>> I now go through the second problem on economic order quantity. We sell a product. Sales price is $300 per unit. The demand is 30 units of product per week. Each time that we order, we order an amount which is enough for 10 weeks of demand or 10 weeks of supply because we assume that throughput is equal to demand, and that means supply is equal to demand. 
And therefore, each time we order 10 weeks multiplied by 30, which is demand per week, each time, we order 300 units. That is Q. We assume 50 weeks per year. Ordering cost S is equal to 225. Purchase price for each unit of product is 150, and carrying cost is 20% of 150 per unit of product per year. Therefore, it is 0.2 multiplied by 150. That is $30 per unit per year, and that is H.
If I divide this one 12, just for example, if I divide it by 12, H would be 2.5 dollars per months. What am I trying to say is, in EOQ formula, if you put demand per year, then you put H per year. You can put demand per month and then put H per month. Both of them ends to the same EOQ. So this is the problem. Flow unit is one dress. Demand or throughput is equal to 30 units per week, 50 weeks per year.
Each time, we order the demand for 10 weeks, which is 300 units. Q is 30 times 10, 300, and demand per year, 30 times 50 is equal to 1,500. Fixed costs of each order is 225. Unit cost is 150. Carrying cost is 20% of 150, which is 30. Compute the total ordering cost and carrying cost under the current policy. Quite simple. Demand is 1,500. Each time, we order 300 units. Therefore, we ordered five times. Cost of each order is $225. 
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Therefore, total ordering costs, ordering cost is equal to $1,125. Now we need to compute carrying cost. Average in winter is 300 divided by 2. Carrying cost per unit of product is 30. Inventory, H per unit of product per year, and that would lead to carrying cost of 4,500. Ordering cost is about $1,000. Carrying costs is about $4,000. 
Now my question for you, my friends, is, is 300 greater than EOQ or less than EOQ? What is the relationship between 300 and EOQ if total ordering cost is about $1,000 and total carrying cost is about 4,000? Is EOQ greater than 300 or less than? We said we have two costs. This is quantity. This is cost. As we know, ordering cost is like this. As quantity goes up, cost comes down. This is ordering cost.
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On the other side, carrying cost is like this. As quantity goes up, carrying cost goes up. Now, in this problem, when we order 300, where are we? Are we here, or we are over there? If you are here, then EOQ is less than 300. If you are here, then EOQ is greater than 300. Let's see where are we. When we did our computations, ordering costs came out about 1,000. About.
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Carrying costs came out about 4,000. Therefore, where am I? Am I here or here? 
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Of course, I am here because carrying cost is greater than ordering cost. Here, ordering cost is greater than carrying cost. 
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Four thousand, 1000. I am here. I am on the right-hand side. I am not on the left-hand side. In this side, ordering cost is greater than carrying cost.
On this side, carrying cost is greater than ordering cost. Therefore, I am on the right side of EOQ. If this is 300 quantity, EOQ is over there. EOQ is less than 300. As simple as that, without any computation. 
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When carrying cost is greater than ordering cost [inaudible] to the right of EOQ because EOQ is here. If this one is greater than this one, I have all the past EOQ, and that is the situation right now.
But if this one, which is ordering cost, is greater than carrying cost, then I am before EOQ. In this case, ordering cost, 1,000. Carrying cost was 4,000. Therefore, I have past EOQ. EOQ is less than 300 without any computation. 
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And total cost, when I add those numbers together, is 5,600. Compute the flow time. 
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Each time, I order 300, it goes to 300, comes down 300, comes down 300, comes down --
Therefore, on average, I have 300 divided by 2. That is my average inventory. Throughput, we said this is 30 units per week. Therefore, throughput and flow time is equal to inventory, 30 times flow time is 150, and T is equal to 5. Five weeks. Why it is five weeks? Because this 30 is in terms of weeks. But we really did not need this computation because the problem by itself says each time we order 10 weeks of supply.
When the order arrives, the first item will go out immediate, and this cycle is 10 weeks because I ordered the amount for 10 weeks. Therefore, the last item will go out after 10 weeks. Zero weeks plus 10 weeks divided by 2. Therefore, flow time is five weeks, and that is how I get it also using the Little's law. What is the average inventory and inventory turn?
You should be able to answer this question in a minute or two. Average inventory. We order for 10 weeks. We order 300. We have 300, goes to 0, so the answer is 150. Inventory turn is equal to demand divided by average inventory -- demand is 1500. Average inventory is 150. If we divide them by each other, we get 10.
But at the same time, we know that inventory turn is R divided by I, and we know that flow time is I divided by R. Therefore, inventory turn is 1 over T. We already know what is T: 5. Therefore, 1 over 5 should be inventory turn. What? Inventory turn should be 1 over 5? Should be 1 over 5? Or it should be 10? Which one? 
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Where did we make a mistake?
Is inventory turn 10, as we compute it based on D or R divided by average inventory? Is this correct? Or inventory turn equal 1/T is correct? Which one of these two is correct? Because one of them gives me 10, the other one, 1 over 5. It is 1 over 5 per week because flow time was five weeks, so this is 1 over 5 per week. One over 5 times per week, it is rotate.
If I multiply it by 50, then I will get 10, which is the same as what I had already. So both procedures reach the same number. 
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What is the optimal EOQ? Put it into the formula. Two DS divided by H; 2, 1500, 225 divided by 30, and as I expected, as I proved it before, EOQ is less than 300. Indeed, it is half of it. The policy that we were following of ordering 300 was twice of the optimal policy, as long as it goes to quantity, and then I will compute the cost.
Total annual cost under this optimal policy is number of orders multiplied by ordering cost. Ordering cost per unit. This is number of orders. If I multiply these two by each other, then that is total ordering cost. This is average inventory. If I multiply it by cost of carrying one unit of inventory per year, that would be total carrying cost. Total ordering cost, total carrying cost.
At EOQ, these two are equal to each other, and that is 4,500. Our previous total cost under 300 was 5,625, 4,500. And therefore, by ordering EOQ, I was able to reduce my total cost by $1,125, 
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which is almost 20%. 
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Thank you for being with me and solving this problem.