
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1. MIE 379 Deterministic Operations Research Todays Goals
Formulate and initialize Transportation Problems
Hillier and Lieberman Sec. 8.1
Signed draft of case study due Today
Case Study due Th. Dec. 11!
Homework #11 Due Thursday. Dec. 4th: 8.1-2ab, 8.1-3a, 8.2-1c
2. Review Transportation problems are a special type of LP.
We use a streamlined version of the simplex method to solve.
Classic problem involves transporting items from one set of nodes to another.
But other problems can be modeled as transportation problems and solved more easily.
3. Review Basically a transportation problem is one in which you are asking:
How many of what should go where?
How many goods should go from which factory to which warehouse?
How many goods should go from which warehouse to which store?
Inventory: How many goods should be made in month i to be available in month j? (i.e. how many goods should go from month i to month j?)
Assigning students to schools.
4. Review Transportation Problem Components:
A source set (Supply Centers / Factories)
A destination set (Distribution Ctrs / Customers)
A cost matrix (Transportation or storage costs)
5. Review Everything you need is in this parameter table
6. Review A basic transportation problem has fixed supply equal to fixed demand and the goal is to find the least cost way to deliver all the goods from supply nodes to demand nodes.
But, we can also handle:
Excess supply (or demand) by adding a dummy demand (or supply)
Infeasible routes (make the cost $M)
Flexible demand (split into two parts)
7. Review - Example 1 from last class The Childfair company has 3 plants producing strollers that are shipped to 4 distribution centers. Plants 1, 2, and 3 can produce 14, 19, and 12 shipments per month. Each distribution center needs 10 shipments per month. The freight cost for each shipment is $100 plus $0.50 per mile. The distance is given in table below.
8. Review - Example 1 from last class Formulate as a transportation problem:
9. Transportation Problem Example 2 The plants produce 60, 80 and 40 units. Firm has committed to sell 40 units to customer 1, 60 units to customer 2, and at least 30 to customer 3. Customers 3 and 4 want as much as they can get.
How do we represent these parameters?
10. Solution
11. Inventory Problems In inventory problems you are asking how much should I make when to sell when?
The sources are the periods in which you produce the goods.
The destinations are the periods in which you sell the goods.
Do the 2nd in-class example problem.
If a particular allocation is impossible, use a big M. (for example, you cant make a boat in Quarter 3 and sell it in Quarter 2).
12. Transportation Problems Inventory Problems How many sailboats to produce each of four quarters?
Demand is projected to be 20, 30, 55 and 35
Demand must be met on time
They start with 10 sailboats
Can produce 40 each quarter
Holding costs are $20/boat/quarter
Total capacity (supply) =
Total demand =
15. Transportation Problems: Algorithm Transportation problems use a slimmed down version of the simplex method.
Because they have equality constraints, we need to find an initial feasible solution.
It turns out this is easy in transportation problems you do not need to use the Big-M method.
16. Initial Allocation Northwest Corner Method You simply start at the upper left hand corner and allocate as much as you can;
Then move right as far as you can;
Then down; then right; etc.
17. Initial Allocation
18. Initial Allocation
19. Initial Allocation
20. Initial Allocation
21. Initial Allocation
22. Initial Allocation
23. Initial Allocation
24. Initial Allocation
25. Initial Allocation
26. Initial Allocation
27. Initial Allocation
28. Formulation vs Allocation
29. Transportation Problems Inventory Problems How many sailboats to produce each of four quarters?
Demand is projected to be 20, 30, 55 and 35
Demand must be met on time
They start with 10 sailboats
Can produce 40 each quarter
Holding costs are $20/boat/quarter
Total capacity (supply) =
Total demand =
32. Transportation Problem - Example Mrs. A has a cookie company along with her 2 friends Mrs. B and Mr. C. They each can cook up to 40 dozen cookies per day, and then have their teenagers deliver them. They have a standing order from the 4 local elementary schools of 60,20,15, and 10. The cost of delivery, per dozen, is given by the table.
