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Lean Manufacturing pp. 242-6 RDQ: 1, 2, 3, 8 Value Chain Mapping 1. Is it possible to have zero inventories? Why or why not? No, you can't literally have zero inventories. You have to have some stuff around. Theoretically, you could have one piece of inventory at each station, and everyone could pass their parts at the same time, and have no inventory that was not being worked on at that exact minute. But that could never happen. More realistically, we want to have no excess inventory. No more inventory than the minimum we can work with. And that is the real difference, making a conscious decision about the amount of inventory to have, not just letting inventory appear; deciding how much you should have and controlling it. 2. In my house, I've done a lot of informal "value stream mapping" over the years, so there's not a lot of waste. I recently put in compact fluorescent light bulbs in the lights that get used the most, to minimize wasted electricity. The other waste that I want to work on is wasted water from the sprinklers. Given the lack of rainfall we've had, I don't want to be wasting any water. So I'm going to be replacing some sprinkler heads and re-orienting others to minimize overspray. I'm also having some work done to better ventilate my attic, so I don't have to spend as much on air conditioning this summer. 3. Why must lean have a stable schedule? Because lean does not have a lot of ability to deal with dramatic changes in production. Everyone up and down the production line is getting small, regular shipments from its supplier. There is no surge capacity to suddenly dramatically crank up production. The line is running at pretty close to capacity all of the time. 8. What are the roles of suppliers and customers in a lean system? Suppliers have a more active role in a lean system. Instead of being told what the customer wants, and being nickled and-dimed to death in haggling over the price, the customer is more likely to tell what kind of performance characteristics they want, and have the supplier, who is the expert in the process, help design the product and the process, to get an end product that can be produced cheaply and with good quality. I'm not sure that the role of the customer is a lot different, for end products. But for someone in the middle of a supply chain, they are going to work much more closely with their suppliers, to get exactly what they want. CASE: VALUE CHAIN MAPPING (p. 245). 1. Elminating the queue of work dramatically quickens the time it takes a part to flow through the system. What are the disadvantages of removing those queues? There used to be a lot of safety capacity in those piles of inventory. If a machine ever went down, if it took a long time to fix, or if a setup took a long time, the downstream processes would not run out of material, unless the process was down for a day or so. Now, that is not true. One machine going down could shut off all production fairly quickly. There are other disadvanges, but that may be the largest. 2. How do you think the machine operators would react to the change? I'm sure they won't like it. People are used to looking at a big pile of inventory, and the protection that that brings, as good thing. There is a feeling of safety in it. Without those piles, there won't be that feeling of safety. Combining machines 1 & 2 may also cause some workier unhappiness, because of the changes in the processes that may be involved, and the new learning that will require. 3. What would you do to ensure that the operators were kept busy? Having everyone producing all of the time doesn't make sense. A pull system reinforces that. When you don't have anything to do, production-wise, you have a great opportunity to clean your area and do some preventive maintenance on your equipment. Doing that reduces the odds that your machine is going to break down on you. So the slack time makes the system more robust, and less vulnerable to breakdowns than it would have otherwise been. , you could have one ve no inventory that e want to have no difference, making a ding how much you a lot of waste. I asted electricity. The we've had, I don't want ers to minimize as much on air ne up and down the o suddenly nts, and being nickled- e product and the the middle of a supply ugh the system. n, if it took a long time ess the process was on fairly quickly. n that that