Question

In manufacturing, there are multiple "parts" to the process. Why is it important to determine what the best solution is when multiple options are available? What are the benefits of using LP (linear programming)? Are there ways to look at the results of LP and evaluate what the best solution is?

Answer 1

The manufacturing process comprises of a number of processes, each one has different constraints associated with it. These constraints are about limits on availability of time, resources, raw materials and other variables that go into the process. These limits are governed by a number of factors like labour availability, material supplies, power availability, stocking capacity and so on. Linear programming is a technique that takes into account, all these constraints to come up to a solution which maximises / minimises a factor. This factor, called objective function, can be either cost ( which needs to be minimised) or profit ( that needs to be maximised) through collective inputs of variables ( which might vary from 2 to a number of them). The results of a linear programming problem is in form of different values of variables ( each in a set), that give different values of the corresponding objective function. The set of variables which corresponds to highest value ( maximisation problem) or minimum value ( minimisation problem) is the optimum solution of the problem. It is that combination of the values of variables that yiled optimum solution to the problem.