Friday, January 27, 2012


Wednesday, May 11, 2011

Gantt Chart


Gantt Chart

During the era of scientific management, Henry Gantt developed a tool for displaying the progression of a project in the form of a specialized chart. An early application was the tracking of the progress of ship building projects. Today, Gantt's scheduling tool takes the form of a horizontal bar graph and is known as a Gantt chart, a basic sample of which is shown below:
Gantt Chart Format
















2 mo.


2 mo.


2 mo.


2 mo.


2 mo.


2 mo.

The horizontal axis of the Gantt chart is a time scale, expressed either in absolute time or in relative time referenced to the beginning of the project. The time resolution depends on the project - the time unit typically is in weeks or months. Rows of bars in the chart show the beginning and ending dates of the individual tasks in the project.

In the above example, each task is shown to begin when the task above it completes. However, the bars may overlap in cases where a task can begin before the completion of another, and there may be several tasks performed in parallel. For such cases, the Gantt chart is quite useful for communicating the timing of the various tasks.

For larger projects, the tasks can be broken into subtasks having their own Gantt charts to maintain readability.
Gantt Chart Enhancements

This basic version of the Gantt chart often is enhanced to communicate more information.



A vertical marker can used to mark the present point in time.

The progression of each activity may be shown by shading the bar as progress is made, allowing the status of each activity to be known with just a glance.

Dependencies can be depicted using link lines or color codes.

Resource allocation can be specified for each task.

Milestones can be shown.

Gantt Chart Role in Project Planning

For larger projects, a work breakdown structure would be developed to identify the tasks before constructing a Gantt chart. For smaller projects, the Gantt chart itself may used to identify the tasks.

The strength of the Gantt chart is its ability to display the status of each activity at a glance. While often generated using project management software, it is easy to construct using a spreadsheet, and often appears in simple ascii formatting in e-mails among managers.

For sequencing and critical path analysis, network models such as CPM or PERT are more powerful for dealing with dependencies and project completion time. Even when network models are used, the Gantt chart often is used as a reporting tool.

Editorial note: The name of this tool frequently is misspelled as "Gannt"

PERT Chart


PERT Chart

Complex projects require a series of activities, some of which must be performed sequentially and others that can be performed in parallel with other activities. This collection of series and parallel tasks can be modeled as a network.

In 1957 the Critical Path Method (CPM) was developed as a network model for project management. CPM is a deterministic method that uses a fixed time estimate for each activity. While CPM is easy to understand and use, it does not consider the time variations that can have a great impact on the completion time of a complex project.

The Program Evaluation and Review Technique (PERT) is a network model that allows for randomness in activity completion times. PERT was developed in the late 1950's for the U.S. Navy's Polaris project having thousands of contractors. It has the potential to reduce both the time and cost required to complete a project.
The Network Diagram

In a project, an activity is a task that must be performed and an event is a milestone marking the completion of one or more activities. Before an activity can begin, all of its predecessor activities must be completed. Project network models represent activities and milestones by arcs and nodes. PERT originally was an activity on arc network, in which the activities are represented on the lines and milestones on the nodes. Over time, some people began to use PERT as an activity on node network. For this discussion, we will use the original form of activity on arc.

The PERT chart may have multiple pages with many sub-tasks. The following is a very simple example of a PERT diagram:
PERT Chart

The milestones generally are numbered so that the ending node of an activity has a higher number than the beginning node. Incrementing the numbers by 10 allows for new ones to be inserted without modifying the numbering of the entire diagram. The activities in the above diagram are labeled with letters along with the expected time required to complete the activity.
Steps in the PERT Planning Process

PERT planning involves the following steps:

1. Identify the specific activities and milestones.
2. Determine the proper sequence of the activities.
3. Construct a network diagram.
4. Estimate the time required for each activity.
5. Determine the critical path.
6. Update the PERT chart as the project progresses.

1. Identify Activities and Milestones

The activities are the tasks required to complete the project. The milestones are the events marking the beginning and end of one or more activities. It is helpful to list the tasks in a table that in later steps can be expanded to include information on sequence and duration.
2. Determine Activity Sequence

This step may be combined with the activity identification step since the activity sequence is evident for some tasks. Other tasks may require more analysis to determine the exact order in which they must be performed.
3. Construct the Network Diagram

Using the activity sequence information, a network diagram can be drawn showing the sequence of the serial and parallel activities. For the original activity-on-arc model, the activities are depicted by arrowed lines and milestones are depicted by circles or "bubbles".

