Thu, 07 Sep 2017

Cost Accounting as a Poorly Defined Constrained Optimization Model

I recently read The Goal, a business novel that introduces the Theory of Constraints as a toolset for managing a business in order to "more money now and in the future". One of the criticisms the book makes of the way businesses are often run is that their use of cost accounting to guide decisions fails to maximize the amount of money the business can make. An alternative called throughput accounting is proposed, but after having completed The Goal, I didn't have a clear understanding of how and why cost accounting fails.

So I bought Throughput Accounting to dig in deeper. The book starts with a great example of a simple decision made using cost accounting.

A factory makes mens and womens shirts. To make a shirt, you need some raw materials, plus the labor to cut fabric and sew fabric.

WomensMens
Price$105$100
Raw Materials$45$50
Cutting Time2 minutes10 minutes
Sewing Time15 minutes10 minutes
Total Time17 minutes20 minutes
Weekly Demand120 shirts120 shirts

Making all 120 womens shirts and 120 mens shirts requires 1,440 minutes (10 min/shirt * 120 mens shirts + 2 min/shirt * 120 womens shirts) of cutting time and 3,000 minutes (10 min/shirt * 120 mens shirts + 15 min/shirt * 120 womens shirts) of sewing time. Since we only have 2,400 minutes of sewing time available, we can't make all of the shirts. How many mens shirts and womens shirts should we make?

Gross profit for mens shirts is $50 ($100 sales price - $50 for raw materials). Gross profit for womens shirts is $60 ($105 sales price - $45 for raw materials). Mens shirts require a total of 20 minutes of labor. Womens shirts require a total of 17 minutes of labor.

Since womens shirts bring in more revenue, have a higher gross margin, and require less labor, it seems like a reasonable answer is to produce 120 womens shirts, and then as many mens shirts as we can with the remaining time we have available.

120 womens shirts take 1,800 minutes on the sewing machine, so we can make 60 mens shirts with the remaining 600 minutes available on the sewing machine. (We're not constrained by cutting.) This results in a net profit of $-300, i.e. a loss.

Revenue$18,600
Raw Materials$8,400
Gross Margin$10,200
Operating Expense-$10,500
Net Profit-$300

Throughput Accounting then explains how to calculate the amount of money (throughput) being made on the constrained resource per minute, the sewing machine, to decide how many of each product to make. But I'm going to use MiniZinc to use a contrained optimization solver to maximize net profit, which will give us the same result.

The constraints above, and the goal of trying to maximize net profit, can be translated into a MiniZinc model as follows (this would be done in a more concise manner if there were many products): 

int: womens_sewing_minutes = 15;
int: womens_cutting_minutes = 2;
int: mens_sewing_minutes = 10;
int: mens_cutting_minutes = 10;

int: womens_price = 105;
int: mens_price = 100;

int: womens_raw_costs = 45;
int: mens_raw_costs = 50;

int: max_sewing_minutes = 2400;
int: max_cutting_minutes = 2400;

int: operating_expense = 10500;

int: womens_demand = 120;
int: mens_demand = 120;

var 0..mens_demand: mens_produced;
var 0..womens_demand: womens_produced;

var int: total_sewing_minutes = womens_produced * womens_sewing_minutes + mens_produced * mens_sewing_minutes;
var int: total_cutting_minutes = womens_produced * womens_cutting_minutes + mens_produced * mens_cutting_minutes;

var int: revenue = womens_price * womens_produced + mens_price * mens_produced;
var int: raw_materials_cost = (womens_raw_costs * womens_produced + mens_raw_costs * mens_produced);
var int: gross_margin = revenue - raw_materials_cost;

var int: total_cost = raw_materials_cost + operating_expense;

var int: net_profit = gross_margin - operating_expense;

constraint total_sewing_minutes <= max_sewing_minutes;
constraint total_cutting_minutes <= max_cutting_minutes;
solve maximize net_profit;

output ["mens: \(mens_produced)\n", "womens: \(womens_produced)\n", "net profit: \(net_profit)\n", "total cost: \(total_cost)"];

And solving the model tells us that we should produce 120 mens shirts and 80 womens shirts for a net profit of $300, rather than a loss. 

$ minizinc clothes.mzn
mens: 120
womens: 80
net profit: 300
total cost: 20100
----------
==========

Intuitively, what's going wrong in the cost accounting solution is that we're lumping together all of the labor and not taking into consideration that the sewing machine is our bottleneck, and that we need to maximize the amount of value we're getting out of the bottleneck. Nonetheless, I struggled to translate this mistake into a MiniZinc model that also gave the wrong answer.

