[MUSIC] In this video, we're going to look at another example of capacity optimization. So in video one from module one we looked at the example, was also a more complex capacity optimization or allocation. Here, we're going to look at just one facility for one country and then we're going to walk through actually in detail how to set this up. So, well, before that you will know the demand. So here we know the demand for a certain product and I also know the production cost and I also know the capacity that I have for each month that I'm interested in analyzing. So this is something that within your organization or the company that you can gather, right, these are typically available demand from your sales history or shipment history, either one. But typically sales would be better and production costs, you can gather from your internal facility or if you outsource, then from your suppliers. And same thing on capacity, you can get it from your internal production plants or from your suppliers. And then so for every, [COUGH] month, but I will have a cost. So if I produce for January to January, for January demand, then it cost me, let's say $24. But if I produce for February in January, it cost me 29, produced from March in January, cost me 34, April produced in January, for April is 39 and so forth. So I won't be able to produce, February for January, cannot go backwards. So I used just a random large number. So for the engine, right, the optimization engine will not consider such a case. This is the way how this is set up here. So then for these in your March for January, April for January and May for January you can just use use 10,000 as a random large number. So February February cost me 27, February, March 32, 37 and 42 and so forth. So I set this up for [COUGH] the five months I have here that I'm interested in analyzing. So then I come down to my decision, right? So my decision, again, same as before. I need to know how much am I producing in which month and for which month. So in this decision matrix, I also know this is my total supply to the market or two in January, sorry. So in January and then total supply in February, total supply in March. And then [COUGH] in the rolls, I know that this is a sum of my total production that I produce in January. [COUGH] Total production in February and so forth. And here these are my production capacity. So this is from row five here, in January, I only have 250 units of capacity. February 225, March 250, April is 200 then May is 225. And similarly on the demand side, rather in January, my total demand is 200, [COUGH] in February 250, March is 150, April is 80 and then May is 120. And so I also do the same, I add these up. These are my supply in January, February and so forth. Okay, so now we have the demand, we have now our capacity, my production cost and also have a cost matrix for the months that I'm interested in analyzing. And I also set up my decision matrix. Then I can go to solving. So this one we're actually going to do it together and also the other one is that I need to set up total cost. Should I put this in my objective function? So total cost is just the, however number of units that I produced times the cost per unit. Right, so some product here, if you're not familiar with. You can take the values in the matrix form, right, form two matrix and multiply them together. So it was easy where you don't have to do, B19 times B10 and then B20 times B11 and so forth. Okay, so now my total cost is my decision objective function. So my objective is, so we're going to do it together in this one. So it's going to set B28 which is my total cost. Okay, and we are trying to minimize our total cost. So I'm going to choose minimize function or option and we're going to change our decision variable matrix. So these are all the values here and then we're going to take these off so we can do it together. So now we have constraints. You always will have constraints. So my first constraint is the my supply, sorry, my production, right? So then whatever I produce, I total production in all the months, it has been less than or equal to the production capacity that I have available. Okay, so I'm choosing, right, so my production capacity that's listed here. And then this is the the unknown it is for now, whatever the optimization engine suggests, it cannot be more than what's here. So it's less than or equal to and we have another constraint which is my supply. And so I have whatever supply I have for each month, it has to equal, is in our case, to the demand. Can I have for each month? Okay, so again, this is the demand I have each month and the supply I have for each month, actually equal to the demand for that month. I hit OK. So we want to check or make sure the account on constrained variables are non negative. This option is checked and also we want to select simplex LP as my optimization method. Okay, so once I have everything set up I can just hit solve. You take a little bit of time to run through the iterations and once again solve or find solution. It tells you that Solver has found a solution and all constraints and optimality conditions are satisfied. So I can choose to keep my solution and I can also select to have a view at my sensitivity report. Right, so I hit OK. So you see that the sensitivity report, another tab gets generated in Excel and then you'll have these optimal decision variables and this is the objective functions of $23,440. It's the minimum cost that I incur based on this mix of production volumes right by from a month to which month. From January to January, I put 200 and from January to February I put 225 and I produce the rest in February and adds up to my supply equals my command, right, 250 equals 250. And then my capacity does not exceed the capacity I have each other month. So they don't necessarily be equal as you see here. And you come over here, the sensitivity report is a bit more complicated but we only need to pay attention to either January or January to Feb. So these forward looking ones, we don't need to pay attention to the backward, those don't make sense. So then you can follow the suggestion from, you can look at the allowable increase allowable decrease to see what you can change. And also look at reduced costs on how to improve the final values on the variable side. In constraint side we can look at the allowable increase and allowable decreases. And the shadow price tells you if you change you make any changes, how much the for each unit to change, how much of the final value go up by, right? That's what the shadow price tells you. Okay, and then as a reminder again, this is allowable increase, if you see, or decrease this infinite number, that means they're not bounded, so there's no upper bound or there's no lower bound.