Speaker 1:	Here, I would like to wrap up some final topics on Economic Audit points. Why we don't want to have extra inventory? Why we like to have just enough inventory in all three main classes of safety inventory, cycle inventory, and pipeline? We like to have just enough inventory because inventory has carrying costs or holding cost. It has physical carrying costs. We need storage, and we need human resources to take care of the inventory. It also has financial costs. It can be in the form of the rate at which we can borrow money or the rate at which we can invest our money, which is the opportunity cost of our funds. We need to have just enough inventory because inventory hides costs. Inventory has devaluation cost components typically drop in price during their inventory life cycle. We have price protection costs, and we need to reimburse customers for drop in the prices. Inventory has return cost. If we send a lot of product to retailers, then if they are not selling them, they will return them, and we need to pay the retailer back. Also, inventory has obsolescence costs. Some new chips come into the market, and if we have a lot of inventory we may need to sell our product or we may need to wait until we produce all our product using what we have and by that time, a large piece of market may have gone. Inventory has hidden costs and inventory hides problems. Even if we produce low quality product, we don't see its impact downstream because there are a lot of inventory. Defective products are easily ignored. If we have a lot of inventory on trustworthy suppliers, machine breakdowns, long changeover times, scraps and defects do not surface. If we have a lot of inventory, we have long flow time, feedback loop is long and we don't have uniform operations. All companies are trying to have just enough inventory, not more than that. In this lecture, I am touching a couple of different topics. What is total cost of Q? Total cost of Q is my ordering cost, demand divided by what I order, times cost of each order, plus carrying cost, which is average inventory, multiplied by cost of carrying one unit of inventory for one year. This is also total cost of EOQ, but we can simplify it. We can replace this Q by EOQ, which is 2DS/H. This part, I have just put it over there, and instead of Q, I have put EOQ formula. Here, H, I also have it over there. Instead of Q, I have put EOQ formula divided by two. Then I have simplified this equation. I have shown that the cost of EOQ is everything including two under square. If I am ordering Q, I can say total cost of Q and total cost of EOQ is demand divided by what I order multiplied by S plus average inventory multiply by H. This is the general total cost formula for Q and also for EOQ. But if I'm specifically talking about EOQ, I can also write TC of EOQ is equal to everything under square. You can do this proof yourself. You can go from here to here for EOQ. In this example, I like to show what will happen if we don't order EOQ. If you go a little bit to the left or to the right. EOQ curve is not like this, it's like this. If I go somehow to the left or somehow to the right of EOQ, my total cost will not increase with the same proportion. We have the data for a product. We have monthly demand and the month is 30 days. Therefore, daily demand is 20, and yearly demand is 12 times this number. This is the holding cost, this cost of the product. This is carrying cost per unit per year. Let me tell you something. In EOQ formula, I don't need to put yearly demand. I can put monthly demand. EOQ is equal to square root 2D, instead of 7,200, I can put 600 times S, which is 100. Divided by H. If H is nine, that is for one unit one year. If I want to change my numbers from year to month, then that H should be stated in terms of month, which is $9/12. I can write EOQ= 2*7,200*100/9. Or I can write it this way. This is also correct because simply, we know that this 12 will go over there and will be multiplied by 600 and will become 7,200. On the same logic, I can also write EOQ= 2(20)(100). The only thing I should do here, I cannot put H per unit per year. I cannot put H per unit per month. I should put H per unit per day, and that is nine divided by in this case, because we have assumed 12 months and each month 30 days, so I should divide 9/360. All of them lead to the same EOQ. EOQ is enough for 20 days. Cycle lens is 20 days. My flow time is 10. Without any computation because the first item which we leave immediately, the last item that leaves will be there for 20 days, therefore, average of these two is 10. Of course, I can also write R*T=I. I is half of this because that is the maximum inventory. Cycle inventory is 400/2, equal to, to put per day is 20, and I'm looking for T, 40T = 400 and T=10. But this was much easier way to do that computation. In total cost, I can compute it in both ways that I showed you. One is this way and the other one is this way, and both of them lead to 3,600. But suppose this product is packed in boxes of 500, not 400. Or suppose transportation cost is lower if we transport in 500 units instead of 400. Increase Q by 25%. Let's see, what would be the impact on the total cost? If I put 500 into the formula, which is not EOQ and therefore I cannot use this formula and I need to use this one. My carrying cost goes up a little bit, my holding cost comes down, but the total goes up. I move from 3600 to 3690. If I divide 3690 by 3,600, I get 2.5% Q went up by 25%, but total cost in this specific example went up only by 2.5%. The curve is flat. It's not like this. You want to show impact of one of the parameters on EOQ. Impact of change in demand. Suppose demand gets quadrupled. What is the change in the optimal order quantity, cycle of stock, and number of orders per year. I have this data. The only difference is now demand is four times what it was before. Our previous EOQ was 400. EOQ1 was 400, EOQ2 is 800. Demand became 4D, but Q just became 2Q because D is under the square root. That four when comes out of square root becomes two. If demand is multiplied by K, EOQ is multiplied by square root of things. How to reduce inventory? EOQ=2RS/H, and as I have explained several times, we use D and R interchangeably. D is demand or is throughput. But we assume demand and throughput are equal. In this formula, when I put D or when I put R, I mean the same thing. We want to reduce EOQ, should I go and reduce R? No sane person does it because what does it mean? We need to beg our customers not to buy our products. One other way of decreasing EOQ is to throw away two and write EOQ=RS/H. But we cannot do that because then it will not be EOQ. Another thing we can do is to increase increase H. We increase H, EOQ goes down. But what does it mean increase H? Increase H means we need to say, people, please come and steal our product. Please come and go on our product and destroy them. Then under those situations, H goes up, and no sane person want to do that. If you want to reduce EOQ by changing one of these parameters, the only thing is S. We need