Math Question: Inbound Flow Question: You are in charge of the department that receives the product in to the building and stows it to the bin where it is accessible by the department. you have two options on how to receive and stow the product. In the first option, you receive the product at 250 units per labor hour and stow it at 100 units per labor hour. You must receive it and stow it for the unit to count for production. This process results in 1% of the units stowed being incorrect. You can find and fix these errors at a rate of 20 units for labor hour with what you believe is almost 100% accuracy. In the second option, you receive and stow the product in one step vs. two. The rate for this process is 80 units per labor hours for receive and stow. This process results in 1.5% of the units being stowed being incorrect. You can find and fix these errors at a rate of 20 units per hour with what you believe is almost 100% accuracy. 1. Which option would you select to process today's units and why? 2. Does your answer change if you are told you must fully process 100,000 units today? If yes, why? 3. Does your answer change if you are told that you have 15 associates today and you must fully produce the maximum amount of units possible? If yes, why?

I like the top answer, but it's a bit complex.....lets make this simple. Start with a setting a production goal at a number that is easy to work with. Lets say 1,000 Units. In option A it would take 4 Labor hours to receive 1,000 units (1,000/250=4) and it would take 10 labor hours to stow 1,000 units 1,000/100=10). 1,000 units X the error rate of .01 = 10 errors. Since you can correct 20 errors in an hour it would take .5 hours to correct the 10 mistakes. So for Option A it would take a total of 14.5 hours (4+10+.5=14.5) to receive and stow 1,000 units. In option B you can receive and stow at a rate of 80 units per hour. So 1,000/80 = 12.5 hours. There is a error rate of 1.5% using this method. So 1000 X .015 = 15 errors. Since we can correct 20 mistakes per hour it would take .75 hours to correct the mistakes. The total hours to receive and stow 1,000 units using this option at 13.25 hours (12.5+.75=13.25). Option B is the best method. Option B will always be the better method, unless we are given new or updated data. I hope this helps.

1st scenario: Assumption - we have 1000 units To receive 1000 units, we would need 4hrs (@250units/hr) and to stow 1000 units, we need 10 hrs (@100 units/hr). # stowed incorrectly @1% = 10 and it takes 0.5 hrs to correct it. So total hrs is14.5 hrs (4+10+.5). Scenario 2: To receive and stow 1000 units, we need 12.5 hrs (@80units/hr). # stowed incorrectly @1.5% is 15 and it would take 0.75 hrs to correct it. Total time = 13.25 hrs (12.5+.75) So option 2 is better in this scenario. Doing the same math for 100000 units, Option 1 takes 1450 hrs and option 2 takes 1325 hrs. So Option 2 is always better, I guess!!!

Please don't let this question confuse you. Option 1 produces about 69 units per hour whereas option 2 produces about 76 per hour. The answer is so much more simple than everyone is making it out to be. In any situation option 2 is going to give you more units per hour which is more productive. The are no special factors or tricks. Option 2. Pause and act like you're doing the math to avoid undue embarrassment.

For the sake of keeping this simple I am going to make the assumption it is 10 hour work day: Option 1: 1hour/250unit + 1hour/100units = 2hours/500units + 5hours/500units = 7hours they produce 500units or 500units/7hours = roughly 71.42 units an hour ; (71.42uph)(10 hours) = 714.2 units that day ; mult by .01 to get number that you count because you screwed them up = 7.14 errors Option 2: (80uph)(10 hours) = 800 units that day; 800 x .015 = 12 errors the amount of time to fix the errors for both are the same so they cancel each other out in my mind and unless adding 15 people will change the units per hour for either of the opitions it doesnt matter. 1 or million units does not change the process.

Basically I just started by equalizing the numbers so they could be easily compared. In Option A - you can receive at a rate of 250/hr but then must stow at a rate of 100/hr therefore it takes you 3.5 hours to receive and stow 250 units. This breaks down to (250/3.5) ~ 71 uph. In Option B - you can receive and stow at a flat rate of 80 uph. Therefore, Option B seems the answer. The percentage errors and the follow up questions seem to be trick questions. In Option A after 1 hour there is 0.71 items misplaced v.s. 1.2 items for Option B or a difference of 0.49 items/hour misplaced, which does not overcome the approximate 9 unit / hour advantage Option B has over Option A and the more hours / units / employees you throw at the problem seem to just compound the advantage of Option B over Option A.

