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If you remember the transportation example, and in that specific example, we decided how much items

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should be sent from supplier to the demand point and the demand at different points are concerned.

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So now we want to expand that to specific example and make it dynamic.

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When we talk about the dynamic kind of modeling, we mean that some decision variables have time.

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Index means t.

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So again, we import the required packages, for example, Palomo non-pay and then we need to define

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an abstract model ie is the set of the suppliers, is a set of the demand and a set of the time steps.

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And as I have already explained, the demand is a parameter which is defined over the node j p mean

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P max r the set of supplier constraints that specify the minimum and maximum capacity of the.

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Suppliers and also the costs of supplier I and also we have added a new parameter called pattern, the

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pattern is going to define how demand is changing and it does have an index t so it is defined over

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the model T and also the distance is also the parameter, which is a stating the distance between supply

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and demand.

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And it is different over real numbers and this geometrical x which was telling us how much item are

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being sent from the supply to demand.

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It also has a T index now.

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OK, so let's continue the pump and the variable P was telling us how much each supplier is supplying,

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no matter what is being said to which demand points, though, the P bounds are.

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This is a function which we have already defined it in order to specify the bounds of my variables.

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OK, ok, so if we continue, we do need a rule C one that's rule is telling us how much it is going

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out of supply at time.

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Step T.

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OK, so the summation of model that X, T.J., for all the JS to all the demands that I'm sending the

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items.

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Hmm.

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And which should be equal to model P dot model that P or.

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So as you can easily see that this specific expression is defined over Tennie.

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That's why my function is defined over Tennie and for the same reason when I want to define my constraint.

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See one I have to define over Model T, model I and the rule is rule C one.

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OK, so next constraint is telling us what.

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It is telling us that whatever is reached the demand point, Jay, at time t, so the variation of the

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whole demand is modeled this way, so concerned number multiplied by something which is changing with

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time.

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So the summation of the model X for every eye in the model eye.

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So it means that whatever is being sent from different suppliers, that demand should be bigger than

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equal to the quantity of that demand at time.

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T.

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And this means that actually if you look at these constraints, is defined over TMJ.

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There is no eye is left in this expression because we have done the summation over.

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I OK, so since that expression is the final word JMT, that means that this should have TMJ here and

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the order of them should be exactly the same as the constraining Model T and G.

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Yeah, OK.

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And finally, the objective function is somehow similar to the previous one means that the summation

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of the operating costs to multiply by the cost of the production over summation over all I an all t

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plus the summation of Excite T.J. multiplied by the distance, which is also telling us how much cost

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is happening and do the summation of RJ and T and.

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OK, so.

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Actually, when we run the objective function here, that that should be very easy because the model,

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a lot of it is a variable that is telling me how much is my overall cost and the sense of the sense

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of the optimization is minimized.

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OK, now what we need to change compared to the, let's say, static kind of version of the transportation

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problem is to update my dad's file.

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So the only thing that I need to change is giving I'm providing the Palomo the pattern of the demand.

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It is assuming that it has only six time steps one, two, three, four, five, six.

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And the pattern of the demand is also specified here.

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And I change the name of the.

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That's fine.

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And I call it here.

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So let me run to code, so first stop, second stop.

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Third tap, so now the problem is solved and the objective function is found, OK?

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And if I want to see the results of the objective optimization problem, you can easily see that at

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twenty one and the values of the suppliers are specified here.

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Eighty four.

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Eighty four.

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Twenty and time two and three and so on and so on.

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So for the time 84 when the coefficient of the pattern is one, we should get exactly the same kind

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of results as we did in the static case.

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So I will show it to you here.

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So at time t one, which is equal, the demand here, the supply of one is three hundred six hundred

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twenty two and supply three is twenty.

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So let's get back to my example.

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Three hundred, six hundred, twenty and twenty.

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And these are objective function is the summation of the all decision variable and the costs associated

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with them for the whole time horizon.

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OK, and there is no drawing for this specific example, but if you want, you can do it easily.

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OK, that's it for this lecture at.