to move and reduce S. Besides reducing S, one other thing we can do is to centralize either spatial or timber. If we can bring demand of all day to two hours, That is what catering company does in India. They bring the demand to a short time period, and they can benefit from a lot of availability in those periods. The other one is spatial centralization. We have four warehouses, we may create a central warehouse. Then standard deviation of this one and standard deviation of this one and standard deviation of these two together, they will not be added. Their variances will be added together, and then that summation will go under square. Let me give you a simple example for a practice on temporal and spatial centralization. Suppose demand per day is 10 units, and standard deviation of demand per day is three. Suppose we have four warehouses, and suppose lead time is nine days, suppose service level is 97.72%, and that is a good service level because then Z will become equal to two. Compute safety stock, demand is 10, we are talking about nine days, so average demand is 9*10=90. But standard deviation of demand is square root of lead time multiplied by standard deviation of daily demand, which is nine. Now for nine days, this is average and this is STD for nine days. But we need to combine it for four warehouses. Average, when we go to four warehouses is equal to 4*90, which is 360. Here, STD would be square root of 4*9, which is 18. Therefore, demand during this period has an average of 360 and standard deviation of 80. Now, if I want to have service level of 97.72, I should multiply 2*18, which makes it 36. I safety is equal to 36. An average demand during this period is 360. Whenever inventory level reaches 396, we place an order. We place an order for what? Suppose our S is the same as the previous 1=100 and H=$9 and S=$100, and demand or throughput per day is equal to 10. Per year, that would be 10*360=3,600. Then we have four warehouses for R=4*3600. Is equal to two times D, which is four times 3,600 times S, which is 100 divided by H, equal to four becomes two, 36 becomes six, nine becomes three, 100 and 100 become 100 square root of two. That is 400 and square root of two. I think square root of two is 1.41. I think multiply by 400, and that would be 465. We also can decrease inventory by commonality. For example, if a piece is used in hip surgery and a piece is used in knee surgery, if we use the same piece, then safety inventory goes lower and also average inventory cycle inventory goes down. Modularization and standardization or other approaches to reduce inventory. Obviously, postponement and delayed differentiation, which we have discussed it earlier are ways to reduce inventory. Just in time, they have tried to reduce setup times. They try to use equipment with low setup times. They try to stay close to the suppliers and develop long term relationship, level loading, low inventories with tight control, small batches and mixed model production. What is mixed model production? We have three products, A, B, and C, 10 minutes per product. Working five days a week, 10 hours a day. Demand downstream, three units of A, two units of B, and one unit of C per hour. But the upstream station, which fits the market, produces (150)A, (100)B, and (50)C. Perhaps because setup time is high. But philosophy of inventory control is to reduce set up time and make small batches. What is mixed model production? We try to produce at the rate customers want. Customer one 3:A, 2:B and 1:C per hour. Why we should produce (150)A? Maybe something happens. Maybe they don't want (150)A. We produce (150)A cycle inventory would be 75 for A. (100)B, 50 cycle inventory, (50)C, 25 cycle inventory. Therefore, we have a cycle inventory of 150. But maybe we do this. We produce 3:A, 2:B, and 1:C. In each hour, we produce six units, The cycle inventory could be half of it, which is three. A better option is even if we produce like this, do not produce (3)A, produce (1)A, and then (1)B, and then another A, and then (1)A, (1)B. Now we have (3)A to B, and then a C here. This one, which is this one is even better than this one. This one definitely is much better than that. This is another example of mixed model production. Suppose we need 1,000 A, 800 B, and 400 C. One approach, if setup time is high, is to produce all A's and then set up the machine for B, produce all Bs, and then set up the machine for C. A better approach maybe this; produce 500 A, then 200 B and 100 C. Again, 200 B, 100 C, and then 500 A, and then repeat it. In this situation, average inventory is much lower. It's like a heuristic. We try to go from situation like this to situation like this and from situation like this to situations like this. To do what? To reduce average inventory. In Toyota, they reduce setup time from several hours to several minutes. One important thing they did, they separated internal and external activities. Internal activities in set up time, are those for which it is essential to have the machine stopped. Examples are adjusting machine speed, placing work on the machine. They try to turn sequential internal activities into parallel internal activities. Two activities if each of them takes 5 minutes and if they are sequential, take together 10 minutes, but if they are parallel, together, still take 5 minutes. They also tried to convert internal activities to external activities. External activities, those for which it is not essential for the machine to be down. Validating work order, searching for tools, looking for material, external activities are done before the actual setup. Actual setup will only cover internal activities which definitely need to have the machine stop. Toyota, they standardized all set up activities. When everything is standardized, over time, they can improve their path to design routines which are perfect with this philosophy, not to take setup time as a parameter that we should obey, but as a variable, which we can change it. They try to eliminate adjustment. They try to have machines that they do not need that much adjustment time and smooth and simplified procedures the company applied Toyota techniques to toothpaste production, and over six months, changeover time dropped from 49 minutes to 15 minutes, and it was translated in 7 million more tubes of Sensodyne and Aquafresh toothpaste. By a simple example, we have the demand, we have all the data that we need. We want our cycle inventory to be 200, that is Q/2, or that is EOQ/2. We want a EOQ to be equal to 400. EOQ formula, and we want it to be equal to 400. That is the formula. We put everything over there. The only thing that we need to play with is S. If we solve this equation, we realize that in this system, if we do have these parameters, we need to reduce our set up time to $160. Information technology can help to reduce setup time and quantity discount will reduce purchaser costs but increases inventory. These were a couple of items that I thought. It is not bad if we touch them too, and thank you very much for attending this session.