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Thread: How Many Stops (delivering various parts to multiple work stations)

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    How Many Stops (delivering various parts to multiple work stations)

    Am I being short changed? I am required to deliver various parts to multiple work stations. I must stop at each station on my 1st of 3 loops and only at stations that require parts on my 2nd and 3rd loop. At one particular station there are 3 separate parts used there. Part #1 requires .27 containers per day, part #2 requires .12 container per day and part #3 requires .06 containers per day. I am paid for 1.3 stops per day based on the following calculation.

    1+.45-.45/3=1.3

    Where,

    1=mandatory 1stop
    .45=total #of containers required per day
    3=# of trips per day

    Does this calculation accurately represent the number of stops I am likely to make at this station each day?
    As the containers are likely to be delivered on different loops, shouldn't they be considered separately vs the total?

    Tanks,

    Dan

  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by Dan Wilson View Post
    Am I being short changed? I am required to deliver various parts to multiple work stations. I must stop at each station on my 1st of 3 loops and only at stations that require parts on my 2nd and 3rd loop. At one particular station there are 3 separate parts used there. Part #1 requires .27 containers per day, part #2 requires .12 container per day and part #3 requires .06 containers per day. I am paid for 1.3 stops per day based on the following calculation.

    1+.45-.45/3=1.3

    Where,

    1=mandatory 1stop
    .45=total #of containers required per day
    3=# of trips per day

    Does this calculation accurately represent the number of stops I am likely to make at this station each day?
    As the containers are likely to be delivered on different loops, shouldn't they be considered separately vs the total?
    I don't understand the reasoning for the "1 + 0.45 - (0.45/3)" computation. Also, surely information is needed regarding the probabilities of parts being needed by the various stations...?

    When you reply, please include the full and exact text of the exercise, the complete instructions, recent topics of study (in your statistics class), and a clear listing of your thoughts and efforts so far. Thank you!

  3. #3
    Quote Originally Posted by stapel View Post
    I don't understand the reasoning for the "1 + 0.45 - (0.45/3)" computation. Also, surely information is needed regarding the probabilities of parts being needed by the various stations...?

    When you reply, please include the full and exact text of the exercise, the complete instructions, recent topics of study (in your statistics class), and a clear listing of your thoughts and efforts so far. Thank you!
    This an actual workplace issue Iím facing, not a classroom exercise. The calculation was provided to me by engineering as justification for paying me to stop at this station 1.3 times per day. Thier calculation doesnít seem to reflect my experience and I do not possess the math skills to question their calculation. Iím hoping you can help me.

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    Quote Originally Posted by Dan Wilson View Post
    This an actual workplace issue Iím facing, not a classroom exercise. The calculation was provided to me by engineering as justification for paying me to stop at this station 1.3 times per day. Thier calculation doesnít seem to reflect my experience and I do not possess the math skills to question their calculation. Iím hoping you can help me.
    As stapel said, the formula doesn't seem to make a lot of sense; perhaps if they explained it, we could judge it better, but it seems that more information would be needed. It's also unclear to me what it even means to be paid per stop; how does it relate to an hourly wage, or to anything else that could be compared to others' pay?

    My recommendation would be to show them that their formula is inadequate by presenting actual data. Record how many stops you make each day (along with any other information that might be useful, such as how long a stop takes), and show them that, over some length of time like a month, it does not average out to match their formula.

    I'll make an attempt to create a formula based on the insufficient information it is based on, to see if there is at least some sense in it.

    Quote Originally Posted by Dan Wilson View Post
    I must stop at each station on my 1st of 3 loops and only at stations that require parts on my 2nd and 3rd loop. At one particular station there are 3 separate parts used there. Part #1 requires .27 containers per day, part #2 requires .12 container per day and part #3 requires .06 containers per day. I am paid for 1.3 stops per day based on the following calculation.