brings, as a in the processes that When you don't have reventive maintenance ou. So the slack time 10 pp. 276-279 RDQ: 2, 4, 5, 6, 8 Pr: 2, 3, 4, 5, 9, 10 2. Examine Exhibit 10.3 and suggest what model you might use for (a) bathing suit demand, I wish this chapter talked about seasonality, because swimsuit sales should be quite seasonal, generally. But I would mostly expect swimsuit sales to be about the same as the last year. So a moving average, or a weighted moving average, or exponential smoothing should all work about the same. But I would use as my inputs the total amount of men's swimsuits, and women's swimsuits, last year and make a separate forecast for each. (b) demand for new houses I would use trend-adjusted moving average. If you want to get fancier, and you always wanted to be an economist, you could study the relationship between new house sales and mortgage interest rates, probably using linear regression. Then as rates go up and down, you could put the new interest rates into your model, to estimate new house sales. (c) electrical power usage A moving average might not be too bad, but I would expect better luck if you use linear regression to study the relationship between daily high temperature and electrical usage. Then, I would look at the weather forecast for the next day and the next week, and put that into my linear regression, to see how much power I am likely to need. (d) new plant expansion plans. I would want to know what sales are expected to be like into the future, the next few years. To do that, a linear regression might be good, or exponential smoothing with a trend. 4. What strategies are used by supermarkets, airlines, hospitals, banks, and cereal manufacturers to influence demand? Well, if this were a marketing class, we could talk all day about this problem. But it's not, so I'll be brief. Supermarkets get you into the store with weekly fliers promising big savings. Once inside, they have free samples, coupons, and big displays to get you to buy more. Airlines get you to keep coming back with frequent flier programs, and periodic sales, which they like to email you about. They raise and lower prices (called yield management) if a plane is a more or less full than they expect, a given amount of time before the date of the flight. Hospvitals try to get you to think they have better technology, or a more caring staff, so you'll choose a health plan that uses their services, and come to them whenever you have a choice. Health fairs, etc., also try to win you over. Banks advertise lower fees on their checking accounts, or higher interest rates on checking, or lower rates on mortgages, Cereal Manufacturers try to convince parents that the food is healthy (if it's not) so they'll buy it for their kids, or that tastes good (if it's healthy), so they think their kids'll like it. 5. How would you get any of the exponential smoothing-based methods started? In class, I suggested that for the first period, you just pretend that you made a perfect forecast. 6. From the choice of moving average, weighted moving average, exponential smoothing, and linear regression, which forecasting method would you consider the most accurate, and why? Of the methods the book considers, I consider the FIT method to be the most accurate. Honestly, I think adding seasonality is the last piece of the puzzle that is very good to add. 8. Discuss the basic differences between the mean absolute deviation and the standard deviation. The mean absolute deviation (MAD) is a linear measure of the amount of error. It tells us, on average, how far off our forecasts were. The Standard Deviation tells us a similar thing, but in a slightly different way, because it squares the errors and then takes a square root. They both tell how far off we are, on average, but the standard deviation will get larger if a method is sometimes off by very large amounts, because of squaring the error term. Problems WMA 3MA ES 2 0.6 Each of these forecasts is really pretty s 0.3 0.2 0.1 Jan 1 12 Feb 2 11 Mar 3 15 Apr 4 12 13.5 12.67 May 5 16 12.8 12.67 Jun 6 15 14.7 14.33 13 Jul 7 15.0 14.33 13.4 a. WMA 15.0 b. 3MA 14.33 c. ES 13.4 d. LR a= 10.8 b= 0.77 e. LR 16.2 3 0.2 Actual Forecast Error In this problem, they seem to have really made the for Jan 1 100 80 20 before hand, instead of just waiting to see what the ac Feb 2 94 84.0 10 demand is, and then pretending that they had come up Mar 3 106 86.0 