>> I have already made a recording on basics of economy order quantity. It is here, if you click on it...
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It will take you to my PowerPoints and the second page is the recording I have. So if you click on this link, or copy it... And paste it in a browser, and then you need to do something with flash, it will allow you to watch. I encourage you to go there and start from about 1 minute 10. That is when I start the concept of economy order quantity. But then now, I am going to solve some problems on that subject. Therefore, I go to inventory problems, which I have opened it here, and I go through solving some of these problems. From the beginning of the semester, and even before the start of the semester, I told you that my teaching style is not injecting some concept into your mind. The idea is to replace push teaching with pull learning. And from day one, I motivated you to form teams with your classmates. And try to use my YouTube lectures and my well animated problems to learn the concepts yourself. I not only motivated you to form teams, but I also said try to find some intra-team connections. And then within the team and within the teams also, you try to learn the material and whenever you encounter problems, you can come to me. And then you need to take these teams and these friends with yourself to the next semester. I'm going to inject a page here and then I paste my recorded lecture here. Now let's go and see what is the nature of the problem that I'm going to discuss with you. In economy order quantity, we do have two types of costs, ordering costs and carrying costs. Each time you order, you have a fixed costs, that is what we call it ordering costs. In this problem, ordering cost is 24 dollars per order. So each time you order, you should pay 24 dollars. It is the cost of preparing the order. The other cost which works on the opposite of this cost is carrying cost. Each unit of inventory, if you carry it for one year, it has a cost. In this problem, it is 60 cents per unit per year. So if you carry one unit of inventory for a whole year, then the cost for you is 60 cents. That is, cost of capital, that is physical cost to put that unit in some storage, have someone to take care of it. And that is also obsolescence cost. Obsolescence cost means if you have a product but either technology changes or customer changes his or her preferences, and that inventory doesn't have a value anymore. And then we have demand. In this problem, demand is 30,000 units of product per year. We need that much product. The first question is how much should we order to minimize our total cost? If each time I order 100 units, I should order 320 times. And each of them has 24 dollars cost. Right? Which is a lot of cost. But if I order at the beginning, I have only 24 dollars. Is this one better or this one better? Of course this is better. But there is something which works on the opposite side. If each time I order 100 units, like the case which is here, I have 100 units at the beginning of the period and 0 at the end of the period. Therefore, during period, I have 100 divided by 2, which is 50. The next period 50, the next period 50. So on average throughout the year, I have 50 units in inventory. 50 times 60 cents is 30 dollars. But if I order it all at the beginning of the year, by the end of the year I have nothing. On average, I have 16,000 units in inventory. 32,000 at the beginning, 0 at the end, average of those two becomes 16,000. And each of those 16,000 units of inventory costs me 60 cents. So that would be about 10,000 dollars inventory carrying cost. If I order in large numbers, holding cost, carrying cost goes up. But ordering cost comes down. And the reverse is correct when I order in small amounts. Let me first see what is my ordering cost in terms of quantity ordered. I'll come here. I go in there. I click on this. And I say open. This Excel sheet gets opened. Now let me show you what I'm going to do. This is what I need. My demand. That demand is 32,000 per year. Suppose the smallest order quantity that I want is 400. I can start from 1, but then I should divide 32,000 by 1, it would become a large number, my Excel chart will come out a little bit out. So I start from 400. I'll go here at tab 400. Right click on this, come a little bit down, go up, release it, series. Go to 4000. With one step, with step of 100. You want it to go in a row, in a column, in a column. And then these numbers are filled. Another way, I go here and I say equal to 400 plus 100. Enter. And then I copy down 4000. But the first procedure is easier because I have control over the last number, right click, go down, limit, series. Go to 4000. With the step of 100. Not in a row, but in a column. Okay? Now I want to know if each time I order 400 units, how many orders should I have? That is equal to my demand, which I show it by D as demand and also by R as throughput. And I assume the demand and throughput are equal to each other. And I lock it at 4 divided by quantity ordered. Enter. If each time that I order I order 400 units, in order to satisfy 32,000, I need to order 80 times. If each time I order 500, I need to order 64 times. And I push the mouse here, click click, these numbers, if you want it, I can add the decimal point to them so they are different numbers. This is the number of orders. Ordering cost is equal to number of orders multiplied by cost of each number and then lock it. Enter. And then click click. So now, I do have the ordering cost. Now I come here, this is my quantity ordered, control, then I go up here and I mark this one too. Insert scatter graph. And I click on this. 
