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OK, this example is the famous transportation problem.

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Suppose we have our factories on the left hand side.

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As one to a three and we have Jay demand points, let's call them, do you want to do, for example?

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And the question is how much we can, uh, produce from each factory in order to minimize the objective

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cost?

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And also, um, knowing that the capacity of each factory is limited, the capacity of each route is

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limited, and also the demand should be satisfied.

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OK, this is a famous transportation problem, and we have some factories on the left hand side and

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we have these are the factories, these are the demand points and we know the demand of each point and

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the capacity of each factory and the cost of production and the cost of transportation.

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So the question is, in order to satisfy the demand on the right hand side, how much each factory should

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produce and from which route we should transport these products from the factories to the demand in

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order to satisfy all the constraints.

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So there are two sections in the objective function.

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So first of all, is telling us that transportation costs depends on the distance between the nodes

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and also how much good are being transported from I to J.

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Hi, this is the transportation problem.

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And in this example, we want to know and if we have some factories and let's call them I and they are

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running from as to history and there are some demand points.

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Do you want to die for?

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And the question is how much each factory should produce.

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And in order to minimize the objective function, which is the summation of their production costs and

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the transportation costs.

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This is the transportation costs and this is the production cost.

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And also there is another thing that should be satisfied that is that and the capacity of the factories

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are limited and they should produce between some specific ranges and also the demand as each point should

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be satisfied.

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OK, so let me talk about the, um, promo codes for solving this problem.

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So first of all, as usual, we have to import the required packages and then, um, define the required

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sets.

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And they are two different sets.

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It's an abstract model.

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Um, we have a demand which is defined over J p mean P max and costs are the parameters.

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So and also the distance between, um, different nodes are, uh, defined as a parameter.

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There's a variable X and telling us how much good is moving from eye to to, uh, from factory eye to

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the demand point J.

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And it is defined, um, as a real number, could be defined as a positive, real.

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And also, uh, it has about between zero and three hundred, for example.

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And there are some bounds for the generation side or the production side.

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You can say that P.

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Mm.

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Is the final.

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The AI is always within this pound.

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Mm hmm.

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And also, um.

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How much you are producing is calculated this way, some version of, um, I NJ Automation of Model

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X, uh, model X IJA for J in Model J.

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Maybe we can improve it.

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What we will see.

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And also, um.

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Um, this is this constraint is on the production side and also this side is ensuring that the demand

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is satisfied.

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I intentionally put it a bigger than equal to demand because it's easier for me to solve it, but it

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will not produce more than what is needed.

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OK, so this term is the production cost and this term is the, uh, transportation cost.

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So, um.

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Everything is fine here and also, um, the objective function, um, is this.

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And we want to minimize that the saw the model, as you can see, it's a linear programming one and

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also we have to.

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We have to specify the data, so as you saw, we have some parameters defined on I saw Param.

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Um, or I want to three p.m. max and calls, and if you have other characteristics, we could put it

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here and also J it is defined over one to four and the demand is specified here in the perimeter distance

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and the distance between each pair of, uh, nodes are given here.

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OK, so you have to specify that in your.

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That's fine.

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And if you solve it, let me run the tabs one by one.

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This one is wrong.

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This one is wrong.

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And also this one is wrong.

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You can see the objective function is calculated here.

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And if you want to visualize the decision variables, you can do it.

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So I run this tab.

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So these are the results, let's, uh, read them, uh, it is telling us that, um.

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And the amount of, um, transportation, uh, between, uh, production one and demand one is zero,

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production one on demand to zero, one on the one, three is three hundred and so on.

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You could visually show that as well.

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So these are the results that are visually shown.

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And you can see the biggest transportation is between, um, point one and demand three.

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And the next one is between two and demand one.

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So if you have a look at that here, it's here.

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So you see the next big quantity to be transported is from point two to demand number one.

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Thank you very much.