I posted a week or so ago and have been successful based on the response I
got. I have a new but similar question that i am trying to solve for with
another layer of complexity:
I Know that it took 6980 hrs to produce the volume below.

ND take twice as long as R and R takes twice as long as M to do. (4T, 2T, T)
I also know that:
based on Coll Complex 1 takes less time then 2 and 2 takes less time then 3
and 3 takes less time then 4.
I also know that:
ND1 1 takes less time then ND 2 which takes less time then 3
same with R items and M items

based on the volume of each type, how long does each type take? can solver
do this?

ND - 1 ND - 2 ND - 3
Coll Complex 1 18 9 9
Coll Complex 2 9 5 5
Coll Complex 3 9 5 5
Coll Complex 4 15 7 7

RD 1 RD 2 RD 3
Coll Complex 1 30 15 15
Coll Complex 2 5 3 3
Coll Complex 3 10 5 5
Coll Complex 4 12 6 6

M 1 M 2 M 3
Coll Complex 1 37 19 19
Coll Complex 2 7 3 3
Coll Complex 3 12 6 6
Coll Complex 4 15 7 7

Hi. If you haven't gotten any responses yet, here is my guess.
I believe you have too many possible combinations that are valid.
To "narrow it down" I tried to see if there were any possible integer solutions.
If we start with the time for the M array, suppose we start with a time s.
One possible array for this first row is

v = {s, c1 + s, c1 + c2 + s};

Where we start with s, and c1 is a time increase for the next column.
The last column is larger than the middle column by adding c2.
We also increase each row by a certain amount k1, k2, and k3.

m = {
v,
k1 + v,
k1 + k2 + v,
k1 + k2 + k3 + v}

The times for RD is twice that of m.

rd = 2*m

And the times for nd are 4 times that of m

nd = 4*m

If we do the math, the equation is reduce to:
394*c1 + 197*c2 + 444*k1 + 333*k2 + 193*k3 + 783*s = 6980

I show there are about 166 integer solutions to this Diophantine equation.
However, many of them have 0 as a start s, so these are infeasible.
I show that there are 29 solutions that are reasonable.

If I pick one of the solutions, say...
{s - 2, c1 - 4, c2 - 4, k1 - 3, k2 - 4, k3 - 2}

Then the times for your M array a

{2, 6, 10},
{5, 9, 13},
{9, 13, 17},
{11, 15, 19}}

The times for your RD array a

{4, 12, 20},
{10, 18, 26},
{18, 26, 34},
{22, 30, 38}}

And the ND times a

{8, 24, 40},
{20, 36, 52},
{36, 52, 68},
{44, 60, 76}}

Again, there are many solutions.
This is just one way limit the search by asking for an integer solution.

--
Dana DeLouis


"Belinda7237" wrote in message ...

I posted a week or so ago and have been successful based on the response I
got. I have a new but similar question that i am trying to solve for with
another layer of complexity:
I Know that it took 6980 hrs to produce the volume below.

ND take twice as long as R and R takes twice as long as M to do. (4T, 2T, T)
I also know that:
based on Coll Complex 1 takes less time then 2 and 2 takes less time then 3
and 3 takes less time then 4.
I also know that:
ND1 1 takes less time then ND 2 which takes less time then 3
same with R items and M items

based on the volume of each type, how long does each type take? can solver
do this?

ND - 1 ND - 2 ND - 3
Coll Complex 1 18 9 9
Coll Complex 2 9 5 5
Coll Complex 3 9 5 5
Coll Complex 4 15 7 7

RD 1 RD 2 RD 3
Coll Complex 1 30 15 15
Coll Complex 2 5 3 3
Coll Complex 3 10 5 5
Coll Complex 4 12 6 6

M 1 M 2 M 3
Coll Complex 1 37 19 19
Coll Complex 2 7 3 3
Coll Complex 3 12 6 6
Coll Complex 4 15 7 7

thanks, i appreciate your thoroughness in explanation - how are you
determining the amount of interger solutions - i think i am using solver
inappropriately which is impairing my ability to solve these on my own?