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And that is my graph. The reason that it looks like this, because I have hidden some rows here. I have hidden from 1000 to 3000, from row 8 to row 20. So what I will do, I click on it, right click, select the data, hidden and empty cells, show data in the hidden cells. Okay. Okay? So this is my ordering costs. While quantity goes up, ordering cost goes down. That is my ordering costs. Therefore the curve here looks like this. If I order 400, I have 400 here. And then I consume it at a constant rate, it goes to 0. Again, I receive 400, consume it, goes to 0. Again, I have 400, and I consume it, it goes to 0. Therefore, on average, here I have 400 plus 0 divided by 2. 400 plus 0 divided by 2. 400 plus 0 divided by 2. On average, I have half of what I have ordered. Goes to Q to 0, Q, 0. And therefore, on the average, in the first cycle, I have Q divided by 2, Q divided by 2, Q divided by 2, Q divided by 2. In general, if each time I order Q, what I will have is Q divided by 2, which I call it cycling inventory. And then I should multiply by H which is cost of carrying one unit of inventory for one year. Therefore, my carrying cost would be equal to Q divided by 2 multiplied by H. So now I'll talk about carrying cost. If I order 400 units on average, I have 400 divided by 2. If I order 500, on average, I have 500 divided by 2. And then click click, I come down. If each time I order 4000 units, on average I have 2000 units in inventory. And carrying cost is cost of carrying one unit for one year, which is 60 cents. Lock it. Multiplied by number of units of inventory per cycle. And then click click. Now I come here, I copy this, copy. I come here. And I paste it. So now, I have two costs... I have two costs. This orange is carrying cost, if I order large amounts, this carrying cost goes up. And this blue is ordering cost. They work at the opposite of each other. Then, I can add these two costs together. Equal to ordering cost plus carrying cost, enter. Click click. Copy. And paste. And this is total cost. Total cost comes down, reach a minimum, and goes up. The minimum appears when these two costs equal it. When ordering cost equals carrying cost. That is the optimal location. And in this problem, I believe that this is around 1600. If I'm going to find it like that... Control 1 in cell 500. I say go by step of 400 and then here, is the maximum of 4000 and 500. I just say 4000. And then click on this. And then I close this. And the instruction of these two is at 1600. Demand, which we also show it by R, by R and D, interchangeably, Demand is 32,000. Carrying cost 60 cent per unit per year. Ordering cost 24 dollars per order. If ordering quantity is Q, therefore number of orders is D divided by Q, which in this case is 32,000 divided by Q. And then multiplied by ordering cost, which is 24. Therefore my total ordering cost, that is ordering cost per order, this many orders, total ordering cost is like this, 24, times 32,000, divided by Q. If I'm going to draw it, it would be like this. As ordered quantity goes up, total ordering cost comes down. Then, if I order Q units, at the beginning it is Q, then it goes to 0. Therefore, the average is Q divided by 2. Q, 0, Q, 0, Q, 0, Q, 0. Therefore, average is Q divided by 2, Q divided by 2, Q divided by 2, and Q divided by 2. On the average, the inventory is Q divided by 2. Carrying cost is H. H times Q divided by 2 is total carrying cost. It will look like this one. This is carrying cost, if ordered quantity goes up, carrying cost goes up. This is ordering cost. If ordered quantity goes up, ordering cost comes down. And this is the total. And the total happens when those two costs are equal. And by this knowledge, that at optimal ordered quantity, carrying cost and ordering cost are equal to each other, we can find that optimal ordered quantity. At EOQ, ordering cost is equal to carrying cost. This is, this is ordering cost. This is carrying. Ordering cost per order multiplied by the number of orders, average inventory multiplied by carrying cost. These two are equal to each other. That is, 24, this is 32,000, that one we don't know. This is .6, this is Q divided by 2. One equation, one unknown, we can solve it. Q2 is equal to this number. If you compute square root of it, it is 1600. In general, this is ordering cost. Demand or throughput divided by Q. Q is what we ordered. Number of orders, multiply cost of each order. This is ordering cost. What we ordered divided by 2 is average inventory. Multiply by carrying cost of one unit per year. These two are equal. And that means Q2 is equal to 2 times D times S divided by H. And therefore, Q is this square root. And if you put those numbers over there, 2 times 32,000 times 24 divided by .6, you get the same thing. I found it here. We can use this knowledge to compute EOQ or we can just memorize EOQ. I expect you to know this. I expect you to know that demand or throughput divided by Q, that is number of orders. And then you multiply by cost of each order, that is your total ordering cost. And then carrying cost is average inventory, which is Q, divided by 2, multiplied by cost of carrying one unit of inventory for one year. And this is carrying cost. And these two are equal at EOQ. So if you know those ratios, you really don't need to memorize EOQ. Nevertheless, in exam, I will give you EOQ. How many times should we order? We have already answered this question. That is equal to D or R, we said we show it by D or R, or demand and throughput, divided by Q. Demand was 32,000. Q was 1600. Each time, we order 1600. If you divide these two numbers by each other, we get 20. 
