OPT Exam

Conveyor vs Path

- Can have initial desired speed for separate conveyors

SIMIO - Property to analyze in experiment

- Choose something like initial capacity of a server - Right click it - Set Referenced Property - Create new reference property - Name it something - Now a variable that can be modified - Go to experiment and can see a new column appeared - Change this value per scenario

SIMIO - Transfer Node

- Conveyor from source to this from two or more locations - Another conveyor from transfer node to server - Definition tab and states · TimeProcessing to create a variable - Click transfernode and add-on process triggers · Something will happen when entity comes in or exits · Double click on entered - This opens processes for this ·-Creating behavior for entities entering · Use decide step - When entity enters node, processing time is decided here - Give condition or probability for decide - Select is.entity1 · Use assign block on each path - ModelEntity.TimeProcessing - Assign a value to this - Do for both - Need to click on server and change Processing Time to ModelEntity.TimeProcessing o Transfernode § If something happens, customers can go to exit § If server reach amount of cakes we want, avoid sending more customers to server because we ran out of cakes o Click on transfer node and double click add on process triggers - entering o Open process modelling page o Use decide block § If amount of entities arriving is more than a certain amount, send elsewhere o Create new property / integer variable in definitions tab § Chocolate_Server_Limit · Default value is 5 § Vanilla_Server_Limit · Default value is 4 o Now want to create a counter, something than can grow in size § Use state variable / integer variable § Chocolate_Counter § Vanilla_Counter o Use node as entrance to server § State Assignment and on entering -> Click § Count how many are entering server § Add new rule § State Variable Name - Chocolate_Counter · New Value is Chocolate_Counter + 1 o Go to animation tab and drag in a status label § Click on it and write in expression Chocolate_Counter o Go back to Processes tab § In decide block, is condition based § Chocolate_Counter<Chocolate_Server_Limit § Put assign block behind true and false paths § Want to change path selection weights so once limit is reached, weight of path to server changes from 1 to 0 and vise versa on path to exit o Go back to definitions and make a new state integer variable § Chocolate_Connector_Weight o Go back to Processes tab § Click on assign for true path (if chocolate cakes still less than limit) § State Variable Name is Chocolate_Connector_Weight § Give value of 1 § For false path, do same but write 0 o Go to model and write for path's selection weight 'Chocolate_Connector_Weight' § Other path (to exit) write in for selection weight "1-Chocolate_Connector_Weight"

Simulation and Probability

- In order to model the objects dynamics with the several objects and components the probability is used - Often this variability is described with the use of probability density function, or distribution functions - A Probability Density Function, f(x) is a positive function whose area is no more than one, and whose area, in a specific interval, describes the probability that a random value lies into such interval

Challenges with Work Scheduling Modelling

- Irregular Work Scheduling, e.g. flex-time. - Irregular work shifts, e.g: People work on individual work shifts, - Many extra irregularities, e.g.: Specific laws, and agreement between workers and employees

Optimal Solution

- Problem of finding best solution from all feasible solutions - Satisfies all constraints with a maximum or minimum objective function value - In linear programming, optimal solution occurs at one or more corner points or on a line segment between two corner points.

SIMIO - Processes

- Processes are useful to force a specific behaviour for a predertermined object.

Feasible Region

- Sample space of x vectors satisfying all the problem constraints - Set of all possible points of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints (all possible feasible solutions)

Steps to Solve SIMIO

1. Think about your model and reflect on the problem. Which elements need to be represented? 2. Identify the parameters you need to insert in your problem. Set time and elements. Focus on Properties of elements. 3. Run a simulation Press run in SIMIO. Set up running time. 4. Reflect on the parameter Results are displayed in the Results Panel. It is important to individuate and the parameters which are essential to study the problem. The resulting panel describes the features and the result of the simulation for each individual object.

System

A combination of components acting together to perform a function, not possible if one of the components is missing

Resource Allocation Models

A common linear programming model involves the allocation of scarce resources to optimize some function, typically the profit margin Allocating limited resources in a best possible (i.e., optimal) way Selecting the level of certain activities that compete for limited resources that are necessary to perform those activities. 1. From allocation of production facilities to products. 2. From allocation of national resources to domestic needs. 3. From requirement to minimum cost. 4. Etc Ex: You sell doors. They need hours on machine and manpower. You only have so much of both. Each door type sells for a certain price. How many doors to produce to max profit?

