>> This is the third example that I solve regarding economic order quantity. Here I would like to discuss the characteristics of that square root. Remember EOQ has a square root. I want to explain what happens due to that square root. I have four warehouses; one, two, three, and four. Suppose demand in all of these warehouses are the same and suppose each warehouse has its own ordering costs and that is the same for all warehouses. And suppose carrying costs is H. Now, each one of these warehouses works independently, then I will have EOQ equal to 2 times the-- times S divided by H. For each one, EOQ, EOQ, EOQ, and EOQ. Each one will have its own EOQ. Each one will have its own total carrying cost, total ordering costs, and so on and so forth. Now suppose we can combine these four warehouses, virtually combine them or physically combine them. What will happen? Now we don't have four warehouses anymore, we only have one warehouse, either physically or virtually. Therefore, the demand of this new warehouse is four D, four times of the demand of each warehouse. H remains the same. Each unit you carry for one year has the same cost if you order centrally or decentralized. But S, when we centralize these four warehouses, S will go up, but it will not become four times of what it was before. And therefore, centralization has some benefits that I explain it in a minute.
^M00:02:34
So, we have four warehouses and we want to combine them and see which one is at our benefit when they work independently or when we combine. Demand for each warehouse is 800 per day and there are 250 days per year. Each unit of product costs 200 and carrying costs, or holding cost is 20% of that 200. 200 multiplied by.2, that is 40 per unit per year; that is holding cost. Ordering cost, when each warehouse orders independently is $99, but when we combine them together and order centrally, it's more than $900, but is not four times $900. So, we have all the data for the problem and there are 250 days per year. Decentralized, four warehouses independently working four different places, centralized, in one place. Carrying costs is the same when we centralize them, combine them, and the same as when they are working decentralized. Carrying cost is 20% of $200 which is $40 per unit per year, both in centralized and decentralized system. Ordering cost when it is centralized is $2025 for each order. But if it is not centralized, it is $900, and that make sense because usually when I order centrally, I should go here, then go over there, then go over here, then come here, and then go back. Perhaps cost is higher than if I do this; I go here and come back, I go here and come back, I go here and come back, I go here and come back. I'll go here, then here, then here, then here, then here. This is one logic for it that when we centralize why ordering cost goes up. Four outlets, demand of each outlet, 800 per day, 250 days, therefore 200,000 per year. Ordering cost 900 if it is not centralized, cost of product, no matter it is centralized or decentralized 200 per unit, carrying costs 20% of cost of the product, 40 per unit per year, and if we combine them ordering costs would be 2000 something. Now the question is what will happen to average inventory in these two systems if you compare them? What will happen to flow time? What will happen to total cost? And answering these questions are not difficult. If you have grasped the concept you can go ahead and solve the problem and then come back and watch my lecture, or just go through the PowerPoints. Decentralized system, demand is 200,000 per year, ordering costs 900, carrying cost 40, and we put these things into the formula, 2DS divided by H; 2 times 200,000 times 900 divided by 40, 3000. Therefore, EOQ for each warehouse is 3000. But we do not have just one warehouse, we have four warehouses and then average inventory is half of 3000, which is 1500. Therefore, four warehouses together we'll have an average inventory of 6000. Average inventory of each warehouse is 3000, divided by 2, that is average. And then we have four of them, therefore it is 6000 average inventory in this system.
^M00:06:52
And we said, when we don't have safety stock, average inventory and cycle inventory are the same. Cycle inventory, at the beginning we have this much. At the end we have zero. Average of these two, which is Q divided by 2, as cycle inventory. Cycle inventory and average inventory when we do not have any safety stock is equal to Q divided by 2. And we don't have any cushioning here. I will discuss safety stock later. Now let's suppose these four warehouses order together. In that case, demand is not 200,000, it is 800,000. H is still 40, but S is 2025. We put it into the equation and we get the answer, which is 9000. If you order together, each time you order 9000, and average inventory or cycle inventory is half of it, which is 4500. Average inventory 4500, average inventory 6000. This one is better because it has lower inventory. Compute the total annual holding cost and ordering cost. In basic EOQ model we do not talk about purchasing cost because purchasing cost does not depend on our strategy. Later, we may discuss the situation of discounting models when the vendor tells you if each time you order more than a specific quantity, they will give you a discount. but it is not the case in this basic inventory model that I have solved, and this is the third problem of that kind. Total cost is this. We have the formula and we just put the numbers over there. Ordering cost, demand, EOQ for each warehouse, H, EOQ divided by 2, which is average inventory. And that is 60,000 plus 60,000, which is 120,000. Therefore, this is cost of each warehouse and we have four warehouses, and the cost of all of them is four times cost of each one, because they all follow the same cost structure, all here for the simplicity we have assumed. So, in centralized system, this is my S. D is four times of D of each warehouse. 9000 is EOQ that we computed earlier. H is the same for centralized and decentralized and this is average inventory. Here the total cost is 360 compared to 480; 25% reduction. If you order centrally, our total cost is reduced by 25% and also our average inventory is reduced from 6000 to 4500. That is also 25% reduction in average inventory.
^M00:10:32
Compute the ordering interval. How often do we order? That is quite simple. In decentralized, demand or throughput is 800 per day. When we centralize them, demand is four times what it was and this 3200 per day. In decentralized, EOQ is 3000. This is EOQ and each day we consume 800, therefore lens of a cycle is 3.75 days from the time that we receive an order until the time that we consume it is 3.75 days. For centralized, EOQ is equal to 9000 and demand for all four warehouses is 3200, therefore cycle from the time that we get an inventory our order until the time we place the next order it is 2.821 days. The second strategy has a shorter cycle. Average flow time in decentralized, throughput is equal to 800, EOQ is equal to 3000, therefore average inventory is EOQ divided by 2, which is equal to 1500.
^M00:12:06
So, I have average inventory of 1500 equal to throughput times flow time. Throughput 800, flow time I am looking for 1500. And therefore, T is equal to 1500 divided by 800. What days, because 800 is in terms of days; 1.875. For centralized, throughput is 3200, average inventory is 4500, and therefore flow time is equal to 1.41. However, I really did not need these two computations because in this system, the first unit which comes goes out immediately; the last one goes out after 3.75 days. Therefore, on average, flow time is 3.75 divided by 2, which is the same as this number. For here it is 2.821 divided by 2 and that is this number. You can do it that way too. And these are those computations.