Major help needed - Iterative Functions

[LiAD]

Hello,

I have a complicated problem which is dificult to explain easily I think.
I will try and lay out the basic concept. What I would like to know is how
can I achieve this in excel.

I have a list of products A B C for example which I will produce during a
set period of gg days on one single machine. The knowns are
- It takes xx hours to produce A, yy for B, zz for C
- If I change from one product to another it takes 4 hours to retool the
machine (from A to B, B to C etc for all changes)
- The production date that each product must be finished

Customers, (being difficult), would like me to deliver in the following
order A B C A C A C B. This presents two potential problems
- Time may be restricted
- If I do follow the customers orders exactly I need to spend a lot of time
changing over my machine. Time wasted that maybe I can use to find more
products or customers.

What would be nice is to have a tool in excel that can answer the question -
can I change the order in which I will manufacture the products and still
meet the customer delivery requirements? If so give me a production schedule.

So I have a table from which I know the products and dates the customer
wants. From the production and tool change times required I can calculate
when it will be possible to make each product. Then I would like to find
some way to get excel to produce a production schedule by optimising the
manufacturing order to reduce the amount of tool changes, (and therefore
total time spent on them), ensuring that all of my orders respect the
customer dates.

The function/method needs to group similar products together providing
- manufacture is finished on or before the customer date
- the resort process does not make any other products late (as in if the
customer asks to have A B A but I re-organise to A A B maybe the A's are
great but I have made the B late).

An important point to consider is that I have only one machine therefore it
is one product after another so the time that product 2 is finsihed is time
of day the line was started + manufacture time for product 1 + tool change
time + time to make product 2.

The function, (in my opinion), needs to iterative as basically it will
re-organise the manufacturing order, check that all orders will be finished
within date, if not re-organise and recheck etc etc.

Is this possible and if so how in terms of function design etc?

Thanks a lot. I hope its clear enough, if not please ask. I'll well stuck
in tables and tables and tables.

LiAD

 

[joel]

The problem can be sove with programming but you need some additional
information to get started. First how much inventory do you have and does
your delivery dates start immediatel or do you have some lead time? Also how
many hours a day are you working and is there any penaties for working over
time?

The solution for the problem is to set up some criteria(s) whre you are
going to retool and then compare the results to determine the best solution.
The best solution would be to minimze being late and to build up as much
inventory as possible. One questtion you didn't specify is if each order is
a custom order or are there standard products. Each product could come in
100 different colors so you wouldn't be able to build up inventory, every
order is a custom order.

One soilution could be to change products every two days. Another solution
would be to continue making one product until you wold become late on one of
the other two products and switch so you are making a product "Just-In-time".

This problem seems like a modeling solution is the best approach. In
modeling your run a 1000 (or any fixed number) of attempts. Set criteria X =
number of days until you retool (make number 1 to 10) and Y when you retool
which product you change to (could be the same product. then keep a history
of the results keeping only the best results.


for i = 1 to 1000
X= int(10*rnd())+1
Y= int(3*rnd())+1 product A = 1 Product B = 2 Product C = 3

for Days = 1 to 100
'run your production line and vaidate if you met your criteria

next Days

next i

 

[LiAD]

To take ur points one at a time. Assume that

- inventory is zero it all needs to be manufactured.
- manufacturing can start at today()
- prod is 24 hours mon-fri
- in reality the product range is massive so its more or less custom orders.
reoccuring orders will be dealt with another way. This tool does not need
to take care of those orders.
- Rather than picking a number of days between retools I would rather than
excel told me when i had too. When I have to could be based on your JIT
approach, perfect. Dates will decide when products will be scheduled.
- no penalties or cost analysis needed just balance what we need to produce
against optimising machine running time.

I could start with the most urgent product. Ask excel to find all products
that are the same as the urgent product, schedule them all together, then
just before the next product will be late schedule a change and so it
continues. Nice approach and i think that would work for this case.

In terms of developing a macro to run this - at the moment thats beyond my
knowledge.

What do you mean by keep and history and the best results? Lots of
schedules are produced and you just pick the best one?

I know details are a bit vague for now, but once i see if the approach may
work then I can put some fat on the bones.

