Transportation algorithm

Asked Aug 16 '18 at 09:10

Active Aug 16 '18 at 09:10

Viewed 39 times

I am attempting Q17 on this worksheet: http://www.statslab.cam.ac.uk/~qb204/teaching/ex_optim_2.pdf

Am i correct in reformulating the problem as : minimise $\sum_{i=1}^{n} \sum_{j=1}^{n} tij $ ? But I don't understand what constraints there need to be. Also in b) it gives me a matrix but to use the transportation algorithm I beloieve I need to be given supplies and demands?

Thank you in advance.

asked Aug 16 '18 at 09:10

MathematicianP

First of all you have to minimize $\sum_{i=1}^{n} \sum_{j=1}^{n} \color{red}{x_{ij}} \cdot t_{ij} $, where
$x_{ij}=\begin{cases} \text{1 , if taxi i pick up costumer j} \ \text{0, if taxi i doesn´t pick up costumer j}\end{cases}$ The values of $t_{ij}$ are fixed. That are the values of the matrix. Is that comprehensible ?
– callculus42 Aug 16 '18 at 14:38
Thank you for your reply . Yes, I understand that, but I am still unsure how to solve the problem. I am trying to use tableaus to solve this but I don't know if this is the right way to go... – MathematicianP Aug 16 '18 at 14:48
I don´t know which method you are supposed to use. One method is the Northwest Corner Method. Which method do you think of? – callculus42 Aug 16 '18 at 14:58
But I don't have the supplies or demands, so how can I apply these methods? – MathematicianP Aug 16 '18 at 15:09
The supply is 1 for every taxi $i$: $\sum\limits_{j=1}^4 x_{ij}=1 \ \forall \ \ i \in {1,2,3,4 }$. And the demand is 1 as well for every costumer $j$: $\sum\limits_{i=1}^4 x_{ij}=1 \ \forall j \in {1,2,3,4 }$. – callculus42 Aug 16 '18 at 15:13
I see, but this does not give me 7 basic variables – MathematicianP Aug 16 '18 at 15:24
Why do you need 7 basic variables? And please tell me what kind of method you are supposed to use? – callculus42 Aug 16 '18 at 15:25
I am trying to apply the transportation algorithm but I don't think it works – MathematicianP Aug 16 '18 at 15:29
Putting all the information in a tableau I get only 4 basic variables (since I am only allowed to place 1 in each column and row once – MathematicianP Aug 16 '18 at 15:30
I hope this makes sense – MathematicianP Aug 16 '18 at 15:32
What is the transportation algorithm in your opinion? Here are several methods provided. 2) Yes, I´ve got 4 basic variables as well.

callculus42

Aug 16 '18 at 15:32

I thought I required 7 basic variables for the method to work. Can I just assign 4 of the multipliers the value 0? – MathematicianP Aug 16 '18 at 15:37

Which method? Please provide a reference. – callculus42 Aug 16 '18 at 15:39

On page 2 of your document: "Thus, the model has m + n - 1 independent constraint equations, which means that the starting basic solution consists of m + n- 1 basic variables" – MathematicianP Aug 16 '18 at 15:43

I would suggest that you try one of the three methods and show it by making an edit of your question. It doesn´t make sense to talk theoretically about the exercise. – callculus42 Aug 16 '18 at 15:48

Transportation algorithm

0 Answers0