Below is an incorrectly defined constrained optimization model that I think reflects where we go wrong when trying to use cost accounting for decision making. The goal is changed from maximizing net profit to minimizing cost. But we don't want to just minimize cost; we could do that by producing zero shirts. We also want to produce as many shirts as we can. I modelled this as a constraint that says that producing one more mens shirt or one more womens shirt should cause us to exceed our cutting or sewing constraints. 

int: womens_sewing_minutes = 15;
int: womens_cutting_minutes = 2;
int: mens_sewing_minutes = 10;
int: mens_cutting_minutes = 10;

int: womens_processing = womens_cutting_minutes + womens_sewing_minutes;
int: mens_processing = mens_cutting_minutes + mens_sewing_minutes;

int: womens_price = 105;
int: mens_price = 100;

int: womens_raw_costs = 45;
int: mens_raw_costs = 50;

int: max_sewing_minutes = 2400;
int: max_cutting_minutes = 2400;

int: operating_expense = 10500;

int: womens_demand = 120;
int: mens_demand = 120;

var 0..mens_demand: mens_produced;
var 0..womens_demand: womens_produced;

var int: total_sewing_minutes = womens_produced * womens_sewing_minutes + mens_produced * mens_sewing_minutes;
var int: total_cutting_minutes = womens_produced * womens_cutting_minutes + mens_produced * mens_cutting_minutes;

var int: womens_revenue = womens_price * womens_produced;
var int: womens_raw_materials_cost = womens_raw_costs * womens_produced;
var int: womens_operating_expenses = operating_expense * womens_produced div (womens_produced + mens_produced);
var int: womens_net_profit = womens_revenue - womens_raw_materials_cost - womens_operating_expenses;

var int: mens_revenue = mens_price * mens_produced;
var int: mens_raw_materials_cost = mens_raw_costs * mens_produced;
var int: mens_operating_expenses = operating_expense * mens_produced div (womens_produced + mens_produced);
var int: mens_net_profit = mens_revenue - mens_raw_materials_cost - mens_operating_expenses;

var int: total_cost = womens_operating_expenses + womens_raw_materials_cost + mens_operating_expenses + mens_raw_materials_cost;

var int: net_profit = womens_net_profit + mens_net_profit;

constraint total_sewing_minutes <= max_sewing_minutes;
constraint total_cutting_minutes <= max_cutting_minutes;

% Maximize the number of items produced by ensuring that it must not be
% possible to produce another item
constraint
   ((mens_produced + 1) * mens_sewing_minutes + womens_produced * womens_sewing_minutes > max_sewing_minutes \/
   (mens_produced + 1) * mens_cutting_minutes + womens_produced * womens_cutting_minutes > max_cutting_minutes)
   /\
   (mens_produced * mens_sewing_minutes + (womens_produced + 1) * womens_sewing_minutes > max_sewing_minutes \/
   mens_produced * mens_cutting_minutes + (womens_produced + 1) * womens_cutting_minutes > max_cutting_minutes);

solve minimize total_cost;

output ["mens: \(mens_produced)\n", "womens: \(womens_produced)\n", "net profit: \(net_profit)\n", "total cost: \(total_cost)"];

Solving this model gives us the original cost accounting result. 

$ minizinc clothes-cost.mzn
mens: 60
womens: 120
net profit: -300
total cost: 18900
----------
==========

business | Permanent Link

Mon, 18 Jan 2016

Requirements in Micro-purchasing

I recently completed an 18F micro-purchase task. It turned out to be a very simple task, tweaking some CSS. I spent more time on bidding, setting up the development environment, and figuring out how to receive payment than on the actual work.

My pull request was accepted, and 18F paid me quickly, but after my changes were merged, Maya Benari pointed out that a simpler solution may have been acceptable, or perhaps even preferable.

It turns out that 18F have drafted U.S. Web Design Standards, and have already given a lot of thought to things like vertical spacing, the subject of my change.

As an independent contractor with no previous experience working with 18F, I didn't know there was a U.S. Web Design Standards document, much less its contents. Had this task been assigned to an internal staff member, they probably would have known that the page being updated should follow the standards, or that if the standards didn't adequately address the requirements for the task, that perhaps a future update to the standards should be planned.

Getting the right level of details in task requirements is often tricky. One doesn't want to spend days writing requirements for a task that can be completed in hours. But one also doesn't want what could have been an hour-long task drag on for days because the requirements were ambiguous.

When working within a long-lived team structure, there is some shared institutional knowledge that doesn't need to be made explicit in every task, like the fact that U.S. Web Design Standards exist. Usually when bringing in an outside contractor or new employee, one is starting a relationship that will last weeks, months, or years, and knowledge transfer is an expected part of the on-boarding. This investment makes sense given the size of the overall engagement.

