System Dynamics

560.657

Homework 5

Problem 1:

Recalling the model we developed in Class 5 (fig. 1), modify it to describe the situation described below.

Figure 1

Business competition for market share is a basic process. Competition favors one or several companies to the disadvantage of their competitors. Sometimes coexistence of competitors is possible, and other at other times, competition may lead to gradual disappearance of disadvantaged competitors.

For two competing companies, A and B, model which is at a greater relative disadvantage (e.g. due to smaller growth rate). Consider under what competition parameters is coexistence of both companies possible.

Both companies grow in proportion to their growth rates (gRA and gRB). Logistic growth is assumed for both the growth rate of populations (gA and gB), with carrying capacity limits (kA and kB). A competition effect parameter (CompEffA and CompEffB) is assumed and a (competition) proportional to the size of both Company A and Company B. The decrease rate is represented by lossA and lossB.

Model Structure Hint

The model is identical to the prey-predator except the following:

•    The red arrows connect, not to the other stock, but to the common variable “competition”.

From here, another arrow connects to losses rates.

•    A new carrying capacity parameter (kA and kB) affect the growth rates (gA and gB).

Parameters and initial states

•    Initial size of Company A = 0.015 [amountA]

•    Initial size of Company B = 0.015 [amountB]

•    gRA = 1 [1/Month]

•    grB = 0.99 [1/Month]

•    kA = 2 (amountA)

•    kB = 2 (amountB)

•    CompEffA = 1 [1/(amountB* Month)]

•    CompEffB = 1 [1/(amountA *Month)]

Model Dynamics

•    competition = Compaby A * Company B [amountA* amountB]

• gA = gRA * CompanyA *(1 – CompanyA / kA) [amountA/Month]

• gB = gRB * CompanyB *(1 – CompanyB / kB) [amountB/Month]

•    lossA = CompEffA *competition [amountA/Month]

•    lossB = CompEffB *competition [amountB/Month]

•    CompanyA = INTEG (gA – lossA, Initial size of Company A) [amountA]

•    CompanyB = INTEG (gB – lossB, Initial size of Company B) [amountB]

Time parameters

•    To  = 0 [Month]

•    Tend  = 25 [Month]

•    tstep  = 0.01 [Month]

Results

•    Provide a screenshot of the Vensim SFD

•    Provide a plot of the progression of CompanyA, CompanyB, and competition.

•    For which values of gA and gB there’s no decrease in the values of CompanyA or CompanyB?

•    What’s the effect of the parameters CompEffectA and CompEffectB on lossesA and B rates?

•    Submit the report and models .mdl.

Problem 2

Given the situation description below:

1.    which of the system archetypes fits the situation best? Why?

2.    What solution would you suggest? (using the archetype diagram)

3.    Please provide drawings of the archetype you select and the solution you’d implement

A list of the archetypes is given in Kim, D. (2000). System Archetypes I. Pegasus and Braun, W. (2002). The System Archetypes. The Systems Modeling Workbook. Both in Canvas Module 5 folder.

In the 1980s, manufacturers developed a strategy for increasing profits and enhance market share of certain non-seasonal consumer products which consisted in offering heavy discounts and promotions.

However, a side effect of this strategy was that it started creating huge costs and difficulties for distributors such as Costco. To improve their own margins, these in turn reacted by buying large quantities of the specific products during the discount period and selling them at regular price later. The sheer quantity of the products sold by Costco, exceeded the manufacturers’ provisions, and severely weakened the manufacturers’ profitability and other logistic problems. This created a war of sorts between manufacturers and retailers like Costco, and both resorted to mutually damaging practices. In the end, short-term profits from promotions were washed away by long-term costs.