20 as a forecast. So I did include the forecast from period Apr 4 80 90.0 10 MAD calculation. May 5 68 88.0 20 Jun 6 94 84.0 10 Jul 7 86.0 15.0 4 linear J-Feb 1 109 123.2 slope = 1.136 200 Mar-Apr 2 104 124.3 intercept = 122.03 May-Jun 3 150 125.4 180 Jul-Aug 4 170 126.6 Sep-Oct 5 120 127.7 160 Nov-Dec 6 100 128.8 140 J-Feb 7 115 130.0 Mar-Apr 8 112 131.1 120 May-Jun 9 159 132.3 100 Jul-Aug 10 182 133.4 Sep-Oct 11 126 134.5 80 Nov-Dec 12 106 135.7 60 J-Feb 13 136.8 60 Mar-Apr 14 137.9 40 May-Jun 15 139.1 Jul-Aug 16 140.2 20 Sep-Oct 17 141.3 Nov-Dec 18 142.5 0 1 3 5 Plotting the data, we see that there seems to be a lot of seasonality to the data. Too bad we didn't get to look at The linear regression does seem to go down the middle of it pretty well, though. 5 TS1 TS2 TS3 1 -2.7 1.54 0.1 5 2 -2.32 -0.64 0.43 4 3 -1.7 2.05 1.08 3 4 -1.1 2.58 1.74 5 -0.87 -0.95 1.94 2 6 -0.05 -1.23 2.24 1 7 0.1 0.75 2.96 0 8 0.4 -1.59 3.02 -1 1 2 3 4 9 1.5 0.47 3.54 10 2.2 2.74 3.75 -2 -3 -4 TS1 is definitely increasing over time. It is not over the limit of 3 or 4, but clearly it is increasing very steadily ov limit any time soon. The method does not seem to be working very well. TS2 seems to vary a lot over time, but there doesn't seem to be any trend to it, so there's no real reason to think working. TS3 has increased to being almost 4. if you're using 4 as a cutoff, it's not there yet, but it's almost there, and cle well, either. 9 Week Forecast Demand Error RSFE Abs Error MAD TS 200 1 140 137 3 3 3 3.000 1.00 2 140 133 7 10 7 5.000 2.00 180 3 140 150 -10 0 10 6.667 0.00 160 4 140 160 -20 -20 20 10.000 -2.00 140 5 140 180 -40 -60 40 16.000 -3.75 6 150 170 -20 -80 20 16.667 -4.80 120 7 150 185 -35 -115 35 19.286 -5.96 100 8 150 205 -55 -170 55 23.750 -7.16 1 For every period, I have computed the Error, RSFE and Absolute Error for each period. Taking the average of compute the MAD that the forecast has generated so far. Dividing the RSFE into the MAD, I get the TS for eac compute the MAD that the forecast has generated so far. Dividing the RSFE into the MAD, I get the TS for eac a. The MAD is pretty straightforward to compute b. The TS isn't too hard, either. c. The TS is really big. The forecast doesn't seem to be doing very well. The problem didn't ask you to graph th forecasts, but I never see trends unless I make graphs. Demand has increased significantly since last year, it a a method that uses a trend. 10 Actual ES F T FIT ES Errors Month Demand 0.3 0.3 0.3 Error 1 31 31 30.00 1 31.0 2 34 31.0 31.00 1.00 32.0 3.00 3 33 31.9 32.60 1.18 33.8 1.10 4 35 32.2 33.55 1.11 34.7 2.77 5 37 33.1 34.76 1.14 35.9 3.94 6 36 34.2 36.23 1.24 37.5 1.76 7 38 34.8 37.03 1.11 38.1 3.23 8 40 35.7 38.10 1.10 39.2 4.26 9 40 37.0 39.43 1.17 40.6 2.98 10 41 37.9 40.42 1.11 41.5 3.09 38.8 41.37 1.07 42.4 MAD = a. Doing the exponential smoothing forecast is pretty straightforward. 44 b. We make an FIT1 = F1 + T1 = 30 + 1 = 31. Notice that, as with all smoothing forecasts, we can't use the smoothing formula 42 for the first period, so they've made up values of F1 and T1 that ended up with the 40 forecast being perfect for the period. 38 So this is our forecast for period 1, which we have made before we have seen the demand in period 1, so there's nothing funny going on. The numbering really isn't 36 bad. Once we see actual demand in period 5, we make F6, T6, and FIT6. Then, once we've seen actual demand in period 1, we compute 34 F2 = FIT1 +0.3(A1-FIT1) = 31+0.3(31-31)=31 We compute a new T2 = T1 + 0.3(F2-FIT1) = 1 + 0.3(31-31) = 1 32 Then, we make a forecast for period 2, FIT2 = F2 + T2 = 31 + 1 = 32 30 When I computed the MAD values, I did not include the "error" for the first period 1 2 in my calculations, because the values of F1 and T1 had been made up to make the first period look perfect. They weren't really future predictions, since they were made after demand was observed. If you graph actual demand, and the ES and FIT forecasts, you see what I've been saying, that ES lags behind the trend, and the farther out we go, the farther it lags behind the actual demand. It's not surprising that the FIT has a much lower MAD. s should be quite t year. So a moving ame. But I would use as my arate forecast for each. ancier, and you always ortgage interest nterest rates into your luck if you use linear n, I would look at the see how much power I am the future, the next few ufacturers to influence ey have free