Micro-purchasing of software development work is unique in this respect. Neither party is committing to a long-term relationship, and therefore unlikely to bear significant knowledge transfer costs. Had the acceptance criteria for my spacing fix task included compliance with the U.S. Web Design Standards, I would have had to bid more to cover the time to read and understand the document. And 18F wouldn't want to bear the cost of making me an expert on U.S. Web Design Standards if I were only going to complete a single task.

It's still early in 18F's micro-purchasing experiment, but if the experiment continues or if other organizations want to try it out, it's worth thinking about what types of tasks are best suited for micro-purchasing, and what level of detail in the requirements is optimal.

Some possible questions to ask about tasks you are considering outsourcing as micro-purchases:

As always when discussing project management, I suggest ordinal prioritization of tasks and confidence interval based estimates. If your existing tools don't support these, I recommend checking out LiquidPlanner (affiliate link).

I like the micro-purchasing model, and I hope that it succeeds and is adopted by commercial organizations.

I've gotten multiple emails from grad students doing research on Github. If you're an economics student interested in industrial organization or open source, micro-purchasing of open source software could be an interesting research project.

business | Permanent Link

Wed, 17 Sep 2014

Fore Close


I thought it'd be a nice gesture to make up some signs for Casey. Actually, I just get a kick out of these. I'm probably the only one.

See the Housing Bubble Blog for some real news.

business | Permanent Link

On Instacart Pricing Transparency

Stephen Klein, a biz dev guy from Instacart, emailed me to ask why I hadn't tried it yet. Here's my response:

Hi Stephen, I was excited to learn about Instacart offering deliveries from Costco. Unfortunately, your current pricing model makes deciding whether to use Instacart too expensive. It's not that your prices are too high. It's that I don't know if your prices are too high; that is, the cost of information is too high.

When deciding whether to use Instacart, my decision is between going to Costco or having Instacart go to Costco for me. In most cases, I would prefer to have Instacart go for me. (Sometimes, I might want to browse.) But to make the decision, I need to know how much it would cost me to use Instacart.

The current pricing model is not transparent enough to determine this cost. Your prices are not the same prices as those offered as Costco, so I don't know what the total cost of using Instacart is, and rather than spend the time trying to figure it out, I simply don't use Instacart.

My recommendation would be to change your pricing model to make explicit the cost of using Instacart. You could charge a fixed percentage above the Costco price, charge a higher delivery fee, or charge a per-item delivery fee, for example; whatever model would be both transparent and profitable.

Christian

business | Permanent Link

Thu, 05 Sep 2013

Estimating Tasks

As described in the previous post about our development process at GreatVines, we use LiquidPlanner for project management. Estimating how long tasks will take is important in most software development projects (and generally any project involving more than one person).

LiquidPlanner provides a great way of estimating tasks using an 80% confidence interval, but estimating tasks like this is a new concept for most developers. Below is a transcript with a developer that recently joined our project. We were able to get from "I have no idea how long it will take" to a decent estimate in about half an hour, but it should only take a minute or two for the next task. 

