Archive for February, 2010

Modeling Bass Diffusion with Rivalry

February 18th, 2010 4 comments

This is the last of a three-part series on the Limits to Growth Archetype.  The first part can be accessed here and the second part here.

Last time, we explored the effects of Type 1 rivalry (rivalry between different companies in a developing market) on the Bass diffusion model by replicating the model structure.  This part will generalize this structure and add Type 2 rivalry (customers switching between brands).

Bass Diffusion with Type 1 Rivalry

To model the general case of an emerging market with multiple competitors, we can return to the original single company case and use arrays to add additional companies.  In this case, everything except Potential Customers needs to be arrayed, as shown below (and available by clicking here).


For this example, three companies will be competing for the pool of Potential Customers.  Each array has one-dimension, named Company, and that dimension has three elements, named A, B, and C, one for each company.  Although each different parameter, wom multiplier, fraction gained per $K, and marketing spend in $K, can be separately specified for each company, all three companies use the same values initially.  All three companies, however, do not enter the market at the same time.  Company A enters the market at the start of the simulation, company B enters six months later, and company C enters six months after that.

Recall that the marketing spend is the trigger for a company to start gaining customers.  Thus, the staggered market entrance can be modeled with the following equation for marketing spend in $K:


The STEP function is used to start the marketing spend for each company at the desired time.  The ARRAYIDX function returns the integer index of the array element, so it will be 1 for company A, 2 for company B, and 3 for company C.  Thus, the offsets from the start of the simulation for the launch of each company’s marketing campaign are 0, 6, and 12, respectively.

This leads to the following behavior:


Note that under these circumstances, the first company to enter the market retains a leadership position.  However, companies B and C could anticipate this and market more strongly.  What if company B spent 50% more and company C spent 100% more than company A on marketing that is similarly effective?  This could be modeling by once again changing the equation for marketing spend in $K, this time to:

STEP(10 + (ARRAYIDX() – 1)*5, STARTTIME + (ARRAYIDX() – 1)*6)

Read more…

Modeling Real World Challenges Inspires Students

February 4th, 2010 No comments

Last summer I had the opportunity to see students from Diana Fisher’s dynamic modeling class at Wilson High School in Portland, Oregon present their modeling projects to participants of the International System Dynamics Society Conference in Albuquerque. The parallel session was filled with educators and professionals from different fields, many of whom are renowned system dynamicists.

I think it is safe to say that we all were very impressed by the quality of the students’ work and how well they understood the dynamics associated with the issues they were presenting.  Perhaps more striking however, was seeing how empowering modeling real-world issues is for young people and the enthusiasm they share for their work.

CC Modeling SystemsNow everyone can see the effect that modeling real-world issues has on students at the CC Modeling Systems web site. Dedicated to helping educators bring dynamic modeling into the classroom, the web site features videos of students presenting their work as compelling evidence to the value of incorporating System Thinking and system dynamics into curriculum.

You’ll be amazed to see what 14-18 year olds are capable of and the excitement they exuberate when addressing challenges such as:

Students are eager to understand the world better and are more than capable of building and understanding relatively sophisticated models in their attempts to understand the dynamics of real-world systems.

—Diana Fisher

Educators and administrators considering dynamic modeling curricula typically face challenges. No matter how compelling the evidence that Systems Thinking and the system dynamics methodology engages students and takes them to a higher level of reasoning, it is still difficult to justify without tying it to National Standards.

The CC Modeling Systems web site devotes an entire section to detailing very specific 21st Century Skills and National Standards addressed by curriculum that incorporates building system dynamics models.   Much of the homework has been done aligning this type of work to standards in the following subject areas:

Many thanks to Diana Fisher for sharing her students and her experiences teaching dynamic modeling with all of us!

To learn more about the modeling course that Diana teaches, I recommend the following links:
Recorded webinar presentation by Diana Fisher
Modeling Dyamic Systems: Lessons for a First Course