hey like to email you about. y expect, a given amount of choose a health plan that to win you over. r lower rates on mortgages, for their kids, or that it g, and linear stly, I think adding average, how far off our because it squares the ndard deviation will get se forecasts is really pretty straightforward. m to have really made the forecast st waiting to see what the actual ending that they had come up with that clude the forecast from period 1 in my Series1 Series2 5 7 9 11 13 15 17 o bad we didn't get to look at seasonality. TS1 TS2 TS3 5 6 7 8 9 10 s increasing very steadily over time, and it will be over the here's no real reason to think the forec asting method is not but it's almost there, and clearly i sn't working too Forecast Demand 1 2 3 4 5 6 7 8 riod. Taking the average of all of the periods so far, I can he MAD, I get the TS for each period. he MAD, I get the TS for each period. lem didn't ask you to graph the demand and the gnificantly since last year, it appears. We should switch to ES Errors FIT Errors Abs(Err) Error Abs(Err) 3.00 -2.00 2.00 1.10 0.78 0.78 2.77 -0.34 0.34 3.94 -1.10 1.10 1.76 1.47 1.47 3.23 0.14 0.14 4.26 -0.81 0.81 2.98 0.60 0.60 3.09 0.54 0.54 2.90 MAD = 0.86 Actual ES FIT 2 3 4 5 6 7 8 9 10 11 Ch 11 pp. 303-05 RDQ: 2, 3, 5 Pr: 2, 6 Review and Discussion Questions 2. What are the basic controllable variables of a production planning system? If we take forecasted demand as a given, then the basic decision we have to make for each period is how much we are going to produce. That determines how much inventory we are going to have, and how much demand will go unmet. In order to realize that level of production, we may need to 1. increase the workforce (hire more workers, hire temp workers), 2. Get more output from the workforce (work overtime) 3. Hire outside help (subcontract), or 4. reduce the size of the workforce (lay off workers or temps). If we want to make significant changes to the level of production, we may also need to increase the capacity of our equipment. What are the four major costs? P. 290, the book says: basic production costs, costs associated with changing the production rate, inventory holding costs, and backordering costs. 3. Distinguish between pure and mixed strategies in production planning. There are 3 pure strategies: Chase, stable workforce-variable work hours, and level. If one approach is strictly followed, that is a pure strategy. Any combination of two or more of those is a mixed strategy. So if you vary the size of the workforce a little, but use subcontracting and overtime, that is definitely a mixed strategy. 5. How does forecast accuracy relate, in general, to the practical application of the aggregate planning models discussed in the chapter? Problem 2 hiring: $100 RT $5 units/hr 0.5 Firing $200 OT $8 Inventory $/Q $5 Hrs/day 8 Backorders $10 Days/Q 60 Fall Winter Spring Summer Forecast 10,000 8,000 7,000 12,000 Starting Inv 500 (2,300) - 200 Start workers 30 30 30 30 Workers used 30 30 30 50 Ending workers 30 30 30 30 RT hours 14,400 14,400 14,400 24,000 OT hours - 6,200 - - RT production 7,200 7,200 7,200 12,000 OT production - 3,100 - - Ending inv (2,300) - 200 200 RT labor 72,000 72,000 72,000 120,000 336,000 OT labor - 49,600 - - 49,600 Hiring cost - - - 2,000 2,000 Firing cost - - - 4,000 4,000 Holding Cost - - 1,000 1,000 2,000 Backorder cost 23,000 - - - 23,000 416,600 From reading the problem, really the only things we can change are: 1. We can use OT in Winter and Spring, and 2. We can hire temps to work for the summer. No OT is available in Fall or Summer. We are supposed to use enough OT in Winter and Spring to make sure we don't have any stockouts. So we need to have 6,200 OT hours in Winter to end Winter with no backorders. We end up carrying a little extra inventory at the end of Spring, 200 units. Then, we hire enough temp workers to end summer with as close to zero inventory as we can manage. 