If done manually, several drafts may be required to correctly portray the relationships among activities. Software packages simplify this step by automatically converting tabular activity information into a network diagram.
4. Estimate Activity Times

Weeks are a commonly used unit of time for activity completion, but any consistent unit of time can be used.

A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion times. For each activity, the model usually includes three time estimates:



Optimistic time - generally the shortest time in which the activity can be completed. It is common practice to specify optimistic times to be three standard deviations from the mean so that there is approximately a 1% chance that the activity will be completed within the optimistic time.

Most likely time - the completion time having the highest probability. Note that this time is different from the expected time.

Pessimistic time - the longest time that an activity might require. Three standard deviations from the mean is commonly used for the pessimistic time.

PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the expected time for each activity can be approximated using the following weighted average:

Expected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6

This expected time may be displayed on the network diagram.

To calculate the variance for each activity completion time, if three standard deviation times were selected for the optimistic and pessimistic times, then there are six standard deviations between them, so the variance is given by:

[ ( Pessimistic - Optimistic ) / 6 ]2

5. Determine the Critical Path

The critical path is determined by adding the times for the activities in each sequence and determining the longest path in the project. The critical path determines the total calendar time required for the project. If activities outside the critical path speed up or slow down (within limits), the total project time does not change. The amount of time that a non-critical path activity can be delayed without delaying the project is referred to as slack time.

If the critical path is not immediately obvious, it may be helpful to determine the following four quantities for each activity:

* ES - Earliest Start time
* EF - Earliest Finish time
* LS - Latest Start time
* LF - Latest Finish time

These times are calculated using the expected time for the relevant activities. The earliest start and finish times of each activity are determined by working forward through the network and determining the earliest time at which an activity can start and finish considering its predecessor activities. The latest start and finish times are the latest times that an activity can start and finish without delaying the project. LS and LF are found by working backward through the network. The difference in the latest and earliest finish of each activity is that activity's slack. The critical path then is the path through the network in which none of the activities have slack.

The variance in the project completion time can be calculated by summing the variances in the completion times of the activities in the critical path. Given this variance, one can calculate the probability that the project will be completed by a certain date assuming a normal probability distribution for the critical path. The normal distribution assumption holds if the number of activities in the path is large enough for the central limit theorem to be applied.

Since the critical path determines the completion date of the project, the project can be accelerated by adding the resources required to decrease the time for the activities in the critical path. Such a shortening of the project sometimes is referred to as project crashing.
6. Update as Project Progresses

Make adjustments in the PERT chart as the project progresses. As the project unfolds, the estimated times can be replaced with actual times. In cases where there are delays, additional resources may be needed to stay on schedule and the PERT chart may be modified to reflect the new situation.

Benefits of PERT

PERT is useful because it provides the following information:



Expected project completion time.

Probability of completion before a specified date.

The critical path activities that directly impact the completion time.

The activities that have slack time and that can lend resources to critical path activities.

Activity start and end dates.


The following are some of PERT's weaknesses:



The activity time estimates are somewhat subjective and depend on judgement. In cases where there is little experience in performing an activity, the numbers may be only a guess. In other cases, if the person or group performing the activity estimates the time there may be bias in the estimate.

Even if the activity times are well-estimated, PERT assumes a beta distribution for these time estimates, but the actual distribution may be different.

Even if the beta distribution assumption holds, PERT assumes that the probability distribution of the project completion time is the same as the that of the critical path. Because other paths can become the critical path if their associated activities are delayed, PERT consistently underestimates the expected project completion time.

The underestimation of the project completion time due to alternate paths becoming critical is perhaps the most serious of these issues. To overcome this limitation, Monte Carlo simulations can be performed on the network to eliminate this optimistic bias in the expected project completion time

Time-Cost Trade-offs


Time-Cost Trade-offs 

There is a relationship between a project's time to completion and its cost. For some types of costs, the relationship is in direct proportion; for other types, there is a direct trade-off. Because of these two types of costs, there is an optimal project pace for minimal cost. By understanding the time-cost relationship, one is better able to predict the impact of a schedule change on project cost.

