eng408-lecture04

8/2/2019 ENG408-lecture04

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Definitions used in Break-Even Analysis:

Fixed Cost:The sum of all costs required to produce the first unit of a product. This amount doesnot vary as production increases or decreases, until new capital expenditures areneeded.

Variable Unit Cost:Costs that vary directly with the production of one additional unit.

Expected Unit Sales:Number of units of the product projected to be sold over a specific period of time.

Unit Price:The amount of money charged to the customer for each unit of a product or service.

Total Variable Cost = (Expected Unit Sales * Variable Unit Cost )

The product of expected unit sales and variable unit cost.

Total Cost = (Fixed Cost + Total Variable Cost )The sum of the fixed cost and total variable cost for any given level of production.


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Definitions used in Break-Even Analysis

Total Revenue:

The product of expected unit sales and unit price.(Expected Unit Sales * Unit Price )

Profit (or Loss):The monetary gain (or loss) resulting from revenues aftersubtracting all associated costs. (Total Revenue - Total Costs)

Break Even:Number of units that must be sold in order to produce a profit ofzero (but will recover all associated costs).(Break Even = Fixed Cost / (Unit Price - Variable Unit Cost))


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Break-Even Analysis

Manufacturing costs are divided into 2 main groups;

Fixed costs,

variable costs

Fixed costs

Examples: rent, property tax, property insurance,wage of permanent employees, depreciation

These costs are fixedthroughout the year

do not depend on the production level. When we have a plant, then the above costs are fixed,

no matter we produce one unit or one million units.


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Break-Even Analysis

Fixed costs

Left graph total fixed costs (F) vs. production volume (Q)

Right graph Fixed costs per unit of production (F/Q) vs. Q


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Break-Even Analysis

In reality they are not completely fixed, usually we have

semi-fixed cost. However, in BEA we assumethey are fixed (at least over the

manufacturing range that we are concerned with).

Total fixed costs (F) vs. Production volume (Q)


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Variable costs

Costs of raw material, packaging material, direct labor,machine utilities are main variable costs.

These costs are fixedper unit of production.

The total variable costs depend on the production

level. The higher the production, the higher the total variable

costs.


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Break Even Analysis (BEA)

The total revenue depends on the production level.

The higher the production, the higher the total variable costs. In BEA, it is assumed that price of product is fixed. Left graph price per unit (P) vs. Production (and sales) volume (Q)

Right graph Total revenue (TR) vs. Production (and sales) volume (Q)


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Break Even Analysis (BEA) Therefore, the overall break-even analysis can be pictorially represented in the

following graph

F = fixed cost V = variable cost per unit Q = production volume P = price per unit Total Cost (TC) = Total Revenue (TR) TC = F + VQ

TR = P Q F+VQ = P Q QBEQ = F / (P-V)


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Example: overall break-even analysis

500,000$ total yearly fixed costs.

150$ / unit variable costs

200$ / unit sale price

QBE=500000/(200-150) =10000 units

If our market research indicates that the presentdemand is > 10000, then this manufacturing system iseconomically feasible.


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BEA and Facilities Layout

Such an analysis is implemented to compare say:

Technology

A Simple technology, an Intermediate Technology,and an Advanced technology.

Machines

General purpose machines, Multi-purpose machines,and Special purpose machines

Layout Process layout, Cellular layout, and Production line

layout.


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BEA and Facilities Layout

In general more advanced technology or more special

purpose technology meanshigher fixed costs and lower variable costs

Product layout

Process layout

Cellular layout


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Reject Allowance Problem

When producing small batches the use of averagevalues is less appropriate.

Example: consider a foundry that produces smallnumbers of custom-designed castings.

If conditions are such that the foundry has only onechance to produce the number of castings required,then the probability of a casting being good should beconsidered when determining the batch size to be

produced.

In determining how many castings to produce, thefollowing questions should be taken care of.


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1. How much does it cost to produce a goodcasting? How much for a bad casting?

2. How much revenue is generated from a goodcasting? How much from a bad casting?

3. What is the probability distribution for thenumber of good castings resulting from aproduction lot.


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Based on the answers a determination can bemade regarding the number of castings toschedule in order to

Maximize the expected profit

OR Achieve a confidence level of not producingfewergood castings than are needed.

