Mathematical optimization & Calculation Techniques
A catering service wants to determine the optimal menu for a wedding reception Objective: The objective of the catering service is to maximize the satisfaction of the guests while minimizing the cost of the menu. Catering Service Problem Constraints: Budget constraint: The total cost of the menu should not exceed the budget of the wedding…
Designing a reservoir for irrigation involves determining the optimal size and shape of the reservoir while considering various objectives and constraints. The objective of the reservoir design is to provide sufficient water for irrigation while minimizing the cost and environmental impact of the project. The following are the typical objectives and constraints that need to…
Project scheduling problem refers to the process of developing a plan that specifies when tasks will be started and completed, and how resources will be allocated to complete the project. The objective of project scheduling is to minimize the time and cost required to complete the project while ensuring that all constraints are met. The…
The decentralization problem refers to the process of delegating decision-making authority and responsibilities from a central authority to lower-level entities or individuals. In this context, the objective is to distribute power and responsibilities to improve efficiency, effectiveness, and responsiveness in decision-making. The decentralization problem can be formulated as a mathematical optimization problem with the following…
Machine scheduling problem involves scheduling a set of jobs on a set of machines while minimizing the overall completion time or makespan. The objective of this problem is to minimize the total time taken to complete all the jobs. Here are some of the constraints and objectives that may be considered when solving a machine…
Data Envelopment Analysis (DEA) is a linear programming-based technique used to measure the relative efficiency of decision-making units (DMUs) with multiple inputs and outputs. The basic idea is to compare the performance of each DMU against a set of “best practice” DMUs called the “efficient frontier”. The efficient frontier represents the most efficient combinations of…
Portfolio selection problem is a classic problem in finance, which aims to select a combination of financial assets to maximize the expected return of a portfolio for a given level of risk or minimize the risk for a given expected return. It is based on the assumption that investors are risk-averse, and they try to…
The diet problem is a classic linear programming problem that aims to find the optimal combination of foods to satisfy a set of nutritional requirements while minimizing the cost. The problem can be formulated as follows: Objective: Minimize the cost of the selected foods. Subject to: In mathematical terms, let ci be the cost per unit…
The Dovetail Model is a type of combinatorial optimization problem that is often used as a test case for optimization algorithms. The problem is defined as follows: Given a set of positive integers a1, a2, …, an, find the smallest positive integers x1, x2, …, xn such that xi ≥ ai for all i, and…
The Knapsack Problem is a classic optimization problem in computer science and operations research. The problem is typically defined as follows: Given a set of items, each with a weight and a value, and a knapsack with a capacity, choose a subset of the items to include in the knapsack such that the total weight…