In this module, we'll talk through the newsvendor model or go into the decision variables that we need to make, to parameters we need to consider, and then how to solve them. For this video, we'll use a Christmas tree CEO as an example. Christmas tree as alluded to in the reading, is a very seasonal item. It only comes once a year. In December, you can say that the selling season for the Christmas tree is between December 1st and December 25th, or some can say is right after Thanksgiving until up to December 25th. You can imagine after the 25th on a 26th, the tree is pretty much worthless. Not many people would desire to buy a tree anymore, maybe a few, but not in mass. Once that season, December 25th is over, there'll be minimal to no demand for the tree. Since it takes a long time to grow the tree and also the procurement of a tree, for every store company to procure these trees, they had to order all the trees at once so they order everything upfront. Then this one, you can imagine it just once a year. They give this one order to the supplier. The decision we need to make in the newsvendor model is the order quantity. How much should I order for this season? The perimeter we need to consider are the unit cost, the cost per tree for the retailer to buy, the revenue, the price that the retailer charges to the everyday consumers like you and I. Salvage value, if at all. If there's a salvage value on December 26th, what can I sell it for? Assuming no one else is going to buy it, and what is the demand? What is the demand from the market? We're going to assume this is a random variable. Is not static or consistent. It may change year-over-year so is something unknown to us. But typically, we assume, and usually based on history, we assume that it follows the demand, follows a normal distribution. One key assumption that we need to make or we need to make sure that it takes place is usually that the revenue is greater than our cost, and our cost is usually greater than a salvage value. Basically, if you need to sell, the salvage value, basically you're selling at a loss, it's less, you get back less than what you pay for it. We need to figure out what's my over-stocking or overage cost and also my under-stocking or underage cost. The over-stocking or overage cost is essentially just my cost, unit cost minus the salvage value. I paid too much. I had too much in my inventory and now I have access and I cannot sell them anymore at the regular price. I need to get rid of it, so I'm actually selling at a loss. The difference between what I paid for it, the cost, and then what I can get back. The cost of under-stocking, this is when I don't have enough. I sell that before December 25th. You can think of it, this is as the profit that we are foregoing. It's revenue minus cost, what I'm charging people, and then versus what I paid for it. This is the profit or opportunity that I'm foregoing because I don't have enough in my inventory. They have gone to another store or somewhere else to buy their tree. The problem is that, the problem statement, the Christmas tree selling season begins December 1st and ends December 25th. The tree has a long lead time and vendor can only place one order for the entire season, so basically for the year. Therefore, the order quantity needs to be decided up front. It's basically way before the season begins, months ahead of December 1st. Each tree, if you sell it for $105 and it costs $15 to buy and has a salvage value of $5. You're satisfying this requirement or this constraint here that my revenue is greater than my cost, and then my cost is greater than the salvage value. We also know that demand follows a normal distribution, so based on historical information, what that means, on average, I sell 30,000 trees a year with a standard deviation of 10,000. This is the distribution of a demand. You can do this by looking at the historical information and this is similar to the video of Module 3 and 2, that you can use the average function in Excel to figure out the mean and also the STDEV value to figure out the standard deviation. If you have historical demand from last year, last two years, three years and so forth, this is something that you can do. Once you have all this information, you have the values for all these parameters, now we can calculate the cost of overage and cost of underage because we need to figure out critical fractile. So here, and this is the equation, is the c(u) is divided by c(u) plus c(o). It's a cost of overage divided by the sum of the overage cost plus the underage cost and this gives us the critical fractile and this is basically Alpha. This is the equivalent of the percentage. There's customer service level that we looked at before like for non newsvendor model that we figured out. We decided on a customer service level and then from there we can figure out the quantity. Once we have that, the equation to determine the optimal quantity is Q equals Mu plus z times s and we need a critical fractile to figure out z, as we saw in Module 3. Mu is actually the mean, that's a Greek word or notation for mean, and an s, which here are used to denote sigma. Sigma denotes standard deviation. So basically, the optimal quantity is just my mean plus the z value times the standard deviation, so it's similar to how we reviewed this in Module 3, with a normal distribution curve. This is telling me how far to the right of my mean then the goal in order to have the optimal quantity for this scenario. Now, we can fill it out the equation and we can compose the equation with the values that are given in the problem. C is the unit cost, unit cost I know it's $15. My revenue, I'm saying is 105, and then this would be b, so my salvage value is only $5. The demand, I know it follows a normal distribution, so it's 30,000, mean of 30,000 and a standard deviation of 10,000. In order to calculate this, the Q optimal, I'll move this down one, so I need to calculate Alpha first. Maybe let me break this down, so I didn't know what my c(o) and c(u) values are. I know c(o) equals my cost less the salvage value. Cost less salvage value. My c(o) cost of overage of our stockings $10 per item. Then cost underage is r minus c is equal to my cost. I made $90 in profit for every tree that I sell. Then if I don't have enough, I'm forgoing $90 for every tree that I'm not able to sell. My Alpha or my critical fractile is c(u) divided by c(u) plus c(o). I get a critical factor, 0.9. Now I can compute this. I know my Q, so my Q optimum is 30,000. Do this in this way. I'm going to do, say another two rows here and then going to put 30,000 as my mean and 10,000 as my standard deviation. Then it will be 30,000 plus. The way we talk about it, figure z, we can use the formula and norms inverse, going into critical fractile, and then times s, s is my standard deviation, Sigma. I figured out value, about 42,000, 43,000 trees, approximately 42,815 or 116 to be more exact. Trees that I need to order for this upcoming season based on the known demand, with the means of 30,000 and standard deviation of 10,000. A critical fractile 0.9. Then put this based on my cost structure. This is one way that we apply the newsvendor model. You can apply this also to, if I change this to selling fashionable items like in the fall season, winter season, spring, and summer, all these different seasonal fashion items like clothing, are you going to replace basically the tree with x clothes? You only have, I say two or three months of selling season and then you retail typically the load heavy upfront. Even before the beginning of the selling season, they have already stock up on the inventory. You don't want to be selling out, then you can think about electronics, phones, maybe computers, when they debut on the market, they already have a heavy load of inventory ready to go. They follow this similar equation to know their costs, their revenues, and the salvage values and they will do an analysis on demand to know the distribution. In this case was [inaudible] is normal, but it could be the distribution as well. I know my means and standard deviations. From there I can calculate my critical fractile and then figure out the optimal value. One last thing is that you can also apply newsvendor model, which is our scope here, but I just mentioned it that to revenue management. Something like selling airline seats or any concerts and sporting events is not on inventory standpoint, but essentially you have fixed inventory. Inventory is my seat, but you need to sell them. The decision point there is to maximize the revenue. This is it for a newsvendor model.