Discrete Event System

A discrete-state, event-driven system, whose state evolution depends by asynchronous discrete event along the time.

Simulator

A machine which imitates the dynamic of a Discrete Event System

Network Definition

A network is defined by a set of points V known as nodes or vertices and ordered pairs of nodes A, known as arcs, that represent possible movement from one node to another. Each supply node i has an amount of material si that needs to be moved to another set of nodes, known as demand nodes. Each demand node j, which could represent customers and has demand dj. There could be other nodes, known as transshipment nodes, that have neither supply nor demand, but through which goods may travel. It is also possible for either an arc or a node to have a capacity associated with it, indicating how much material can pass to or through it. In addition, each arc can have a per-unit cost associated with it

Feasible Solution

A solution that satisfies all the constraints

Discrete Event System Simulator

Allows observing the evolution of the state of the system along the time, through the imitation that the model creates for a specific simulation. The observation of the parameters, variables and events along the time, support the changes to support to the model system to improve the efficiency of the system.

Work Scheduling Models

Another example of resource allocation comes in the form of determining minimum cost solutions for satisfying various requirements. A common example of this is the design of work schedules to meet labor requirements. Design work schedules for all the employees at a given location to meet certain service requirements Ex: People start a 8 hr shift on various hours. Need to determine how many start on x hour. Ex: - Once an employee begins working, he or she will be there continuously for the entire shift, except for either a meal break or short rest breaks - Requirement that a minimum number of employees needed on duty for each X hour interval over a 24-hour day (and these requirements can change from day to day over a 7-day week) - Estimate how many employees of each shift length should begin work at what start time over each 24-hour day of a 7-day week?

Each element has a buffer

Can decide queue parameters

Network Models

Certain models have a special structure that allows them to be solved using specialized algorithms These models can be formulated on some graph-like, or network, structure Often in network models, we are interested in the "flow" of material from one location (node) to another. Our variables are typically the amount sent over each arc; thus, there would be variables xij for each arc (i, j).

Blending Models

Creating a product from ingredients in the most cost efficient way possible Blending or mixing ingredients to obtain a product with certain characteristics or properties. 1. Gasoline blending, where petroleum ingredients were blended to obtain various grades of gasoline. (THECLASSICAL) 2. Chemical industry for mixing chemicals to other chemical products. 3. Food industry to food production. 4. Steel industry for steel production. 5. Etc. Ex: 3 types of ingredients. Each has a cost and max amount. Each has a rating. For two products, they need at least/most x% of ingredient x. Product itself has demand and profit. How much ingredient to use on each product?

Matrix

Is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Transportation Models

Delivering goods from one locale to another at minimum cost All nodes are either supply nodes or demand nodes. Source or supply nodes have material coming out of it. Should be sum of these paths is <= the amount of supply there Sink or demand nodes have material coming in. Should be sum of these is >= the amount of demand there.

Interarrival Time Property

Described as a random variable which creates a flow of entities. Such values are commonly described through Probability Density Functions.

Why Use SIMIO

Discrete Event System Simulator allows observing the evolution of the state of the system along the time, through the imitation that the model creates for a specific simulation. The observation of the parameters, variables and events along the time, support the changes to support to the model system to improve the efficiency of the system. Respect to a computational and analytical tool the Discrete Event System Simulator can provide a sequence of approximated output-parameters, for a specific solution to a problem, in order to support the decision making and to observe how the changes of the model parameter are influencing each other

Solving 2D LP Problems

Draw lines for constraints, find points of intersection as solution is a corner point or intersection of two constraints. Map obj function slope and move up or down until corner point is hit.

Source

Element It is the generator of the entities, normally at the beginning of the chain.

Sever

Element It represents a machine or an operator which/who processes the entities. Property: ProcessingTime It is the time between two Entities are processed by the Server

Sink

Element Normally at the exit of the process, it destroys the entities. Property: InterarrivalTime It is the time between two Entities are generated

Entity

Element of SIMIO It represents a product in a chain, an object, or a user.

