PERT & CPM - PROJECT MANAGEMENT

PROJECT MANAGEMENT

PROJECT MANAGEMENT

A PROJECT IS A WELL DEFINED TASK WHICH HAS A DEFINABLE BEGINNING AND A DEFINABLE END AND REQUIRES ONE OR MORE RESOURCES FOR THE COMPLETION OF ITS CONSTITUENT ACTIVITIES, WHICH ARE INTERRELATED AND WHICH MUST BE ACCOMPLISHED TO ACHIEVE THE OBJECTIVES OF THE PROJECT. PROJECT MANAGEMENT IS EVOLVED TO COORDINATE AND CONTROL ALL PROJECT ACTIVITIES IN AN EFFICIENT AND COST EFFECTIVE MANNER. THE SALIENT FEATURES OF A PROJECT ARE:

• A PROJECT HAS IDENTIFIABLE BEGINNING AND END POINTS.
• EACH PROJECT CAN BE BROKEN DOWN INTO A NUMBER OF IDENTIFIABLE ACTIVITIES WHICH WILL CONSUME TIME AND OTHER RESOURCES DURING  THEIR COMPLETION.
• A PROJECT IS SCHEDULED TO BE COMPLETED BY A TARGET DATE.
• A PROJECT IS USUALLY LARGE AND COMPLEX AND HAS MANY INTERRELATED ACTIVITIES.
• THE EXECUTION OF THE PROJECT ACTIVITIES IS ALWAYS SUBJECTED TO SOME UNCERTAINTIES AND RISKS. 

NETWORK TECHNIQUES

THE NETWORK TECHNIQUES OF PROJECT MANAGEMENT HAVE DEVELOPED IN AN EVOLUTIONARY WAY IN MANY YEARS. UP TO THE END OF 18^TH CENTURY, THE DECISION MAKING IN GENERAL AND PROJECT MANAGEMENT IN PARTICULAR WAS INTUITIVE AND DEPENDED PRIMARILY ON MANAGERIAL CAPABILITIES, EXPERIENCE, JUDGMENT AND ACADEMIC BACKGROUND OF THE MANAGERS. IT WAS ONLY IN THE EARLY OF 1900'S THAT THE PIONEERS OF SCIENTIFIC MANAGEMENT, STARTED DEVELOPING THE SCIENTIFIC MANAGEMENT TECHNIQUES. THE FORERUNNER TO NETWORK TECHNIQUES, THE GANTT CHART WAS DEVELOPED, DURING WORLD WAR I, BY HENRY L GANTT, FOR THE PURPOSE OF PRODUCTION SCHEDULING. AN EXAMPLE OF GANTT CHART 

NETWORK CONSTRUCTION 

A NETWORK IS THE GRAPHICAL REPRESENTATION OF THE PROJECT ACTIVITIES ARRANGED IN A LOGICAL SEQUENCE AND DEPICTING ALL THE INTERRELATIONSHIPS AMONG THEM. A NETWORK CONSISTS OF ACTIVITIES AND EVENTS.

ACTIVITY

AN ACTIVITY IS A PHYSICALLY IDENTIFIABLE PART OF A PROJECT, WHICH CONSUMES BOTH TIME AND RESOURCES. ACTIVITY IS REPRESENTED BY AN ARROW IN A NETWORK DIAGRAM 

THE HEAD OF AN ARROW REPRESENTS THE START OF ACTIVITY AND THE TAIL OF ARROW REPRESENTS ITS END. ACTIVITY DESCRIPTION AND ITS ESTIMATED COMPLETION TIME ARE WRITTEN ALONG THE ARROW. AN ACTIVITY IN THE NETWORK CAN BE REPRESENTED BY A NUMBER OF WAYS: (I) BY NUMBERS OF ITS HEAD AND TAIL EVENTS (I.E. 10-20 ETC.), AND (II) BY A LETTER CODE (I.E. A, B ETC.). ALL THOSE ACTIVITIES, WHICH MUST BE COMPLETED BEFORE THE START OF ACTIVITY UNDER CONSIDERATION, ARE CALLED ITS PREDECESSOR ACTIVITIES. ALL THOSE ACTIVITIES, WHICH HAVE TO FOLLOW THE ACTIVITY UNDER CONSIDERATION, ARE CALLED ITS SUCCESSOR ACTIVITIES 

