Illinois Investment Network


Recent Blogs


Pitching Help Desk


Testimonials

"Joined, submitted, we're moving forward. Excellent site, thanks again... "
Steve Smith - EquipmentFX

 BLOG >> Recent

A Non-Stationary Revenue Model [Business Models
Posted on June 27, 2013 @ 09:10:00 AM by Paul Meagher

The underlying process that generates revenue for a line-of-business can be stationary or non-stationary in nature. A stationary revenue process is one in which the parameters for the probability distribution representing a revenue factor (e.g., average lobster price) is specified once for the period that your revenue model covers. A non-stationary revenue process is one in which you must specify the parameters multiple times (e.g., average lobster catch size) during the period that your revenue model covers. In my last blog I argued that in order to construct a more realistic revenue model for a lobster fishing season, we should take into account the fact that lobster catch sizes diminishes over the course of a season because the rate of extraction from the lobster fishing grounds exceeds the rate of replenishment as the season progresses. I argued that an exponential decay function is a useful function to use to represent how the catch size diminishes over the course of a season. I showed a worked example of the math required to estimate the relevant decay parameter k that captures how the catch size decreases over the course of the season.

In this blog, I want to illustrate how to integrate this non-stationary factor (i.e., catch size) into our lobster fishing revenue model. The essential observation is that we cannot be content to set the parameters of our catch size distribution (average catch size and standard deviation) only once, but instead need to set these parameters multiple times as we iterate through each catch of the season. In other words, the catch size distribution that we sample from changes after each catch; specifically, the mean and standard deviation parameters are reduced by a constant percentage after each catch. This better represents the true state of affairs with respect to how revenue is generated over the course of a lobster fishing season. Our first attempt at creating a revenue model for a lobster fishing season assumed that the lobster catch-size distribution was stationary over the course of a fishing season. Now we are assuming it is non-stationary so that we can construct a more realistic revenue model.

The new script that I developed to model lobster fishing is called lobster_revenue_with_decay.php and the code for that model is illustrated below. I was also informed that instead of the lobster season consisting of 28 trips, it will consist of around 40 trips this season so that is one other change to the revenue model I presented previously.

What is critical to note in this code is that we set the parameters of our $lobster_catch_distribution multiple times according to our exponential decay function for the mean catch size and the standard deviation of the catch size. In general, a non-stationary process involves re-setting parameters inside the loop that generates revenue for each time unit in your model. In contrast, the parameters for the $lobster_price_distribution is only set once outside the loop and remains constant for each time unit of the model. This structure will be common to all revenue models that consist of stationary or non-stationary factors that determine revenue.

This is what the output of our new lobster fishing revenue model looks like.

Catch # Price/LB Weight(LB) Revenue
1 $3.57 629 $2245.53
2 $3.67 853 $3130.51
3 $3.67 1065 $3908.55
4 $3.33 819 $2727.27
5 $3.50 848 $2968.00
6 $3.49 1075 $3751.75
7 $3.72 1038 $3861.36
8 $3.75 933 $3498.75
9 $3.57 756 $2698.92
10 $3.58 731 $2616.98
11 $3.54 610 $2159.40
12 $3.29 822 $2704.38
13 $3.56 757 $2694.92
14 $3.31 501 $1658.31
15 $3.59 644 $2311.96
16 $3.35 649 $2174.15
17 $3.34 718 $2398.12
18 $3.61 415 $1498.15
19 $3.22 842 $2711.24
20 $3.28 626 $2053.28
21 $3.49 464 $1619.36
22 $3.48 588 $2046.24
23 $3.37 234 $788.58
24 $3.42 530 $1812.60
25 $3.88 256 $993.28
26 $3.05 321 $979.05
27 $3.43 575 $1972.25
28 $3.37 420 $1415.40
29 $3.23 554 $1789.42
30 $3.35 420 $1407.00
31 $3.55 498 $1767.90
32 $3.63 305 $1107.15
33 $3.44 407 $1400.08
34 $3.24 335 $1085.40
35 $3.00 455 $1365.00
36 $3.53 359 $1267.27
37 $3.79 242 $917.18
38 $3.31 177 $585.87
39 $3.43 440 $1509.20
40 $3.74 293 $1095.82
  Totals 23204 $80695.58

What you should note about this output is how the revenue is greater at the beginning of the season than towards the end of the season. This gives us a better sense of what type of cashflow to expect over the season. It conforms better to the day-to-day revenue expectations a fisherman has over the course of a lobster fishing season.