Path - SIMIO

It connects the objects of the model. Property: SpeedLimits It is the speed at which the Path is supposed to be crossed by the Entities Property: Logical Length Length of the Path

Uniform Distribution

It describes a random event which always has the same probability to be verified. 1/(b-a)

Triangular Distribution

It is normally used for applications in which it is possible to identify the minimum and maximum value at which a random value could be associated. The probability for this distribution is described by the equation. The triangular distribution is defined with the extreme values a,b and its mean. f = 2 / (b-a)

Multi-Objective Optimization Problems (MOOPs)

For these problems the different parts of the object function often have: (a) different units (this can make an object function problematic to work with) and (b) conflicts with each other (that means part of the objective function cannot be improved because the different parts of the object function counteract). Example of a problem where company wants to minimizing the total transport time duration to the customer centres and the company also wants to minimize the number of trucks, warehouses and customer centres in order to reduce operating costs Above example is in conflict because o adding more trucks will reduce the total transport time duration to the customer centres, but increase the costs and o increasing the number of warehouses and customer centres will reduces the duration of the routes, but increases operation costs. Obj also expressed in different units: time and cost The huge challenge with MOOPs are the nature of the objective function (no definable unit and the different parts of the object function can conflicts with each other). The method most often used in MOOPs to compare solutions is the Pareto dominance relation Relevance Within Engineering - Manufacturing of a product from raw materials to final product: Can include assembly processes, a quality assurance process, a corrective/preventive maintenance process, etc. - Product quality vs cost. - Product development vs cost. - Container management: volume, weight, value. - Transport sector: This might include work schedule problem, stock optimization, transportation planning challenge etc

MOOPs Definitions - Pareto Improvement, Pareto Optimal, Pareto Frontier

Given a set of feasible solutions, and several objective functions, a Pareto improvement is defined as a step which brings at least one of the objective functions to improve without making the other function go worse. A Pareto optimal is a solutions where no Pareto improvements are possible anymore. The Pareto Front (frontier)is the set of all Pareto optimals, also called the Pareto solutions (i.e. you cannot say that one Preto optimal are more correct than another.) Is the set of all Pareto efficient solutions It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering the full range of every parameter

Transshipment Models - Setup

Has middle nodes Set up solver so things coming out of source is +1 and less than or equal to the supply. Sink nodes are +1 and more than or equal to demand. Middle nodes should be balanced so -1 on things coming in and +1 on things coming out while equal to 0.

How to Solve MOOPs

Have a list of solutions for Obj 1 and Obj 2 with same variables used in each row We observe, from solution B to C: Obj.-1 goes down, but obj.-2 goes up, therefore this is a Pareto improvement since Obl.-1 is a minimization object function and Obl.-2 is a maximization object function. Based on similar arguments we can easy observe that going from D to C and A to C are also improvement. We can therefore conclude that the Pareto front for this case are point C, thus the optimal solution for this problem is point C. Look at graph where Obj 1 is on one axe and Obj 2 is on the other Look for Pareto Front If both obj functions are min, look towards 0,0. If both are max, look at top right. If mixed, look in opposite corners

Shortest Path Setup

Have path lengths, a part of the obj function. Source twos are +1 and =1 as only one path will come out. Middle nodes have paths coming in that are -1 and those coming out are +1. Sink has paths coming in as -1 and constraint is equal to -1 since only one path coming in.

Unbounded Problem

If the objective function can be improved indefinitely without violating the constraints and bounds (Optimal feasible solution cannot be determined)

Path - Network

In a network, a path is an ordered sequence of arcs (i, j) such that any node i is "visited" at most once.

Shortest Path Models

In this case, the nodes represent starting/ending points in time, arcs represent some activity to be performed, and we are interested in "paths" through the network that help us determine which activities to perform Similar to transshipment but paths leaving source or supply should be equal to 1. Same for sink except paths are negative and equal to -1 (i.e. -x24 -x34 = -1). Can also all be equal to 1 and positive. Anything inbetween should be equal to 0. The theoretical interest in the problem is due to the fact that it has a special structure, in addition to being a network, that results in very efficient solution procedures. Shortest-path problem often occurs as a subproblem in more complex situations, such as the subproblems in applying decomposition to traffic-assignment problems. For problems of many variables algorithms can be much faster than the LP method.

