Random generation of employee assignments

[Blue Max]

We have 65 work assignments and must randomly re-assign them to our
employees each month. We have given each work assignment a number 1-65.
How do we randomly re-shuffle a list of 45 whole numbers at the beginning of
each month?

Once we have learned how to perform the random re-shuffle above, we would
also like to learn how to tailor the random assignments as follows:

First, how do we prevent an employee from being re-assigned the same
assignment they performed last month or perhaps the last 3 months?

Second, how do we prevent employees from receiving certain random numbers
that represent tasks they are not capable of performing? In other words,
how do we prohibit an employee from being assigned a subset of certain tasks
(task numbers) included in the comprehensive list of tasks?

Thank you for any help with this question.

[JoeU2004]

"Blue Max" <mailr...@msn.com> wrote:
> We have 65 work assignments and must randomly re-assign
> them to our employees each month. We have given each
> work assignment a number 1-65. How do we randomly re-shuffle
> a list of 45 whole numbers at the beginning of each month?

I'm confused. Do you have the same number of work assignments as employees?
Or do you have 45 employees that you need to assign randomly to 65 work
assignments?

The first (same number) is easy.

Ostensibly, create a column of 65 cells, say A1:A65, with the formula
=RAND(). Then create a column of 65 cells, say B1:B65, with the following
formula in B1 and copy it down:

=RANK(A1,$A$1:$A$65)

Pay close attention to the use of relative and absolute references.

Gotcha!.... The RAND() values will change every time you modify any(!) cell
in the workbook and every time you open the file, normally. Presumably that
is not what you want.

One simple way to avoid that is use the following macro and replace =RAND()
with =myrand():

Function myrand(Optional arg)
Dim first
If first = 0 Then Randomize: first = 1
myrand = Rnd
End Function

The optional arg makes it easy to generate a new set of random values.
Simply use =myrand($C$1). Then, a new set of random values are generated
whenever C1 is changed (e.g. pressing Delete).

> Once we have learned how to perform the random
> re-shuffle above, we would also like to learn
> how to tailor the random assignments as follows:

Applying these constraints are feasible. But they require, or at least are
best implemented by, a macro. A good design of that macro is non-trivial
and goes beyond the scope of what I can deal with here. My suggestion is
that you higher an experienced Excel/VB programmer to implement it.

FYI, a "bad design" is certainly easier. A "bad" design will iterate the
random selection until the necessary constraints are met. Such a design is
not guaranteed to work in a finite amount of time, and if it does work, it
may or may not take a very long time, depending on stochastic properties.
Caveat emptor!

----- original message -----

"Blue Max" <mailr...@msn.com> wrote in message
news:D313B623-94FF-49A4...@microsoft.com...

[Blue Max]

Thanks Joe. In our case, we have 65 employees and 65 unique schedule
configurations (not tasks) that combine specific tasks in differing order.

I appreciate your suggestions, especially the controllable macro. How about
using the 'Data Analysis' pack included with Excel? Does it include any
additional functionality?

Thanks

*********************
"JoeU2004" <joeu...@hotmail.com> wrote in message
news:uEhnuvS...@TK2MSFTNGP06.phx.gbl...

[JoeU2004]

"Blue Max" <mailr...@msn.com> wrote:
> How about using the 'Data Analysis' pack included
> with Excel? Does it include any additional functionality?

Sorry, I'm not familiar with that.

> we have 65 employees and 65 unique schedule configurations (not tasks)
> that combine specific
> tasks in differing order.

I provided a solution for exactly what you asked for initially, namely:
"How do we randomly re-shuffle a list of 45 whole numbers [...]?"

But I suspect the following might be more useful.

Suppose you have a column of configurations in A1:A65 and a column of
employees in C1:C65. Fill D1:D65 with the formula =myrand() or =RAND().
Then put the following formula into B1 and copy down through B65:

=INDEX($C$1:$C$65,RANK(D1,$D$1:$D$65))

Again, pay close attention the use of relative and absolute references.

This randomly assigns employees in B1:B65 to respective configurations in
A1:A65.

----- original message -----

"Blue Max" <mailr...@msn.com> wrote in message

news:5FE30397-64CC-49F8...@microsoft.com...

[Rob Jordan]

I have a solution that should work for you, and implements all the features
you wanted. Hopefully these steps are easy to follow. If not, let me know.

We need to first build the table that holds the tasks the the employees
cannot do. In a new workbook, on Sheet2, enter "EE - Task", "EE ID", and
"Task ID" into A1:C1. In A2, enter the formula "=B2&" - "&C2". In B2 and C2,
enter the Employee unique identifier (ee id, or SSN or possibly name), and a
SINGLE task id that that employee cannot complete. Fill out the rest of the
table by copying down the formula in column A and entering the EE ID and Task
ID. Name this whole table TaskTable (just select the whole table and type
TaskTable in the Name Box).