50 units makes ending inventory negative, 50 makes it positive. Given the number of workers i plan to be using during a quarter, I compute the RT hours they will work, and the labor I will get from that. I add in the OT hours they will work, and the units from that. I take beginning inventory + production - demand to get ending Problem 6 Jan Feb Mar Apr May June Total Forecast 5,000 4,000 6,000 6,000 5,000 4,000 30,000 Employees 25 RT hours 4,000 4,000 4,000 4,000 4,000 4,000 24,000 work day/mo 20 OT hours 1,200 1,200 1,200 1,200 1,200 - 6,000 Ending "Inv" 200 1,400 600 - - - 2,200 $/hr Ending "backorder" - - - 200 - - 200 RT labor 30 OT labor 45 RT Labor 720,000 "Holding" $5 OT Labor 270,000 "backorder" $10 Holding 11,000 Backorders 2,000 Total 1,003,000 Above, I have shown my final cost, but below I will walk you through the process I used to arrive at it. We have 25 employees, who work 20 days (or 160 hours) per month, RT, = 4,000 hours OT can be at most 30% of that, or 1,200 hrs per month. Notice that RT = 4,000, which is our smallest forecasted quantity, al so. So we have no choice but to do a "hire for the minimum, and produce extra" approach. We can't outsource, so all we can do is pro duce extra. We may have to produce extra some months and hold inventory. I started by trying to meet demand in January, so I did 1,000 hours of OT. There is no reason to do less - I pay a penalty if I don't get the work done and end up doin it late. I can do 1,000, (it's less than 1,200) so the cheapest thing is to do it then. In February, I don't need to produce anything extra, so I penciled in 0 OT hours. Then in March and April, I can't get it al l done in time, so I put down 1,200 OT hours for both. In May, I need to use 1,000 hours of OT, so I put that in, and no OT in June At this Jan Feb Mar Apr May June Total Forecast 5,000 4,000 6,000 6,000 5,000 4,000 30,000 RT hours 4,000 4,000 4,000 4,000 4,000 4,000 4,000 OT hours 1,000 - 1,200 1,200 1,000 - 4,400 Ending "Inv" - - - - - - - Ending "backorder" - - 800 1,600 1,600 1,600 5,600 Overall, I am 1,600 hours short. I need to produce 800 more hours for March, and 800 more for April. I could do 200 more OT in January, 1,200 in February, 200 in May, and 1,200 in June. Each month I do something early costs $5 per hour, doing it late costs $10, so early is better than late. I want to carry as little inventory as possible, and take care of any backorders as soon as possible. I could do 800 in February, and that would take care of March's needs. So now it looks like this: Jan Feb Mar Apr May June Total Forecast 5,000 4,000 6,000 6,000 5,000 4,000 30,000 RT hours 4,000 4,000 4,000 4,000 4,000 4,000 4,000 OT hours 1,000 800 1,200 1,200 1,000 - 5,200 Ending "Inv" - 800 - - - - 800 Ending "backorder" - - - 800 800 800 2,400 I need 800 more hours for April. I could do 400 more hours in Feb. Each moth early costs $5 per hour. So work done in February for April incurs a holding cost of $5 unit/month * 2 months = $10. The alternative is to do things one month late in May, for the same cost of $10 unit. Overall, I'd rather pay holding cost than have irate customers with late orders. So I put in 400 more hours in February. Jan Feb Mar Apr May June Total Forecast 5,000 4,000 6,000 6,000 5,000 4,000 30,000 RT hours 4,000 4,000 4,000 4,000 4,000 4,000 4,000 OT hours 1,000 1,200 1,200 1,200 1,000 - 5,600 Ending "Inv" - 1,200 400 - - - 1,600 Ending "backorder" - - - 400 400 400 1,200 I'm still 400 units short for April. I can do 200 units in May, for a backorder cost of $10 per unit. I can do work early i n January, which is 3 months early, and is a cost of $15 per unit. So May is a better option, as far as it goes. So I will do 200 units in May, and have to do the other 200 units I still need in January, which brings me to my final solution. I've talked about doing so many hours of work early in a particular month, saying it's for work due in a particular month. Th e important thing is that I produce enough to satisfy demand. But in the end it doesn't matter if the OT in January is specif ically for March or April demand; I hold the same number of units for the same amount of time, no matter how you slice it. Ch 12, pp 339-343 RDQ: 4, 5, 8 Pr: 1, 2, 5, 10, 12 Case: HP 4. Under which conditions would a plant manager elect to use a fixed-order quantity model as opposed to a fixed-time period model? If there are quantity discounts, it makes sense to use an ordering policy that will try to take advantage of it. If there is a lot of demand variability, the lower level of safety stock from a fixed order quantity will be significant. If holding cost is high (either because of the interest rate, or unit value), for the same reason. If there are no savings from coordinating orders from a supplier to try to save on transportation costs. What are the disadvantages of using a fixed-time period model? The main disadvantage as I see it is that you end up carrying more safety stock, and therefore have higher holding costs. On the other hand, there are a number of advantages: 1. You have better possibilities of taking advantage of quantity discounts from a supplier. 