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Concurrent and sequential networks — implications for project management
Engineering Management International, 3 (1986) 279-282 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
279
CONCURRENT AND SEQUENTIALNETWORKS IMPLICATIONSFOR PRWECrPMANAGEMENT Larry A. Smith and Joan Mills College of Business Administration,
Florida
International
University,
Bay Vista Campus, North Miami. FL 33181
fU.S.A.1
ABSTRACT Timely completion of projects is one of the essential goals of project management. The present authors have developed aprobabilitybased explanation of the latenessphenomenon as it relates to network complexity. Concur-
rent activities within a network are greater determinants of the delay than are comparable sequential activites. The implications for project management are discussed.
An effective project management system should address three interrelated resource parameters - time, cost, and performance (Kerzner, 1979). During the project planning stage, and through Work Breakdown Structures, time, cost, and performance estimates are determined. This information normally is used in developing a PERT/CPM network which serves as a tool in managing and controlling the project. Schonberger (1981) attributes the “phenomenon of projects always being late” to a faulty estimation procedure based on critical path analysis. According to Schonberger, the deterministic critical path understates the likely project duration but continues to be popular because it is simpler to understand, easier to use, and cheaper than an alternative, such as Monte-Carlo simulation. He recommends the continued use of traditional critical path analysis but with certain modifications. The modifications involve using one time estimate in place of the customary three estimates and subjectively re-evaluating the event completion dates based upon (1) activity time variability among concurrent project path seg-
ments and (2) the relative “fatness” of the network (i.e. preponderance of coneurrent activities). The present authors have developed a prob;?bility-based explanation of the lateness phenomenon as it relates to the complexity of the network and will discuss the implications of this concept for project management.
0167-5419/86/$03.50
AN EXAMPLE When the budgetary process starts in the county, the budget director issues a set of guidelines for each of the departments to follow. Upon receiving all the departmental (Fire, Police, etc.) requests, the director duplicates and collates their requests for evaluation at a staff meeting. These evaluations and :2commendations are then formulated, typed, collated and presented to middle level managers at a working session. Their input is appended to the original report and sent to the County Manager for review by his staff. This report is then rewritten, typed, bound and submitted to the commission for their input
o 1986 Elsevier Science Publishers B.V.
280 SUBNETWORK
Fire
Department
Pobce
SUSNETW ORK
A
B
I
Department
Transportation Malntenance Personnel Finance/
Summary Version
Admlnistratlon
Parks
&
Water
Management
A
Staff
A
Summary
1VEvaluationVRevislon
Recreatlon
& Recommendahons
Mlddle fi A 1 UManagement”Revlslon Workshop
ommlssloners,-,
Summary
WorkshopsURevwon
Fig. 1. An example
of a concurrent
subnetwork
(A) and sequential
subnetwork
and modification. Then it must be presented for public hearing, Once approved, the budget is then compiled in final form, typeset, bound and distributed to all concerned. The sequence of activities is described in Fig. 1. The Budgetary process can be divided into two subnetworks, A and B. Subnetwork A consists of twelve departments, each concurrently developing their budgets, and in subnetwork B, twelve activities must be performed sequentially. Subnetwork A is estimated that each department will require a mean of 36 working days - normally distributed with a standard deviation of six days. In order to obtain Summary Version 1 all twelve departments must submit their budgets. What is the probability that all twelve departments will submit their requests within 45 days? The probability that a department will submit a budget within 45 days is 0.933 (see Fig. 2). Therefore, the probability of all twelve departments submitting budgets within 45 days is (0.933)12 or 0.44 with the probability It
Summary
fl
County
2”Manager & Staff Meeting
,q Pubhc n 4uHearllngsVApproval
~~~~ @I
(B).
36
45 tz1.5
Fig. 2. The normal probability distribution of all twelve departments submitting their budget requests within 45 days (Subnetwork A).
of taking longer than 45 days to collect all the departments’ budgets equaling 1 - 0.44 or 0.56. So it becomes evident that if one activity takes longer than X days to complete then Subnetwork A will take longer than X days to complete. By similar calculations, Table 1 was developed. Subnetwork B Suppose each of the twelve activities is estimated to take three days with a standard
281 TABLE 1 The cumulative probability tion time of Subnetwork A
distribution
X = Number days to complete Subnetwork A
Probability of finishing within X days
36 37 38 39 40 41 52 43 44 45
0.00 0.00
for comple-
Probability of taking more than X days
work A is six days and the standard deviation of Subnetwork B is also six days. Yet, the probabilities of completing each subnetwork varies considerably as demonstrated by the graph presented in Fig. 3.
