OPTIMAL PRICING STRATEGY: A SYSTEM DYNAMICS SIMULATION STUDY Balaji Janamanchi Ph.D. Assistant Professor of Management Texas A&M International University, Division of International Business and Technology Studies, COBA 5201, University Boulevard, Laredo, Texas 78041, Phone: (956)326-2537 Fax : (956)326-2494, Email: [email protected] James R. Burns, Ph.D., P.E., CIRM Professor of Operations Management and Information Technology Rawls College of Business Administration ISQS Area, P.O. Box 42101 Texas Tech University Lubbock, TX 79409-2101 (806)742-1547 Fax-(806)742-3193 Email: [email protected]

ABSTRACT As business systems grow in complexity by the day, the need for a new breed of tools capable of dealing with such ever increasing complexity arises. Systems thinking and system dynamics belong to such a breed of tools that help managers first, to understand the complexity that is inherent in modern business systems and next, to develop appropriate managerial perspectives necessary to formulate effective policies. The complexity being studied is dynamic and behavioral complexity rather than detail complexity. Behavioral complexity in business systems is caused by nonlinear relationships, delays, and feedback loops. This study demonstrates the effects of nonlinear relationships between system variables when system operates close to its boundary or limiting conditions. 1. INTRODUCTION Jay W. Forrester, the founder of System Dynamics, while analyzing the characteristics of socioeconomic systems remarked, “…social systems exhibit a conflict between short-term and long-term consequences of a policy change.” Forrester further elaborates, “A Policy that produces improvements in the short run is usually one that degrades a system in the long run. Likewise policies that produce long-run improvements may initially depress behavior of a system” (Forrester, 1971). Though these statements were made in the context of systems that may be guided by a totally different set of goals and objectives than the modern-day business systems, the substance of these statements is also true of complex modern-day business systems. 312

Peter Senge (1990) makes a similar observation while explaining his famous laws of systems thinking, and states, “system behavior grows better before it grows worse.” An improvement in the behavior of systems is not necessarily a sure indicator of continuing improvement but could very well be a false indicator that may be indicating a downtrend in the long-run. From these observations, one can deduce that short term system trends do not tell the complete story; hence, a capture of the behavior-over-time (BOT) of the system variables is necessary to gain a deeper and better understanding of complex system behavior. For instance, consider the dilemma facing management when determining the product pricing strategy. Pricing the product high will obviously yield a higher margin per unit sold and will yield a higher profit in the immediate short run. Buy such high price may hamper sales growth and become counter productive in terms of sustaining increased growth in profitability. On the other hand a low price strategy may quickly attract large numbers of customers in the short run, but may leave the manufacturer with little or no profit margin and consequently earning much lower profit than he would make at lower levels of volume with higher prices. This is a typical dynamic complexity issue. The business system is so complex with so many interrelated and interacting system components that it‟s is very hard to visualize the behavior of the system variables without the help of some visual tools like behavior-over-time (BOT) charts. The complexity gets confounding when the system in question operates close to its boundary or operating limits because under those circumstances the nonlinear relationships between the system variables are more pronounced than at any other level of system operation. The rest of this paper is organized as follows. Section 2 discusses the modeling tool used and explains the general outline of a typical market setting being modeled. The results from the simulation of the model under three alternate strategies of High, Mid, and Low sale price for the product are presented in section 3 with a control variable growth rate with lower and higher growth rate normal options. This is followed by discussion of inferences and insights that may be drawn and developed respectively, from these results. Finally, in section 4 we describe the contributions and limitations of the current model. 2. MODEL DESCRIPTION System dynamics is a modeling methodology that characterizes processes, systems as flows of goods, materials, cash, resources that are controlled by information transfers (Sterman, 2000). System Dynamics modeling has been shown to be an effective tool to study business dynamics by the system dynamicists (Forrester, 1958, 1961; Sterman, 2000). In this paper, we shall utilize system dynamics to model a hypothetical business enterprise operating in a small city. The enterprise vends a consumer product that needs to be consumed on-site or alternatively one that can‟t be stocked or transferred to another place from where it was produced because of its inherent nature and character. The simulation model is developed using the simulation software Vensim (Ventana, 2007a). Brief overview of the market set up. The market being modeled is of a city that has approximately 200,000 initial population, and is growing at a rate applicable to a typical city in Texas. For this purpose we chose Laredo, Texas as the basis (CensusScope, 2007). As stated already, the hypothetical business is dealing in a product that needs to be consumed on-site or 313