2. There is the chance to combine orders to reduce shipping costs. 3. Ordering costs may be lower because you will place fewer orders from each supplier, because you may order all of the items from supplier A every other Wednesday. 5. What two basic questions must be answered by an inventory-control decision rule? 1. How much should we order at one time? 2. When is it time to order more? 8. Which type of inventory system would you use in the following situations? a. Supplying your kitchen with fresh food. As I described in class, we only have time to shop for groceries once a week. So we use a periodic ordering policy. b. Obtaining a daily newspaper. I guess you could try to buy a week's worth all at once, but I don't think it'd really work. This has to be periodic. c. Buying gas for your car. Our minivan gets refueled whenever it gets low, so that's a fixed-order quantity, pretty much. Our smaller car is being driven to Minden for a class every week, so I stop in Carson City and fill up on their cheaper gas, which makes for a periodic ordering quantity. To which of these items do you impute the highest stockout cost? Running out of gas. There is always something you could eat in the house, you just get less and less appetizing options. But once you're out of gas, you're stuck. If you completely, totally ran out of food in your house, though, I guess you'd die. Pr. 1 Supermarket boxes of lettuce Cost = 4 avg = 250 P <= 0.7059 Sales price = 10 stdev = 34 z= 0.5414 salvage = 1.5 C_o = 2.5 Q= 268.41 C_u = 6 Pr. 2 Super Discount Airlines C_o = 250 avg = 25 P <= 0.3333 C_u = 125 stdev = 15 z= -0.4307 Q= 18.54 If the airline underestimates the number of people who don’t show up, it loses out on $125 per unsold ticket. If it overestimates the number of people who won't show up, that means more people show up than it expects, and they will have people show up who can't get on the plane. So cost of overestimating is Pr. 5 Charlie's Pizza Reordering Period (wks) = 4 In a fixed-time period model (p. 328), we want to place an LT to ship (wks0 = 3 order each time so that what we have on hand plus our order quantity brings us up to some level, which I call the Pepperoni per wk avg = 150 "Order up to level." st dev wkly pepp used= 30 Probability don't run out= 98% The thing to remember is that our Order up to level has to z= 2.054 protect us against all of the demand uncertaintly that can happen in the next 7 weeks. So we figure out the average demand over 7 weeks, and the standard deviation of the d-bar(T+L) = 1050 demand over 7 weeks. stdv T+L = 79.4 Order up to level = 1213 Inventory on hand = 500 Order to place = 713 Pr. 10 Given annuald demand, ordering cost and holding cost, we can Demand/yr = 15,600 compute the EOQ of 3,120. Demand/wk= 300 To figure out the safety stock, we need to first figure out the stdv / wk = 90 standard deviation of demand over the lead time. Stdv of LT demand = sqrt of the lead time * standard deviation Order cost = 31.20 of demand per week. Inv cost/yr = 0.10 Service level = 98% The average demand over the LT is 4 * 300 = 1200 z= 2.054 So the Reorder Point is the average + SS = 1200 + 370 EOQ = 3120 To answer the second part, about a 50% reduction in safety LT (wks) = 4 stock, we first figure out how much safety stock we'll have: DLT 1,200 0.5 * 370 = 185 units. stdv LT dem 180 SS = 369.67 Then we need to figure out the percentage of time we won't ROP = 1,570 have a shortage. To do that, we need to know how many standard deviations of demand that will be. The standard deviation of LT demand is 180, so SS of 185 is 1.027 standard deviations above the mean. Then, look up the probability demand is 1.027 standard deviations or less below the mean. SS reduction 50% New ss = 184.84 # std dev. = 1.027 service = 84.8% Exact EOQrounded Pr. 12 Item X EOQ = 89.44 90 Cost = $25 Annual Ordering costs $ 223.61 $ 222.22 Holding/yr = $5 Annual Holding costs $ 223.61 $ 225.00 Order cost = $10 $ 447.21 $ 447.22 Demand /yr= 2,000 When I compute ordering and holding costs, I did it using the exact EOQ value of 89.44, and the ordering and holding costs are exactly the same, to as many decimal places as you want to look at. If I round the EOQ to 90 