Show According to the optimization model, interference varies inversely with the strength of a trace, where trace strength is proportional to its frequency of activation (Brainerd, 1995). From: Advances in Psychology, 1998 Optimisation is using a set of mathematical techniques to find the best possible solution to a business problem, generally minimising costs, maximising yields, specific resource assignments and exploring best possible time of activities. Here are some examples of optimisation in achieving business goals (individual or in combination):
The process involves an optimisation model (objective function, decision variables, constraints), data (to create the instance of the model) and an optimisation engine/solver (algorithms to solve the model instantly). In mathematical term, the purpose of optimisation is to find the values for the decision variables to satisfy all constraints and optimise the objective function. Optimisation Engine / SolverAn optimisation engine or solver is a set of algorithms. Different algorithms solving different types of optimisation problems. The algorithm is a search mechanism to find better and better solutions efficiently (fast enough) among the different possible alternatives based on the model (type). Algorithms have been measured how fast they can solve a problem in function of the size (worst-case / average …) Read: Optimization Engines Make The Industry Efficient Optimisation ModelThe typical optimisation model development cycle is
Objective FunctionWe need to first identify the objective in performing optimisation. As well as the metric(s) or Key Performance Indicators (KPIs) we would use, to compare and determine the best solution among the solutions. Objective function is a mathematical representation of the business objectives or goals to be achieved. It always starts with “maximise” or “minimise” of the outputs, for example, minimising costs, idle or time, also, maximising revenue, throughput, profitability, customer satisfaction or employee preferences. It can be a simple expression involving a single objective or a more complex expression combining several objectives. Each alternative (solution) is measured by a goal (function = cost, time, #people), that is, alternative 1 is better than alternative 2 if the measurement on alternative 1 is better than the (same) measurement on alternative 2. It is said that a solution is optimal if it is the best alternative among all the possible solutions, measured by a goal. Decision variablesEach model has several variables. Each variable has several possible values. Decision variables are the values or decisions that can be changed to arrive at the best solution possible for the objective function. They are determined during the solution process (solver engine) or possible initial guess. The inputs can be the demand to be met, resources available, costs, yields & recipes, operational constraints & customer preferences and business goals. They have a domain (a set of possible variables), bounds (upper and lower limit of the domain) and a type (: integer, boolean…). It is important to choose the decision variables well, in which will impact the formulation of the constraints.
ConstraintsConstraints define the relationship between different decision variables. They represent the limits within which the solution should exist. There are 2 types of constraints:
Global operating constraints
Individual operating constraints and preferences
Optimization TechniquesThere are two main optimisation techniques, which are Mathematical Programming (MP) and Constraint Programming (CP). Mathematical (MP)
Constraint (CP)
When problems are particularly hard, some hybrid approaches are known to bring "the best of both worlds" - typically a MP + CP approach. This is how batching + detailed scheduling is done in many optimisation tools for manufacturing. We can help you identify the best technology to solve your problem, create suitable models and benchmark them, using all of the best engines (CPLEX/CPO, Gurobi, LocalSolver and FICO Xpress). |