Determining the number of additional unitstoallow when scheduling low-volume productionwhere rejects randomly occur is called thereject allowance problem


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Reject Allowance Problem Let

x = random variable representing the number of good units produced.

p(x) =probability of producing exactly x good units

Q = quantity of units to produce

C(Q,x)= cost of producing Q units, of which exactly x are good units

R(Q,x) = revenue from producing Q units, of which exactly x are goodunits

P(Q,x) = profit from producing Q units, of which exactly x are goodunits

P(Q,x) = R(Q,x) - C(Q,x)


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E[P(Q)] = expected profit from producing Q units

Q

E[P(Q)] = P(Q,x) p(x)

x=0

Q

E[P(Q)] = {R(Q,x)C(Q,x)} p(x)

x=0

probability


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Example: Reject Allowance Problem

If maximum expected profit is desired ,the value of Qcan be determined by enumerating over various values ofQ.

A foundry produces castings to order. An order for 20custom-designed castings has been received. The casting

process cost $ 1,100 per unit scheduled. If a casting is notsold, it has a recycle value of $ 200. The customer hasindicated a willingness to pay $2500 per casting for 20acceptable castings-no more no less. Based on historical

records, the probability distribution given in table 2.6 havebeen estimated. How many castings should be scheduledfor production to maximize expected profit? What is theprobability of loosing money at this production level?


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Example: Reject Allowance Problem

If x < 20 (good castings do not meet the requirement )

All wasted = $ 200 * Q

If x >= 20 then you will get the revenue that is

$ 20 * 2500 but the additional castings were a waste

$ 200 * (Q-20) what ever is excess (>20)

Cost of producing one casting $1100

Cost of producing Q castings = $1100 * Q


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Equipment Fractions The quantityof equipmentrequired for an operation

is referred to as the equipment fraction. The equipment fraction may be determined for an

operation by dividing the total time required to perform

the operation by the time available to complete theoperation.

The total time required to perform an operation is theproduct of the standard timefor the operationand

the number of times the operation is to be performed. Example: if it takes hr to duplicate a paper and if six

papers are to be duplicated in 2 hrs.

E i F i


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Equipment Fractions Total time = standard time of the operation * numbers

of times the operation is to be performed Total time = * 6 = 3 hrs Time available =2 hrs Equipment fraction = total time / time available = 3/2 = 1.5

1.5 duplicating machines are required It actually depends on the following questions1. Are the papers actually being duplicated according to

the hr per paper standard?2. Is the duplicating machine available when needed

during the 2-hr period?3. Are the standard time , the number of papers, and

the time the equipment is actually available knownwith certainty and fixed over time?


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Equipment Fractions1. The first question may be handled by dividing the standard

time by the historical efficiency of performing the operation.

2. The second question may be handled by multiplying the timethe equipment is available to complete an operation by thehistorical reliability factor for the equipment.

The reliability factor is the percentage of timethe equipment is

actually producing and is not down because of malfunction orplanned maintenance.

3. The third question dealing with uncertainty and time-varyingnature of machine fraction variables can be an importantfactor in determining process requirements.

If considerable uncertainty and variation over time exists, itmay be useful to consider using probability distributions,instead of point estimates for the parameters, and utilize aprobabilistic machine fraction model.

Deterministic model to


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Deterministic model toestimate the equipment fraction

F = S Q / HER

F = number of machines required per shift

S = standard time (minutes) per unit produced

Q = number of units to be produced per shift

E = actual performance, expressed as a percentageof standard time

H = amount of time (minutes) available per machine

R = reliability of machine, expressed as percentuptime


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Equipment requirement Additionally equipment requirements are a function of the

following factors Number of shifts (same machine can work in more than one

shift)

Setup times (if machines are not dedicated, the longer thesetup, the more machine needed)

Degree of flexibility (customers may require small lot sizes ofdifferent products delivered frequentlyextra machine capacitywill be required to handle these requests)

Layout type (dedicating manufacturing cells or focused

factories to the production of product families may require moremachines).

Total productive maintenance (will increase machine up timeand improve quality, thus fewer machines will be needed).


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Example

A machine part has a standard machinery time of 2.8

min per part on a milling machine. During an 8-hr shift200 units are to be produced. Of the 480 min availablefor production, the milling machine will be operational80% of the time. During the time the machine is

operational, parts are produced at a rate equal to 95% of the standard rate. How many milling machinesare required?

