[nateo]

More beer on tap doesn't necessarily increase sales. Especially if one of your beers has a high margin, and another you're breaking even on, you're cannibalizing profitable sales from yourself if they buy the less-profitable beer. The more beer you have (made or bought) the more cash you need upfront to pay for the beer or ingredients. Unless you have so much cash that cash flow doesn't matter, I would be very concerned about carrying too much inventory that doesn't move or isn't profitable enough.

[tschmidlin]

It's not about increasing beer sales necessarily, it is about increasing total sales.  It's a pub, and if people will sit longer trying different beers or come back more often to try the variety then they are more likely to buy some food too.  Adding a couple of taps in the build-out is way cheaper than adding them later.

But hey, that's what I would do.  His place, his decision.

[nateo]

Luckily, once we have an idea of what the costs are, we can use math to determine the optimal solution to maximize profit. Maybe 20, or 16 or 8 taps is the optimal solution. Without any numbers it's impossible to say definitively.

[Thirsty_Monk]

I agree with nateo. Less taps less inventory. To some extend.

It also depends on how much people you attract in your area.
We had a pub with 27 tap and they did pretty well. Then they added 13 more lines and they stopped to pay the bills. Sales were the same as with 27 taps just had to carry more inventory.

[tschmidlin]

Well, clearly there's a limit.  I don't know where that is though, I think it depends on the market.  There are places in my area with 160 taps that seem to be doing fine.  There are some with 60+ that are doing well, and the place I go most has 25+ taps (he just added 8 more) and is doing fine.  The local brewery (not a pub, just a production place with a taproom) has roughly 18 taps at two bars, so there is some duplication for now but when they open a new (and bigger) production facility I expect that will change.

Anyway, my point is I think it depends on the market.  I can't imagine a decent sized pub with fewer than 8 taps though, around here they all have more.

[nateo]

Here's an example of what I was talking about. You could use hundreds of constraints and variables if you wanted to, but to keep it simple I'll just use a few, and avoid sticky widgets like amortizing cost for equipment or multi-period inventory management, although you can include all of those and more in a more detailed analysis. This is an incredibly powerful tool for analyzing business decisions, and will give you an optimal solution, as well as identify the range in which the answer remains optimal if costs or demands change.

Let's say you run a 3bbl British brewpub.
You have $5000 cash at the beginning of the week in your beer budget.
You need at least 20 kegs of beer, but you never need more than 60 kegs per week.
The costs of brewing your beer, how much you sell it for per pint, and profit per keg:
mild - $40 / $3 / $320
stout - $50 / 4 / 430
IPA - $60 / 4 / 420
barley-wine - $90 / 5 / 510
The costs of beer you can buy
bitter for $70 / 3 / 290
ESB for $80 / 4 / 400
porter for $90 / 4 / 390
foreign stout for $100 / 5 / 500
(There are 120 pints per keg.)
No more than 1/4 of your sales volume will be from $5 pints, at least 1/3 of your sales volume will be from $3 pints.

You want to maximize profit:
Max: 320m + 430s + 420i + 510bw + 290b + 400e + 390p + 500fs

subject to the following constraints:
1) 40m + 50s + 60i + 90bw + 70b + 80e + 90p + 100fs <= $5000
2) m + s + i + bw + b + e + p + fs >= 20
3) m + s + i + bw + b + e + p + fs <= 60
4) (bw + fs) <= 0.25(m + s + i + bw + b + e + p + fs)
= 0.75bw + 0.75fs - 0.25m - 0.25s - 0.25i - 0.25b - 0.25e - 0.25p <= 0
5) (m + b) >= 0.33(m + s + i + bw + b + e + p + fs)
= 0.67m + 0.67b - 0.33s - 0.33i - 0.33i - 0.33bw - 0.33e - 0.33p - 0.33fs >= 0

The results tell us that the optimal solution is $24822 profit, from 20 kegs of mild, 25 kegs of stout, and 15 kegs of barleywine. It also tells you that for every keg of IPA you add, the profit decreases by $46. For every keg of bitter or esb, it'll decrease by $30, for porter $40, and for foreign stout $10.

[anthony]

For the math muggles like me, what did you use to solve that function?

[nateo]

My prof uses Management Scientist. That's the most "user friendly" program I've seen, but it's pretty pricey to buy new and hasn't been updated in a while (it won't work with Win 7). I found an old copy of the textbook with the software for under $10 on amazon (An Introduction to Management Science : Quantitative Approaches to Decision Making by Anderson and Sweeney). 

I have http://lpsolve.sourceforge.net/ at home. It's free, but it's a little more cumbersome to program. I've heard good things about GLPK, but I haven't used it.

