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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
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      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


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y expect, a given amount of

choose a health plan that
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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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