S =2.8 Q = 200 E=0.95 H=8 * 60 = 480 min

R = .80 F = 2.8 * 200 / 0.95 * 480 * .80 = 1.535 machines per

shift


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Machine Assignment problem

the combination of product, process, and schedule

design decisions significantly influences the numberof employees involved in producing the product.

Decisions regarding the assignment of machines tooperators can affect the number of employees.

Human machine chart or multiple activity chart

A two-column, multiple-activity process chart listingthe steps performed by an operator and the

operations performed by a machine and showing thecorresponding idle times for each. Also known asman-machine chart.

Man Machine Chart - One Operator Running Three Machines


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Timer Pro

http://www.acsco.com/Video.htm

The multiple activity chart can prove useful inanalyzing the activities or each operator and eachmachineduring transient and steady-stateconditions.

Fig 2.17

A model can be developed to determine the optimumnumber of machines to assign an individual operator.

It is assumed the machines are identical, time requiredto load and unload each machine are constant.

Semiautomatic production equipment

assignment of machines t operators
http://www.acsco.com/Video.htmhttp://www.acsco.com/Video.htm


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assignment of machines to operators

It takes 0.5 minute to travel between machines

1.0 minute to load a machine

1.0 minute to unload a machine

6 minutes to automatic machine time

0.5 minute to inspect and pack a finished part.

The analysis begins with each machine empty and the operatorstanding in front of machine 1 (M 1)

The operator loads M1, walks to M-2 loads M-2 walks to M3,load M3, walks to M1 unloads M1, loads M1, inspects andpacks the part removed from M1, travels to M2, unloads m2..

It takes 12 minutes for the operator and three machines toachieve a steady-state condition, thereafter a repeating cycle of9 minutes (provided no interruption )


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Facilities Design Once the product, process, and schedule design decisions

have been made, the facilities planner needs to organize the

information and generate and evaluatelayout, handling,storage, and unit load designalternatives.

Some typical business objectives include breakthrough in production cost, on-time delivery, quality, and lead time. In 1950 Dr. W.E. Deming proposed a model for continuous

process improvementthat involves four steps.

1. Planning and goal settings2. Doing or execution3. Checking or analysis4. Specifying corrective actions

Japanese:


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Japanese:seven management and planning tools

1. Affinity Diagram

2. Interrelationship Digraph

3. Tree Diagram

4. Matrix Diagram

5. Prioritization Matrices

6. Process Decision Program Chart (PDPC)

7. Activity Network Diagram

seven management and planning tools


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seven management and planning tools1. Affinity Diagram

a tool to group ideas.

a group of people write down ideas on "sticky notes." Then those notes are stock on a large piece of paper on the

wall randomly.

Then a select group will move the notes into logical groupings

without talking (no one in the room will talk). People can move notes that other people have moved.

Those moving the notes around will place titles over the notesto capture the theme of the notes.

As things seem to be basically set (little or no currentmovement of notes) the facilitator will call an end to the silentmovement.

1 Affi it Di


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1. Affinity Diagram Then people can discuss the logical groups, interconnections,

etc..

Why should teams use the Affinity process? The Affinity process is a good way to get people to work on a

creative level to address difficult issues. It may be used in situations that are unknown or unexplored by

a team, or in circumstances that seem confusing or

disorganized, such as when people with diverse experiencesform a new team, or when members have incompleteknowledge of the area of analysis.

One benefit of this tool is to encourage participation fromeverybody.

Those who are less vocal will be able to write their notes andmove notes without the normal pressures of those who aremost vocal dominating the process.


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When shouldn't we use the Affinity process?

As a rule of thumb, if less than 15 items of informationhave been identified, you can skip the Affinity process.

Instead, you can clarify and combine the ideas andthen use one of the Decision-Making Tools to identifythe highest priority items.

What Is an Affinity Diagram?

A tool that gathers large amounts of language data(ideas, opinions, issues) and organizes them intogroupings based on their natural relationships.

H i Affi i Di d?


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How is an Affinity Diagram created?

Affinitizing is a process performed by a group or team.

The idea is to meld the perspectives, opinions, andinsights of a group of people who are knowledgeable

about the issues.

The process of developing an Affinity Diagram seems

to work best when there are no more than five or sixparticipants.