If you're interested in this sort of thing, I'd recommend picking up a copy of the textbook. Formulating the problems isn't always intuitive, and the results would be incomprehensible if you're not sure what each parameter means.

[nateo]

I should add, so you don't need to do the math, that the binding constraint in that example is the demand (60 kegs). You'd only be using $3400 of your budget for the optimal solution, but you'd decrease your profit and increase your expenses if you need to pursue a sub-optimal solution.

For instance if you wanted to carry all 8 different beers. You could add constraints to make it so the program has to pick at least a certain number of each type of beer. Like m>=1, esb >=1, etc. But in this case, the program would select the minimum number of the other kegs it can, because they're less profitable.

If you have to buy kegs on a contract or something, like if you have to buy at least 5 kegs of bitter it'd be b>=5x, or b-5x>=0 where bx would be binary: zero if you buy zero, and 1 if you buy any non-zero amount.

If you have a tied-distribution, like if you want to buy a keg of ESB you have to buy a keg of bitter, it'd be esb = b, or esb - b = 0, because all of the programs I know of can't compute solutions with variable on the right-hand side of the equations.

[narvin]

So, that's all well and good, but the assumptions you're making are pretty big ones for a a local brew pub.   For example, that there's demand for that much mild.  Or that IPA won't bring in a bigger crowd to eat your food.

This isn't budweiser level distribution where you can calculate their exact demand for each product reliably. You can play with the math all you want, but the result is only going to be as good as your model.

[nateo]

So, that's all well and good, but the assumptions you're making are pretty big ones for a a local brew pub.   For example, that there's demand for that much mild.  Or that IPA won't bring in a bigger crowd to eat your food.

This isn't budweiser level distribution where you can calculate their exact demand for each product reliably. You can play with the math all you want, but the result is only going to be as good as your model.

Yeah, but the math will always be better than your gut feeling.

And like I said, you can include hundreds of variables if you want to. If you think your IPA sales will increase your food volume, you can include your food demand and margin, and assign a coefficient to food volume that's a function of IPA sales. You need to make some educated guesses, but you should be able to get in the ballpark.

We're talking about a business, right? And we want to make a profit at that business, maybe even enough to pay ourselves well?

You can run a business from your gut. I've done it. It was already a successful, established business, so I've succeeded despite my ignorance, but if you want to build something from scratch, I wouldn't recommend being as stupid as I was.

[narvin]

So, that's all well and good, but the assumptions you're making are pretty big ones for a a local brew pub.   For example, that there's demand for that much mild.  Or that IPA won't bring in a bigger crowd to eat your food.

This isn't budweiser level distribution where you can calculate their exact demand for each product reliably. You can play with the math all you want, but the result is only going to be as good as your model.

Yeah, but the math will always be better than your gut feeling.

And like I said, you can include hundreds of variables if you want to. If you think your IPA sales will increase your food volume, you can include your food demand and margin, and assign a coefficient to food volume that's a function of IPA sales. You need to make some educated guesses, but you should be able to get in the ballpark.

We're talking about a business, right? And we want to make a profit at that business, maybe even enough to pay ourselves well?

You can run a business from your gut. I've done it. It was already a successful, established business, so I've succeeded despite my ignorance, but if you want to build something from scratch, I wouldn't recommend being as stupid as I was.

Sure, "the math" is always better than your gut feeling at solving a specific problem, but what are you solving?  A problem that you set the parameters for based on your gut feeling.  I'd be much more inclined to look at sales data and use some simple math based on margins than to start from scratch by building a complex simulation of something as volatile as a small brewpub.  A tool is just a tool, and any tool can use the wrong tool for the job    I could tell you that you need differential equations and control theory to solve the true problem, which is creating demand, but that doesn't mean linear programming is "mathematically" incorrect.

[nateo]

The "specific problems" here are the presumptions that IPA sales increase food sales, and therefore net profit, or that having 30 beers on tap vs 20 beers increases beer sales, and therefore net profit. All I'm saying is there is a mathematical way to determine if those presumptions are true or not, and under what conditions they're true or false.

[tschmidlin]

I'm with Narvin on this one.  Your model may tell you what beers are most profitable, but my experience tells me that if you don't have at least one IPA on tap in this market you aren't going to sell as much beer.  You have to have an IPA here according to the pro brewers I know.  You don't make beers based on which make you the most money, you make beer based on what sells.

[jeffy]

I'm with Narvin on this one.  Your model may tell you what beers are most profitable, but my experience tells me that if you don't have at least one IPA on tap in this market you aren't going to sell as much beer.  You have to have an IPA here according to the pro brewers I know.  You don't make beers based on which make you the most money, you make beer based on what sells.

We went to Big Time this summer, where you are, and they had three of their own IPA's  on tap.