Thanks a lot for your help
LiAD

 

[joel]

I don't have any idea on the quantities or time to make each item so it is
hard to get to a correct solution. A JIT approach would require finding the
latest date to start an order and the time required to make the item.

to try evvery combination would requir e chaing the which orderr you build
first, then 2nd and thrid going though every combination or build sequencies.
if you had 10 orders then try each combination

Below is a table of the orders and the sequence built. the 1st row is
building the order in sequence. The 2nd row is the same except building
order 10 before order 9.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1, 2, 3, 4, 5, 6, 7, 8, 10, 9
1, 2, 3, 4, 5, 6, 7, 9, 8, 10
1, 2, 3, 4, 5, 6, 7, 9, 10, 8
1, 2, 3, 4, 5, 6, 7, 10, 8, 9
1, 2, 3, 4, 5, 6, 7, 10, 9, 8
1, 2, 3, 4, 5, 6, 8, 7, 9, 10
1, 2, 3, 4, 5, 6, 8, 7, 10, 9
and so on

the solution would be to try every combination and determine how many orders
were late, the number of times you had to retool, and the number of days you
shipped before the due date.

 

[LiAD]

So from one input table I would need to create every possible output
combination then select the one thats best. Seems workable.

What function or type of macro is best to use that would to generate all the
tables automatically?

Thanks

 

[LiAD]

Just made a quick calculation to see if this is possible.

My production schedule will be 40-80 lines long. 80! = a huge number, a lot
more than the 65000 lines thats in excel meaning I would not have space to
generate every possible version of the table.

Would there be a way of excel just outputting an optimised solution?

Thanks
LD

 

[joel]

It would be a recursive algorithm. I have a bunch of them that I mdofiy as
required. You would need to re-run the program as new order are placed like
every night or once a week becaue plans always change.

Here is the recursive code that will put the combination on sheet 1 so you
can see the results. Put a small number in becasue the combinations are
large and may exceed the number of rows you can have in a worksheet. You
willnot be saving all the combinations so the size of the worksheet is not a
factor.

Public Orders()
Public combo
Public RowCount As Long
Sub permuations()

NumberofOrders = InputBox("Enter Number of orders")
ReDim Orders(NumberofOrders)
For i = 1 To NumberofOrders
Orders(i) = i
Next i

ReDim combo(NumberofOrders)
Level = 1
RowCount = 1

Call recursive(Level)
End Sub
Sub recursive(ByVal Level As Integer)

Length = UBound(Orders) + 1

For i = 0 To (Length - 1)

'for combinations check if item already entered
found = False
For j = 0 To (Level - 2)
'combo is a count of the combinations,not the actual data
'123
'132
'213
'231
'312
'321
'data is actually in InStrings
If combo(j) = i Then
found = True
Exit For
End If
Next j

If found = False Then

combo(Level - 1) = i

If Level = Length Then
ComboString = ""
For j = 0 To (Length - 1)
ComboString = ComboString & Orders(combo(j))
Next j
Sheets("Sheet1").Range("A" & RowCount) = ComboString
RowCount = RowCount + 1
Else
Call recursive(Level + 1)
End If
End If
Next i
End Sub

 

[LiAD]

I've laid out the data as follows on sheet 1.

Col A - product A B C A B C
Col B - time to produce in days (0,5, 0,4, 0,3)
Col C - delivery date
Col D - calculation for eithers todays date + prod time for first item, or
date finished last product + time to produce next one
Cell F1 - to days date

When I run the macro Iìm getting a complile error as a whole list of things
are not allowed as public memebers of object modules.

 

[joel]

That is why a recommended a modeling approach. You randomly try 10,000 (or a
fixed number) different approaches from the 80! and choose the best.

Running a PC overnight is a reasonable solution. When you get the code
running test measure how long it takes to run one approach and that will
determine how many trials you run.

This is an artificial inteligence problem. You can try things like like
sorting the orders by products and then not running more than 10 orders of
the same product before switching products. I've taken Graduate Level
modeling courses in college and understand the complexity of this problem.
What yo will see if you run 10,000 combinations 4 or 5 different times you
won't see a significant difference in the results. This will give you a
confidence level that the random solution is a godd solution.

 

[Bernie Deitrick]

LD,

The best approach to this problem is to use a bit of common sense, and to work backwards from
required date/times. It is way too complicated to program in a simple macro.

