Process Flow StructuresThe 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 refineryThese 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 CharacteristicsProjectJobShopBatchProcessAssemblyLineContinuousFlow

FlowNoneContinuous

FlexibilityHighLow

No. of ProductsHighLow

Capital InvestmentLowHigh

Variable CostHighLow

Labor ContentHighLow

Labor SkillHighLow

VolumeLowHigh

The following sections describe each of the architectures, highlighting their differentiating characteristics.Project Flow - no flow Flexibility - very high Products - unique Capital investment - very low Variable cost - very high Labor content and skill - very high Volume - oneIn 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 process structure 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 - lowA 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 - moderateA 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 - highLike 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 highLike 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 SelectionThe 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.Process AnalysisAn operation is composed of processes designed to add value by transforming inputs into useful outputs. Inputs may be materials, labor, energy, and capital equipment. Outputs may be a physical product (possibly used as an input to another process) or a service. Processes can have a significant impact on the performance of a business, and process improvement can improve a firm's competitiveness.The first step to improving a process is to analyze it in order to understand the activities, their relationships, and the values of relevant metrics. Process analysis generally involves the following tasks: Define the process boundaries that mark the entry points of the process inputs and the exit points of the process outputs. Construct a process flow diagram that illustrates the various process activities and their interrelationships. Determine the capacity of each step in the process. Calculate other measures of interest. Identify the bottleneck, that is, the step having the lowest capacity. Evaluate further limitations in order to quantify the impact of the bottleneck. Use the analysis to make operating decisions and to improve the process.Process Flow DiagramThe process boundaries are defined by the entry and exit points of inputs and outputs of the process.Once the boundaries are defined, the process flow diagram (or process flowchart) is a valuable tool for understanding the process using graphic elements to represent tasks, flows, and storage. The following is a flow diagram for a simple process having three sequential activities:Process Flow Diagram

