Mathematical Modeling Approach for Decision-Making in Competitive Markets

Estimated reading time: 7 minutes

In today’s world, running a business is like playing a high-stakes game. Since the rules are not there over time and change constantly. Not only that, but the minds of customers change, while on the other hand, market competitors are trying to one-up each other. Due to that, making the right move leads to breaking or moving your company’s market. In such crucial decision making, mathematical modeling helps a lot.

So that businesses stay ahead and make good choices when things are unpredictable, the best weapon is mathematical modeling. It is the way to convert and translate real-world problems, including business problems, into language that mathematics can easily understand and is tractable to solve. It is not bonded to mathematicians or economists. Mathematical modeling is a tool that can be utilized to make predictions and plan to profit better.

For instance, mathematical modeling helps businesses to make decisions in supply chains for the sake of competitiveness and more focused sustainability. It considers a simple supply chain of a manufacturer and retailer, whereby customers can select from options a traditional product and a greener(Basiri & Heydari, 2017).  And analyzed three ways of making decisions:

1. Deconsecrated – concentrated only on maximizing own profit.
2. Concentrated – aiming to increase the net income for the supply chain                                                                                                                              
3. Cooperative – consider working together to amend performance.

[image]

What Is Mathematical Modeling and why we Use it in Market Decision?

Mathematical modeling is a tool that can easily translate scenarios to mathematical language with assumptions of the scenario considered. Which means developing equations to represent supply and demand by utilizing optimization techniques. And can be used to simulate and thereby test different alternatives for effective lane to dice. In militant markets, this modeling includes:

• How price impacts demand?
• How production costs affect profit?
• How businesses react to competitors?

These mathematical models are very important for companies navigating complicated situations, as the majority of businesses are constantly deepening their products and prices. Using techniques of be-level programming, taking these decisions as problems of optimization, companies predict what competitions will do, evaluate contrary strategies, and maximize their profits by finding the solution. Fundamentally, these models extend a systematical, data-driven method that goes beyond elementary guesswork. They admit businesses to simulate different results, assess the pros and cons of each option, and in the end make informed determinations that better their competitiveness and profitableness(Beresnev & Suslov, 2010).

Many factors can influence the market: Markets are influenced by multiple factors: price, preference of consumers, activity of competitors, and resource constraints. Mathematical models, on the other hand, help us to make decisions: in order to predict behaviors of consumers, to optimize level of productions, to balance supply and demand interest, to react to competitors, and in order to minimize the loss or maximize profit. Modeling can provide an integrated way to analyze the outcomes before taking action. Rather than purely relying on trial and error.

Simple Example of Model in Action

Supply and Demand Model

One of the most fundamental mathematical models for decision making in economics uses two functions are

Demand: D(p)=a−bp and Supply: S(p)=c+dp.

In this functions corresponds the intercept on the quantity axis that is  when price is zero, on the other hand    corresponds the slope or inclination of the curve which means how quantity changes when price  fluctuate, and represents the price of the good. In demand functions, the negative sign of  is indicating an inverse relationship between price and quantity demanded. Where as in supply functions, the positive sign of    shows a direct relationship between price and quantity supplied.  

The following simulation represents the supply and demand model with parameter values of a = 100, b = 2, c = 20, and d = 1.5.

Real-Life Applications

If we see the areas where mathematical models for decision making are applicable, it is very wide and used in different sectors. For example:

• in the agriculture sector, mathematical models will be used to optimize crop choice and irrigation (Mellaku & Sebsibe, 2022);

• in the retail sector, shops will use mathematical models to put dynamic prices depending on demand forecasting;

• in the transport and logistics sector, companies use mathematical models to minimize fuel and time costs;

• in the policy-making sector, mathematical models will be used by governments to simulate tax effects on local markets;

Conclusion

Mathematical modeling is not only for economists or data scientists but also it is a practical and approachable tool for anyone who is interested and wants to make appropriate and data-driven determinations in a competitive world. Whatever you are learning, a mathematical model for decision-making will provide you with an edge and ground to clearly understand and pilot challenges.

Additionally, to stay updated with the latest developments in STEM research, visit ENTECH Online. Basically, this is our digital magazine for science, technology, engineering, and mathematics. Furthermore, at ENTECH Online, you’ll find a wealth of information.

FAQs

Q1. What type of data is needed for a mathematical model based decision making in order to build?

Answer: To build a mathematical model for decision-making, you need previous historical data of sales and market research data. Historical data helps identify patterns and trends, while market research provides crucial insights into consumer behavior and market conditions.

Q2: In a competitive market, what type of mathematical model will be used for decision making?

Answer: Linear programming and dynamic programming can the mathematical models of choice for decision making in a competitive market.

Q3: In the context of a competitive market, what is mathematical modeling used for decision making?

Answer: Mathematical modeling for decision making in competitive market is the process that represents real-world scenarios using mathematical equations.

References:

1. Mellaku, M. T., & Sebsibe, A. S. (2022). Potential of mathematical model-based decision making to promote sustainable performance of agriculture in developing countries: A review article. Heliyon, 8(2), e08968. https://doi.org/10.1016/j.heliyon.2022.e08968
2. Beresnev, V. L., & Suslov, V. I. (2010). A mathematical model of market competition. Journal of Applied and Industrial Mathematics, 4(2), 147–157. https://doi.org/10.1134/s199047891002002x
3. Basiri, Z., & Heydari, J. (2017). A mathematical model for green supply chain coordination with substitutable products. Journal of Cleaner Production, 145, 232–249. https://doi.org/10.1016/j.jclepro.2017.01.060