Bill of Materials

Independent - customer demand (Lady Shoe) Dependent - Leather, soles, glue Can make a schedule from BOM if you know lead time each element takes Affects purchase orders in MRP Use this to make material plans with (MRP record) § Give - gross requirements § Get - planned order receipt § Have - projected available § Need - net requirements

Corner Point

Intersections of two or more constraints where a solution can be found for an LP problem

MRP

Is a push system because release made to this schedule without regard on system status so no WIP limit exists Customer orders and forecast demand go into master production schedule which goes into material requirements planning (also takes BOM and inventory records), returns purchase orders, materials plans, and work orders

Problem Constraints

Logical conditions that a solution to an optimization problem must satisfy.

LP-Problem

Method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships.

Intro to Network Problems - Their Characteristics

Network Flow Problem 1. A flow capacity is assigned to each arc. 2. A per-unit cost is specified along each arc. 3. To each node · 1. a given material supply, source (+) node 1, · 2. demand, sink (-), node 4, or · 3. intermediate points (often referred to as transshipment nodes. · 4. The objective is to find the min-/maximum-cost flow pattern to fulfill demands from the source nodes. Transportation Problem (Ex of Network Flow) 1. A unit cost /capacity can be specified along each arc. 2. To each node a capacity/demand can be assign. · 1. a given material supply, source (+) node 1, · 2. demand, sink (-), node 2. 3. The objective is to find the min-/maximum-cost flow pattern to fulfill demands from the source/sink nodes.

Transportation Models - Setup

Network with no middle nodes, all are sources or sinks. Have any path coming form a source +1 and make source material amount a constraint. Have any sink +1 and amount demanded the constraint. Stuff flowing out should not be more than what is coming out. Demand is minimum for stuff coming in.

Infeasible Problem

No solution that satisfies all the constraints

OPT and ERP Link

Obj: Meet customer expectations with on-time delivery of correct quantities of desired specification without excessive lead times or large inventory levels. Two Basic Approaches: Push Systems: -Material Requirements Planning -General - Provides a planning hierarchy

Typical Network Flow Problems

Problem - Nodes - Arcs - Flow Urban Transportation - Intersections/Bus Stops - Roads - Vehicles Air Traffic - Airports - Air Lanes - Aircrafts Water Resources - Pumping Stations/Lakes/Reservoirs - Pipelines/Channels/Rivers - Water Fluids Energy Grid - Power Plant/Transformers Stations/End Users - Electric Cables - Electricity Water Supply - Pumping Stations - Pipes - Fluids

Decision Variables

Problem choices; an unknown in an optimization problem.

Scientific Method

Real world data gathering -> Translate -> Mathematical Model -> Analyze -> Solve -> Setup -> Mathematical Solution -> Interpret -> Real-world Prediction and Analysis -> Test ->

SIMIO - Bring in two entities

Select entity type in source properties

Solving LP Problem with Excel Solver

Set objective as the objective function. Select min or max. Define constraints. Select Simplex as solving method.

SIMIO

Simio is a tool to simulate processes and in particular: - How to model and simulate a process - Analysis of results - How to modify the logic and behavior of a specific component

Objective Function

The function being maximized or minimized

Linear Programming

The goal is to find the best solution for a class of extremal problems by finding the extremum value of a linear function of several values that have to satisfy a number of linear inequalities.

Multiperiod Models

These models arise when decisions are made for more than one period, such as determining production processes and inventory levels over multiple months. Planning over a time horizon of many time periods: - i.e. where decisions for the current planning period affect the future, and - requirements in the future need action. Examples include: - Production/inventory planning. - Human resource staffing. - Investment problems. - Capacity expansion. Need to make two products to meet demand each month. Each cost labor hours and supplies. Any extra go into inventory each month and carried over to next month. Cheapest way to deliver demand?

Linear Function

Those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx.