units, the two costs are not exactly the same any more. They differ by a couple of dollars. But the total ordering and holding costs go up by $0.01. HP CASE STUDY Make no mistake about it, this is not easy. But it's really what HP did when we talked about postponement earlier in the semester, so it's an interesting application of using inventory management. Nov Dec Jan Feb Mar Apr May Jun Jul A 80 - 60 90 21 48 - 9 20 AB 20,572 20,895 19,252 11,052 19,864 20,316 13,336 10,578 6,095 AU 4,564 3,207 7,485 4,908 5,295 90 - 5,004 4,385 AA 400 255 408 645 210 87 432 816 430 AQ 4,008 2,196 4,761 1,053 1,008 2,358 1,676 540 2,310 AY 248 450 378 306 219 204 248 484 164 Total 29,872 27,003 32,344 18,054 26,617 23,103 15,692 17,431 13,404 T= 14 days reorder interval 250 printer value L= 42 days LT 25% holdling cost T+L= 56 service 98% z= 2.054 Currently, they keep one month's supply of each product as safety stock. I computed the average monthly demand f safety stock they have. This totals 23, 034 printers. If they are going to keep all of the printers different, the way they are now, they should compute the safety stock in a deviation of monthly demand for each product. For AB it is 5,624.7. Now comes the one tricky step. Reading "Fixed case isn't exactly clear about how often Europe orders. In my spreadsheet, I originally had, T=7, because it says the mean that they order every product every week. So I have a cell where I can change the reorder interval to Using 14 days as T, and 42 days as L, the average demand over T+L for AB is 29,549 with a standard deviation of How did I get that? The average per month is 5624. If we assume that represents 30 days worth of sales, divide by average over 49 days. The VARIANCE works the same way, so if you want to know the standard deviation, take the 49, and then take the square root to get the standard deviation. You can do that a little more directly if you multiply th 49/30, and you will get the same answer. For a 98% service level, we want to be 2.05 standard deviations over the mean, so the safety stock should be We compute the amount of safety stock needed over T+L, instead of just over L, because how ever much we order o We compute the amount of safety stock needed over T+L, instead of just over L, because how ever much we order o order would come in. Since we'll place that next order T days from now, and it will come in L days after that, that nex Doing that for all the products, and summing them up, they should have inventory of 26,346. This would give them th If they switched to a generic printer, the demand for the generic printer would be equal to the total demand for all of th each product, and we would have total demand of of 23,033.5 per month, with a standard deviation of 6304. Switching to a generic printer, we would need a SS of 17,688 printers. This would save us $2.2m in inventory, which $541k. 35000 30000 25000 A AB 20000 AU AA 15000 AQ AY Total 10000 5000 0 Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sept Oct as opposed to a be significant. e higher holding you may order all of c ordering policy. be periodic. smaller car is being which makes for a ess appetizing house, though, I per unsold ow up than it estimating is ant to place an and plus our which I call the to level has to aintly that can out the average eviation of the holding cost, we can rst figure out the standard deviation 370 duction in safety ock we'll have: of time we won't ow how many The standard standard the probability s below the mean. , and the ordering and differ by a couple of about postponement monthly T+L Order up change Aug Sept Oct avg stdev stdev avg SS SS 54 84 42 42.3 32.4 44 79 90.95 48.62 14,496 23,712 9,792 15,830.0 5,624.7 7,685 29,549 ######## (47.24) 5,103 4,302 6,153 4,208.0 2,204.6 3,012 7,855 6,185.96 1,977.96 630 456 273 420.2 203.9 279 784 572.21 152.04 2,046 1,797 2,961 2,226.2 1,220.6 1,668 4,156 3,424.93 1,198.77 363 384 234 306.8 103.1 141 573 289.36 (17.48) 22,692 30,735 19,455 23,033.5 6,303.7 8,612 42,996 ######## (5,345.71) Amount of Safety Stock they have 23,034 they SHOULD have 26,346 Generics 17,688 Inventory savings $ 2,164,595 Holding cost savings $ 541,149 verage monthly demand for each product, and assumably, that is how much pute the safety stock in a smarter way. I have computed the standard icky step. Reading "Fixed-Time Period Models" in the book may help. The , because it says they receive orders