ACTIVITY	IMMEDIATE PREDECESSOR
A	_
B	A
C	A
D	B
E	C

ACTIVITY	IMMEDIATE SUCCESSOR
A	B,C
B	D
C	E

 AN ACTIVITY, WHICH IS USED TO MAINTAIN THE PRE-DEFINED PRECEDENCE RELATIONSHIP ONLY DURING THE CONSTRUCTION OF THE PROJECT NETWORK, IS CALLED A DUMMY ACTIVITY. DUMMY ACTIVITY IS REPRESENTED BY A DOTTED ARROW AND DOES NOT CONSUME ANY TIME AND RESOURCE 

AN UNBROKEN CHAIN OF ACTIVITIES BETWEEN ANY TWO EVENTS IS CALLED A PATH.

EVENT

AN EVENT REPRESENTS THE ACCOMPLISHMENT OF SOME TASK. IN A NETWORK DIAGRAM, BEGINNING AND ENDING OF AN ACTIVITY ARE REPRESENTED AS EVENTS. EACH EVENT IS REPRESENTED AS A NODE IN A NETWORK DIAGRAM. AN EVENT DOES NOT CONSUME ANY TIME OR RESOURCE. EACH NETWORK DIAGRAM STARTS WITH AN INITIAL EVENT AND ENDS AT A TERMINAL EVENT. EACH NODE IS REPRESENTED BY A CIRCLE AND NUMBERED BY USING THE FULKERSON'S RULE. FOLLOWING STEPS ARE INVOLVED IN THE NUMBERING OF THE NODES:

• THE INITIAL EVENT, WHICH HAS ALL OUTGOING ARROWS AND NO INCOMING ARROW, IS NUMBERED AS 1.
• DELETE ALL THE ARROWS COMING OUT FROM THE NODE JUST NUMBERED (I.E. 1). THIS STEP WILL CREATE SOME MORE NODES (AT LEAST ONE) INTO INITIAL EVENTS. NUMBER THESE EVENTS IN ASCENDING ORDER (I.E. 2, 3 ­ETC.).
• CONTINUE THE PROCESS UNTIL THE FINAL OR TERMINAL NODE WHICH HAS ALL ARROWS COMING IN, WITH NO ARROW GOING OUT, IS NUMBERED.

AS A RECOMMENDATION IT MUST BE NOTED THAT MOST OF THE PROJECTS ARE LIABLE FOR MODIFICATIONS, AND HENCE THERE SHOULD BE A SCOPE OF ADDING MORE EVENTS AND NUMBERING THEM WITHOUT CAUSING ANY INCONSISTENCY IN THE NETWORK. THIS IS ACHIEVED BY SKIPPING THE NUMBERS (I.E. 10, 20, 30…).

RULES FOR DRAWING NETWORK DIAGRAM

RULE 1: EACH ACTIVITY IS REPRESENTED BY ONE AND ONLY ONE ARROW IN THE NETWORK.

RULE 2: NO TWO ACTIVITIES CAN BE IDENTIFIED BY THE SAME END EVENTS.

RULE 3: PRECEDENCE RELATIONSHIPS AMONG ALL ACTIVITIES MUST ALWAYS BE MAINTAINED.

RULE 4: DUMMY ACTIVITIES CAN BE USED TO MAINTAIN PRECEDENCE RELATIONSHIPS ONLY WHEN ACTUALLY REQUIRED. THEIR USE SHOULD BE MINIMIZED IN THE NETWORK DIAGRAM.

CPM AND PERT

THE CPM (CRITICAL PATH METHOD) SYSTEM OF NETWORKING IS USED, WHEN THE ACTIVITY TIME ESTIMATES ARE DETERMINISTIC IN NATURE. FOR EACH ACTIVITY, A SINGLE VALUE OF TIME, REQUIRED FOR ITS EXECUTION, IS ESTIMATED. TIME ESTIMATES CAN EASILY BE CONVERTED INTO COST DATA IN THIS TECHNIQUE. CPM IS AN ACTIVITY ORIENTED TECHNIQUE.

