Hours/ability

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Carinca86

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Jul 23, 2020
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Hi, I wonder if someone can help me putting a formula together to calculate an ability.

Example:

I have 100h available on my shift.

We are picking and packing.
Picking: 86 units per hour
Packing: 20 parcels per hour (each parcel consist of 1.9 units in average)

Problem: how many units can be picked and how many parcels can be packed per shift having 100h available in total?

Thanks in advance!
 
P.S. I tried to work it out per hour.
Packing 14 parcels and picking 26.6 (with average 1.9 unit per hour) will take 61.95 mins. That's the closest to an hour that I've managed to work out but it was more trial an error calculation. I still need a formula that I can put onto a spreadsheet that will calculate ability depending on hours available.
 
86+20 = 106. You want 100. What do you multiply 106 by to get 100? Multiply 86 and 20 by this special number.
 
Carinca86 said:
I have 100h available on my shift.

We are picking and packing.
Picking: 86 units per hour
Packing: 20 parcels per hour (each parcel consist of 1.9 units in average)

Problem: how many units can be picked and how many parcels can be packed per shift having 100h available in total?
Click to expand...
Carinca86 said:
P.S. I tried to work it out per hour.
Packing 14 parcels and picking 26.6 (with average 1.9 unit per hour) will take 61.95 mins. That's the closest to an hour that I've managed to work out but it was more trial an error calculation. I still need a formula that I can put onto a spreadsheet that will calculate ability depending on hours available.
Click to expand...

I don't understand the work. I thought the 1.9 units per hour was for packing 1 parcel, not for picking.

In any case, it seems to me that in 100 hours you could pick 86*100 units, or pack 20*100 parcels, which is 20*1.9*100 units; or you could combine in many ways. Or is there a constraint, such as that the number of units picked and packed must be equal?

Must the number of parcels, or units, be a whole number?
 
Thanks for answers, I have worked it out.

I had to calculate it by order, not hour.

So...

We pack 20 parcels per hour so 1 parcel in 3 minutes. There is in averege 1.9 units in parcel. We pick 86 units per hour, to pick 1.9 units it takes 1.33 minutes. So to pick an pack 1 parcel: 3+1.33= 4.33.

My formula:

Hours available per shift*60/4.33

That will tell me how many orders can be completed per shift.

Example:

100 hours available

100x60/4.335=1384.68
1384.68*1.9=2630.89

So... Having 100 hours available and taking into consideration we have to pick 1.9 units per parcel I can estimate that we will pick 2630.89 units and pack 1384.68 parcels.
 
How many parcels do 86 units produce? How long does it take to pack this number of parcels? You now know the total time it takes to pick 86 units and pack them into parcels. You can proportion this to find out how much you can pick and pack in 100 hours.
 
I think I understand what you're after. Phrasing a question in math is a pretty hard problem. Please respond if I've misunderstood. And since you're not a student I'm going to give you most of the answer, but I'll leave some work for you to complete at the end!


Let x = total units picked
Let y = total parcels packed
Let \(c_1\) = 1.9 = average units in a parcel

Let t = total time (hours)
Let \(t_x\) = time spent picking (hours)
Let \(t_y\) = time spent packing (hours)

A) Pick 86 units per hour

[math]t_x = \frac{x}{86}[/math]
B) Pack 20 parcels per hour

[math]t_y = \frac{y}{20}[/math]
C) Each parcel consists of c1 units

[math]x = y \cdot c_1[/math]
D) Time constraints

[math]t=t_x+t_y[/math]
A and B into D gives...

E) [math]t = \frac{x}{86} + \frac{y}{20}[/math]
Using C...

[math]t = \frac{y\cdot c_1}{86} + \frac{y}{20}[/math]
[math]t = y\cdot \left( \frac{c_1}{86} + \frac{1}{20} \right)[/math]
[math]y = \frac{t}{ \frac{c_1}{86} + \frac{1}{20}}[/math]
[math]= \frac{20 \times 86 \times t}{20c_1 + 86}[/math]

If t=1, then y≈13.8709677

NOW can you rearrange equation E so that you can tell me the value of x (given that we know the value of y)
 
I am answering only the original OP.
Following my leads earlier gives a four line solution.
In one hour, you pick 86 items; these produce 86/1.9 parcels.
These parcels take 86/(1.9 x 20) hours to pack.
So (1 + 86/(1.9 x 20)) = (38 + 86)/ 38 = 124/38 hours to pick and pack for 86 items.
So in 100 hours you pick and pack 86 x (38/124) x 100 = 2635 items. From which you easily calculate the number if parcels.
 
For some reason posts#6 and #7 didn't appear on my screen before I made my post #8. Perhaps the forum is running slow today (or maybe I need more coffee). But I guess it can be good to see that there are many ways to approach/ solve a problem!

EDIT: actually the posts were probably awaiting moderator approval, because they are within the first five posts made by those people
 
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Carinca86 said:
Hi, I wonder if someone can help me putting a formula together to calculate an ability.

Example:

I have 100h available on my shift.

We are picking and packing.
Picking: 86 units per hour
Packing: 20 parcels per hour (each parcel consist of 1.9 units in average)

Problem: how many units can be picked and how many parcels can be packed per shift having 100h available in total?

Thanks in advance!
Click to expand...
I wonder if the problem ACTUALLY is:

how many units can be (picked and packed) per shift having 100h available in total?
 
Subhotosh Khan said:
I wonder if the problem ACTUALLY is:

how many units can be (picked and packed) per shift having 100h available in total?
Click to expand...

...or "how many units can be picked and packed, such that all of the picked units end up being packed, within a shift of 100h"

EDIT: Actually, after several re-readings, I think Subhotosh's way of writing the question does imply that each picked unit has to end up being packed. I'm not always very good with words!
 
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