The symbols in a process flow diagram are defined as follows: Rectangles: represent tasks Arrows: represent flows. Flows include the flow of material and the flow of information. The flow of information may include production orders and instructions. The information flow may take the form of a slip of paper that follows the material, or it may be routed separately, possibly ahead of the material in order to ready the equipment. Material flow usually is represented by a solid line and information flow by a dashed line. Inverted triangles: represent storage (inventory). Storage bins commonly are used to represent raw material inventory, work in process inventory, and finished goods inventory. Circles: represent storage of information (not shown in the above diagram).In a process flow diagram, tasks drawn one after the other in series are performed sequentially. Tasks drawn in parallel are performed simultaneously.In the above diagram, raw material is held in a storage bin at the beginning of the process. After the last task, the output also is stored in a storage bin.When constructing a flow diagram, care should be taken to avoid pitfalls that might cause the flow diagram not to represent reality. For example, if the diagram is constructed using information obtained from employees, the employees may be reluctant to disclose rework loops and other potentially embarrassing aspects of the process. Similarly, if there are illogical aspects of the process flow, employees may tend to portray it as it should be and not as it is. Even if they portray the process as they perceive it, their perception may differ from the actual process. For example, they may leave out important activities that they deem to be insignificant.Process Performance MeasuresOperations managers are interested in process aspects such as cost, quality, flexibility, and speed. Some of the process performance measures that communicate these aspects include: Process capacity - The capacity of the process is its maximum output rate, measured in units produced per unit of time. The capacity of a series of tasks is determined by the lowest capacity task in the string. The capacity of parallel strings of tasks is the sum of the capacities of the two strings, except for cases in which the two strings have different outputs that are combined. In such cases, the capacity of the two parallel strings of tasks is that of the lowest capacity parallel string. Capacity utilization - the percentage of the process capacity that actually is being used. Throughput rate (also known as flow rate ) - the average rate at which units flow past a specific point in the process. The maximum throughput rate is the process capacity. Flow time (also known as throughput time or lead time) - the average time that a unit requires to flow through the process from the entry point to the exit point. The flow time is the length of the longest path through the process. Flow time includes both processing time and any time the unit spends between steps. Cycle time - the time between successive units as they are output from the process. Cycle time for the process is equal to the inverse of the throughput rate. Cycle time can be thought of as the time required for a task to repeat itself. Each series task in a process must have a cycle time less than or equal to the cycle time for the process. Put another way, the cycle time of the process is equal to the longest task cycle time. The process is said to be in balance if the cycle times are equal for each activity in the process. Such balance rarely is achieved. Process time - the average time that a unit is worked on. Process time is flow time less idle time. Idle time - time when no activity is being performed, for example, when an activity is waiting for work to arrive from the previous activity. The term can be used to describe both machine idle time and worker idle time. Work In process - the amount of inventory in the process. Set-up time - the time required to prepare the equipment to perform an activity on a batch of units. Set-up time usually does not depend strongly on the batch size and therefore can be reduced on a per unit basis by increasing the batch size. Direct labor content - the amount of labor (in units of time) actually contained in the product. Excludes idle time when workers are not working directly on the product. Also excludes time spent maintaining machines, transporting materials, etc. Direct labor utilization - the fraction of labor capacity that actually is utilized as direct labor.Little's LawThe inventory in the process is related to the throughput rate and throughput time by the following equation:W.I.P. Inventory = Throughput Rate x Flow TimeThis relation is known as Little's Law, named after John D.C. Little who proved it mathematically in 1961. Since the throughput rate is equal to 1 / cycle time, Little's Law can be written as:Flow Time = W.I.P. Inventory x Cycle TimeThe Process BottleneckThe process capacity is determined by the slowest series task in the process; that is, having the slowest throughput rate or longest cycle time. This slowest task is known as the bottleneck. Identification of the bottleneck is a critical aspect of process analysis since it not only determines the process capacity, but also provides the opportunity to increase that capacity.Saving time in the bottleneck activity saves time for the entire process. Saving time in a non-bottleneck activity does not help the process since the throughput rate is limited by the bottleneck. It is only when the bottleneck is eliminated that another activity will become the new bottleneck and present a new opportunity to improve the process.If the next slowest task is much faster than the bottleneck, then the bottleneck is having a major impact on the process capacity. If the next slowest task is only slightly faster than the bottleneck, then increasing the throughput of the bottleneck will have a limited impact on the process capacity.Starvation and BlockingStarvation occurs when a downstream activity is idle with no inputs to process because of upstream delays. Blocking occurs when an activity becomes idle because the next downstream activity is not ready to take it. Both starvation and blocking can be reduced by adding buffers that hold inventory between activities.Process ImprovementImprovements in cost, quality, flexibility, and speed are commonly sought. The following lists some of the ways that processes can be improved. Reduce work-in-process inventory - reduces lead time. Add additional resources to increase capacity of the bottleneck. For example, an additional machine can be added in parallel to increase the capacity. Improve the efficiency of the bottleneck activity - increases process capacity. Move work away from bottleneck resources where possible - increases process capacity. Increase availability of bottleneck resources, for example, by adding an additional shift - increases process capacity. Minimize non-value adding activities - decreases cost, reduces lead time. Non-value adding activities include transport, rework, waiting, testing and inspecting, and support activities. Redesign the product for better manufacturability - can improve several or all process performance measures. Flexibility can be improved by outsourcing certain activities. Flexibility also can be enhanced by postponement, which shifts customizing activities to the end of the process.In some cases, dramatic improvements can be made at minimal cost when the bottleneck activity is severely limiting the process capacity. On the other hand, in well-optimized processes, significant investment may be required to achieve a marginal operational improvement. Because of the large investment, the operational gain may not generate a sufficient rate of return. A cost-benefit analysis should be performed to determine if a process change is worth the investment. Ultimately, net present value will determine whether a process "improvement" really is an improvement.Linear ProgrammingOperations management often presents complex problems that can be modeled by linear functions. The mathematical technique of linear programming is instrumental in solving a wide range of operations management problems.Linear Program StructureLinear programming models consist of an objective function and the constraints on that function. A linear programming model takes the following form:Objective function:Z = a1X1 + a2X2 + a3X3 + . . . + anXnConstraints:b11X1 + b12X2 + b13X3 + . . . + b1nXn < c1b21X1 + b22X2 + b23X3 + . . . + b2nXn < c2 . . . bm1X1 + bm2X2 + bm3X3 + . . . + bmnXn < cmIn this system of linear equations, Z is the objective function value that is being optimized, Xi are the decision variables whose optimal values are to be found, and ai, bij, and ci are constants derived from the specifics of the problem.Linear Programming AssumptionsLinear programming requires linearity in the equations as shown in the above structure. In a linear equation, each decision variable is multiplied by a constant coefficient with no multiplying between decision variables and no nonlinear functions such as logarithms. Linearity requires the following assumptions: Proportionality - a change in a variable results in a proportionate change in that variable's contribution to the value of the function. Additivity - the function value is the sum of the contributions of each term. Divisibility - the decision variables can be divided into non-integer values, taking on fractional values. Integer programming techniques can be used if the divisibility assumption does not hold.In addition to these linearity assumptions, linear programming assumes certainty; that is, that the coefficients are known and constant.Problem FormulationWith computers able to solve linear programming problems with ease, the challenge is in problem formulation - translating the problem statement into a system of linear equations to be solved by computer. The information required to write the objective function is derived from the problem statement. The problem is formulated from the problem statement as follows:1. Identify the objective of the problem; that is, which quantity is to be optimized. For example, one may seek to maximize profit.2. Identify the decision variables and the constraints on them. For example, production quantities and production limits may serve as decision variables and constraints.3. Write the objective function and constraints in terms of the decision variables, using information from the problem statement to determine the proper coefficient for each term. Discard any unnecessary information.4. Add any implicit constraints, such as non-negative restrictions.5. Arrange the system of equations in a consistent form suitable for solving by computer. For example, place all variables on the left side of their equations and list them in the order of their subscripts.The following guidelines help to reduce the risk of errors in problem formulation: Be sure to consider any initial conditions. Make sure that each variable in the objective function appears at least once in the constraints. Consider constraints that might not be specified explicitly. For example, if there are physical quantities that must be non-negative, then these constraints must be included in the formulation.The Effect of ConstraintsConstraints exist because certain limitations restrict the range of a variable's possible values. A constraint is considered to be binding if changing it also changes the optimal solution. Less severe constraints that do not affect the optimal solution are non-binding.Tightening a binding constraint can only worsen the objective function value, and loosening a binding constraint can only improve the objective function value. As such, once an optimal solution is found, managers can seek to improve that solution by finding ways to relax binding constraints.Shadow PriceThe shadow price for a constraint is the amount that the objective function value changes per unit change in the constraint. Since constraints often are determined by resources, a comparison of the shadow prices of each constraint provides valuable insight into the most effective place to apply additional resources in order to achieve the best improvement in the objective function value.The reported shadow price is valid up to the allowable increase or allowable decrease in the constraint.Applications of Linear ProgrammingLinear programming is used to solve problems in many aspects of business administration including: product mix planning distribution networks truck routing staff scheduling financial portfolios corporate restructuring