Now for the task assignment page.
1. On Sheet1, type the following column headers into A1:H1 : Employee, Rand,
New Task, Current Task, Last Task, Prior Task, Is New Task, Can do Task
2. Type "=Rand()" into B2
3. Type "=RANK(B2,$B$2:$B$66)" into C3
4. Type "=AND(C2<>D2,C2<>E2,C2<>F2)" into G2.
5. Type "=ISNA(MATCH(A2&" - "&C2,TaskTable,0))"
6. Copy row 2 down to row 66.
7. Cells A2:A66 need to uniquely identify the Employee. You can use EE IDs
or SSNs or whatever works for you. The values you entered in the TaskTable
must be a subset of these values.
8. Cells D2:F66 track the employees' three months history of task IDs. These
should be integers from 1 to 65.

Now we'll add the row that checks for a valid solution.
9. In A68, type "Found Solution?"
10. In C68, enter the formula "=SUM(C2:C66)=COUNT(C2:C66)*(COUNT(C2:C66)+1)/2"
11. In G68, enter the formula "=AND(G2:G66)"
12. In H68, enter the formula "=AND(H2:H66)"
13. In I68, enter the formula "=AND(C68,G68,H68)"

In order to generate a solution, hit the F9 key (which recaluates the
formulas, generating new random numbers). Watch cell I68. When this cell
shows TRUE, you have a valid solution. You may want to turn on Manual
Calculation so that the workbook doesn't automatically recalculate and reset
your solution.

--
Rob Jordan
Powered by Creative Laziness

[Blue Max]

Thanks Rob, this looks promising, but will take me awhile to fully digest.
When I get a handle on your example I may have more questions. Any way to
send me a sample worksheet with your example? Meanwhile, I do have one
question. What if the employee has several tasks they are incapable or
unauthorized to perform? Your example, on the surface, appears to only
accommodate one invalid task.

For example, can the list of unauthorized tasks for an employee be saved as
an array and used in the process to narrow the available population of tasks
for that employee? For example, can we start with a total array of 65
tasks, reduce it by any limitations, randomly select a task for the first
employee, and then pass the residual array on to the subsequent employee for
making a similar assignment until all tasks are assigned out?

If I had to summarize our problem in narrative I would do so as follows: We
have a total population of 65 tasks (or schedule assignments). They are
assigned to successive employees without replacement until all 65 tasks are
assigned out. Each successive employee is given an assignment from a
diminishing population of available tasks. Furthermore, the population of
tasks available to any successive employee may be further reduced by the
tasks that they are not authorized to perform. Off course, this means we
may need to process employees with limitations first so that we don't end up
with a residual population that offers no authorized tasks for an employee.

Thanks for your help.

************************
"Rob Jordan" <RobJ...@discussions.microsoft.com> wrote in message
news:AB9C3C74-77AA-4629...@microsoft.com...

[Mukayi Mutsago]

Hello Joe,

I have a similar problem to what you posted here except that all my employees can do any task. Did you ever got this to work. If so can you send me a copy of how you wrote your excel formulas. In Rob's example I can find out how Sheet1 is linked to sheet2. I typed everything as he said but my employees and tasks in sheet2 are not connected to sheet1 at all. Let me know.

Thanks
Muk

[Auric__]

Mukayi Mutsago wrote:

> I have a similar problem to what you posted here except that all my
> employees can do any task. Did you ever got this to work. If so can you
> send me a copy of how you wrote your excel formulas. In Rob's example I
> can find out how Sheet1 is linked to sheet2. I typed everything as he
> said but my employees and tasks in sheet2 are not connected to sheet1 at
> all. Let me know.

Dude. The original post was 11 years ago.

> On Tuesday, October 6, 2009 at 11:41:23 PM UTC-4, Blue Max wrote:

^^^^^^^^^^^^^^^^^^^^^^^^

Rather than reply to a long-dead thread, why not just, y'know, ask a
question? I for one am not will to go dig through the Google archives to read
the original posts.

--
A wise man distrusts his neighbor.
A wiser man distrusts both his neighbor and himself.
The wisest man of all distrusts his government.

[Auric__]

Auric__ wrote:

> Mukayi Mutsago wrote:
>
>> I have a similar problem to what you posted here except that all my
>> employees can do any task. Did you ever got this to work. If so can you
>> send me a copy of how you wrote your excel formulas. In Rob's example I
>> can find out how Sheet1 is linked to sheet2. I typed everything as he
>> said but my employees and tasks in sheet2 are not connected to sheet1
>> at all. Let me know.
>
> Dude. The original post was 11 years ago.
>
>> On Tuesday, October 6, 2009 at 11:41:23 PM UTC-4, Blue Max wrote:
> ^^^^^^^^^^^^^^^^^^^^^^^^
>
> Rather than reply to a long-dead thread, why not just, y'know, ask a
> question? I for one am not will to go dig through the Google archives to
> read the original posts.

Ah, I see. You did ask. Well, wait for someone to answer, or google it, or
figure it out for yourself. Replying after 11 years is silly.

--
If you can write out an idea in English,
you're halfway to writing it in C.