Using Model to Solve Problem

Let’s look at this step-by-step approach using a sample problem:

Imagine we are planning a trip and we want to visit as many cities as possible, but we have a limited budget for travel. This is a problem domain, and our goal is to maximize the number of cities visited within our budget constraint.

Step 1: Examine the Problem

In this step, we identify the key elements of the problem and understand its structure. Here, our problem is a classic optimization problem, with the goal of maximizing the number of cities visited given a budget constraint.

Key elements in this problem are:

  • Objective: Maximize the number of cities visited
  • Variables: The cities we can visit and the cost of traveling to each city
  • Constraints: The total budget we have for the entire trip

Step 2: Construct the Model

A model is an abstract representation of the problem that simplifies the real situation. In our case, we can represent each city as a node in a graph and each trip between cities as an edge. The cost of travel between cities can be the weight of the edges.

This model simplifies the actual problem but captures the essential features that we need to make a decision. In this case, we are excluding factors like the quality of travel, time spent in each city, or personal preferences about each city from our model. Including these factors would add complexity, but if they aren’t critical to our decision-making, then our model is better off without them.

Step 3: Solve the Model

Now we apply algorithms or techniques to solve the model. For our travel problem, we can use an algorithmic approach like the Greedy Algorithm, where we always choose the city with the lowest travel cost that we haven’t visited yet. We continue this process until we run out of budget.

By following these three steps, we can systematically address problems within their domain. This approach helps us focus on the core elements of the problem and create actionable solutions. Please note that the model’s effectiveness and the solution depend on how well we’ve identified and represented the key aspects of the problem. If our model doesn’t capture something crucial about the problem, the solutions we come up with might not work in the real world.

This process applies not only to this travel problem but also to various other situations in computer science, mathematics, business, etc., where defining variables, constraints, and objectives is essential to problem-solving.