Normal Distribution

Tt represents a random value with completely casual behaviour. It is often used to represent when an event can happen in a total random case. It is indicated by f = N (mean, variance) where the mean indicates where the distribution it is centred (even if could be biased) and the variance how much the function is "spread" into the axis.

Slack Variable

Variable added to an inequality constraint to transform it to an equality.

Surplus Variable

Variable that is subtracted to an inequality constraint to transform it to an equality.

Transshipment Models

When "middlemen" are present in a network Same as transportation except the transshipment nodes should be balanced i.e. what comes in is equal to what comes out.

SIMIO Intro

is a Discrete Event System Simulator A Discrete Event System Simulator is a system (for example a software) which imitates the dynamic of a Discrete Event System.

Probability Density Functions

f(x) is a positive function whose area is no more than one, and whose area, in a specific interval, describes the probability that a random value lies into such interval

Enterprise resource planning (ERP)

links all areas of a company including order management, manufacturing, human resources, financial systems, and distribution with external suppliers and customers into a tightly integrated systems with shared data and visibility Focus of study is on activities prior to the ERP adoption decision. In a typical manufacturing environment, the master production schedule (MRS) specifies the quantity of each finished product required in each planning period; it is a set of time-phased requirements for end items § ERP therefore has evolved from its predecessors to play an integrated supporting roles in the creation of a value chain Advanced planning in supply chain management. APSs employ algorithms to model and analyze the supply chain constraints to develop plans that provide optimal or near-optimal solutions Components, Personnel, Finance, Distribution, Accounting into Manufacturing Operations and Customer

Pull Research

o Both of these papers described the mechanics of kanban and the requirements for its implementation - Because it represented the first system to be termed a "pull" system o What is So Special About Pull? § The first, and easiest, step in understanding Kanban in specific, and pull in general, is to characterize its benefits § (1) Reduced WIP and Cycle Time: By limiting releases into the system, kanban regulates WIP, and hence results in a lower average WIP level § (2) Smoother Production Flow: By dampening fluctuations in WIP level, kanban achieves a steadier, more predictable output stream. § (3) Improved Quality: A system with short queues cannot tolerate high levels of yield loss and rework because these will quickly shut down the line. Additionally, short queues reduce the time between creation and detection of a defect. As a result, Kanban both applies pressure for better quality and provides an environment in which to achieve it. § (4) Reduced Cost: By switching the control from release rate to WIP level (card count), kanban provides an explicit means to "stress" the system. § There are three primary logistical reasons for the improved performance of pull systems: § (1) Less Congestion: Comparison of a open queueing network with an "equivalent" closed one shows that the average WIP is lower in the closed network than in the open network given the same throughput § (2) Easier Control: This is a fundamental benefit that results from several observations: · (a) WIP is easier to control than throughput because it can be observed directly. · (b) Throughput is typically controlled with respect to capacity · (c) Throughput is controlled by specifying an input rate. § (3) WIP Cap: The benefits of a pull environment are more a result of the fact that WIP is bounded, than to the practice of "pulling" everywhere § In the mid-1990s "pull" shifted in popular usage from being synonymous with kanban to shorthand for make-to-order Difference between push and pull Pull production system is one that explicitly limits the amount of work in process that can be in the system Push production is one with no explicit limit on amount of work in process in system

SIMIO - Interarrival Time

o Change interarrival time under properties for source o Random.NameofDistributionType() o Change processing time of a server in the same way

SIMIO = Scenarios

o Creation of multiple tests o Project Home -> New Experiment o Have a scenario o Can choose amount of replications o Pivot Grid shows results