Subnetwork
1.00 1.00 1.00 0.99 0.97 0.93 0.88 0.78 2 c2 0.56
0.00
0.01 0.03 0.07 0.12 0.22 0.32 0.44
A
0.9 0.8 0.7 0.6
-
0.2 -
TABLE 2
0.1 -
The cumulative probability tion time of Subnetwork B
distribution
for comple-
X = Number days to complete Subnetwork B
Probability of finishing within X days
Probability of taking more than X days
36 37 38 39 40 41 42 43 44 45
0.5 0.56 0.63 0.69 0.75 0.80 0.84 0.88 0.91 0.93
0.5 0.44 0.37 0.31 0.25 0.20 0.16 0.12 0.09 0.07
deviation of 1.7 days, normally distributed. Then the twelve activities in Subnetwork B will require an average time of 36 days and variance of 12 X 3 = 36 or standard deviation of 436 = 6. Therefore the time duration to complete Subnetwork B can be calculated using the normal distribution and produces Table 2. Subnetwork A and Subnetwork B both require the same average time of 36 days. The standard deviation of each activity on Subnet-
I
I
I
I
I
36
37
36
39
40
41
42
Number
of
Days
Fig. 3. A comparison work A (concurrent)
1
I
I
43
I
44
I
45
46
of completion times for Subnetand Subnetwork B (sequential).
CONCLUSION The probability of missing a completion date for a subnetwork with concurrent activities (Subnetwork A) is greater, in general, than a subnetwork with sequential activities (Subnetwork B). Subnetwork A requires more monitoring, less coordination between activities, less communication between activities, and more independence of activities, while subnetwork B requires more team work, more coordination, greater dependence, less monitoring, and more communication. Webster (1981) advises project managers to “avoid unnecessary meddling which is detrimental to morale and progress” and to determine the appropriate degree of attention for each organizational unit. With information on the probability of project delays related to network complexity, the project manager can
individualize attention control process.
during the program
REFERENCES Kenner, Harold, 1979. Project Management - A Systems Approach to Planning, Scheduling, and Controlling. Van Nostrand Reinhold, New York.
Schonberger, Richard J., 1981. Why projects are always late: a rationale based on manual simulation of a PERT/CPM network. Interfaces, 11: 66 70. Webster, Francis M., 1981. Ways to improve performante on projects. Project Management Quarterly, September: 21-26.
279
CONCURRENT AND SEQUENTIALNETWORKS IMPLICATIONSFOR PRWECrPMANAGEMENT Larry A. Smith and Joan Mills College of Business Administration,
Florida
International
University,
Bay Vista Campus, North Miami. FL 33181
fU.S.A.1
ABSTRACT Timely completion of projects is one of the essential goals of project management. The present authors have developed aprobabilitybased explanation of the latenessphenomenon as it relates to network complexity. Concur-
rent activities within a network are greater determinants of the delay than are comparable sequential activites. The implications for project management are discussed.
An effective project management system should address three interrelated resource parameters - time, cost, and performance (Kerzner, 1979). During the project planning stage, and through Work Breakdown Structures, time, cost, and performance estimates are determined. This information normally is used in developing a PERT/CPM network which serves as a tool in managing and controlling the project. Schonberger (1981) attributes the “phenomenon of projects always being late” to a faulty estimation procedure based on critical path analysis. According to Schonberger, the deterministic critical path understates the likely project duration but continues to be popular because it is simpler to understand, easier to use, and cheaper than an alternative, such as Monte-Carlo simulation. He recommends the continued use of traditional critical path analysis but with certain modifications. The modifications involve using one time estimate in place of the customary three estimates and subjectively re-evaluating the event completion dates based upon (1) activity time variability among concurrent project path seg-
ments and (2) the relative “fatness” of the network (i.e. preponderance of coneurrent activities). The present authors have developed a prob;?bility-based explanation of the lateness phenomenon as it relates to the complexity of the network and will discuss the implications of this concept for project management.
0167-5419/86/$03.50
AN EXAMPLE When the budgetary process starts in the county, the budget director issues a set of guidelines for each of the departments to follow. Upon receiving all the departmental (Fire, Police, etc.) requests, the director duplicates and collates their requests for evaluation at a staff meeting. These evaluations and :2commendations are then formulated, typed, collated and presented to middle level managers at a working session. Their input is appended to the original report and sent to the County Manager for review by his staff. This report is then rewritten, typed, bound and submitted to the commission for their input
o 1986 Elsevier Science Publishers B.V.
