Mean Project Completion Time in Dynamic Markov PERT Networks

Amir Azaron, Hideki Katagiri, Kosuke Kato, Masatoshi Sakawa
1 2
actually known and assumed to be ( s 2 , s2
) . Table 2 shows the values of
1 2
V ( s , s ) for m = 1,
2 , i = 1,
2 and l=1,2,3,4. Taking into account this
l
m
1
m
2
i
table, the approximation of mean project completion time in the dynamic
Markov PERT network of Figure 1 is equal to 0.597 year.
1 2
If the initial sate vector of system is assumed to be ( s 1 , s1
) , or the worst
case for the strike and the inflation rate, then, the approximation of mean project
completion time would be equal to 1.89 year. The approximation of mean
project completion time in the worst case would be more than 3 times of this
1 2
quantity in the best case, or the state of ( s 2, s2
) . Therefore, in the real world
problems, the actual mean project completion time is so sensitive to the transitions
of social and economical problems over the planning horizon, and we
should consider the dynamic behavior of social problems in the classical PERT
networks.
1 2
Table 2. V ( s , s ) for m = 1,
2 , i = 1,
2 and l=1,2,3,4
l
m
1
m
2
i
V 1
2 V V 3
4 V
1 2
( s 1 , s1
) 1.89 1.274 1.182 0.25
1 2
( s 1 , s2
) 1.214 0.724 0.414 0.167
1 2
( s 2 , s1
) 0.902 0.629 0.466 0.125
1 2
( s 2 , s2
) 0.597 0.385 0.249 0.1
780