2013-09-05 11:16:52: <Christian G. Warden> have you guys reviewed all of the
                     tasks for the september release?
2013-09-05 11:20:44: <Ben H> yes, but many of the tickets refer to parts of the
                     code I have no experience with so I have no idea how much
                     work they will be.
2013-09-05 11:23:11: <Christian G. Warden> you can put wide estimates on tasks
                     like that.  can you give me an example, and i'll walk you
                     through it?
2013-09-05 11:25:15: <Ben H> 10631525- Make Modal Form Fields scroll-able: I
                     have no idea where contacts are viewed in the application,
                     I haven't had any reason to look at their controller/model
2013-09-05 11:25:52: <Ben H> so any time estimate I would come up with would be
                     a sheer guess
2013-09-05 11:26:38: <Christian G. Warden> ok, no problem.  what's the
                     likelihood it will take you more than 2 weeks to complete
                     the task given what you currently know about the app?
2013-09-05 11:27:21: <Ben H> darn near 0% I would figure
2013-09-05 11:27:26: <Christian G. Warden> phew :) 
2013-09-05 11:27:31: <Christian G. Warden> how about 1 week?
2013-09-05 11:28:29: <Ben H> that's still very high, so 2%?
2013-09-05 11:28:38: <Christian G. Warden> how about 3 days?
2013-09-05 11:28:40: <Ben H> given that it looks like pure GUI work
2013-09-05 11:30:03: <Jim Thompson> yeah Ben the problem is that one customer
                     has put so many fields in the FieldSet that you can't see
                     the entire modal, the Save and Cancel buttons scroll below
                     the page
2013-09-05 11:30:33: <Ben H> I guess 3-4 days (if it is pure GUI work then 1-2
                     should be more then enough, unless there's something
                     unseemly complex)
2013-09-05 11:30:45: <Jim Thompson> I am going to move this task beneath the
                     Performance items Christian
2013-09-05 11:30:47: <Jim Thompson> (and Ben)
2013-09-05 11:32:20: <Christian G. Warden> would you say there's a 10%
                     probability that it will take more than 4 days?
2013-09-05 11:33:34: <Jim Thompson> at 12-32 hours it might have to drop off
                     the list, or at least to the bottom
2013-09-05 11:34:40: <Christian G. Warden> jim, we'll go through the tasks and
                     reprioritize after the estimates are updated.
2013-09-05 11:34:57: <Jim Thompson> ok, I also moved "New Task" and "New Event"
                     to October, which is when we promised it
2013-09-05 11:35:39: <Christian G. Warden> you're interrupting my estimation
                     lesson    :) 
2013-09-05 11:36:02: <Ben H> (yeah, he's been high balling for tutorial
                     purposes)
2013-09-05 11:36:11: <Jim Thompson> ok im out
2013-09-05 11:37:50: <Christian G. Warden> no, i want to come up with realistic
                     estimates.  if they're wide right now because of
                     uncertainty as to what it will take to complete them,
                     that's fine.  once we have estimates, we can decide
                     whether to invest time to come up with tighter estimates.
2013-09-05 11:38:44: <Christian G. Warden> so, do you think 4 days as a high
                     estimate is accurate?
2013-09-05 11:39:29: <Ben H> for this example I put 12-24, it's really wide and
                     most likely most of that will be learning about how that
                     GUI element is working and making the tests
2013-09-05 11:39:57: <Ben H> the range is more to show that it could go
                     horribly wrong if there is something there I have no idea
                     of
2013-09-05 11:40:24: <Ben H> but 12 still seems really high
2013-09-05 11:40:30: <Christian G. Warden> what's the likelihood that you will
                     complete the task in 2 hours?
2013-09-05 11:41:14: <Ben H> the likihood I'll complete it in 6 hours I would
                     meet the 10% threshold
2013-09-05 11:41:26: <Ben H> *likelihood
2013-09-05 11:41:38: <Christian G. Warden> ok, so, let's make it 6-24
2013-09-05 11:45:29: <Christian G. Warden> and you can check yourself by
                     imagining we're going to a casino.  you can choose from
                     two wagers:
                     1) roulette - there are 10 numbers on the roulette wheel.
                     if 1 or 10 comes up, you lose. if 2 through 8 comes up,
                     you win $100.
                     2) the bookmaker - if you complete the task in less than 6
                     hours, you lose. if you complete the task in more than 24
                     hours, you lose.  if you complete the task between 6 and
                     24 hours, you win $100. which wager do you want to take?
2013-09-05 11:47:25: <Ben H> bookmaker, it also means I can spend some
                     speculative time trying different approaches to find one
                     that solves the problem better
2013-09-05 11:47:34: <Ben H> if things go well
2013-09-05 11:49:16: <Christian G. Warden> so it's not really an 80% confidence
                     interval.  it might be more like a 90% confidence
                     interval.  you should make the range narrower.
2013-09-05 11:49:52: <Ben H> how then do you show the risk if (I doubt in this
                     case) that 10% could be really bad
2013-09-05 11:52:19: <Christian G. Warden> it's ok if there's an outlier
                     occasionally.  we want to get an accurate estimate across
                     all of the tasks.
2013-09-05 11:56:09: <Christian G. Warden> you should narrow the range until
                     you're ambivalent between taking the two wagers.  and
                     widen the range when you'd rather play roulette.
2013-09-05 11:58:02: <Christian G. Warden> but we've already gone from "i have
                     no idea how long it will take" to "i'm 90% confident, it
                     will take between 6 and 24 hours".
2013-09-05 11:59:40: <Ben H> I'm just worried it's misplaced confidence
2013-09-05 12:00:03: <Ben H> either way, given the range, I am (90%) confident
                     that I can get it done within the range
2013-09-05 12:07:07: <Christian G. Warden> nobody dies if you're wrong.  you're
                     expected to be wrong 20% of the time (once you narrow it
                     to an 80% confidence interval).  if we decide we need to
                     know with more certainty when something will be done, we
                     might ask you to spend an hour to do a little research so
                     you can come up with a tighter estimate, after which you
                     would adjust the high and/or low estimate.  for now,
                     though, estimate the tasks based on what you currently
                     know.
2013-09-05 12:07:50: <Ben H> ok