"Dana DeLouis" wrote:

Hi. If you haven't gotten any responses yet, here is my guess.
I believe you have too many possible combinations that are valid.
To "narrow it down" I tried to see if there were any possible integer solutions.
If we start with the time for the M array, suppose we start with a time s.
One possible array for this first row is

v = {s, c1 + s, c1 + c2 + s};

Where we start with s, and c1 is a time increase for the next column.
The last column is larger than the middle column by adding c2.
We also increase each row by a certain amount k1, k2, and k3.

m = {
v,
k1 + v,
k1 + k2 + v,
k1 + k2 + k3 + v}

The times for RD is twice that of m.

rd = 2*m

And the times for nd are 4 times that of m

nd = 4*m

If we do the math, the equation is reduce to:
394*c1 + 197*c2 + 444*k1 + 333*k2 + 193*k3 + 783*s = 6980

I show there are about 166 integer solutions to this Diophantine equation.
However, many of them have 0 as a start s, so these are infeasible.
I show that there are 29 solutions that are reasonable.

If I pick one of the solutions, say...
{s - 2, c1 - 4, c2 - 4, k1 - 3, k2 - 4, k3 - 2}

Then the times for your M array a

{2, 6, 10},
{5, 9, 13},
{9, 13, 17},
{11, 15, 19}}

The times for your RD array a

{4, 12, 20},
{10, 18, 26},
{18, 26, 34},
{22, 30, 38}}

And the ND times a

{8, 24, 40},
{20, 36, 52},
{36, 52, 68},
{44, 60, 76}}

Again, there are many solutions.
This is just one way limit the search by asking for an integer solution.

--
Dana DeLouis


"Belinda7237" wrote in message ...
I posted a week or so ago and have been successful based on the response I
got. I have a new but similar question that i am trying to solve for with
another layer of complexity:
I Know that it took 6980 hrs to produce the volume below.

ND take twice as long as R and R takes twice as long as M to do. (4T, 2T, T)
I also know that:
based on Coll Complex 1 takes less time then 2 and 2 takes less time then 3
and 3 takes less time then 4.
I also know that:
ND1 1 takes less time then ND 2 which takes less time then 3
same with R items and M items

based on the volume of each type, how long does each type take? can solver
do this?

ND - 1 ND - 2 ND - 3
Coll Complex 1 18 9 9
Coll Complex 2 9 5 5
Coll Complex 3 9 5 5
Coll Complex 4 15 7 7

RD 1 RD 2 RD 3
Coll Complex 1 30 15 15
Coll Complex 2 5 3 3
Coll Complex 3 10 5 5
Coll Complex 4 12 6 6

M 1 M 2 M 3
Coll Complex 1 37 19 19
Coll Complex 2 7 3 3
Coll Complex 3 12 6 6
Coll Complex 4 15 7 7

Hi. Feel free to send my your email address, and I'll send a workbook over to you.
You can look at it to get some general ideas.
Let me know what Excel version you have also.

--
Dana DeLouis


"Belinda7237" wrote in message ...

thanks, i appreciate your thoroughness in explanation - how are you
determining the amount of interger solutions - i think i am using solver
inappropriately which is impairing my ability to solve these on my own?

"Dana DeLouis" wrote:


<snip

thanks, its and I have Excel 2003

"Belinda7237" wrote:

I posted a week or so ago and have been successful based on the response I
got. I have a new but similar question that i am trying to solve for with
another layer of complexity:
I Know that it took 6980 hrs to produce the volume below.

ND take twice as long as R and R takes twice as long as M to do. (4T, 2T, T)
I also know that:
based on Coll Complex 1 takes less time then 2 and 2 takes less time then 3
and 3 takes less time then 4.
I also know that:
ND1 1 takes less time then ND 2 which takes less time then 3
same with R items and M items

based on the volume of each type, how long does each type take? can solver
do this?

ND - 1 ND - 2 ND - 3
Coll Complex 1 18 9 9
Coll Complex 2 9 5 5
Coll Complex 3 9 5 5
Coll Complex 4 15 7 7

RD 1 RD 2 RD 3
Coll Complex 1 30 15 15
Coll Complex 2 5 3 3
Coll Complex 3 10 5 5
Coll Complex 4 12 6 6

M 1 M 2 M 3
Coll Complex 1 37 19 19
Coll Complex 2 7 3 3
Coll Complex 3 12 6 6
Coll Complex 4 15 7 7