TYPES OF FLOATS AND THEIR CALCULATION

OPERATIONS RESEARCHTYPES OF FLOATS AND THEIR CALCULATIONMADE BY:YATIN GUPTA(35)VISHAL GUPTA(34)CRITICAL PATH ANALYSISGives the shortest time in which whole network can be completed.It is chain of activities with the longest time durations.These activities are called CRITICAL ACTIVITIES.

Steps for calculation of critical path-:Calculation of time schedule for each activityCalculation of time schedule for the completion of the entire project.Identify the critical activities and find the critical path.Important TermsEarliest Start Time(E):Represents the time at which the activity can begin at the earliest.Calculated by using forward path method .

Latest Finish Time(L):Represents the latest by which an activity must be completed in order that the project may not be delayed beyond its targeted completion time.Calculated by using backward pass method.

Earliest Finish Time( TEF ): E + tij Latest Start Time ( TLS ) : L - tijImportant Terms

FLOATSIt is defined as positive difference between the finish time or the positive difference between start times.Mathematically, F = L TEF F = TLS - EThere are four types of floats. Total Float, Free Float, Interfering Float and Independent Float.TYPES OF FLOATS1)Total float(T.F) : It is the difference between the maximum time available to perform the activity and the activity duration.Maximum available time = L ETherefore, Total Float = L E tij = (L tij) - E = TLS - E =L (E + tij ) = L TEFTotal float represents the maximum time within which an activity can be delayed without affecting the project completion time.TYPES OF FLOATS2) Free Float(F.F): It is that portion of the total float within which an activity can be manipulated without affecting the floats of subsequent activities.Free Float = T.F (L E) of head event j

Thus free float is the time by which completion of an activity can be delayed without delaying its immediate successor activities.TYPES OF FLOATS3) Independent Float: It is that portion of the float within which an activity can be delayed for start without affecting the floats of preceding activities.

Independent Float = F.F (L E ) of tail event iTYPES OF FLOATS4) Interfering Float: It is defined as the difference between the latest finish time of the activity under consideration and the earliest start time of the following activity.It is also the difference between the total float and the free float of the activity.

Interfering float = T.F F.F = (L E ) of the head event j

Other termsSubcritical Activity: Activity having next higher float other than the critical activity is called the subcritical activity.

Supercritical Activity: An activity having negative float is called supercritical activity.

Slack: It is the time by which occurrence of an event can be delayed. S = L E Float is used for activities and slack for events.TIME COST TRADE OFFThe objective of the time-cost trade-off analysis is to reduce the original project duration, determined form the critical path analysis, to meet a specific deadline, with the least cost.Reducing project duration can be done by adjusting overlaps between activities or by reducing activities duration.By scheduling weekend or evening work, the completion time for an activity as measured in calendar days will be reduced. However, extra wages must be paid for such overtime work, so the cost will increase.