within the vicinity of the place of provision. This product could very well be any normal consumable product that a vendor sells such as shaven ice, hot chocolate, movie show, and boatride or like product or service. There are no other businesses (sellers) offering this product/service in the market, but the seller is not free to demand a monopoly price because such decision may drive the consumers to other alternatives. Let‟s assume that based on past history the consumption norms of the product/service are available, as is the consumer sensitivity to price. Model Structure. Exhibited below in Figure 1, is the system dynamics structure for the sales and market sector of the model. The fundamental logic and constructs for the model structure are drawn from the state-of-the-art models presented in Sterman (2000). Only the required constructs from this source referred above have been adopted. Suitable programming constructs have been incorporated to capture the logic of price-demand elasticity subject to the ceiling in demand as limited by the potential market size. Potential market size is limited by the population of the city, which in turn is limited by the historical population growth rates as adopted from CensusScope (2007). Sales and Potential Market View SALES GROWTH RATE NORMAL

SALES DECLINE RATE NORMAL

PRICING STRATEGY

Qty Sold decrease rate

increase rate Strategy multiplier



AVERAGE CUSTOMER CONSUMPTION RATE

market share

Strategy multiplier Tab

growth rate

Potential customer population

CUSTOMER GROWTH RATE NORMAL

exit rate CUSTOMER EXIT RATE NORMAL

Figure 1: Sales and Potential Market View A month is the unit of time in this model. In the lower half of the figure, the population stock with net growth is captured. The growth rate and exit rate (per month) are adopted after carefully analyzing (and manually calibrating) the net growth rate as given by CensusScope (2007) for a typical city in Texas. Initial population is set at 200,000 persons. In effect, the mathematical equation of the population is 314

t

Population (t) = OR

to

[ growth exit ]

Population (to)

Population(t) = INTEG (+growth rate-exit rate, 200000) Where the units is „person‟ Similarly, the mathematical equation for Qty Sold is t

QtySold (t) = OR

to

[increase decrease]

QtySold (to )

QtySold(t) = INTEG (+increase rate-decrease rate, 1e+006) Where the unit is unit of product/service sold

The average consumption rate is set at 10 units (per person * per month). Initial customer population * average consumption rate yields the total potential market. Depending upon the sale price being charged, the seller is able to capture a certain portion of this potential market, which we term as “market share” for the limited purpose of this study. At the start of the simulation, the business is selling 1,000,000 units per month reflecting a capture or market share of 50% of the potential market. Depending upon the pricing strategy adopted by management, a strategy multiplier is chosen from a table lookup to reflect the elasticity in demand in response to price variations. Similarly, the pricing strategy also affects the potential market. For example, the potential market is limited to 80% if the pricing strategy is higher than a „medium‟ price. A rate of decline in sales is incorporated to reflect the exiting of customers from the market or otherwise. The following structure of the financial metrics depicted in Figure 2 captures the behavior-over-time of the financial metrics for the given changes in the pricing strategies. normalizing factor

Financial Metrics View

variable cost per unit

gross profit per Unit

VARIABLE COST COMPONENT

Strategy cost multiplier

FIXED COST COMPONENT

sale price



total revenue

total costs

price tab lookup Gross profit GP Ratio

OVERHEAD EXPENSES

monthly net profit accumulation rate

MACHINERY DEPRECIATION profits before tax



net profit after tax

monthly depn accumulation rate

taxation accumulated depreciation

cumulative profit profit per unit

cumulative retained profits

Figure 2: Financial Metrics View 315

As may be noticed, this view is primarily concerned with accumulating revenues and costs based on the volume of operations and reporting of the resulting profit numbers. The beauty of the system dynamics modeling is the capability to capture the non-linear interrelationships between the variables (feedback loop effects) and the depiction of the behavior of the variables over time (BOT). By carefully writing out the relevant equations, it is possible to capture all the aspects of the business decisions and the resulting behavior in a simulation model. The complete alphabetical listing of all equations used in the model is provided as Appendix A. Initial Parameter/Policy Setting. Table 1 given below lists the initial values for the major stocks and policy parameters of the model. Parameter Average Customer Consumption Rate Customer growth rate normal Customer exit rate normal Final time Fixed Cost component Machinery Depreciation Overhead Expenses Potential Customer Population Pricing Strategy Price: High Price: Medium Price: Low Quantity Sold Sales Decline Rate Normal Sales Growth Rate Normal Sales Growth Rate Normal (higher) Taxation Variable cost component