Option B all the way. 250/ hour for receiving and 100/hour for stowing= 3.5 man hours/ 250. Option 1 has 71 uph Option 2 has 80 UPH With these facts and my main goal is productivity: 1) Option B 2) Option B takes 1325 man hours for receiving, stowing and corrections Option A takes 1450 man hours for the same. So option B is chosen 3) I am assuming a 10 hour shift for the 15 people so 150 man hours. In 150 man hours, option A yields 10,543 correct pieces at 1% error rate option B yields 11,820 correct pieces at 1.5% error rate option B again. option B all the way

Option 2 is the answer for both Q1 & Q2 just because it's done in one step hence generating a greater throughput in any time frame and for any target volume. In 1 hour you have received 250 units in Option 1 but have not stowed any units since it's a 2-step process and the receiving must be done first. On the other hand, in 1 hour you have received and stowed 80 units in Option 2. Option 2 is also the answer for Q3 because in 1 hour you have received and stowed 80*16 = 1,280 units meaning the stow rate is then 1,280 uph. There are 15 associates plus myself equaling 16 laborers. Alternatively in Option 1, the most efficient way to allocate the associates is at a receiving:stowing ratio of 1:2.5 so that the two rates are identical. Hence the maximum number of associates that can be allocated to stowing is then 11 (it's actually 11.43 but that's not feasible). Hence within 1 hour Option 1 can stow a total amount of 11*100 uph = 1,100 units meaning the stow rate is then 1,100 uph. As you can see then the stow rate from Option 1 is lower than that from Option 2 hence the answer is Option 2 for Q3 as well.

so many different answers above.. anyone has true answer to part C? I think 1st 2 questions are more clear - option B is better... but w/ 15 associates, I tend to think option A is better.. but not sure... anyone has a more recent math problem presented at on-site interview?

30 associates, 2 are indirect (they don't count towards the production) 150 units p/h per associate 5 day week 8 hour days, 2-15 min breaks. How much production in 40 hour workweek. I came up with 165900 units per week for the crew. Follow up: We want to increase production by 10000 units per week, how many additional associates do we need? With production per associate at 5925 per week, 1 is too few, 2 will give us some leeway as we will have extra production capacity.

First Option: Assume 'x' units have to be processed a day - Total no of people required in first case will be (x/250) for receiving+(x/100) for stowing +(1/100)(x/20) for correcting the errors = 0.0145x Second option requires : (x/80) for both receiving and stowing +(1.5/100)(x/20) for error correction = 0.01325x So second option requires less workforce for whatever quantity of x it may be

What I did was the following: Compare production if I had 10 people working on each project. It could have been 10 or 4 or 1,085 as long as they were equal. Option 1 at 10 people: 3 people to receive and 7 to stow helped to do 750 units/hr receiving and 700 units/hr stowing. Therefore production is really 700 with 50 that still needed to be stowed at .5 labor hour. Option 1 error rate at 700 units was 70. That takes 3.5 labor hours to correct Option 2 at 10 people = 800 units per hour received and stowed Option 2 error rate at 800 was 120. That takes 6 labor hours to correct. Option 2 looks better because at 10 people, if I used 9 to do the receiving/stowing I would still produce 720 and would have 1 person to correct all errors during the same shift with some time left over. For Option 1 if I went 3 people to receive (750) and 6 to stow (600) and 1 to correct errors (3.5 hrs) and stow (4.5 hrs) 55 units I'd still have some excess to stow. I can't figure out the exact equation, but Option 2 definitely looks better. I think most organizations want managers who can figure out the best, if not most precise, solution. Then, they want the manager to get back to work to take care of people. Also, people aren't fractions. You can fractionate their days by giving them different tasks but I think you have to take a pragmatic approach to creating a real solution. I chose Option 2 and I don't think it matters whether there were 100,000 units required or 1,000,000. The equation is still going to be less efficient during Option 1 because of the requirement to receive and stow separately.

Option 1 says that the parts should be received and stowed for you thing into production...so per hour count will just be 100 units/hr. Comparing that with Option 2 ( which has a lower units/hr and higher error rate), option 1 would be favorable.

Option 2 is always favourable as the scenario reads 80UPH for receiving and stowing, it a one step process rather than a two step process for option 1. with this in mind option 1 will take 14.5 hours and option 2 will take 13.25 hours. regardless of the scale of the order, option 2 is always more productive, efficient and effective.

I’m cross trained in every thing it doesn’t work like this the yard has at least 250 k just sitting there and the bins are at 102% full being a vet there option one just to get it in the yard option A but I would go wit

option two appears to be the best option as it only takes 80 labor units to get the product stored....with a 1.5% error rate...go with option 2

15 associates Option 1: 4 receiving (1000uph) and 10 stowing (1000uph) with 1 for errors (10uph so we are wasting .5 hours or he can work at a slower pace). Total output of 15 associates PER HOUR is 1000 Option 2: 14 receiving and stowing (1120uph) with 1 for errors (16.8uph so we are wasting less time). Total output of 15 associates per hour is 1120. Remember for both examples the errors are corrected, you just waste resources (1 associate) to have them correct. I looked at a lot of answers so this may be wrong. Using 1000 units also gives the same answer - option B