The roulette idea comes from Douglas Hubbard's How to Measure Anything.

business | Permanent Link

Wed, 24 Aug 2011

Self-Employment Tax Thoughts

I filed my taxes Tuesday night. It wasn't quite the relief it usually is though. This was the first year in which my income was mostly 1099 income. That means that self-employment tax reared its big ugly head. I knew it was coming, but when it looks you in the eyes, it's still frightening. After writing off my business expenses, my total taxes were actually about $3,000 less than the rough estimate I made last year when filling out my 1040-ES. Nonetheless, I still owed the feds over $10,000 of the almost $19,000 total tax liability.

What makes the number so shocking is when you compare it to a return for which all of the income is W-2. With W-2 income, the section of the 1040 labeled Other Taxes is generally blank. As an employee, you pay 7.65% of your wages for Social Security and Medicare insurance, but this amount doesn't show up on your tax return. When your self-employed, the 15.3% tax on your net business profit shows up under Other Taxes, increasing the bottom line (line 62, that is) substantially.

One nice thing about being self-employed is being able to write off business expenses that employees typically can't. This year, I expensed gas and other automotive expenses, internet access, office supplies, part of my rent and utilities, and depreciated computer equipment and part of my car. Working from home, I don't have too many expenses so I was only able to reduce my gross income by about 6% in calculating my net profit. I was also able to write off my health insurance premiums, but that only reduces my adjusted gross income rather than business income, and thus doesn't reduce the SE tax. So I was left with a large amount of self-employment tax to pay.

In 2005, I'm going to set up and contribute to a SEP-IRA and a Health Saving Account which will reduce my income tax, but not my SE tax unfortunately. To reduce my SE tax, I may form an S Corporation. Paying myself half the corporate income in salary, which is subject to SE tax, and rest as a distribution, which is not, would probably be fair and would reduce my SE tax by quite a bit.

business » taxes | Permanent Link

Slovak Spas

Over on TJ's Weblog, they picked a company planning on opening a spa in Slovakia as one of their top 3 business plans.

TOP 3 - comes in MAGMA ZAFÍR s.r.o. that aims to develop a hot water spa in Slovakia. Central Europe has been less then well served with wellness facilities so far and has the advantage of cheap labor costs. A world-class spa for clients from Germany and Austria could easily fill a market void.

I'd be interested in reading their business plan. Slovakia already has a number of spas, and Piestany has attracted foreigners from around the world to its spas for a long time, even during Communism.

Slovaks, in general, see spas as places for the elderly and infirm, but that may start to change. When I was in Slovakia a few weeks ago, there was an article in a magazine describing a visit to a spa by a young woman. She hadn't been too thrilled about her assignment to visit and write about her experiences at a spa. She figured she had twenty or thirty years before she should start visiting spas. She was delightfully surprised by her experience and concluded that visiting spas was a great way for young professionals to relax.

I think there could be a good opportunity in marketing spas to Slovaks between 20 and 40.

business » marketing | Permanent Link

State Government Irony

The State of California publishes a booklet called Striking Gold in California. This is the most absurd name they could have come up with. Striking Gold describes the various bureaucracies to which a business must send forms and pay taxes.

Every year in California, thousands of new small businesses start up. Unfortunately, thousands of companies also go out of business each year.

The probably go out of business partially because they have to spend so much time filing forms with various government agencies, not to mention, sending them money.

The booklet is for sole proprietorships, so it doesn't cover the forms corporations must file. Here's a short list of the forms mentioned.

They forgot the 1099s that have to be filed with the IRS, the FTB and the EDD.

Also, your city or county may have tax or license requirements not covered in this publication. See the government listings in the white pages of your telephone book.

Yep, City of Los Angeles has a Business Tax of 0.5% of gross sales.

business | Permanent Link

Tue, 28 Nov 2006

Gold Almost at $500

Gold almost hit $500/oz today.

business | Permanent Link

Fri, 24 Nov 2006

Creative Talent Tax Exemption

I had to pay business tax to the city of Los Angeles last month since I receive 1099 income. The city took $600 from me, but it turns out that "creative artists" who earn up to $300,000 are exempt from the business tax thanks to the lobbying of the Screen Writers Guild. I should move to New Hampshire.

business » taxes | Permanent Link

The state is that great fiction by which everyone tries to live at the expense of everyone else. - Frederic Bastiat