Types of Costs

The costs associated with a project can be classified as direct costs or indirect costs.
  • Direct costs are those directly associated with project activities, such as salariestravel, and direct project materials and equipment. If the pace of activities is increased in order to decrease project completion time, the direct costs generally increase since more resources must be allocated to accelerate the pace.
  • Indirect costs are those overhead costs that are not directly associated with specific project activities such as office space, administrative staff, and taxes. Such costs tend to be relatively steady per unit of time over the life of the project. As such, the total indirect costs decrease as the project duration decreases.
The project cost is the sum of the direct and indirect costs.

Compressing the Project Schedule

Compressing or crashing the project schedule refers to the acceleration of the project activities in order to complete the project sooner. The time required to complete a project is determined by the critical path, so to compress a project schedule one must focus on critical path activities.
A procedure for determining the optimal project time is to determine the normal completion time for each critical path activity and a crash time. The crash time is the shortest time in which an activity can be completed. The direct costs then are calculated for the normal and crash times of each activity. The slope of each cost versus time trade-off can be determined for each activity as follows:
Slope = (Crash cost - Normal cost) / (Normal time - Crash time)
The activities having the lowest cost per unit of time reduction should be shortened first. In this way, one can step through the critical path activities and create a graph of the total project cost versus the project time. The indirect, direct, and total project costs then can be calculated for different project durations. The optimal point is the duration resulting in the minimum project cost, as show in the following graph:
Project Cost Versus Duration

Attention should be given to the critical path to make sure that it remains the critical path after the activity time is reduced. If a new critical path emerges, it must considered in subsequent time reductions.
To minimize the cost, those activities that are not on the critical path can be extended to minimize their costs without increasing the project completion time.

Time-Cost Model Assumptions

The time-cost model described above relies on the following assumptions:
  • The normal cost for an activity is lower than the crash cost.
  • There is a linear relationship between activity time and cost.
  • The resources are available to shorten the activity.

The model would need to be adapted to cases in which the assumptions do not hold. For example, the schedule might need to take into account the need to level the load on a limited resource such as a specialized piece of equipment.

Additional Considerations

There are other considerations besides project cost. For example, when the project is part of the development of a new product, time-to-market may be extremely important and it may be beneficial to accelerate the project to a point where its cost is much greater than the minimum cost.
In contract work, there may be incentive payments associated with early completion or penalties associated with late completion. A time-cost model can be adapted to take such incentives and penalties into account by modeling them as indirect costs.
Because of the importance of the critical path in compressing a project schedule, a project planning technique such as the Critical Path Method or PERT should be used to identify the critical path before attempting to compress the schedul

Process Flow Structures


Process Flow Structures

The flow structure of the process used to make or deliver a product or service impacts facility layout, resources, technology decisions, and work methods. The process architecture may be an important component in the firm's strategy for building a competitive advantage.
When characterized by its flow structure, a process broadly can be classified either as a job shop or a flow shop. A job shop process uses general purpose resources and is highly flexible. A flow shop process uses specialized resources and the work follows a fixed path. Consequently, a flow shop is less flexible than a job shop.
Finer distinctions can be made in the process structure as follows:
  • Project - Example: building construction
  • Job shop - Example: print shop
  • Batch process - Example: bakery
  • Assembly line - Example: automobile production line
  • Continuous flow - Example: oil refinery

These process structures differ in several respects such as:

  • Flow - ranging from a large number of possible sequences of activities to only one possible sequence.
  • Flexibility - A process is flexible to the extent that the process performance and cost is independent of changes in the output. Changes may be changes in production volume or changes in the product mix.
  • Number of products - ranging from the capability of producing a multitude of different products to producing only one specific product.
  • Capital investment - ranging from using lower cost general purpose equipment to expensive specialized equipment.
  • Variable cost - ranging from a high unit cost to a low unit cost.
  • Labor content and skill - ranging from high labor content with high skill to low content and low skill.
  • Volume - ranging from a quantity of one to large scale mass production.
It is interesting to note that these aspects generally increase or decrease monotonically as one moves between the extremes of process structures. The following chart illustrates how the process characteristics vary with structure.
Comparison of Process Structures and Characteristics

None  Continuous
High  Low
No. of Products
High  Low
Capital Investment
Low  High
Variable Cost
High  Low
Labor Content
High  Low
Labor Skill
High  Low
Low  High

The following sections describe each of the architectures, highlighting their differentiating characteristics.