Work Breakdown StructureA complex project is made managable by first breaking it down into individual components in a hierarchical structure, known as the work breakdown structure, or the WBS. Such a structure defines tasks that can be completed independently of other tasks, facilitating resource allocation, assignment of responsibilities, and measurement and control of the project.The work breakdown structure can be illustrated in a block diagram:Work Breakdown Structure Diagram

Because the WBS is a hierarchical structure, it may be conveyed in outline form:Work Breakdown Structure OutlineLevel 1Level 2Level 3

Task 1

Subtask 1.1

Work Package 1.1.1

Work Package 1.1.2

Work Package 1.1.3

Subtask 1.2

Work Package 1.2.1

Work Package 1.2.2

Work Package 1.2.3

Task 2

Subtask 2.1

Work Package 2.1.1

Work Package 2.1.2

Work Package 2.1.3

Terminology for Different LevelsEach organization uses its own terminology for classifying WBS components according to their level in the hierarchy. For example, some organizations refer to different levels as tasks, sub-tasks, and work packages, as shown in the above outline. Others use the terms phases, entries, and activities.Organization by Deliverables or PhasesThe WBS may be organized around deliverables or phases of the project life cycle. Higher levels in the structure generally are performed by groups. The lowest level in the hierarchy often comprises activities performed by individuals, though a WBS that emphasizes deliverables does not necessarily specify activities.Level of DetailThe breaking down of a project into its component parts facilitates resource allocation and the assignment of individual responsibilities. Care should be taken to use a proper level of detail when creating the WBS. On the one extreme, a very high level of detail is likely to result in micro-management. On the other extreme, the tasks may become too large to manage effectively. Defining tasks so that their duration is between several days and a few months works well for most projects.WBS's Role in Project PlanningThe work breakdown structure is the foundation of project planning. It is developed before dependencies are identified and activity durations are estimated. The WBS can be used to identify the tasks in the CPM and PERT project planning models.Gantt ChartDuring 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 FormatTaskDurationJanFebMarAprMayJunJulAugSepOctNovDec

12 mo.