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Creating an Affinity Diagram

Step 1 - Generate ideas

Step 2 - Display ideas

Step 3 - Sort ideas into groups

Step 4 - Create header cards

Step 5 - Draw finished diagram


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seven management and planning tools2: Interrelationship Digraph

a chart showing the relationship between factors.

All the factors to be considered are placed in a box on a pieceof paper.

Then lines are drawn from each box that has an impact onanother box to that box (with an arrow pointing in the direction

of impact). This tool is used in complex situations with many factors.

It is among the least used tools (and in my experience that isfor good reason, it just is not that useful - John).

The diagram will show which factors have the largest numberof factors that they influence (by counting the number of arrowsdrawn from the box).



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seven management and planning tools2: Interrelationship Digraph

Relations Diagrams are drawn to show all the differentrelationships between factors, areas, or processes.

Why are they worthwhile? Because they make it easy to pick out the factors in asituation which are the ones which are driving many ofthe other symptoms or factors.

For example, a relations diagram of urban povertymight start out something like this:


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T t R l ti Di


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To create a Relations Diagram:

Agree on the issue or question.

Add a symbol to the diagram for every element involved in theissue. Compare each element to all others. Use an "influence" arrow

to connect related elements. The arrows should be drawn from the element that influences to

the one influenced. If two elements influence each other, the arrow should be

drawn to reflect the stronger influence. Count the arrows. The elements with the most outgoing arrows will be root causes

or drivers. The ones with the most incoming arrows will be key outcomes

or results.



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seven management and planning tools3: Tree Diagram

Tree Diagram (Breakdown Structure) - displays the tasks, and

sub tasks, associated with achieving a goal. Starting with the goal "branches" are added to the "tree" to

show the items that must be addressed to reach the objective.

Then those "branches" are further broken out into smallerbranches.

Thus large projects can be illustrated in detail to allow for betterunderstanding of what tasks must be accomplished to meet theoverall goal.

The ultimate goal is shown on the left with more details being

shown on the right of the diagram. The farthest right of the diagram will consist of action items.

The Tree Diagram is a very useful project management tool.


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seven management and planning tools4: Matrix Diagram

The Matrix Diagram is an analysis tool that facilitates the

systematic analysis of the strengths of relationships betweentwo or more sets of elements.

It consists of a table whose main rows and columns containthe elements being inter-related, with the rest of its cellscontaining symbols or numbers that denote the strengths ofrelationship between the elements.

The elements being inter-related in a matrix diagram may be in

the form of information, concepts, conditions, activities, or otherintangible items, as well as physical things such as people,equipment, tools, and materials.



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The matrix diagram can be used in almost all types of decision

making that involves several options or alternatives, or isaffected by several factors. Examples of these include: 1) equal distribution of major and minor assignments among

members of a given project;

2) selection of a process, equipment, or material for a givenpurpose; 3) identifying the most critical factors affecting a given problem

area; 4) matching of tasks to objectives, etc.

The elements belonging to the same row or column shouldhave something in common, so that they comprise a set thatrepresents something.



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For instance, a matrix diagram that relates various reliabilitytests to various failure mechanisms might show in its main rowindustry-standard reliability tests and on its main columncommonly-encountered failure mechanisms.

The strength of relationship between each reliability test andeach failure mechanism may then be denoted on the cell wherethey intersect with a symbol or a number (say, 1-3, with 3

denoting the strongest relationship).

A Matrix Diagram Relating Reliability Tests to


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A Matrix Diagram Relating Reliability Tests toFailure Mechanisms

Table shows a simplified version of such a matrix diagram.

This matrix diagram shows, for instance, that if one wants tocheck the reliability of a set of samples with respect to packagecracking and ball lifting, then TCT should be the reliability test

used instead of PCT or HTOL.



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seven management and planning tools5: Prioritization Matrix

The Prioritization Matrix provides a way of sorting a

diverse set of items into an order of importance.

It also enables their relativeimportance to be identifiedby deriving a numerical value of the importance of

each item.

Deciding what is really important from a list of issuescan be very difficult, especially if there is no objectivedata available and the people involved have adifference of opinion about which should be actedupon first.

How to understand it


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How to understand it

For example, when customers are asking for a list of

product enhancements, how do you decide which toimplement?