THE PERT (PROJECT EVALUATION AND REVIEW TECHNIQUE) TECHNIQUE IS USED, WHEN ACTIVITY TIME ESTIMATES ARE STOCHASTIC IN NATURE. FOR EACH ACTIVITY, THREE VALUES OF TIME (OPTIMISTIC, MOST LIKELY, PESSIMISTIC) ARE ESTIMATED.  OPTIMISTIC TIME (T_O) ESTIMATE IS THE SHORTEST POSSIBLE TIME REQUIRED FOR THE COMPLETION OF ACTIVITY. MOST LIKELY TIME (T_M) ESTIMATE IS THE TIME REQUIRED FOR THE COMPLETION OF ACTIVITY UNDER NORMAL CIRCUMSTANCES. PESSIMISTIC TIME (T_P) ESTIMATE IS THE LONGEST POSSIBLE TIME REQUIRED FOR THE COMPLETION OF ACTIVITY. IN PERT Β-DISTRIBUTION IS USED TO REPRESENT THESE THREE TIME ESTIMATES 

 AS PERT ACTIVITIES ARE FULL OF UNCERTAINTIES, TIMES ESTIMATES CAN NOT EASILY BE CONVERTED IN TO COST DATA. PERT IS AN EVENT ORIENTED TECHNIQUE. IN PERT EXPECTED TIME OF AN ACTIVITY IS DETERMINED BY USING THE BELOW GIVEN FORMULA:

CALCULATION OF TIME ESTIMATES IN CPM

IN THE PROJECT NETWORK GIVEN IN FIGURE BELOW, ACTIVITIES AND THEIR DURATIONS ARE SPECIFIED AT THE ACTIVITIES. FIND THE CRITICAL PATH AND THE PROJECT DURATION.

CALCULATIONS IN NETWORK ANALYSIS

THE FOLLOWING CALCULATIONS ARE REQUIRED IN NETWORK ANALYSIS IN ORDER TO PREPARE A SCHEDULE OF THE PROJECT.

1. TOTAL COMPLETION TIME OF THE PROJECT
2. EARLIEST TIME WHEN EACH ACTIVITY CAN START (I.E. EARLIST START TIME)
3. EARLIEST TIME WHEN EACH ACTIVITY CAN FINISH (I.E. EARLIST FINISHED TIME)
4. LATEST TIME WHEN EACH ACTIVITY CAN BE STARTED WITHOUT DELAYING THE PROJECT (I.E. LATEST START TIME)
5. LATEST TIME WHEN EACH ACTIVITY CAN BE FINISHED WITHOUT DELAYING THE PROJECT (I.E. LATEST FINISH TIME)
6. FLOAT ON EACH ACTIVITY (I.E. TIME BY WHICH THE COMPLETION OF AN ACTIVITY CAN BE DELAYED WITHOUT DELAYING THE PROJECT)
7. CRITICAL ACTIVITY AND CRITICAL PATH

THE SYMBOLS USED IN THE CALCULATIONS ARE SHOWN IN TABLE BELOW.

SYMBOL	DESCRIPTION
EI	EARLIEST OCCURANCE TIME OF EVENT I
LJ	LATEST ALLOWABLE OCCURANCE TIME OF EVENT J
TEI-J	ESTIMATED COMPLETION TIME OF ACTIVITY (I,J)
(EST)IJ	EARLIEST STARTING TIME OF ACTIVITY (I,J)
(EFT)IJ	EARLIEST FINISHING TIME OF ACTIVITY (I,J)
(LST)IJ	LATEST STARTING TIME OF ACTIVITY (I,J)
(LFT)IJ	LATEST FINISHING TIME OF ACTIVITY (I,J)

THE COMPUTATIONS ARE MADE IN FOLLOWING STEPS. 

(A) FORWARD PASS COMPUTATIONS :

 (B) BACKWARD PASS COMPUTATIONS :

(C) CALCULATION OF SLACK:

EVENT SLACK IS DEFINED AS THE DIFFERENCE BETWEEN THE LATEST EVENT AND EARLIST EVENT TIMES.

THE CALCULATIONS FOR THE ABOVE TAKEN EXAMPLE NETWORK ARE SUMMARISED BELOW IN THE TABLE.

PREDECESSOR EVENT I	SUCCESSOR    EVENT J	TEI-J	(EST)IJ	(EFT)IJ	(LST)IJ	(LFT)IJ	S(I) SLACK
5	10	7	0	7	0	7	0
5	15	12	0	12	7	19	-
5	20	17	0	17	5	22	-
10	20	15	7	22	7	22	0
10	25	9	7	16	21	30	-
15	30	11	12	23	19	30	7
20	25	5	22	27	25	30	-
20	30	8	22	30	22	30	0
25	35	10	27	37	30	40	3
25	45	15	27	42	35	50	-
30	35	10	30	40	30	40	0
30	40	8	30	38	35	43	-
35	45	10	40	50	40	50	0
40	45	7	38	45	43	50	5

(D) DETERMINATION OF CRITICAL PATH:

THE SEQUANCE OF CRITICAL ACTIVITIES IN A NETWORK IS CALLED THE CRITICAL PATH. THE ACTIVITIES WITH ZERO SLACK OF HEAD EVENT AND ZERO SLACK FOR TAIL EVENT, ARE CALLED AS CRITITCAL ACTIVITIES. IN THE TAKEN NETWORK, THE FOLLOWING ACTIVITIES ARE CRITICAL ACTIVITIES: 5 - 10, 10 - 20, 20 - 30, 30 - 35, 35 - 45.
THUS THE CRITICAL PATH IS A - E - G - K - M.
CRITICAL PATH DURATION IS 7 + 15 + 8 + 10 + 10 = 50.

CALCULATION OF EXPECTED TIME AND VARIANCE OF A PATH IN PERT

THE EXPECTED TIME OF A CHAIN OF ACTIVITIES IN SERIES, IS THE SUM OF THEIR EXPECTED TIMES. SIMILARLY THE VARIANCE OF THE PATH, IS THE SUM OF VARIANCES OF ACTIVITIES ON THE PATH. IN FIGURE BELOW, THREE ACTIVITIES A,B AND C ARE CONNECTED IN SERIES, (I.E. FORM A PATH). THEIR TIME ESTIMATES TO-TM-TPARE GIVEN ALONG THE ACTIVITY ARROWS. THE EXPECTED TIME OF THE PATH 1-2-3-4 IS CALCULATED AS: 

AS THE LENGTH OF THE PATH ,THAT IS THE NUMBER OF ACTIVIES CONNECTED IN SERIES INCREASES,THE VARIANCE OF THE PATH AND HENCE THE UNCERTAINTY OF MEETING THE EXPECTED TIME ALSO INCREASES.

AN EXAMPLE

IN THE NETWORK OF FIGURE BELOW, THE PERT TIME ESTIMATES OF THE ACTIVITIES ARE WRITTEN ALONG THE ACTIVITY ARROWS IN THE ORDER TO-TM-TP. COMPUTE THE EXPECTED TIME AND VARIANCE FOR EACH ACTIVITY. ALSO COMPUTE THE EXPECTED DURATION AND STANDARD DEVIATION FOR THE FOLLOWING PATHS OF THE NETWORK.

           (A) 10-20-50-80-90

           (B) 10-30-50-70-90

           (C) 10-40-60-80-90 

THE COMPUTATION OF EXPECTED TIMES AND VARIANCES FOR DIFFERENT ACTIVITIES ARE CARRIED IN A TABLE GIVEN BELOW.

ACTIVITY I              J	TIME ESTIMATES TO           TM          TP	EXPECTED TIME TE	VARIANCE Σ2
10           20	6             9           12	9.00	1.00
10           30	3             5            9	5.33	1.00
10           40	10         14           18	14.00	1.78
20           50	7           10           13	10.00	1.00
20           70	3             4             8	4.5	0.69
30           50	4           10           12	9.33	1.78
40           50	8           11           14	11.00	1.00
40           60	5          10           15	10.00	2.78
50           70	3            4            5	4.00	0.11
50           80	11           15          17	14.67	1.00
60           80	7             9           12	9.17	0.69
70           90	4             8            10	7.67	1.00
80           90	6             7           9	7.17	0.25

REFERENCES:-  www.nptel.iitm.ac.in/