Help with payback calculation

[moosetracks555]

I am having a difficult time coming up the savings figure for the following situation. I am almost certain the solution is a rate calculation involving calculus. However, it has been so long I don’t know where to start.

We have logs that degrade when not sprinkled with water. Our inventory has grown and we have more logs than capacity to sprinkle. We estimate a 2% / week loss on logs that are not sprinkled. I am trying to find the cost savings of adding some additional capacity to our sprinkler system. We will continue to add inventory at about the same rate as consumption. However we will use the oldest logs first.

Here is a generic example…
Assume the logs cost $100 a piece
Week 1 we have 1000 logs not sprinkled, and we use 100 logs.
Week 2 we have 900 logs not sprinkled for 1 week, and we add 100 new logs
Week 3 we have 800 logs not sprinkled for 2 weeks, 100 logs not sprinkled for 1 week, and we add 100 new logs

If we upgrade the sprinklers we will have 500 logs not sprinkled
Week 1 we have 500 logs not sprinkled, and we use 100 logs.
Week 2 we have 400 logs not sprinkled for 1 week, and we add 100 new logs
Week 3 we have 300 logs not sprinkled for 2 weeks, 100 logs not sprinkled for 1 week, and we add 100 new logs

How would you calculate a cost savings?

 

[zekeman]

My take on this if you have a survival rate of .98 per week for the unsprinkled logs so in equilibrium it takes 10 weeks to clear the added 100/ week ; so the overall survival is 0.98^10= 0.817 or an 18.2% loss.
If you add the sprinkler system then you clear the inventory in 5 weeks so the survival rate is .98^5=.904 or a 10%loss.
So if you ship 100 logs a week, you lose 18 logs/week now vs a loss of 10 logs/week after your new system is in place.
However, this does not mean you go out and buy the new system, since perhaps the large inventory (1000 logs) might be questioned.

 

[zekeman]

After rereading your comments, your assumption that the rate of loss is 2% per week of unsprinkled logs,surprisingly independent of the time they are unsprinkled ( I think you mean unsprinkled for that particular week, but my answer is the same), means your loss is .02*n where
n is the inventory of unsprinkled logs
For n=1000 the loss is 20/week regardless of the input or output, only the amount of unsprinkled inventory is involved.
If you are allowing the unsprinkled inventory to decline to 5000 then the loss is 10/week.
I think the decision is based on the cost of 10 logs in the short term until you get the overall inventory down.

 

[dvd]

Can you start a side business that buys the logs cheap? How much does the sprinkler cost compared to some other type of equipment that makes use of the "ruined" logs? Seems like you are not thinking about alternatives.

 

[rb1957]

can you "use" bad logs ?

i mean, if you took a bad log out of inventory, wouldn't you toss it away and take another ?

aren't the bad logs scrap ?

 

[moosetracks555]

The ends of the logs start cracking and then the log starts to rot. We assume 2% degrade on each log / week. The logs are never trash, but the number of viable board feet you get from the log goes down a little each week. I don't have data to know when it tapers off, probably around 25% degrade.

 

[ivymike]

that would be a completely different simulation, then... no simulation needed, really.

 

[tomwalz]

Can you rent sprinklers or a sprinkler service?

Here the gold courses aren’t watering yet. Construction is slow. Maybe, as a temporary measure, use those crappy Melnor sprinklers from a Big Box store. They fall apart pretty fast but they are cheap.

Many, many mills had committed to buy logs that they now can’t use. You have to estimate how much lumber you will cut and commit a long time ahead, maybe years. No one wants excess timber now except for a few very special cases.

If you have a 16 foot log you can get two eight foot pieces of lumber out of it end to end. If you lose a bit on the ends you can get one 12 foot piece of lumber out of it and cut the rest into chips for paper, which is a huge loss.


Thomas J. Walz
Carbide Processors, Inc.

http://www.carbideprocessors.com

Good engineering starts with a Grainger Catalog.

 

[rb1957]

and i supppose that not all the logs are the same size, nor the same species (hence not the same value), and the 100 in and 100 out, oh and 1000 inventory, are just numbers ... oh, and the logs on the bottom of the pile start to rot (too much water)

 

[swearingen]

You've got to keep in mind what you're selling! Let's look at the total revenue for the 20 weeks:

For 1000 unsprinkled logs, selling 100 FIFO per week at a declining value of 2% each week, you'd get the following:
Week 1: 100 logs x $100 = $10000 revenue
Week 2: 100 logs x $98 = $9800 (he did say value drop, not wasteage)
Week 3: $9600
Week 4: $9400
and so on down to Week 10 where 100, 9 week unsprinkled logs sell for $82 each = $8200. Since at this time we reach steady state, using FIFO, each 100 logs after this point sells for $8200.

So, for 20 weeks, we get:
10000+9800+9600+9400+9200+
9000+8800+8600+8400+(11)*8200 = $173,000 in revenue for the 20 weeks.

We need more info for the sprinkled case because, as has been mentioned before, if you only sprinkle 500 of the logs, only sell the unsprinkled ones, and never move the logs from sprinkled to unsprinkled, then 500 logs would just sit there wet and the unsprinkled inventory would be the only set that would get turned over. To get past this, I'm assuming that you'll take 50 unsprinkled logs and 50 sprinkled logs and sell that each week. When you buy your 100 new logs, 50 go to the sprinkled pile and 50 go to the unsprinkled. When you lay that out, the total revenue after 20 weeks would be calculated as follows:

Week 1: 100 logs x $100 = $10000
Week 2: 50 x $98 + 50 x $100 = $9900
Week 3: 50 x $96 + 50 x $100 = $9800
Week 4: $9700
and so on down to week 10 where you're selling 50, 9 week unsprinkleds for $4100 plus 50 sprinkleds for $5000 for a total of $9100 per week from week 10 to 20. For the 20 weeks, we get:

10000+9900+9800+9700+9600+
9500+9400+9300+9200+(11)*9100 = $186,500

Granted, it is a simple model - you can throw in compounding for the 2% reduction and interest on your money, but even when you do, it looks like you'd have plenty of money to buy a nice sprinkler system for the 20 week haul...


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm

 

[rb1957]

a good analysis but the OP says (i think) that the 2% wasteage/week isn't true wastage (ie 2% of stock becomes scrap) but rather 2% of stock loses some value (due to cracking at the ends reducing the usefull product.

 

[swearingen]

Exactly - which is why I devalued the wood instead of throwing it out as some previous posts did.


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm

 

[rb1957]

mea culpa ... almost asked why do things level off after 9 weeks, then i thought about it for a little.

 

[swearingen]

Maybe this will help a little - I set up a spreadsheet to illustrate how I attacked it. See what you think...


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm

 

[zekeman]

quote"New Postswearingen (Civil/Environme)
19 May 09 10:40
Exactly - which is why I devalued the wood instead of throwing it out as some previous posts did."


I don't think anybody is suggesting you "throw out" whole tainted logs.
When they say you lose x number of logs they mean the sum of the scrap calculated in whole logs.

 

[swearingen]

12 May 09 11:38 - Moosetracks555
"We loose [sic] 2% of the logs [sic] value every week."

This is the OP's statement that I was referring to. I take it that they can sell the log, but for an average of a 2% loss per week of not being sprinkled.



If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm

 

[swearingen]

moosetracks555 -

I'm curious - what was the outcome? I would imagine you could get a sprinkler system for less than $13.5k. Did they go for it?


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm