P&LProcess

5/27/2018 P&LProcess

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Process

Introduction.

Types of Processes.

Process Strategy in the industry.

Factors affecting Process Design.

Tools


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Process Introduction

Classification of Processes Process strategies at the Industry

Factors that affect (or are affected by) the ProcessSelection.

Tools SPC, SMED

Documents

Work Measurement and Standards

Job Place Design

Line Balancing

Measuring Process Performance

Queueing Theory


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Introduction The information generated during the product design phase specifies

how the product must be, but not how to organize the productionprocess to make it (equipment, labor skills required, etc.).

Process Design specifies how the activities that Operations must carry

out should be developed:

Guiding the election and selection of technologies.

Clarifying the quantity and type of resources to be acquired, when to beacquire and their availability.

Process design and redesign is intimately related to Product Design:

Concurrent or Simultaneous Engineering.
http://d/cursos/curso%20gesti%C3%B3n%20sector%20automovil/fordANTIGUO.MPGhttp://d/cursos/curso%20gesti%C3%B3n%20sector%20automovil/fordANTIGUO.MPG


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Process Selection and System Design

Forecasting

Product and

Service Design

Technological

Change

Capacity

Planning

ProcessSelection

Facilities and

Equipment

Layout

Work

Design


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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The process-focused Project ShopCharacteristics

1. Unique products with certain complexity (boats, aircrafts, trains, motorways)

2. The production process is managed like a project3. Makes a one-of-a-kind product (volume = 1)

4. Uses general purpose equipment

5. Has informal relationships with many vendors

6. Very little vertical integration

7. Flexible layout often with factors of production moving to job


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TheJob ShopA process structure suited for low volume production of a great variety of non-standard

products (highly customized products).

Custom or workshop: Low specialized operations carried out by the same worker or groupof workers that follow up the whole process for the order.

Batch: More specialized operations carried out by different workers or group of

workers (need for more specialization and standardization).

Characteristics

1. Makes many products in small volume

2. Uses general purpose equipment, grouped by the same function in Work Centres

3. Has informal relationships with vendors

4. Very little vertical integration

5. Departmentalized layout with chaotic flow
http://d/pielsa.mpghttp://d/pielsa.mpg


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The Large Batch (Cell, Flow Shopor

Hybrid Shop)

A process structure that produces a variety of standard

products at relatively low volumes. This variety of

standard products has a similar sequence of operations:

The equipment is laid out in line, instead of grouped by

the same function.

After completing one batch, equipment adjustments for

the next one are made and the next batch produced.

Characteristics

1.Makes several families of products in moderate volume

2.Uses general purpose equipment often customized

3.Little vertical integration

4.Similar product follows the same path, produced inbatches to reduce the impact of setup time.

5.Hybrid layout with flow lines
http://d/gres%20de%20nules.mpghttp://d/gres%20de%20nules.mpg


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A process structure designed to make discrete parts. Parts are moved

through a set of specially designed workstations at a controlled rate.

Characteristics

1.Makes few products in large volume

2.Uses specialized high-volume equipment

3.Has formal relationships with vendors

4.May use vertical integration

5.Product-based layout with linear flow

Assembly Line
http://d/ponepuerta.mpghttp://d/ponepuerta.mpg


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Continuous FlowAn often automated structure that converts raw

materials into finished products in one continuousprocess.

Same operations are made in the same equipment to make

the same product, reducing waiting time.

Objectives: Improvement of material flow and operations.

Workers specialization:

Increasing speed and added value.
http://d/valor1.mpghttp://d/valor1.mpg


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Types of Processes Flexibility and Costs

By Projects

Job Shop

Flow Shop

Assembly Line

Continuous

Flexibility

Fixed CostVariable Cost

Unit Cost

+

- +

-


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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Process Strategy in the industry

Manufacturing Process Life Cycle

Processes go through different phases as

products do.

Interdependency between Product and

Process Life Cycles: Process Life Cycle: Affects manufacturing costs,

quality and production volumes, which affects

sales volumes.

Product Life Cycle: Influences the type of

manufacturing process that can be economically

and financially justified.


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Process Strategy in the industry

Product-Process Matrix

IV.

Continuous

Flow

III.Assembly

Line

II.

Batch

I.

Job

Shop

Low

Volume,

One of a

Kind

Multiple

Products,

Low

Volume

FewMajor

Products,

Higher

Volume

HighVolume,

High

Standard-

ization

CommercialPrinter

French Restaurant

Heavy

Equipment

Automobile

Assembly

Burger King

Sugar

Refinery

Flexibility (High)

Unit Cost (High)

Flexibility (Low)

Unit Cost (Low)

These are

the major

stages ofproduct and

process life

cycles


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Process Strategy in the industry The Product-Process matrix and the Competitive Advantage

The Product-Process matrix helps companies define where theircompetencies are, concentrating their attention in a limited groupof decisions and process alternatives, as well as a limited groupof Marketing options.

When the company considers at the same time products andprocesses, it can increase its probability of success.

Place in the matrix and Competitive priorities

Organization of the Operations and the Product-Processmatrix


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Place in the matrix and Competitive priorities Operations Management priorities change as the Product-

Process combinations change.

I.e.- Flexibility vs. Standardization

Each company has to take into account its traditional focus when

positioning in the matrix: Market oriented: Flexibility and Quality.

Manufacturing oriented: Costs and Process Leadership.

Organization of the Operations and the Product-Processmatrix


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Place in the matrix and Competitive priorities Organization of the Operations and the Product-Process matrix

Paying attention to the process that makes the company morecompetitive, the company will be able to manage thedevelopment of the operations involved per line of products.

The knowledge about how the different positions in the matrixaffect manufacturing will lead the company to suggest changes inOperations Management.

Companies that compete with several products in differentmarkets will probably have their products in different stages of thelife cycle:

Companies should separate and organize their processes in differentareas focalized in the different life cycles.


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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Process Selection and System Design

Forecasting

Product and

Service Design

Technological

Change

Capacity

Planning

ProcessSelection

Facilities and

Equipment

Layout

Work

Design


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Factors affecting Process Design

Capital Investment

Flexibility

Vertical Integration / Outsourcing

Nature of Demand

Quality of the product or service

Customer participation

The Learning effect

Financial Planning and Evaluation


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Capital Investment

Combination of equipment and human resources

at the manufacturing process.

The new manufacturing technologies provide a

wide variety of available options: As the mechanical and/or automated operations

increase, more capital is required.

Most of the available options require a high capital

investment, which create a high risk in case our sales

volumes (and therefore our production volumes) arelower than the expected.


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Flexibility

A production process is more flexible when their

equipment and human resources are able to

manage a wider variety of products, outputs,

responsibilities and functions, at a reasonable

cost and time frame.

Capital vs. Flexibility

Flexibility

Capital

Traditional

technologies

New

technologies


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Flexibility

Flexibility affects the type of human resources

required and their job stability:

More training is required.

Job stability is more variable for companies working by

projects or job shop type of process.

Flexibility is one of the best ways to get a reliable

customer service and reduces bottle necks.


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Factors affecting Process Design Vertical Integration/Outsourcing

The degree of vertical integration is related to the numberof processes at the supply chain that are carried out by theown company.

The vertical integration can generate savings when thecompany has the necessary skills to carry out some

processes at a lower cost and better quality. If the resources acquired are basic, the company may

loose competitiveness with non-vertical integration.

Outsourcing is interesting when a resource consumption islow, and its efficient management has a certain economy of

scale. Outsourcing is used as well when the technology to be

used is so complex that being competitive requires a bigeffort not balanced with the benefits obtained.


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Factors affecting Process Design Nature of the demand

Manufacturing processes have to have the necessary capacity tosupport the demand of products and services that the company is

going to offer.

Seasonality, tendency and other characteristics of the demand are

going to affect the capacity required over the time.

Some processes are able to expand and contract more easily than others. The final selection of processes will be affected by the estimated demand.

Price:

If its high, consumers will tend to buy less and vice versa.

To fix the price, the company has to take into account factors like

advertising costs, sales force, financial conditions, services provided to thecustomer, specific designs, inventory and delivery policy, quality, etc., at

the same time than the costs related to manufacturing.

It should be coordination between product price and process selection, due

to the competitive advantages provided by the different types of processes


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Factors affecting Process Design Quality of the product or service

Quality is a competitive advantage in the current businessenvironment.

The level of quality to be offered will affect directly the selection of the

production process.

The level required is directly related to the level of automation of the

process, since the automatic equipment manufactures products witha high and consistent uniformity.

Customer participation

Services that require higher contact with the customer generally

need less capital investment and have more flexibility.

Customer presence normally affects the process efficiency in anegative way, which increases cost.


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Factors affecting Process Design The Learning effect

The working hours required per unit of product represent adecreasing function of the number of cumulative production units.

This reduction of working hours (and therefore cost) are

based on the gain of experience in design of products and

services, automation and capital investment, as well as

changes in methods and experience of the working force. Companies competing in price try to have high

manufacturing volumes to take advantage of the learning

effect, and therefore have a lower cost.

Production volume

Working

hoursperunit


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Financial Planning and Evaluation

Operation managers are continuously looking for

new and different ways of producing that:

Increase productivity.

Follow the Operations Strategy.

Provide sufficient profit to justify the capital investment

required.

Each type of process has different capital

requirements, thus limiting the companys

possibilities of process selection in case of limited

financial resources.


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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Tools and Concepts

Simplify/Mechanize/Automate/Integrate

SMED

CAD/CAM

Statistical Process ControlBottlenecks


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How much is the profit?

A company manufactures 2 products P & Q. Sale price of P is

90and Q price is 100/unit. Weekly Demand is 100 units for Pand 50 units for Q.

Both products require the same PC component, the rawmaterial of which worths 20 /unit. To transform PC 15 minutesof a given resource B are required and 5 minutes of a givenresource C.

Product P also requires Component 1 (C1) that should betransformed from a raw material that cost 20 /unit, and itrequires 15 minutes of a given resource A and 10 minutes of C.

To assembly PC with C1 a new component C3 is required witha cost of 5/unit and 5 minutes of the D resource.

Product Q follows a very similar process. To manufacture C2raw material with a cost of 20 /unit is needed, and it isprocessed using 20 minutes of A and 15 minutes of B. Thenresource D assembles PC with C2 during 5 minutes.

Each week has 5 days of 4 hours. Total cost are 3600/week.


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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Work Measurement and Standards The Purpose of Work Measurement is to set time standards for a job.

Such standards are necessary for 4 reasons:

To schedule work and allocate capacity. To provide an objective basis for motivating the workforce.

To bid for new contracts and to evaluate performance on existing ones.

To provide benchmarks for improvement.

Methods

Time Study (stop watch) Work Sampling (observing a sample)

Predetermined times

Elementary standard data

Reference points.

Reference Book (B.W. Niebel, Motion and Time Study)


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Time Study A time study is generally made with a stopwatch, either on the spot

or by analyzing a videotape for the job. The job or task to be studied is separated into measurable parts

and then timed individually.

Some general rules

Define each work element to be short in duration but long enough

to be timed and the time can be written Separate activities related with machine from the rest.

Define any delays or acyclic activities.

After a number of repetitions, collection times are averaged.

Normal Time = Observed Performance Time x Performance Rating

Standard Time = NT x (1 + Allowances)


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Work Sampling Three primary applications

Determine the activity-time percentage for personnel orequipment.

Performance measurement to develop a performance index forworkers.

Evaluate time standards to obtain the standard time for a task.

Five Steps Identify the specific activities that are the main purpose for the

study.

Estimate the proportion of time of activity of interest of the totaltime.

State the desired accuracy in the study results.

Determine the specific times when each observation is to bemade.

At two or three intervals during the study period recompute therequired sample size by using the data collected thus far.


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Get Put

Move with Weight (5 UMT)

Grasp (6 UMT)

Bend Down (29 UMT)

Stand up (32 UMT)

Apply Presure (14 UMT)

Eye Movement (7 UMT)

Step (18 UMT)

Coger funda GDF 25

Coger "tinta" GDF 25Poner "tinta en funda" PDN 19

Coger y Poner GEN+PEN 5+8

Aplicar Presin 14

Coger caperuzn GDF 25

Reajustar tras coger 6

Poner caperuzn PDN 19

Aplicar Presin 14

Dejar bolgrafo PEF 14

6.3 seconds

N X F

PE 5 9 14

PD 19 22 28

N X FGE 8 13 16

GD 17 20 25

Predetermined Motion Times (MTM, MODAPTS, )


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Classification of Processes

Process strategies at the Industry


Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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Documents Flowchart.A flowchart is a

graphical representation of aprocess, depicting inputs,

outputs and units of activity. Itrepresents the entire process ata high or detailed (depending onyour use) level of observation,allowing analysis andoptimization of workflow.It canserve as an instruction manual.

Assembly Drawing: Anexploded drawing containing aset of number parts combined tomake a complet product.

Value Stream Map: Value

stream mapping is a paper andpencil tool that helps you to seeand understand the flow ofmaterial and information as aproduct or service makes itsway through the value stream.


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Operation

Begin or end

Information

input

Information

output

Shampoo directions

1. Lather

2. Rinse3. Repeat

Process Documentation using Flowcharts

Basic flowchart symbols

Example: Any problems

with the followingset of directions?

Question

yes/no?

Shampoo?

Begin shampoo

Rinse hair with

warm water

Lather shampoo

into hair

Select bottle

Wet hair with

warm water

Information

on bottle

No

Yes

Hair

clean?

NoEnd shampoo

Yes


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Process Flow Diagram (PFD)A process flow diagram is a mapping of the specific processes that raw materials

parts, and subassemblies follow as they move through a plant.

Builds on the concept of flowcharting.Activity

A more constrained version of the operation symbol used in flowcharting

1. Requires a resource

2. Resource has a capacity constrain

3. Adds value

Flow

1. Arrow indicates the flow of jobs

2. Multiple flow units (types of jobs) possible

Buffer

Buffer or inventory location

1. Normally does not have a capacity

2. Multiple units possible

Trees

RM

DebarkStems

WIP

Scan SawAcceptable

Lumber

FG

GrindChips

FG

Acceptable


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Flow Diagrams


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Single Object Process Chart


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Assembly Process Chart Assembly charts

Disassembly charts


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Action Decision Flow Diagram

M l i A i i Ch


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Multi Activity Charts


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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Job Design (I)

Job design is the function of specifying the work activities of an

indidividual or a group in an organizational setting. The objective is to develop job structures that meet the

requirements of the organization and its technology and thatsatisfy the job holders personal and individual requirements.

Trends of Job Design Decisions Quality control as part of the workers job

Cross training workers to perform multiskilled jobs Employee involvement and team approaches to designing and

organizing work

Informating ordinary workers through internet, email

Extensive use of temporary workers

Automation of heavy manual work

Organizational commitment to providing meaningful and rewardingjobs for all employees.


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Job Design (II) The improvement of the job methods leads to a higher level of

specialization.

A workplace with a high level of specialization covers a narrow set oftasks, high repetitive levels, and, hopefully, high efficiency and quality.

Specialization produce benefits as quicker training and faster workingrates.

This way of working has also some disadvantages as workerdemoralization, reduces flexibility and increases the work of upper levelsof management.

To avoid those disadvantages: Wider jobs

Job enlargement (horizontally expanded)

Job enrichment (vertically expanded)

Job Rotation

Socio-Technical Systems Task variety

Skill variety

Feedback

Task identity

Task autonomy


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing


Queueing Theory


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Line Balancing

Introduction

Line Balancing

Mathematical Programming Model

Heuristic Methods

Yamazumi

Duration of the Tasks Longer than Cycle Time

Other Considerations.

Mixed Model Assembly Line


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Introduction

The design of the line, constraints the alternatives whenscheduling the activity of the line.

A decision on the productive system (in the long term):

Defines the allocation of facilities.

Constrains the sequence (lines with mixed models).

Constrains the production volumes (lines multi-model).


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Assembly line

Manufacturing

Made and bought inventory of

components and subassemblies

Conveyor moving at constant speed

WorkStation 1

WorkStation 2

WorkStation m

Final

product

inventory
http://localhost/var/www/apps/conversion/tmp/scratch_1/vistaaereaVALDESA.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/kanbanlineaford.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/kanbanlineaford.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/ponepuerta.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/estacionmontajebumper.MPGhttp://localhost/var/www/apps/conversion/tmp/scratch_1/estacionmontajebumper.MPGhttp://localhost/var/www/apps/conversion/tmp/scratch_1/ponepuerta.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/kanbanlineaford.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/kanbanlineaford.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/vistaaereaVALDESA.mpghttp://localhost/var/www/apps/conversion/tmp/scratch_1/kanbanford.MPG


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1 2 3 4 NIn Out

1 2 3 4 NIn Out

1 2 3 4 NIn Out

single model line

batch model line

mixed model line

Production Organization


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Use of the Assembly line

Advantages

Performance increase due to the learning effect.

Reduces the difficulty of the task.

Increases the team work, avoiding isolations. Constant rate of work.

Ongoing quality control.

Disadvantages

Alienation.

Less flexibility.


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Line Balancing. Definition.

Line Balancing consists of assigning operations to theworkstations of such form that the sum of their durations ineach station is as similar as possible.

With this procedure bottlenecks should be avoided,

unproductive time will be reduced and the productivity ofthe line will increase.

This implies that:

Each operation will be assigned to an one only and onlyone workstation.

Relations and bounds between operations will berespected.

Times of the stations will not exceed their cycle time.


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Objectives.

Capacity Minimization of total idle time (maximization of the use of the

line).

Minimization of product flow-time.

Balance the levels of capacity used at the workstations.

Cost

Minimization of the machinery costs, tools or idle equipment.

Minimization of the costs of materials or reworks.

Minimization of the costs by adjustment and change.

Organizational-social Job Enrichment

Modifications at the Line balancing

General definitions (I)


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General definitions.(I) Operation:Smaller unit of work than cannot be divided without creating an

unnecessary interference.

Workstation:Segment of the line where a set of operations is executed.

Characterized by its surface, machinery or type of assigned work. Line Balancing:Process to assign operations to workstations. It intends to

assign personal or equipment of efficient way to obtain the performancemaximum.

Cycle time:Amount of time between two consecutive products.

Balance Efficiency: It indeed represents the percentage of invested totaltime in making products.

Station Pitch:The distance of a product and the one that follows to him inthe conveyor belt.

ProductionForecast

TimeAvalaibleTimeCycle

Stations NxCycle Time

Operations Total TimeEfficiency


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General Definitions. (II) Bounds between operations.

Precedence Relations.

Imposed generally by technological constraints.

Operation'' cannot be made if before the 'h' has not

taken place

In the case of linear configurations, this implicates

that 'h' will have to be in the same station that 'i' or in

a previous one, but never in a following one.


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General Definitions. (III) Positive Zoning.

It is compulsory to locate an operation in

the same station that another one.Operations that need the same toolOperations that need the same ability on the part of the

workerOperations that need the same physical training conditions

Negative Zoning or incompatibility.

It is demanded that an operation is not inthe same station that another one.

Position of the unit in the line (Operations to be made at theright side

are not compatible with those to be made at the left)

Exigency of a high specialized workers

Processes of painted sandpapering and of surfaces

Allocation of varied activities to avoid monotony.

Limit Zone.

It is demanded that certain operations areassigned to stations previous or next toone given

Fixed zone of material arrival.

Zone of preparation or control.

G l D fi i i ( V)


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General Definitions. (IV)

ji

ij tTO m1,...,=j;

Line Speed

Productivity

Operation Time in a station

Minimum number of workstations

LV=L/C

CP

1

C

t

N

n

i

i

ws

1

1 minute

TOTO 1 minute

C C

G l D fi i i (IV)


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General Definitions. (IV)

Idle time of a station

Total idle time of a station or delay

Station saturation

Efficiency

Delay

n

i

i

m

j

j tCmTOCD11

)(

...

0.9 minutes

1 minute1 minute

m1,...,=j;ij TOCDI

m1,...,=j;CTOS ij

100(%) 1

Cm

t

E

n

i

i

(%)100(%) ER

Li B l i


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Line Balancing

Introduction

Line Balancing


Heuristic Methods


Other Considerations.

Mixed Model Assembly Line

Resolution Procedures for problem SALBP 1


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Resolution Procedures for problem SALBP 1.

Exact methods

Mathematical Programming Models

Exact algorithms of directed exploration and dynamic

programming.

Heuristic methods

Constructive. Based on rules and strategies

Heuristic of a single one happened.

Simple

Composed

Heuristic with backward movement

Approaches from exact algorithms

Others

Model of PLM of problem SALBP1


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Model of PLM of problem SALBP1.

Variables of allocation xij:

Binary variables that they

indicate if operation i is

assigned to station j.

Variables of existence yj:

Binary variables that theyindicate if station j exists.

This existence comes

imposed when not being

able to assign but

operations to anyone of

the stations already

defined.

mmax

j

jyzMIN

1sujeto a:

mmax

j

jix1

, 1 i=1n [1]

n

ijjii yCxt

1, j=1mmax [2]

mmax

j

mmax

j

jpji xjxj1 1

,, i precede a p [3]

ij yy 1 j=1mmax-1 [4]

jix ji ,1,0,

jy j 1,0

H ri ti pr d r


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Heuristic procedures Although nonexact, some heuristic

procedures provide solutions thatcan be considered acceptable.

The known procedures of

constructive type more are the

bound ones to the duration of the

task or the number of consequent. One of them chooses to assign to

the open station the task with

greater duration than still it fits in the

station.

The alternative procedure chooses

to assign to the open station the

task with greater number of

consequent.

Y i


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Yamazumi

1

2 3

4

5 6

7

8

9

10

11

12

CY

C

L

E

TI

M

e

Obj i


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Objectives.

Capacity Minimization of total the idle time (maximization of the use of

the line).

Minimization of products flow-time in the line.

Balance the levels of capacity use at the workstations.

Cost

Minimization of the machinery costs, tools or idle equipment.

Minimization of the costs of materials or reworks.

Minimization of the costs by adjustment and change.

Organizational-social Job Enrichment

Modifications in the Line balancing

Li B l i


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Line Balancing

Introduction

Line Balancing


Heuristic Methods

Yamazumi


Other Considerations. Mixed Model Assembly Line

A real Example


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Operation Time Preceding Task Operation Time Preceding Tas1 0,175 - 16 0,200 -

2 0,139 - 17 0,084 -

3 0,078 1 18 0,116 13;15

4 0,349 - 19 0,199 18

5 0,007 - 20 0,079 19

6 0,050 - 21 0,103 19

7 0,211 4 22 0,098 98 0,158 - 23 0,116 19

9 0,230 8 24 0,210 23

10 0,080 9 25 0,140 24

11 0,075 - 26 0,210 25

12 0,395 9 27 0,177 26

13 0,219 12 28 0,234 2714 0,188 - 29 0,090 -

15 0,122 12

A real Example


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3

4

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78

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212223

24

25

26

27

28

29

16

14 9

12

13

1510

11

Yamazumi Graphics Example


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2

3

4

56

78

17

18

19

20

2122 23

24

25

26

27

28 29

1614

9

12

13

1510

11

Yamazumi Graphics Example

Process


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing Measuring Process Performance

Queueing Theory



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Productivity: Ratio of Output to Input

Effiency: Ratio of Actual output to some standard.

Utilization: Ratio of the time that a resource is actually activatedrelative to the time that it is available for use.

Cycle time (takt time): Average time between the completion ofsuccesive units.

Run Time: time required to produce a batch of parts

Setup Time: is the time required to prepare a machine to make aparticular item.

Operation Time: sum of setup and run time.

Throughput time: time that unit spents actually being transformedor waiting.

Throughput rate: output rate that the process is expected toproduce over a period of time.

Process velocity: Total throughput divided by Value Added Time

Value Added Time: Time that useful work is actually done

Process


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Tools SPC, SMED

Documents


Job Place Design

Line Balancing Measuring Process Performance

Queueing Theory

Queueing Theory


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Queueing Theory Littles Law: The size of a queue is proportional to the input

rate and the average throughput time.

L= W

Lq = Wq

1

qWW

P&LProcess

Documents

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