 Decision models transform inputs, the data, the uncontrollable variables, and the decision variables, things you can control, into outputs which allow us to evaluate the quality of our decisions. Building decision models is more of an art than a science, but there are some basic steps to consider. Let's look at a typical problem. A news boy sells daily newspapers and he must make a decision about how many to buy. If he buys too few, he will not be able to satisfy the demand and will miss out on some profit. If he buys too many, he will have to lower the price to sell the papers at the end of the day and lose money. Since this is a quantitative model, we need to define our variables. R is the selling price, which is set by the publisher. C is the cost of a paper, which is also set by the publisher, as is S, the discount price. Demand D is uncontrollable by the news boy, but Q is his decision to make. Finally, QS is the quantity of papers that he sells, and SQ is the surplus number of papers, the number that he buys but fails to sell in the normal work period. To build a model, we need some basic relationships to find. Logically, R must be greater than C, must be greater than S, if anything is to make sense. And as usual, profit equals revenue minus cost. Revenue in this problem is equal to R, the price that he can sell the papers for times the quantity sold, plus the surplus price times the surplus quantity. And cost is equal to the cost of the paper C times the quantity he buys Q. If he knew the demand D, then he should buy Q equal to D, which will give him the max profit. If Q is less than D, then he is missing some of the profit, because he's got papers he could have sold, but he didn't have the papers to sell. If Q is greater than D, then he must sell the papers at a loss, and thus he will lower his profit. So let's build this model in Excel. This is one way to build the model in Excel. The way I've set it up here, I put my data up in top, and these are the values that were given in the problem statement. Usually in this case, we're given that the price of each newspaper is 18 cents, the cost of each newspaper is 12 cents, and the discount price, the price that he can sell them for, if they're out of date, is 9 cents. And those are all established by the publisher. The model is down here. The part in blue, the demand and the purchase quantity, now those are variables, the demand we can't control, but here we're assuming it to be 4,000, and I'm starting out the decision variable and saying it's also 4,000. And yellow are our outputs here. The first part is the quantity sold, QS, and it's 4,000, and it's the minimum of the demand or the quantity that he purchases, Q. And the reason for that, he cannot sell more than demand and he cannot sell more than Q. So it's the minimum of those two, and that's the formula with the sale references. The surplus quantity, SQ, zero in this case, because the demand and the quantity match, has to be the max of zero because we don't want a negative surplus quantity. And that's what you would have if the demand was greater than Q. So it's the max of zero or Q minus D, and that's set up with the formula max, zero comma and the sale references. The profit is just the formula that we talked about on the previous slide. It's the selling price R times the quantity sold, QS, plus the surplus price times the surplus quantity, SQ, minus the cost, which is the cost of each paper times the number that were purchased. And that is the formula and sale references here. You can see if he buys exactly the demand, then he gets a profit of $240. If he buys too many, let's say he buys 4,200, and you need to exercise your model to make sure it makes sense. If he buys more than a demand, then he has a surplus, and the surplus reduces his profit down to $234. If he buys fewer than the demand, it drops again, because this time he doesn't have a surplus, but he lost the profit on those 200 newspapers he didn't buy. So this is a basic decision model. All the decision models you make will be something like this. Of course, they will be more complicated with the more information you're given and the more relationships you have to build into your model. But this is a basic and it's a good place to start.