Interesting question and one that will require some review BEFORE the interview!!!! Keep focused on what the questions are specifically what information is provided and what information is omitted!! I will provide my response first than provide workflow to how I derived my understanding. The Questions 1. Which option would you select to process today's units and why? 2. Does your answer change if you are told you must fully process 100,000 units today? If yes, why? 3. Does your answer change if you are told that you have 15 associates today and you must fully produce the maximum amount of units possible? If yes, why?" My Response: 1. no information provided on inbound units or available associates; my choice is Step 2 the receive and stow option. Reasons that will be supported later; the time required to complete 1000 inbound units (made up number) is completed faster with option 2 than in option 1 even including the high error rate with option 2. 2. My answer will not change because the information for associates are not provided and the rate of production per hour remains the same. Option 2 is still the faster method. 3. 15 associates and still no provided information of inbound units, my answer will change to Option 1 as this is the faster option. My workflow: Doing a chart with a preset 1000 inbound units i set up a chart for each step and computed the production per 1,5,10,15,20,30 associates.One may compute production per hour however, I look at how long a specific job will take because one's superior wants 'how long' so consider this an efficient at-a-glance and on-the-spot estimation..... Error Rates/1000 Unit 1% @ Step 1 (1000*.01) 10 errors per 1000 units --> 30 minuets add for error 1.5% @ Step 2 (1000*.015) 15 errors per 1000 units --> 45 minuets add for error Check your error math: Error Correction rate Per Hour (60/20) ---> 3 corrected units per minuets 10 errors (3*10) = 30 minuets 15 errors (3*15) = 45 minuets Step 1: Receive then Stow (250 units/hour + 100 units/hour) Step 1 Receive Receive Units Associates 1 5 10 15 20 30 Inbound Units 1000 250 Units/Hour Units/Hour 250 1250 2500 3750 5000 7500 Hours 4 0.8 0.4 0.266666667 0.2 0.133333333 Minuets 240 48 24 16 12 8 Step 1 Stow Associates 1 5 10 15 20 30 Stow Units 1000 100 Units/Hour Units/Hour 100 500 1000 1500 2000 3000 Hours 10 2 1 0.666666667 0.5 0.333333333 Minuets 600 120 60 40 30 20 Hours 14 2.8 1.4 0.933333333 0.7 0.466666667 Minuets 840 168 84 56 42 28 Add Error 30 30 30 30 30 30 Minuets 870 198 114 86 72 58 Hours 14.5 3.3 1.9 1.433333333 1.2 0.966666667 Step 2: Receive and Stow (80 units/hour) Step 2 Associates 1 5 10 15 20 30 Inbound Units 1000 80 R+S units/Hour Units/Hour 1000 400 800 1200 1600 2400 Hours 12.5 2.5 1.25 0.833333333 0.625 0.416666667 Minuets 750 150 75 50 37.5 25 Add Error 45 45 45 45 45 45 Minuets 795 195 120 95 82.5 70 Hours 13.25 3.25 2 1.583333333 1.375 1.166666667 Now take a deeeeeep breath, the math is not intensive, the objective with the above is only to understand the productive relationship between each option. The differences between each are very close meaning that one option was only minuets better than the other and really wont have a serious impact on overall production which ever option one chooses; however, the merits of the question are for one to understand the differences and define why one chooses which option. my answer changed from option 2 to option 1 in question 3 because option 1 actually completed the job 9 minuets faster per the chart....which suggests that the number of associates significantly influence production regardless of error rate......I hope this helps and not further confuses anyone. Great luck to all of you in your interviews.

a: I would choose option 2. It is a more productive operation using less hours per day. You need 2.5 times more stowers in option 1 to manage the receiving or you get backed up. Stowing 250/hr generates 2.5 error/hr, so 20 errors that shift should be fixed by the same crew of 4x. Option 2 generated 1.2/hr x 8 or 10 errors in a shift. Fixable by the crew of 3x. X being the unknown variable of how may units can an employee manage per hour. You would produce less units but do it it a more efficient/productive manner cost wise. b. I would then use option A, it produces more units per hour. It costs one labor unit more but would be needed for a bottleneck to process more jobs per hour when needed. Up the stowing crew to balance with receiving and you are stowing 250/hr. c. Option A produces more units/hr with lower errors but higher net labor cost. If the goal is only unit driven you would likely want to do A. If errors were also a high concern, I would do a hybrid version of this. Unless the receiving/stowing ratios are constraints related to equipment or plant design, then you would use A. Hired? Hope os, first interview on Tuesday. (bites nails) Side note: The error rates seem low to me on both. 250/hr gets you 3 units wrong per hour. Not that it insignificant but I would guess the team could absorb and correct them with less than a unit of the labor variable.

I would have thought Opt 1 is better. Purely for the number of items being churned out and lower error rate. Sean: The error rate is 1% so would be 7 and not 70!!!