    1+.45-.45/3=1.3

    Where,

    1=mandatory 1stop
    .45=total #of containers required per day
    3=# of trips per day
    Presumably you deliver only whole containers, so you stop as many times as there are whole containers needed. In 100 days, you would then stop at the station 27 times for the first part, 12 times for the second, and 6 for the third. If we suppose that you never stop for two reasons at once, this means 45 stops per 100 days; in reality this would be somewhat less. So the total number of stops per day would be 1 (the required stop) + 0.45 (delivering a container) - 0.45/3 (the number of times a container would be needed on the required stop that is already counted).

    So it does make some sense. But it's a rather simplistic calculation, so if I made it, I would welcome actual data that showed it's wrong, and would then try to figure out what it is about the frequency of deliveries that made the calculation wrong, in order to improve it.

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    Quote Originally Posted by Dr.Peterson View Post
    My recommendation would be to show them that their formula is inadequate by presenting actual data. Record how many stops you make each day (along with any other information that might be useful, such as how long a stop takes), and show them that, over some length of time like a month, it does not average out to match their formula.
    I should have added that you should also record how many containers are used, in order to compare your number of stops to the actual calculation using real numbers.This could also help check the assumptions they seem to be making. If I were to look at your data, I would want to do all of this.

  6. #6
    Quote Originally Posted by Dr.Peterson View Post
    I should have added that you should also record how many containers are used, in order to compare your number of stops to the actual calculation using real numbers.This could also help check the assumptions they seem to be making. If I were to look at your data, I would want to do all of this.
    The significance of the number of stops is that there are a certain number of pre set timed elements associated with each stop such as acceleration/deceleration, walking to the work station etc. The job is timed/paid based on a per day basis, hence the partial container calculation. The constants are that there are three trips per day and it is mandatory to stop at each station on the first trip.

    There are three different parts delivered to a particular station based on the usage of Part #1 at .27 containers per day part #2 at .12 containers per day and Part #3 at .06 containers per day. The parts could be delivered on any of the three trips. One, two, three or none could be delivered on any trip but since the usage is < one container per day, no more than one container of any part # would be delivered on a given day. I believe this would create 61 separate delivery possibilities. i.e. Day one - none on the first trip, part #2 on the second trip, none on the third trip, requiring 2 stops - the first trip mandatory stop and for a delivery on the 2nd trip. Day 2 - Part 3 on 1st trip, none on 2nd and part #3 n 3rd. again 2 stops. etc

    Based on the low frequency of deliveries for these part #'s collection of actual data would be extremely time consuming. Also, frequency changes on a regular basis. Having said that, I hoping for a calculation, based on the above information to determine how many times per day I am likely to stop at this station. Given that I must stop on he 1st trip I believe it is, 1+ the possibility I would deliver parts on the 2nd and/or 3rd trip.

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    Quote Originally Posted by Dan Wilson View Post
    There are three different parts delivered to a particular station based on the usage of Part #1 at .27 containers per day part #2 at .12 containers per day and Part #3 at .06 containers per day. The parts could be delivered on any of the three trips. One, two, three or none could be delivered on any trip but since the usage is < one container per day, no more than one container of any part # would be delivered on a given day. I believe this would create 61 separate delivery possibilities. i.e. Day one - none on the first trip, part #2 on the second trip, none on the third trip, requiring 2 stops - the first trip mandatory stop and for a delivery on the 2nd trip. Day 2 - Part 3 on 1st trip, none on 2nd and part #3 n 3rd. again 2 stops. etc
    If we need to come up with a better theoretical formula, we might have to dig into this level of detail and more. At the moment, I'm more interested in confirming your sense that the formula isn't working, and for that we need data. (And that would probably be more convincing than any theory we come up with.)

    Quote Originally Posted by Dan Wilson View Post
    Based on the low frequency of deliveries for these part #'s collection of actual data would be extremely time consuming. Also, frequency changes on a regular basis. Having said that, I hoping for a calculation, based on the above information to determine how many times per day I am likely to stop at this station. Given that I must stop on he 1st trip I believe it is, 1+ the possibility I would deliver parts on the 2nd and/or 3rd trip.
    Perhaps you're picturing a different sort of data collection than I am; or I may have an entirely wrong picture of what you do. (I imagine there's a lot more you aren't telling us, such as that there are really hundreds of different parts you're dealing with.)