weekly. But that doesn't necessarily eorder interval to 14 days or whatever I want to look up. a standard deviation of 7,685, . worth of sales, divide by 30 to get daily sales, then multiply by 49 to get the andard deviation, take the VARIANCE per month, divide by 30, multiply by re directly if you multiply the standard deviation by the square root of ety stock should be 15,783. how ever much we order one day, it has to be enough to last us until the NEXT how ever much we order one day, it has to be enough to last us until the NEXT L days after that, that next order will come in T+L days from now. . This would give them the 98% service level they need. he total demand for all of the products. So we just add up the demands for m in inventory, which would translate to annual holding cost savings of Looking at a graph of demand, there is a little bit of variability in total sales that could be similar from one year to the next. If it is the same from year to year, we would have to call it seasonality. Sales spike in September, which could be a back-to-school surge. But only AB, the top seller really went up a lot, so maybe there was a sale on those or something. Since the other models were not affected, it is probably not real seasonality. In any case, we are not making any attempt to factor seasonality into the model. Ch 13, pp. 367-369 RDQ: 3, 6, 7 Pr: 2, 4 3. What is the role of safety stock in an MRP system? Theoretically, an MRP system has computed exactly how much we are going to ened, and when, so you might think that there would not be any need for safety stock. But that is not the case. Shipments may be delayed, or may be too small. In which case, safety stock can be a lifesaver. On p. 359, the book explains how safety stock fits into the reorder quantity calculation, and on p. 360, in Item C, they show how to take SS into account. 6. "MRP just prepares shopping lists. It does not do the shopping or cook the dinner." Comment. True. It does not do the production, nor does it even make sure that the kitchen has a big enough stove to cook it all, nor that it has a fridge large enough to store all the food. It just tells us what parts we would need, and when, if we were to try to produce a given quantity. 7. What are the sources of demand in an MRP system? Are these dependent or independent, and how are they used as inputs to the system? The two types of demand in an MRP system are dependent demand, and independent demand. Dependent demand arises from planned production of some other item. Independent demand is demand from an outside source. So demand for car water pumps might come primarily from the production line that will produce the cars they go into. But there also will be demand for water pumps from the spare parts division that sells to dealers to replace those that fail. Problem 2 0 1 2 3 4 5 Gross Req 75 50 70 On-Hand 40 40 40 40 0 0 0 Net Req 0 0 35 0 50 70 Pl Ord Rec 0 0 35 0 50 70 Pl Ord Rel 0 35 0 50 70 0 Problem 4 Z =IF(a>b, c, d) A(2) B(4) a=10, b=5, 10>5, do"c" C(3) D(4) E(2) Z 0 1 2 3 4 5 6 7 8 9 10 B 4 Gross Req 0 0 0 0 0 0 0 0 0 50 Gross Req On-Hand 0 0 0 0 0 0 0 0 0 0 0 On-Hand Net Req 0 0 0 0 0 0 0 0 0 50 Net Req Pl Ord Rec 0 0 0 0 0 0 0 0 0 50 Pl Ord Rec Pl Ord Rel 0 0 0 0 0 0 0 50 0 0 Pl Ord Rel A 2 0 1 2 3 4 5 6 7 8 9 10 C 3 Gross Req 0 0 0 0 0 0 0 100 0 0 Gross Req On-Hand 0 0 0 0 0 0 0 0 0 0 0 On-Hand Net Req 0 0 0 0 0 0 0 100 0 0 Net Req Pl Ord Rec 0 0 0 0 0 0 0 100 0 0 Pl Ord Rec Pl Ord Rel 0 0 0 0 0 0 100 0 0 0 Pl Ord Rel D 4 0 1 2 3 4 5 6 7 8 9 10 E 2 Gross Req 0 0 0 0 0 0 400 0 0 0 Gross Req On-Hand 0 0 0 0 0 0 0 0 0 0 0 On-Hand Net Req 0 0 0 0 0 0 400 0 0 0 Net Req Pl Ord Rec 0 0 0 0 0 0 400 0 0 0 Pl Ord Rec Pl Ord Rel 0 0 0 0 0 400 0 0 0 0 Pl Ord Rel 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 200 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 200 0 0 0 0 0 0 0 0 0 200 0 0 0 0 0 0 0 0 200 0 0 0 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 300 0 0 0 0 0 0 0 0 0 300 0 0 0 0 0 0 0 0 300 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 800 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 800 0 0 0 0 0 0 0 0 0 800 0 0 0 0 0 0 800 0 0 0 0 0 0 0

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Shane Acker, Elijah Wood, Jennifer Connelly, John C. Reilly, Breaking News, Tim Burton, Martin Landau, Christopher Plummer, September 9, Timur Bekmambetov

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