280 SUBNETWORK
Fire
Department
Pobce
SUSNETW ORK
A
B
I
Department
Transportation Malntenance Personnel Finance/
Summary Version
Admlnistratlon
Parks
&
Water
Management
A
Staff
A
Summary
1VEvaluationVRevislon
Recreatlon
& Recommendahons
Mlddle fi A 1 UManagement”Revlslon Workshop
ommlssloners,-,
Summary
WorkshopsURevwon
Fig. 1. An example
of a concurrent
subnetwork
(A) and sequential
subnetwork
and modification. Then it must be presented for public hearing, Once approved, the budget is then compiled in final form, typeset, bound and distributed to all concerned. The sequence of activities is described in Fig. 1. The Budgetary process can be divided into two subnetworks, A and B. Subnetwork A consists of twelve departments, each concurrently developing their budgets, and in subnetwork B, twelve activities must be performed sequentially. Subnetwork A is estimated that each department will require a mean of 36 working days - normally distributed with a standard deviation of six days. In order to obtain Summary Version 1 all twelve departments must submit their budgets. What is the probability that all twelve departments will submit their requests within 45 days? The probability that a department will submit a budget within 45 days is 0.933 (see Fig. 2). Therefore, the probability of all twelve departments submitting budgets within 45 days is (0.933)12 or 0.44 with the probability It
Summary
fl
County
2”Manager & Staff Meeting
,q Pubhc n 4uHearllngsVApproval
~~~~ @I
(B).
36
45 tz1.5
Fig. 2. The normal probability distribution of all twelve departments submitting their budget requests within 45 days (Subnetwork A).
of taking longer than 45 days to collect all the departments’ budgets equaling 1 - 0.44 or 0.56. So it becomes evident that if one activity takes longer than X days to complete then Subnetwork A will take longer than X days to complete. By similar calculations, Table 1 was developed. Subnetwork B Suppose each of the twelve activities is estimated to take three days with a standard
281 TABLE 1 The cumulative probability tion time of Subnetwork A
distribution
X = Number days to complete Subnetwork A
Probability of finishing within X days
36 37 38 39 40 41 52 43 44 45
0.00 0.00
for comple-
Probability of taking more than X days
work A is six days and the standard deviation of Subnetwork B is also six days. Yet, the probabilities of completing each subnetwork varies considerably as demonstrated by the graph presented in Fig. 3.
Subnetwork
1.00 1.00 1.00 0.99 0.97 0.93 0.88 0.78 2 c2 0.56
0.00
0.01 0.03 0.07 0.12 0.22 0.32 0.44
A
0.9 0.8 0.7 0.6
-
0.2 -
TABLE 2
0.1 -
The cumulative probability tion time of Subnetwork B
distribution
for comple-
X = Number days to complete Subnetwork B
Probability of finishing within X days
Probability of taking more than X days
36 37 38 39 40 41 42 43 44 45
0.5 0.56 0.63 0.69 0.75 0.80 0.84 0.88 0.91 0.93
0.5 0.44 0.37 0.31 0.25 0.20 0.16 0.12 0.09 0.07
deviation of 1.7 days, normally distributed. Then the twelve activities in Subnetwork B will require an average time of 36 days and variance of 12 X 3 = 36 or standard deviation of 436 = 6. Therefore the time duration to complete Subnetwork B can be calculated using the normal distribution and produces Table 2. Subnetwork A and Subnetwork B both require the same average time of 36 days. The standard deviation of each activity on Subnet-
I
I
I
I
I
36
37
36
39
40
41
42
Number
of
Days
Fig. 3. A comparison work A (concurrent)
1
I
I
43
I
44
I
45
46
of completion times for Subnetand Subnetwork B (sequential).
CONCLUSION The probability of missing a completion date for a subnetwork with concurrent activities (Subnetwork A) is greater, in general, than a subnetwork with sequential activities (Subnetwork B). Subnetwork A requires more monitoring, less coordination between activities, less communication between activities, and more independence of activities, while subnetwork B requires more team work, more coordination, greater dependence, less monitoring, and more communication. Webster (1981) advises project managers to “avoid unnecessary meddling which is detrimental to morale and progress” and to determine the appropriate degree of attention for each organizational unit. With information on the probability of project delays related to network complexity, the project manager can
individualize attention control process.
during the program
REFERENCES Kenner, Harold, 1979. Project Management - A Systems Approach to Planning, Scheduling, and Controlling. Van Nostrand Reinhold, New York.
Schonberger, Richard J., 1981. Why projects are always late: a rationale based on manual simulation of a PERT/CPM network. Interfaces, 11: 66 70. Webster, Francis M., 1981. Ways to improve performante on projects. Project Management Quarterly, September: 21-26.