    I'm picturing that you just record which stations you stop at on each trip, and what containers you deliver at each. I would not be surprised if at least the latter is already reported somewhere. I'd just want that information each day for a month or so. Specifically, I want the actual number of stops you make per day, for comparison with the output of the formula, and if possible the actual number of containers used per day, for comparison with the input to the formula, in case that is wrong.

    But you also say that the frequencies change regularly. Do you mean that the numbers in the formula may change from day to day? Or just that they don't stay the same long enough to collect consistent data for a month? Where do those numbers come from? That data, too, may be already available!

    As far as the formula is concerned, I've shown you that it does make sense theoretically, at least in terms of a very simplistic model, and may even overestimate the number of stops you make. I want to know how far it is from reality, in order to decide whether it is worth the effort to make a more complete model (given that I know very little about the whole reality of your situation, and there may be other issues that are more important to the model than what you've told us). Without both clear evidence that it is needed, and enough information to be sure I'm modeling accurately, I'm not about to try making a better formula.

    Can you at least tell me what it is that leads you to think the formula is wrong? You must have some sort of evidence.

  8. #8
    Quote Originally Posted by Dr.Peterson View Post
    If we need to come up with a better theoretical formula, we might have to dig into this level of detail and more. At the moment, I'm more interested in confirming your sense that the formula isn't working, and for that we need data. (And that would probably be more convincing than any theory we come up with.)

    Perhaps you're picturing a different sort of data collection than I am; or I may have an entirely wrong picture of what you do. (I imagine there's a lot more you aren't telling us, such as that there are really hundreds of different parts you're dealing with.)

    I'm picturing that you just record which stations you stop at on each trip, and what containers you deliver at each. I would not be surprised if at least the latter is already reported somewhere. I'd just want that information each day for a month or so. Specifically, I want the actual number of stops you make per day, for comparison with the output of the formula, and if possible the actual number of containers used per day, for comparison with the input to the formula, in case that is wrong.

    But you also say that the frequencies change regularly. Do you mean that the numbers in the formula may change from day to day? Or just that they don't stay the same long enough to collect consistent data for a month? Where do those numbers come from? That data, too, may be already available!

    As far as the formula is concerned, I've shown you that it does make sense theoretically, at least in terms of a very simplistic model, and may even overestimate the number of stops you make. I want to know how far it is from reality, in order to decide whether it is worth the effort to make a more complete model (given that I know very little about the whole reality of your situation, and there may be other issues that are more important to the model than what you've told us). Without both clear evidence that it is needed, and enough information to be sure I'm modeling accurately, I'm not about to try making a better formula.

    Can you at least tell me what it is that leads you to think the formula is wrong? You must have some sort of evidence.
    First, I would like to say thanks for sticking with this for me!

    Second, you are correct in assuming that there is more to the story so to speak. There are a number of similar delivery jobs that would have 40-50 different work stations/stops. Each stop could have 1-6 different containers of parts associated with it. The volume of parts are determined by consumer demand (various options, colours etc.) and are projected 1 week in advance. For example, the the volumes used for the 3 part #'s in my example regularly change significantly week to week. Considering the vast number of parts at the vast number of stops and the frequency of volume changes, gathering hard data to compare to a formula would be very difficult. That data I agree is be recorded somewhere but I do not have access.

    Breaking it down, their formula calculates that I would likely stop once for the mandatory stop, plus the average number of containers delivered daily minus the number of containers divided by the number of trips made per day (presumably to account for the number of containers likely delivered on the first trip). Although I used one workstation in the example above, I'm basically looking for a tool to predict the number of stops I would make at each of several work stations based on the volume of parts, which may be a partial container, per day. The current method does make sense but I was wondering if there was a more accurate method. Also, does using the cumulative total number of containers vs individual container volumes affect the calculation.