For each of your unique products, find the earliest due date. Then work from the latest unique
product backwards, like in this made up example:

Say you need 40 A on April 4, 50 B by April 5, and 60 C by April 6, and all must be shipped by Noon
on the due date. And then you need 30 A on April 9, 45 B by April 10, and 90 C by April 11.

Start at Noon on April 6, and calculate when you need to start work on the 60 Cs to finish by then,
including change-over time. If that start time is later than the B's are due, leave the time
between the two unassigned, and then do the same for the 50 Bs. Again, if B's start time is after
the As are due, leave that time unassigned, and do the same for the 40 As. That gives you your
absolute latest start time for each product. Then, you need to decide what to do with the
intermediate times. You can move up or expand production of A to include the next 30 units, in the
time before A needs to start, or into the time after A is due and before B needs to start. You can
move up production of the first 40 A, keeping the production the same, and expand Bs production to
include the extra 45 B, and so on.

But the decision on how to move things around will depend on a lot of things, especially future
volumes. If the slack time in the first cycle would allow you to produce all of the A needed in a
future cycle, then move that production of A up, and you will save the switch-over time associated
with that batch. Basically, you are trying to fit blocks of production into the schedule in such a
way that you remove the need for the change-over, and that requires judgment, something that Excel
is famously bad at.

HTH,
Bernie
MS Excel MVP

 

[joel]

Bernie: This isn't an excel problem. It is a general programming problem.
There are software packages commercially available that is desgned to solve
these type problems. But no software can solve this problem because the BEST
solution is deterministic. The program is only as good as its inputs.

A simplistic solution can be programmed in Basic to solve the problem. That
is why I'm recommending the random approach.

 

[LiAD]

I can do the working backwards bit. Its producing the final improved version
that I am getting stuck on - apparently its not easy either! At least that
re-assures me a bit.

If producing the final schedule cannot be automated on excel then such is
life.

I will try the random approach and see what that yields in the meantime -
something close might be better than the nothing I have now.

Thanks

 

[LiAD]

Thanks Joel,

is it possible you could give me an idiots guide on how i should lay things
out to run this macro.

If i understand correctly I will get a lot of tables out from which I then
pick the best?

Thanks again

 

[joel]

You don't have to save a lot of history/results. Just enough so at the end
you can pick the solution you want to use. No matter which way you get the
answer you need to determine the acceptable criteria. I would start by
figuring out your criteria for an acceptable solution.

I was watching a National Geogrphic show on cable last night. they showed a
modeling package to determine how animal move. to generate a simulation of
the animals they fed into a computer the sizes of the bones and the muscles
that pulled the bones. the computer tries every method possible to get the
ideal solution. they show when the computer starts the model runs and the
animal falls down then final solution after 72,000 tries the animal can move
a 28 miles per hour. They showed the compuer simulations for Apes, and
Horses. the optimqal solution was the one where the animal moved the
quickest. The show was really about Dinosaurs. The scientist were trying to
understand the speed and movements of animals that were dead for 70 million
years.

The point is that trying to caculate the solution isn't always possible.
Trying different solutions is sometimes the best method.

 

[Bernie Deitrick]

I'm think a more structure apporach would work better. I've been thinking about the optimum
'algortihm' that you would use - start with the first full cycle:

A1 B1 A2 B2 C1 A3 C2 B3

the first "cycle" would be A1 B1. So start with B1, and work backward to A1. Then ask - can I fit
in all of A2, A3, ... Ax in the slack time? If so, do pick the largest of the A2 to Ax lots that
will fit, and do so. If not, can you fit in any of B2, B3, .... Bx? and so on.

But if none of the whole lots fit (the answer to all of those questions are "No"), then move both A1
and B1 to the earliset times, and then go onto the next cycle A2, B2, and C1, and apply the same
logic, with the exception that the first question is: can I fit in one of the B2... Bx first, since
the machine is set up for B already, without affecting A?

HTH,
Bernie
MS Excel MVP

 

[Bernd P]

Hello,

Would it also be reasonable to produce more items than ordered during
periods of low order volume (based on historical seasonal information
about past orders and taking in account storage space, budget, risk of
getting out of date with regards to technical features or fashion,
etc.)?

Is the task a homework exercise (aiming to get students to read Donald
Knuth's Art of Computer Programming, for example) or a real production
challenge? Which budget (time and money) could be invested for an
acceptable solution?

Regards,
Bernd