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That is the number of orders that we place. R or D equal to 32,000, EOQ 1600, divide the value of Q 20 times. What is the length of ordering cycle? We order 20 times. And a year in this example is 240 days. 240 divided by 20 is 12. That is the length of an ordering cycle. From the time that we place an order until the time that inventory on hand goes to 0 and we get the next order. 1600, it will go to 0. And then the next 1600 will arrive. And then it will go to 0. And then the next 1600 will arrive. From here to here is 12 days. Because we ordered 20 times. And a year is 240. That is one way of computing it. There is also a different way for 240 days, we need 32000. How many days... we will last to consume 1600. That is 1600 multiplied by 240 divided by 32000. Again, if you divide this one by this one, here you get 20. So this will cross out, that will cross out, it is 240 divided by 20, which is again, 12. 20 times 240 divided by 12, alternately 32,000 is required for 240 days, therefore each day you consume 32000 divided by 240. And if I have 1600, if I divide this 1600 by this, I will get 12 days. Compute the total ordering cost and total cost. Ordering cost is equal to demand or throughput, both of them are the same, divided by Q or EOQ, in this situation. This is the number of orders multiplied by S. S is ordering cost per order. D was 32,000 divided by 1600. We already know this is 20 multiplied by 240. The total ordering cost is equal to 480. To compute total cost, I know that at EOQ, ordering cost and carrying cost are equal to each other. Therefore, if this one is 480, the other one is also 480. 480 plus this 480 is equal to 960, as simple as that. Alternatively, D divided by Q or EOQ times S. That is carrying cost is H times Q divided by 2. And that is multiplied by Q, which was 1600, divided by 2. This is equal to 480 and this one is equal to 480, so the total cost is 960. Compute the average inventory. Average inventory, 1600 divided by 2, 800. Compute the total carrying cost, we have already done it, Q divided by 2, which is 800, multiplied by cost of carrying one unit of inventory per year, .6 times 1600 divided by 2 is 480. Compute the total cost. Summation of those two. Or you can take one of them and multiply by 2. Compute the flow time. This is very interesting. This tries to tell you that I don't teach in isolated islands. If I teach process flow, and then I teach inventory, you will find a way to connect these things together. Flow time, flow time. What is flow time? We remember that throughput times flow times is equal to inventory. We know that we are looking for this. But is throughput? Throughput is 32,000 per year. Flow time is T. What is average inventory? It is 1600, which is what we order each time, divided by 2, which is 800. Now if I divide 800 by 32,000, it would be 1 over 40. 1 over 40 what? Flow time is 1 over 40 what? 1 over 40 year. Why year? Because this is in terms of years. So that is 1 over 40 year. If I multiply by the number of these per year, which is 240, 240 multiplied by 1/40 is equal to 6. Flow time is 6. That is one way of computing it. Let me show you a second way. Throughput times flow time is equal to inventory. Inventory we know is 1600. Flow time we don't know, but throughput, it is 32,000 per year. A year is 240 days. 32,000 divided by 240. That is throughput per day. If you multiply it by T, that is equal to 1600. If you do the computation T is equal 1600 multiplied by 240 divided by 32,000. That one also gives you 6 days. Do I know any easier way? Yes. This is what I get and this is when it's consumed. 0, 1600. We have already computed that we ordered 20 times. And a year is 240. Therefore, from here to here is 12 days. Now look at this. I can assume it is logical to assume that the first unit which arrives is consumed immediately. The last unit that I consumed is after 12 days. Therefore immediately consumed after 12 days, 0 plus 12 divided by 2 is equal to 6. So I showed you several ways to find it out, what is the flow time? Demand 32,000, throughput, 32,000 per year. EOQ 1600. Average inventory, because the ending inventory is 0, is 1600 divided by 2. Q divided by 2 or EOQ divided by 2, we also call it cycle inventory. When we have no safety stock, average inventory, and cycle inventory are equal. In this problem, we don't have safety stock, but later, I will discuss safety stock. So average inventory is 800. Demand is 32,000 per year. The flow time is 1 over 40 years. And then I multiply by 240, that is 6 days. Or from the beginning, I could have divided 32,000 by 240 to have demand per day. And this is the other alternative, which we said the first item's consumed immediately, the last item after 12 days, so on average, item will be 0. 12, 0 plus 12 divided by 2, 6. Compute the inventory turns. Inventory turn is defined as demand divided by average inventory. 32,000, average inventory is 1600 divided by 2, therefore inventory turn is 40 times. That means its unit which goes into inventory, it will rotate 40 times throughout the year. This is an accounting term. So each unit goes there, and is replaced 40 times. 240 divided by 40 is 6. That is what we computed it as average flow time. A year is 240 days, and items are replaced 40 times. Therefore, each item on average is there for 6 days. And that is what we called flow time. Let me show you something interesting. Inventory turn, we defined it as demand divided by average inventory. And then we also know that throughput times flow time is equal to inventory. And therefore, we know that flow time is equal to inventory divided by throughput. Now look at these two equations.
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I divided by R or D and D or R divided by I. So this is I divided by R or D, I divided by D. And this is D divided by I. So they are the reciprocal of each other. Therefore, inventory turns is equal to 1 over flow time. Inventory turn is D divided by I, flow time is I divided by D. This is also a neat insight. That ends my discussion of the first problem.