  • Flow - no flow
  • Flexibility - very high
  • Products - unique
  • Capital investment - very low
  • Variable cost - very high
  • Labor content and skill - very high
  • Volume - one

In a project, the inputs are brought to the project location as they are needed; there is no flow in the process. Technically, a project is not a process flow structure since there is no flow of product - the quantity produced usually is equal to one. It is worthwhile, however, to treat it as a processstructure here since it represents one extreme of the spectrum.
Projects are suitable for unique products that are different each time they are produced. The firm brings together the resources as needed, coordinating them using project management techniques.
Job Shop

  • Flow - jumbled flow
  • Flexibility - high
  • Products - many
  • Capital investment - low
  • Variable cost - high
  • Labor content and skill - high
  • Volume - low

job shop is a flexible operation that has several activities through which work can pass. In a job shop, it is not necessary for all activities to be performed on all products, and their sequence may be different for different products.
To illustrate the concept of a job shop, consider the case of a machine shop. In a machine shop, a variety of equipment such as drill presses, lathes, and milling machines is arranged in stations. Work is passed only to those machines required by it, and in the sequence required by it. This is a very flexible arrangement that can be used for wide variety of products.
A job shop uses general purpose equipment and relies on the knowledge of workers to produce a wide variety of products. Volume is adjusted by adding or removing labor as needed. Job shops are low in efficiency but high in flexibility. Rather than selling specific products, a job shop often sells its capabilities.
Batch Process

  • Flow - disconnected, with some dominant flows
  • Flexibility - moderate
  • Products - several
  • Capital investment - moderate
  • Variable cost - moderate
  • Labor content and skill - moderate
  • Volume - moderate

batch process is similar to a job shop, except that the sequence of activities tends to be in a line and is less flexible. In a batch process, dominant flows can be identified. The activities, while in-line, are disconnected from one another. Products are produced in batches, for example, to fill specific customer orders.
A batch process executes different production runs for different products. The disadvantage is the setup time required to change from one product to the other, but the advantage is that some flexibility in product mix can be achieved.
Assembly Line Process

  • Flow - connected line
  • Flexibility - low
  • Products - a few
  • Capital investment - high
  • Variable cost - low
  • Labor content and skill - low
  • Volume - high

Like a batch process, an assembly line processes work in fixed sequence. However, the assembly line connects the activities and paces them, for example, with a conveyor belt. A good example of an assembly line is an automobile plant.
Continuous Flow Process

  • Flow - continuous
  • Flexibility - very low
  • Products - one
  • Capital investment - very high
  • Variable cost - very low
  • Labor content and skill - very low, but with skilled overseers
  • Volume - very high

Like the assembly line, a continuous flow process has a fixed pace and fixed sequence of activities. Rather than being processed in discrete steps, the product is processed in a continuous flow; its quantity tends to be measured in weight or volume. The direct labor content and associated skill is low, but the skill level required to oversee the sophisticated equipment in the process may be high. Petroleum refineries and sugar processing facilities use a continuous flow process.
Process Selection

The primary determinants of the optimal process are the product variety and volume. The amount of capital that the firm is willing or able to invest also may be an important determinant, and there often is a trade-off between fixed and variable cost.
The choice of process may depend on the firm's marketing plans and business strategy for developing a competitive advantage. From a marketing standpoint, a job shop allows the firm to sell its capabilities, whereas flow-shop production emphasizes the product itself. From a competitive advantage perspective, a job shop helps a firm to follow a differentiation strategy, whereas a flow shop is suited for a low cost strategy.
The process choice may depend on the stage of the product life cycle. In 1979 Robert H. Hayes and Steven C. Wheelwright put forth a product-process matrix relating process selection to the product life cycle stage. For example, early in a product's life cycle, a job shop may be most appropriate structure to rapidly fill the early demand and adjust to changes in the design. When the product reaches maturity, the high volumes may justify an assembly line, and in the declining phase a batch process may be more appropriate as product volumes fall and a variety of spare parts is required.
The optimal process also depends on the local economics. The cost of labor, energy, equipment, and transportation all can impact the process selection.
A break-even analysis may be performed to assist in process selection. A break-even chart relates cost to levels of demand in various processes and the selection is made based on anticipated demand