Methods for solving ‘or’ models
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This document discusses three main methods for solving operational research (OR) models: analytical methods, iterative methods, and the Monte-Carlo method. Analytical methods use tools like calculus and graphs to find closed-form solutions. Iterative methods are used when analytical methods are too complex; they start with a trial solution and iteratively improve it until optimal. The Monte-Carlo method experiments on a model by inserting random variable values and observing their effects on the criterion over time.
Methods for solving ‘or’ models
- 1. Methods for Solving ‘OR’ Models By Jishnu R
- 2. • In OR, we do not have a single general technique that solves all mathematical models that arise in practice. • A peculiarity of most OR techniques is that solutions are not generally obtained in (formula-like) closed forms. • Instead, they are determined by algorithms. • An algorithm provides fixed computational rules that are applied repetitively to the problem with each repetition (called iteration) moving the solution closer to the optimum.
- 3. Generally three types of methods are used for solving OR models. • Analytical Method • Iterative Method • The Monte-Carlo Method
- 4. Analytical Method • If the OR model is solved by using all the tools of classical optimization techniques such as: differential calculus and finite differences and graphs. • Analytical methods are non iterative methods to obtain an optimal solution of a problem. • Such type of solutions are called analytic solutions.
- 5. Example • To calculate economic order quantity (optimal order size), the analytical method requires that the first derivative of the mathematical expression be taken and equated to zero as the first step towards calculating, EOQ(Q) • TC=(𝐷/𝑄) 𝐶𝑜 + (𝑄/2) 𝐶ℎ Where, • TC total variable inventory cost • 𝐶𝑜 ordering cost per order • 𝑄 size of an order • 𝐷 annual demand • 𝐶ℎ carrying cost per time period;
- 6. • EOQ(Q)= 2𝐷𝐶𝑜/𝐶ℎ • This is because of the concept maximum and minimum used for optimality
- 7. Iterative Method • If classical methods fail because of complexity of the constraints or of the number of variables, then we are usually forced to adopt an iterative method. • Such a procedure starts with a trial solution and a set of rules (algorithms) for improving it towards optimality. • The trial solution is then replaced by the improved solution, and the process is repeated until either no further improvement is possible or the cost of further calculation cannot be justified.
- 8. Iterative method can be divided into three groups: • a. After a finite number of repetitions, no further improvement will be possible. • b. Although successive iterations improve the solutions, we are only guaranteed the solution as a limit of an infinite process. • c. Finally we include the trial and error method, which, however, is likely to be lengthy, tedious, and costly even if electronic computers are used
- 9. The Monte-Carlo Method • Method is based on idea of experimenting on a mathematical model by inserting into the model specific values of decision variable for a selected period of time under different conditions and then observing the effect on the criterion chosen. • In this method, random sample of specified random variable are drawn to know how the system is behaving for a selected period of the time under different conditions. • The random sample form a probability distribution, the value of the desired random variable can be estimated.
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