The Prioritization Matrix provides a way of sorting a

diverse set of items into an order of importance. It also enables their relativeimportance to be identified

by deriving a numerical value of the importance ofeach item.

Thus an item with a score of 223 is clearly far moreimportant than one with a score of 23, but is not muchmore important than one with a score of 219.

seven managemen an p ann ng oo s


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seven managemen an p ann ng oo s5: Prioritization Matrix

In order that the items can be compared with one another inthis way, each item is scored against each of a set of keycriteria, and the scores for each item are then summed.

For example, a potential solution of 'Use high grade materials'will get a high score on the criterion of, 'Low cost ofmaintenance', but will get low score on 'Low cost of materials'.

A good criterion reflects key goals and enables objectivemeasurements to be made.

Thus 'material cost' is measurable and reflects a business profitgoal, whilst 'simplicity' may not reflect any goals and be difficultto score.

When there are multiple criteria, it may also be important totake into account the fact that some criteria are more importantthan others.

This can be implemented by allocating weightingvalues to eachcriteria, as Fig 1, below.



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se e a age e t a d p a g too s5: Prioritization Matrix

5: Prioritization Matrix


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When to use it

Use it to prioritize complex or unclear issues, where there aremultiple criteria for deciding importance.

Use it when there is data available to help score criteria andissues.

Use it to help select items to be actioned from a larger list ofpossible items.

When used with a group, it will help to gain agreement onpriorities and key issues.

Use it, rather than simple Voting, when the extra effort that isrequired to find a more confident selection is considered to beworthwhile.



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g p g6: Contingency Diagram

A Contingency Diagram is used anytime you want to

brainstorm ideas. It takes advantage of human nature by utilizing the critic that

resides in all of us.

With this tool, you change the brainstorming topic to be the

opposite of what you really want. For example, if your team is supposed to brainstorm ideas for

reducing cost, the team brainstorms ways to increase cost.

If you want to improve attendance, brainstorm ideas to reduce

attendance. You then take each idea and work on how to eliminate it from

your environment.

6: Contingency Diagram


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This tool takes advantage of negative energy and is especially

useful if you have a team that is in a negative mood.

After the team has filled the wall with ideas for lowering moraleor chasing away customers, you are ready to get down to

identifying potential solutions to your problem.



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Ask the team to analyze the list and develop ideas for solving

the problem. Many solutions can be found simply by reversing some of the

ideas on the list.

Others can be discovered through patterns and interesting

combinations of negative ideas. In either case, the list of "bad" ideas is a tremendous stimulus

for generating "good" ideas.

Next time you face the same old problems and a team tired of

trying to solve them, cut the team loose on ways to make theproblem worse.

It will be fun, energizing, and most of alleffective.



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g p g7: Activity Network Diagram

An activity network diagram is a schedule for the completion ofa complex project.

The Activity Network Diagram (AND), also referred to as anArrow Diagram or PERT Diagram, is used to identify the time-sequence of events necessary to achieve an objective.

When timing is critical, this tool helps teams to understand thespecific sequence of events that drives the time required toachieve the objective.

The AND is also helpful in managing the implementation of a

project requiring multiple activities.

7: Activity Network Diagram


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7: Activity Network Diagram

This analysis has its origins in engineering and constructionproject management (PERT stands for Program EvaluationReview Technique) but has been applied widely.

The Critical Pathway method of identifying and standardizingpatient, hospital and doctor activities draws heavily on thisconcept.

When should we use an activity network


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ydiagram?

An activity network diagram can help you work out the most

efficient sequence of events needed to complete your project. You can use it if you want to create a realistic project schedule

by graphically showing:

the total amount of time needed to complete the project;

the sequence in which tasks must be carried out;

which tasks can be carried out at the same time; and

which are the critical tasks that you need to keep an eye on.

Some tips on how to do this:


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Some tips on how to do this:

Beginning with the first task, calculate the earliest time each

task could be started (Early Start: ES). You do this by adding the duration of each task to the

cumulative duration of its previous tasks.

This is called the forward pass.

For example:


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Starting at the last task, calculate the latest time each task

could be started and still finish the project on schedule (LateStart: LS).

You do this by starting at the end with total implementation timeand subtracting the duration of each task from the latest starttime of its successor.

This is called the backward pass. For example:

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