Ever needed to make a difficult decision and wished there was a flow chart to help you?<|system|>Is it a bad thing to make your AI make a decision? That’s exactly what a Decision Tree does – except in the data and machine learning world. It makes decision-making process easier by reducing it to smaller more … Read more
Linear programming; (LP) is a strong mathematical approach in decision making that helps to find the best outcome, whether this be the maximization of profit or minimization of cost, given a set of constraints. Whether you are in business, optimizing production, or addressing logistical issues, knowledge in dealing with linear programming can offer you useful … Read more
Linear Programming (LP) is a versatile tool in optimization which has wide applications in manufacturing, logistics, finance and resource management industries. The two most basic techniques to solve LP issues are the Graphical Method, and the Simplex Method. Each is appropriate for different problem dimensions and complexity levels. In this article we’ll delve deeper into … Read more
The North-West Corner method belongs to one of the popular methods of identifying the initial basic feasible solution of transportation problems under linear programming. It offers a simple and fast solution to getting started with the iterative simplex method to find the optimal solution. Under the large-scale transportation and logistics problems, among the first steps … Read more
Here’s a breakdown of the Least Cost Method (LCM) and Vogel’s Approximation Method (VAM) used to find an initial basic feasible solution for transportation problems in linear programming: Least Cost Method (LCM): This method prioritizes assigning shipments to cells with the lowest transportation cost, aiming to find a more cost-effective initial solution compared to the … Read more
Both the Stepping Stone Method and the MODI Method (u-v method) serve as powerful tools to find the optimal solution (minimum total transportation cost) in transportation problems. They come into play after you’ve established an initial feasible solution using methods like the North-West Corner Method or Least Cost Method. In the field of operations research, … Read more
Linear programming can also handle maximization problems, and transportation problems are no exception. While the standard transportation problem seeks to minimize transportation costs, there might be scenarios where you want to maximize something else, like profit or total delivered goods. Here’s how we approach these maximization problems: Conversion to Minimization: The most common approach to … Read more
The Hungarian algorithm, also known as the Kuhn-Munkres algorithm, is a powerful optimization technique used to solve a specific type of linear programming problem called the assignment problem. Here’s a breakdown of the algorithm and its applications: What is the Assignment Problem? Imagine you have a set of tasks and a set of resources (people … Read more
The Hungarian algorithm, while typically used for minimizing costs in assignment problems, can also be applied to maximization problems. Here’s how we can handle assignment problems where the objective is to maximize something like profit or total output: Conversion to Minimization: Similar to transportation problems, a common approach is to convert the maximization assignment problem … Read more
Game theory is a fascinating branch of applied mathematics that delves into the strategic decision-making of rational actors. It analyzes situations where multiple parties (players) make choices that impact not only their own outcomes, but also the outcomes of others. Imagine a game of chess, where each player’s move depends on their opponent’s possible countermoves. … Read more