# Simulation Optimization

From Training Material

## Contents

- 1 Overview
- 2 Need for Simulation Optimization
- 3 Mathematical methods vs Simulation
- 4 Heuristic
- 5 Metaheuristic
- 6 Metaheuristics
- 7 Problems with Simulations
- 8 Metaheuristics
- 9 Optimization of Simulation Models
- 10 Applications
- 11 Black-box Model
- 12 Simulating Result
- 13 Uncertaintiy
- 14 Academic Approaches
- 15 Pragmatic Approach
- 16 Evolutionary Approaches
- 17 Constraints
- 18 Constraints and Feasability

## Overview

- BPMS offers simulation capabilities
- Simulation is "a means to evaluate the impact of process changes and new processes in a model environment through the creation of “what-if” scenarios"
- decisions can be tested before going life
- simulation allow forecast with a level of uncertainty

## Need for Simulation Optimization

- analyst wants to find a set of model optimal performance (parameters and structure)
- range of parameter values and the number of parameter combinations is too large for analysts to simulate all possible scenarios
- they need a way to find a good solutions

## Mathematical methods vs Simulation

- many problems are too complex to be modelled in analytical way
- pure optimization models alone are incapable of capturing all the complexities and dynamics of the system
- simulation cannot easily find the best solutions
**Simulation Optimization**combines both methods (analytical optimization of the simulation or vice versa)

## Heuristic

- Greek: "Εὑρίσκω": find, discover
- technique designed for solving a problem more quickly when classic methods are too slow
- finding an approximate solution when classic methods fail to find any exact solution (by trading optimality, completeness, accuracy, and/or precision for speed)
- e.g. rule of thumb, an educated guess, an intuitive judgement

## Metaheuristic

- designates a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality
- make few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions
- do not guarantee an optimal solution is ever found
- implement some form of stochastic optimization.

(Wikipedia)

## Metaheuristics

## Problems with Simulations

- Optimization models were thought to over-simplify the real problem
- this was improved by research in
**metaheuristics**along with improved statistical methods of analysis

## Metaheuristics

- Coined in 1986 by Dr. Fred Glover
- "describe a master strategy that guides and modifies other heuristics to produce solutions beyond those that are normally generated in a quest for local optimality"

- There are algorithms to guide a series of simulations towards good results in the absence of tractable mathematical structures
- Quality of different solutions can compared
- commercial products use discrete-event or Monte Carlo simulation to performs search for optimal values of input parameters
- tool for commercial simulation software, employs metaheuristics (
**scatter search**,**tabu search**,**neural networks**)

## Optimization of Simulation Models

- develop simulation model for a system or a process
- set performance measure (for possible set of choices)
- find a configuration that produce good results

- Extreme Methods

- trial-and-error
- enumeration of all possible configurations

## Applications

- configuration of machines for production scheduling
- layouts, links, and capacities for network design
- investment portfolio for financial planning
- utilization of employees for workforce planning
- course scheduling

## Black-box Model

- Input

- input parameters and/or structural design that lead to optimal performance (
**factors/levels**,**decision variables**)

- Output

- performance measures (
**responses**- used to model an objective function and constraints)

- Goal

- find out which factors have the greatest effect on a response
- combination of factor levels that minimizes or maximizes a response
- subject to constraints imposed on factors and/or responses

- Constraints

- constraint for both: decision variables and responses need to be formulated

- Example
- manufacturing facility
- factors - number of machines of each type, machine settings, layout, and the number of workers
- responses - cycle time, work-in-progress, and resource utilization
- goal - reduce cost, minimize cycle time, minimize resource utilization (subject to constraints)

## Simulating Result

- "Changes proposed to business processes can be simulated"
- "
**Sensitivity**of making the changes on the ultimate objectives can be examined and quantified, reducing the risk of actual implementation"

- Changes

- adding, deleting, and modifying processes
- process times
- resources required
- schedules
- skill levels
- budgets

- Performance objectives

- throughput
- costs
- inventories
- resources/capital utilization
- cash flow
- waste

## Uncertaintiy

In BPM:

- simulation: a way to understand and communicate the uncertainty related to making the changes,
- optimization: provides the way to manage that uncertainty

## Academic Approaches

- Stochastic approximation (gradient-based approaches)
- (sequential) response surface methodology
- random search
- sample path optimization (also known as stochastic counterpart)

## Pragmatic Approach

- Commercial simulation software employs metaheuristics

## Evolutionary Approaches

- commercial simulation uses evolutionary approaches
- Evolutionary approaches: builds and evolves population of solutions
- e.g.
**Genetic Algorithms**and**Scatter Search**.

- a simulation model can be thought of as a

“mechanism that turns input parameters into output performance measures” (Law and Kelton, 1991)

- simulation model is a function that evaluates the merit of a set of specifications, typically represented as set of values
- Looking at simulation model as a function encouraged family of approaches to optimize simulations based on
**response surfaces**and**metamodels**.

## Constraints

- speciying constraints is important feature of simulation optimization
- constraints define the feasibility of trial solutions
- specified as mathematical expressions or as logic statements
- usually formulated with input factors or/and responses

## Constraints and Feasability

- constraints in a simulation optimization model depend only on input parameters -> new trial solution can be checked for feasibility before running the simulation
- infeasible trial solution may be discarded or may be mapped to a feasible one when its feasibility depends only on constraints formulated with input parameters
- constraints depend on responses -> feasibility of a solution is not known before running the simulation