22 mo.

32 mo.

42 mo.

52 mo.

62 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 EnhancementsThis 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 PlanningFor 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.Alternative spellings: The name of this tool frequently is misspelled as "Gannt Chart".CPM - Critical Path MethodIn 1957, DuPont developed a project management method designed to address the challenge of shutting down chemical plants for maintenance and then restarting the plants once the maintenance had been completed. Given the complexity of the process, they developed the Critical Path Method (CPM) for managing such projects.CPM provides the following benefits: Provides a graphical view of the project. Predicts the time required to complete the project. Shows which activities are critical to maintaining the schedule and which are not.CPM models the activities and events of a project as a network. Activities are depicted as nodes on the network and events that signify the beginning or ending of activities are depicted as arcs or lines between the nodes. The following is an example of a CPM network diagram:CPM Diagram

Steps in CPM Project Planning1. Specify the individual activities.2. Determine the sequence of those activities.3. Draw a network diagram.4. Estimate the completion time for each activity.5. Identify the critical path (longest path through the network)6. Update the CPM diagram as the project progresses.1. Specify the Individual ActivitiesFrom the work breakdown structure, a listing can be made of all the activities in the project. This listing can be used as the basis for adding sequence and duration information in later steps.2. Determine the Sequence of the ActivitiesSome activities are dependent on the completion of others. A listing of the immediate predecessors of each activity is useful for constructing the CPM network diagram.3. Draw the Network DiagramOnce the activities and their sequencing have been defined, the CPM diagram can be drawn. CPM originally was developed as an activity on node (AON) network, but some project planners prefer to specify the activities on the arcs.4. Estimate Activity Completion TimeThe time required to complete each activity can be estimated using past experience or the estimates of knowledgeable persons. CPM is a deterministic model that does not take into account variation in the completion time, so only one number is used for an activity's time estimate.5. Identify the Critical PathThe critical path is the longest-duration path through the network. The significance of the critical path is that the activities that lie on it cannot be delayed without delaying the project. Because of its impact on the entire project, critical path analysis is an important aspect of project planning.The critical path can be identified by determining the following four parameters for each activity: ES - earliest start time: the earliest time at which the activity can start given that its precedent activities must be completed first. EF - earliest finish time, equal to the earliest start time for the activity plus the time required to complete the activity. LF - latest finish time: the latest time at which the activity can be completed without delaying the project. LS - latest start time, equal to the latest finish time minus the time required to complete the activity.The slack time for an activity is the time between its earliest and latest start time, or between its earliest and latest finish time. Slack is the amount of time that an activity can be delayed past its earliest start or earliest finish without delaying the project.The critical path is the path through the project network in which none of the activities have slack, that is, the path for which ES=LS and EF=LF for all activities in the path. A delay in the critical path delays the project. Similarly, to accelerate the project it is necessary to reduce the total time required for the activities in the critical path.6. Update CPM DiagramAs the project progresses, the actual task completion times will be known and the network diagram can be updated to include this information. A new critical path may emerge, and structural changes may be made in the network if project requirements change.CPM LimitationsCPM was developed for complex but fairly routine projects with minimal uncertainty in the project completion times. For less routine projects there is more uncertainty in the completion times, and this uncertainty limits the usefulness of the deterministic CPM model. An alternative to CPM is the PERT project planning model, which allows a range of durations to be specified for each activity.

PERTComplex 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 DiagramIn 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 ProcessPERT 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 MilestonesThe 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 SequenceThis 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 DiagramUsing 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 TimesWeeks 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 ) / 6This 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 ]25.Determine the Critical PathThe 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 timeThese 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 ProgressesMake 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 PERTPERT 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.LimitationsThe 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-offsThere 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 CostsThe 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 salaries, travel, 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 ScheduleCompressing 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 AssumptionsThe 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 ConsiderationsThere 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 schedule.