Conclusion

In this blog I've illustrated how stationary and non-stationary factors are included in a revenue model. Although I am focusing on a lobster fishing example, the programmatic lessons about how to incorporate stationary and non-stationary factors into a revenue model is more general and you can use this model as a template for constructing a revenue model for your own line-of-business. When specifying the non-stationary component of your revenue model you have many choices as to what function might be used to determine the parameter settings for probability distribution representing that component. I used an exponential function but there are a large number of other possible functions you might use. One common function would be a sine wave function if your revenue model has a seasonal component. Gompertz functions are often used in situations where the sales are brisk at first then die off rapidly thereafter, such as happens when a new movie is released. Piecewise linear functions are also very useful and flexible.

I'm not quite done with revenue modelling as there is one more aspect that I want to add to the lobster-fishing model make it more realistic. Stay tuned for my next blog to find out what else we might do to make our revenue models more realistic.

Permalink 

 Archive 
 

Archive


 November 2023 [1]
 June 2023 [1]
 May 2023 [1]
 April 2023 [1]
 March 2023 [6]
 February 2023 [1]
 November 2022 [2]
 October 2022 [2]
 August 2022 [2]
 May 2022 [2]
 April 2022 [4]
 March 2022 [1]
 February 2022 [1]
 January 2022 [2]
 December 2021 [1]
 November 2021 [2]
 October 2021 [1]
 July 2021 [1]
 June 2021 [1]
 May 2021 [3]
 April 2021 [3]
 March 2021 [4]
 February 2021 [1]
 January 2021 [1]
 December 2020 [2]
 November 2020 [1]
 August 2020 [1]
 June 2020 [4]
 May 2020 [1]
 April 2020 [2]
 March 2020 [2]
 February 2020 [1]
 January 2020 [2]
 December 2019 [1]
 November 2019 [2]
 October 2019 [2]
 September 2019 [1]
 July 2019 [1]
 June 2019 [2]
 May 2019 [3]
 April 2019 [5]
 March 2019 [4]
 February 2019 [3]
 January 2019 [3]
 December 2018 [4]
 November 2018 [2]
 September 2018 [2]
 August 2018 [1]
 July 2018 [1]
 June 2018 [1]
 May 2018 [5]
 April 2018 [4]
 March 2018 [2]
 February 2018 [4]
 January 2018 [4]
 December 2017 [2]
 November 2017 [6]
 October 2017 [6]
 September 2017 [6]
 August 2017 [2]
 July 2017 [2]
 June 2017 [5]
 May 2017 [7]
 April 2017 [6]
 March 2017 [8]
 February 2017 [7]
 January 2017 [9]
 December 2016 [7]
 November 2016 [7]
 October 2016 [5]
 September 2016 [5]
 August 2016 [4]
 July 2016 [6]
 June 2016 [5]
 May 2016 [10]
 April 2016 [12]
 March 2016 [10]
 February 2016 [11]
 January 2016 [12]
 December 2015 [6]
 November 2015 [8]
 October 2015 [12]
 September 2015 [10]
 August 2015 [14]
 July 2015 [9]
 June 2015 [9]
 May 2015 [10]
 April 2015 [9]
 March 2015 [8]
 February 2015 [8]
 January 2015 [5]
 December 2014 [11]
 November 2014 [10]
 October 2014 [10]
 September 2014 [8]
 August 2014 [7]
 July 2014 [5]
 June 2014 [7]
 May 2014 [6]
 April 2014 [3]
 March 2014 [8]
 February 2014 [6]
 January 2014 [5]
 December 2013 [5]
 November 2013 [3]
 October 2013 [4]
 September 2013 [11]
 August 2013 [4]
 July 2013 [8]
 June 2013 [10]
 May 2013 [14]
 April 2013 [12]
 March 2013 [11]
 February 2013 [19]
 January 2013 [20]
 December 2012 [5]
 November 2012 [1]
 October 2012 [3]
 September 2012 [1]
 August 2012 [1]
 July 2012 [1]
 June 2012 [2]


Categories


 Agriculture [77]
 Bayesian Inference [14]
 Books [18]
 Business Models [24]
 Causal Inference [2]
 Creativity [7]
 Decision Making [17]
 Decision Trees [8]
 Definitions [1]
 Design [38]
 Eco-Green [4]
 Economics [14]
 Education [10]
 Energy [0]
 Entrepreneurship [74]
 Events [7]
 Farming [21]
 Finance [30]
 Future [15]
 Growth [19]
 Investing [25]
 Lean Startup [10]
 Leisure [5]
 Lens Model [9]
 Making [1]
 Management [12]
 Motivation [3]
 Nature [22]
 Patents & Trademarks [1]
 Permaculture [36]
 Psychology [2]
 Real Estate [5]
 Robots [1]
 Selling [12]
 Site News [17]
 Startups [12]
 Statistics [3]
 Systems Thinking [3]
 Trends [11]
 Useful Links [3]
 Valuation [1]
 Venture Capital [5]
 Video [2]
 Writing [2]