﻿ Optimization Explained

Optimization Explained

The mathematical optimization provided by Solve helps you to use limited resources to produce the best possible outcome based on a variety of inputs and settings.

The process of optimization starts with a mathematical model of some aspect of your business - also known as a "Business Model". The business model is then extended into a "Decision Model" which includes the resources that are required for your business process (people, trucks, raw materials), the constraints to be satisfied (parts available, minimum order satisfied, geographical availability), and your objective (minimizing cost, minimizing late deliveries, maximizing profit). "Decision variables" are items whose values can be changed to find the best possible value of the objective. A mathematical optimization "solver" then combs through all possible solutions to find the best one.

The Solve plug-in lets users build such models through the Tabulate spreadsheet interface.

Optimization Examples

The following examples are provided to help users better grasp the use case for such analyses and models

• An e-commerce company wants to minimize the time taken to complete an order - this is the objective. The constraints might include the space available in different parts of the warehouse, and the logistics of moving items from one part of the warehouse to another. The decision variables are what items to put in different areas.
• A landlord wants to optimize the performance of their elevators at different times of day. Their high-performance elevators are designed to learn traffic patterns by time of day and place themselves in the optimal positions. For example, the restaurant floors at the top of a building might be busy in the evenings, so the elevators should be positioned there - whereas a lot of people are coming into the building early in the morning, so the elevators should be at the bottom. The objective is the time that people must wait for an elevator, which must be minimized. The constraints are the number and capacity of the elevators, and the number of floors - a full elevator must empty its passengers before it can take on another load. The decision variables here are the positions at which the empty elevators wait.
• A solar panel manufacturer needs to reduce costs regularly to remain competitive. The objective here is the unit cost, which must be minimized; the constraints are the costs of running the factories, and the expense of the machines required. The decision variables might relate to the time of day to run the machines, or how long to run them for continuously.
• A marketing team tries different pricing strategies and promotions for a given product, location, and customer. The objective in this case is to maximize the revenue from sales of the product. The constraints might relate to the cost price of the product - there is no point in discounting a product so much that it becomes unprofitable to make. The decision variables relate to the selling price - not so low that it makes the product 'not viable', not so high that it becomes unattractive to purchasers.

Explanation of Terms used in Optimization

The following terms are frequently used in optimization. Variables can be integers, and optimization problems always involve constraints, and decision variables. Optimization often focuses on finding a local maximum, rather than a global one, and optimization techniques are often referred to as linear programming.

Integers

When some, or all, of the variables are integers (whole numbers) - for example, numbers of people, cities, or engineering parts - the problem can be more difficult to solve than one with no integers.

Tip: When using Solve, you may want to make use of some of the Advanced Settings that help with integer problems such as this. For more information, see Advanced Settings.

Constraints

Constraints specify limits on resources, which must be followed for the solution to be valid. Decision variables are values that can be adjusted to find the best solution that satisfies the constraints.

Global Maximum, versus Local Maximum

While a local maximum is the best answer in a certain range of values, a global maximum is the best of all possible answers.

Finding the global maximum (over all possible values) might take too much time, or too many resources, or the maximum might not satisfy the constraints. If this happens, the local maximum is found, with all constraints satisfied.

Linear Programming

Linear programming (LP), also called linear optimization, seeks to achieve the best outcome (such as maximum profit or minimum cost) in a model whose requirements are represented by linear relationships.

Summary

Optimization can involve finding either the maximum value (profit, for example), or minimum value (cost, for example) for a given scenario. The optimization solution might require you to set a particular price or produce a specific number of items. The solution can be constrained, depending on factors such as lack of resources, or a requirement to use a certain minimum number of items. Any solution that finds the optimal value must satisfy these constraints if it is to be usable.