Units of measurement

Units/ (person * Month) Dmnl/Month Dmnl/Month Months Dollars/Month

Qty 10 0.00415 0.001 120 50,000 0.1 0.1 200,000 3(medium) 1.50 1.25 1.00 1,000,000 0.001 0.02 0.025 0.25 0.25

Dollars/(units*Month) Dollars/(units*Month) Person Dmnl Dollars/Unit Dollars/Unit Dollars/Unit Units/month Dmnl/Month Dmnl/Month Dmnl/month Dmnl dollars/units Table 1: Initial and Key Parameter Settings The other parametric settings may be seen from the equation listing given in Appendix A. 3. RESULTS FROM ALTERNATE POLICIES

Below we shall simulate three alternate scenarios of adopting a High, Medium and Low price strategies to ascertain which strategy appears to yield better results in terms of sustained profitability under a reasonable growth rate normal for the sales. Predictably, the Low price strategy results in the highest volume of sales as may be seen from Figure 3 depicted below.

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Figure 3: Quantity sold, under three alternate price strategies However, the cumulative retained profits tell a different story as seen in Figure 4 below.

cumulative retained profits 200 M 2

150 M dollars

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cumulative retained profits : LP cumulative retained profits : MP cumulative retained profits : HP

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Figure 4: Cumulative retained profit, under three alternate price strategies We repeat the same three strategies under a higher growth rate normal for the sales (using growth rate normal as a control variable). The difference in the runs is relatively less because the system is operating close to it boundary conditions (approaching the limit of potential customer demand). This is evident from the fact that the increase in sales recorded despite the higher growth rate normal is very minimal as shown in Figure 5 below. Its is also interesting to note the non-linear rate of increase (less than proportionate, in this case) despite increase in the stock of 317

quantity sold, while holding the growth rate normal steadily constant. As for the cumulative retained profit, the Medium price strategy is a clear winner once again as seen in Figure 6 below.

increase rate 60,000 1

45,000 units/Month

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30,000

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increase rate : LP increase rate : MP increase rate : HP 6

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84

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Figure 5: Increase in sales, under various strategy options

cumulative retained profits 200 M 2

dollars

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cumulative retained profits : LP_Hgrn cumulative retained profits : MP_Hgrn cumulative retained profits : HP_Hgrn

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Figure 6: Cumulative retained profit, under alternate scenarios with a higher Growth rate normal assumption Optimization run to fine tune the policy choice: Having inferred from the above figures that Medium price strategy is performing better than low and high price strategies, the study proceeded to find what further fine tuning is possible in the pricing strategy to improve the 318

cumulative retained profits. Vensim offers excellent support for such optimization by allowing users to specify the results that need to be optimized with possible variation in the independent input variables (user can choose the range of values that an input variable can assume). Vensim software has built-in „Powell‟s hill climbing algorithm‟ (Powell, M.J.D., 1964) to perform search for the parameter optimization (Ventana Systems Inc., 2007b). We seek to optimize the cumulative retained profits by allowing the pricing strategy to vary between 1 and 5 (low-to-high price strategies). The optimization run returns a pricing strategy value of 3, meaning a recommendation for medium price strategy.

cumulative retained profits 200 M

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48 60 72 84 96 108 120 Time (Month) cumulative retained profits : Optimal_sp 1 1 1 1 1 1 cumulative retained profits : LP_Hgrn 2 2 2 2 2 2 cumulative retained profits : MP_Hgrn 3 3 3 3 3 3 cumulative retained profits : HP_Hgrn 4 4 4 4 4 4

Figure 7: Optimization run, endorses medium price strategy

Obviously, if the system were to pick a fractional number between 2 and 3 or 3 and 4, it would mean a product mix of certain proportion of Low price product and Medium price product, or a combination of Medium price product and High price product. Will the recommendations be different, if the average consumption rate increases? To answer this question, we can set the consumption rate higher and rerun the optimization option to ascertain the pricing strategy values. The average consumption rate is now increased from 10 units/(per person * per month) to 15 units/(per person* per month). Once again, the optimization run returns a strategy close to Medium price strategy at 2.97 which is almost equal to 3. It is interesting to note that the strategy is leaning slightly towards the Low price than High price direction. Table 2 below summarizes the alternate simulation run results.