  9. #9
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    Quote Originally Posted by Dan Wilson View Post
    Second, you are correct in assuming that there is more to the story so to speak. There are a number of similar delivery jobs that would have 40-50 different work stations/stops. Each stop could have 1-6 different containers of parts associated with it. The volume of parts are determined by consumer demand (various options, colours etc.) and are projected 1 week in advance. For example, the the volumes used for the 3 part #'s in my example regularly change significantly week to week. Considering the vast number of parts at the vast number of stops and the frequency of volume changes, gathering hard data to compare to a formula would be very difficult. That data I agree is be recorded somewhere but I do not have access.

    Breaking it down, their formula calculates that I would likely stop once for the mandatory stop, plus the average number of containers delivered daily minus the number of containers divided by the number of trips made per day (presumably to account for the number of containers likely delivered on the first trip). Although I used one workstation in the example above, I'm basically looking for a tool to predict the number of stops I would make at each of several work stations based on the volume of parts, which may be a partial container, per day. The current method does make sense but I was wondering if there was a more accurate method. Also, does using the cumulative total number of containers vs individual container volumes affect the calculation.
    So, you don't actually have any specific reason to think the formula is wrong and you are being shortchanged, as you initially said ("Their calculation doesnít seem to reflect my experience"); you just want to find a better formula. If you do think it is wrong, then it could be either because the formula is wrong (which is why I hoped to find out how many stops you are actually making as compared with what they are getting from the formula), or because they are putting bad data into the formula (which is why I hoped you could compare the estimated numbers of containers to reality, over whatever time frame makes sense). If you do want to challenge the formula, you could ask the people who do know to check their data for you. Basing your pay on unsupported estimates of what they think you are going to have to do, rather than what you actually do, seems like a "formula" for conflict. And as I've suggested, showing that the formula is actually producing inaccurate results will be far more impressive than telling them someone you found online told you that such and such a formula is better ...

    But let's leave that behind. I'll suppose you just want to be able to predict more accurately how many stops you have to make.

    The calculation they are doing seems to give you the benefit of the doubt, by supposing that the only "collisions" of different needs are with the mandatory stop. It just imagines that you will make an average of 0.45 deliveries per day (which means about one every 2.2 days). Then it assumes that your three trips per day are evenly spaced, and the time of any part being needed is random (evenly distributed), so that the probability that the next trip on which it would be needed would be the mandatory one is 1/3. This is the part that could be quite wrong, and possibly in a bad direction. Consider these examples, imagining for ease of calculation that there are 9 working hours in a day (I want to be able to divide by 3):


    1. Suppose you reach this station on the mandatory trip at the very start of the day, hour 0, and on your other two trips at hour 3 and hour 6. Then if needs are at random times, the need will arise between hour 6 and hour 9 1/3 of the time, so 1/3 of the .45 deliveries per day will be on the mandatory trip, and the formula will be exactly right. You will make the mandatory trip plus 2/3 of the .45 = .30, for a total of 1.30 stops.
    2. Suppose your trips are not evenly spaced, but are at hours 1, 6, and 8. Then needs that arise from 8 to 9 or 0 to 1 will be met on the mandatory trip, only 2/9 of the time; 7/9 of the .45 is .35, so you make 1.35 stops.
    3. If your trips are at hours 1, 3, and 5, on the other hand, 5/9 of all needs will be filled on the mandatory trip, and you will make only 1.20 stops per day on average.


    So the accuracy of the formula can certainly vary; but we'd need a lot more knowledge in order to make a better prediction.

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    If your pay is based on a daily rate, what difference does it make? This kind of formula may be based on the opportunity cost of delays if items are not delivered in a timely manner or other considerations over and above what you perceive to be an efficient use of your time. Sub-optimization, meaning optimization against the wrong objective, is always a potential problem. If we do not know what objective function is being optimized, we cannot possibly prove it right or wrong. Moreover, if the formula is being adjusted weekly, any conclusion we reach will be likely obsolete by the time anyone can consider it.

    Seriously, if you believe the formula is not optimal, ask what the criteria are for defining optimality, and then let us think about the rule that you are following relative to the desired optimization.
    Last edited by JeffM; 12-13-2017 at 01:06 AM.

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