Sequence Tables

o For addressing the entities directly to the objects and to associate specific processing times to each of the entities o Go to data tab and Tables § Add data table § Name PathsTable § In ribbon, select object reference property and entity § Name top of column 'Parts Name' § Automatically both entities are included and select one for each row § Create a new property from ribbon above, integer names PartsMixture § This is probability that a part will be created by the source § Set Entity column as key (select from above) § Create a new property from ribbon above, integer names PartsMixture § This is probability that a part will be created by the source § Set Entity column as key (select from above) o Go to model § Click on source and select entity type as PartsTable.PartsName § Go to Table Row References and Before Creating Entities and Action Type select reference existing row § Table name is PartsTable § Row number is PartsTable.PartsMixture.RandomRow o Make new sequence table § Go to ribbon and click foreign key property Name it PartsKeyColumn § Need to link this column to other table § Go the column properties and click Value - Table Key and select PartsTable.PartNames § Then click on property and select real for a new column § Name it ProcessingTime · Will hold processing time associated with each machine and part § Click on sequence column and select Input@Machine1 for part 1 § New row and part 1 and Input@Machine2 § New row and part 1 and Input@Exit § Same thing for part 2 § Give values for processing time o Need to link tables to model now § Click on the output nodes and select routing logic - entry destination type - by sequence § Click on the servers and change processing time to SequenceTable.ProcessingTime

Work Schedules

o Have server that is on and off and one that is always on o Go to data tab § Go to Work Schedules § Need to make sure start date is same as run time § Define a standard day in Day Patterns § Define when it works o Go back to model and on and off server o Select capacity type to WorkSchedule o Select StandardWeek below § Don't want parts queuing if machine is off § Add transfer node § Click on it and go to add-on process triggers and entered o Add a state variable § VarWeight o Go to add-on processes from above and add decide block o Place two assign blocks o For decide, write in condition 'OnOffServer(ServerName).ResourceState o When server is out of schedule, is true - Select if 4 § Click assign on that path § Variable name is ModelEntity.VarWeight § Give value of 0 o Go to other assign block and give value of 0.5 o Go to path and make Selection Weight ModelEntity.VarWeight o Other side, put 1-ModelEntity.VarWeight

SIMIO - Initial Capacity for Servers

o Maybe server can process more than one at a time - Initial capacity under properties change to another number (4 means 4 can be processed at one time) - Change capacity of a buffer in its properties same way (ex 2 from infinity) means no more than 2 cars in buffer at a time - Any other cars should be destroyed by the system (go away)

Network Modelling Problem Types

o Network Flow Models - Transportation Models (Source-Demand) - Minimum Cost Network Flow Models - Shortest Path Models o The Traveling Salesman Problem o Facility Location o Vehicle Routing Problem

SIMIO - Counters

o To create a counter is necessary to create a variable that can increase at each event Now want to create a counter, something than can grow in size § Use state variable / integer variable § Chocolate_Counter § Vanilla_Counter o Use node as entrance to server § State Assignment and on entering -> Click § Count how many are entering server § Add new rule § State Variable Name - Chocolate_Counter · New Value is Chocolate_Counter + 1 o Go to animation tab and drag in a status label § Click on it and write in expression Chocolate_Counter o Want to see how many are exiting § Do another state variable named Exited § Click on node before sink § State Assignments - On Entering § Add § Exited is state variable name § New value is Exited + 1 § Bring in status label and make its name Exited

SIMIO - Expressions in Scenarios

§ Go to definitions § Create new integer properties § Name Max_Inter_Cust, Min_Inter_Cust, Mean_Inter_Cust § Define Default Values o Go to model § Inset these values in Random.Triangular() within interarrival time in server o Make a new experiment § These properties are now columns § Can change values o Make a counter § Go to definitions § Make a state variable named Cust_Counter o Go to model § Click on node before server § Click on state assignments and click on entering § State variable cust_counter § New value: cust_counter + 1 o Add status label from animation and give expression of cust_counter o Profit of 10dkk for each customer going into server o Add response o Name profit § In properties, write in expression '10*cust_counter' § Can specify a currency unit

MRP II

§ In the 1990s MRP II was further expanded into ERP § It is intended to improve resource planning by extending scope of planning to include more of the supply chain than MRP II. § Key difference between MRP II and ERP is than MRP II focused on planning and scheduling of internal resources, ERP strives to plan and schedule supplier resources as well as dynamic customer demands and schedules § MRP and MRP II applications may not be up to the challenge presented by manufacturers seeking to capitalize on the competitive advantage offered by an integrated supply chain

Pull and Lean

§ The terms pull and lean production have become cornerstones of modern manufacturing practice § Specifically, we argue that pull is essentially a mechanism for limiting WIP, and lean is fundamentally about minimizing the cost of buffering variability