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Simulation run name

(Unit of measurement) LP MP HP LP_Hgrn MP_Hgrn HP_Hgrn Optimal_SP Optimal_AboveAvgCon

Price Strategy 5=High 3=Medium 1=Low

Dmnl 1 3 5 1 3 5 3 2.97

Growth rate normal

Avg Consumption normal

Qty Sold

Cumulative Retained Profit

dmnl/month 0.02 0.02 0.02 0.025 0.025 0.025 0.025 0.025

Unit/(per person*per month) 10 10 10 10 10 10 10 15

Units in Millions 2.765 2.587 1.654 2.795 2.666 1.778 2.666 3.990

Dollars in Millions 140.38 155.87 120.69 143.90 163.93 127.42 163.93 229.21

Table 2: Summarized results for alternate policy scenarios Its may easily be noted that whether sales growth rate is normal or higher, the medium price strategy yields better results than Low and High price strategy (note the rows for MP and MP_Hgrn in Table 2, paying specific attention to Cumulative Retained Profit). Thus, the optimal price strategy at the current consumption rate as well as the increased consumption rate is to stick with medium price. System dynamics models provide the managers with decision support in cases involving dynamic complexity. As Sterman observes, the “…mental models people use to guide their decisions [in dynamic complex systems] are dynamically deficient” (Sterman, 2000, pp. 27). While, simplified system dynamics models like the one developed in this study may not be able to capture to stochastic behavior of market forces, they can provide reasonably reliable decision support under the assumption of market forces remaining what they are at present. As was done in this case, alternate scenarios with likely changes (as with average consumption rate, or sales growth rate normal) can be simulated to find out likely responses in the system behavior or system variables behavior. It will not be out of place here to recall the Policy Sensitivity Test recommendation, namely, “If two plausible sets of parameters can lead to the same policy, then recommendation of such policy will have greater validity than otherwise” (Forrester and Senge, 1979). We definitely have such recommendation in support of Medium price strategy. 4. CONTRIBUTIONS AND LIMITATIONS This study has shown that System Dynamics modeling can provide decision support for highly complex business systems. We have also seen the benefits of optimization runs facilitated in the Vensim simulation environment. Managers can make use of simulation tools to study and analyze the business problem situations in a systemic perspective and assess the impact of alternate policy options before implementing the same in real world business. This study has shown that by carefully analyzing and suitably modeling the business operations and the financial record keeping, managers can assess the financial implications of alternate policy options. 320

In summary, the contributions of this study are: First, a general hypothetical case is modeled, analyzed with the model and then optimized, providing some general insight into the problem class characterized, namely, retail vendors who provide on-the-spot products/services. Second, the paper demonstrates the applicability of system dynamics modeling technique as a commercial decision support system for the class of users characterized. Third, all retailing vendors must make pricing decisions and this study has prototyped a tool for assistance in regard to that decision. Some Limitations: However, it must be understood that no single tool is comprehensive enough to provide decision support in all decision situations. Managers should try to develop alternate perspectives with the help of alternate tools/models so they can take robust decisions based on insights developed from such alternate approaches.

References CensusScope, 2007, Population Growth, Laredo, TX at the http://www.censusscope.org/us/m4080/chart_popl.html accessed on September 14th.

URL

Forrester, Jay W, 1958, “Industrial dynamics: a major breakthrough for decision makers,” Harvard Business Review 36(4); 37-66. Forrester, Jay W, 1961, Industrial Dynamics, MIT Press, Cambridge, MA (now available from Pegasus Communications, Waltham, MA). Forrester, Jay W., 1971, “Counterintuitive Behavior of Social Systems,” MIT System Dynamics literature collection, D-4468-2, pp11 Forrester, J.W., Senge, P.M., 1979, “Tests for Building Confidence in System Dynamics Models,” MIT system dynamics literature collection, D-2926-7. Powell, M.J.D., 1964, “An efficient method for finding the minimum of a function of several variables without calculating derivatives” Computer Journal., Vol. 7, pp 155-162, July. Senge, Peter M., 1990, The Fifth Discipline: The art and practice of the learning organization, Doubleday/Currency, 1st edition. Sterman, John D., 2000 Business Dynamics-Systems Thinking and Modeling for a Complex World McGrawHill Companies Inc. Ventana Systems Inc, 2007a at http://www.vensim.com/new.html accessed on September 14th. Ventana Systems Inc, 2007b at URL http://www.vensim.com/optimize.html Vensim documentation, accessed on September 14th. -o0oNote: List of equations used in the model are available upon request from the first author. 321