Production and Operation Managements Project Scheduling Dr.Na GeNG Prof.Zhibin JIANG Department of Industrial Engineering Management Shanghai Jiao Tong University
Production and Operation Managements Dr. Na GENG Prof. Zhibin JIANG Department of Industrial Engineering & Management Shanghai Jiao Tong University Project Scheduling
Content The nature of project management Techniques for project scheduling Resource constraints Activity crashing Incorporating uncertainty in activity times 国 Problems with implementing critical path analysis Monitoring projects 2 上浒充通大粤
Content The nature of project management Techniques for project scheduling Resource constraints Activity crashing Incorporating uncertainty in activity times Problems with implementing critical path analysis Monitoring projects 2
Incorporating uncertainty in activity times Estimating activity duration distribution In PERT model,the duration for each activity is assume to follow Beta Distribution with pdf Tp+qx-to)P-1(4,-x)9-1 f(x)=r(p)r(q) (tp-to)p+q-2 where .totp-the lower and upper control point ·r(m)=6xm-1e-xdx Expected value: p,q-the shape parameters -o+e,-o49 Variance: 5=（6p-to'p+90+q+西 pq 3
Incorporating uncertainty in activity times Estimating activity duration distribution • In PERT model, the duration for each activity is assume to follow Beta Distribution with pdf ൌ ݔ ݂ ݍ Г Г Г ݍ ݐെݔ ିଵ ݐ ݔ െ ିଵ ݐ ݐ െ ାିଶ where • t o, tp – the lower and upper control point • Г η ൌ ଵିݔ ݔ݀௫݁ି ஶ • p, q - the shape parameters 3 Expected value: ݐൌߤ ݐ ݐ െ ݍ Variance: ܵ ൌ ݐ ݐ െ ݍ ଶ ݍ 1ݍ ଶ
Incorporating uncertainty in activity times Estimating activity duration distribution A typical Beta distribution is commonly used to describe the duration of uncertain activities. Optimistic time(A):the duration of an activity if no complications or problems occur. Most likely time (M):the duration is most likely to occur. Pessimistic time (B):the duration of an activity if extraordinary problems arise. 01,Gm,=A+4M+B 350-98 Expected value: 5容9由 A+4M+B sideT ni be g=B-A行5Da5d orr bait 6 1a0800d2v t三 6 P (duration <A)=0.01 P (duration B)=0.01 Standard Variance: 6.01 oldeT B-A Days A M B 0三 Optimistic Most Mean Pessimistic iwL-1-8-O-A 6 Time Likely Time Time Time ong5由1 o noistitn t.出H的a
Incorporating uncertainty in activity times Estimating activity duration distribution • A typical Beta distribution is commonly used to describe the duration of uncertain activities. • Optimistic time (A): the duration of an activity if no complications or problems occur. • Most likely time (M): the duration is most likely to occur. • Pessimistic time (B): the duration of an activity if extraordinary problems arise. 4 Expected value: ൌ ݐ ܤ ܯ4 ܣ 6 Standard Variance: ൌ ߪ ܣെܤ 6
Incorporating uncertainty in activity times Project completion time distribution 1)For every activity,obtain estimates of A,M,B. 2)Use t=(A+4M+B)/6 to calculate the expected activity durations, and perform critical path analysis using the expected activity durations t. 3)The expected project completion time T is assumed to be the sum of the expected durations of activities on critical path 4)The variance of project completion time o2r is assumed to be the sum of the variances of activities on the critical path. 5)Probabilities regarding project completion time can be determined from standard normal tables. 5 上浒充通大粤
Project completion time distribution 1) For every activity, obtain estimates of A, M, B. 2) Use t=(A+4M+B)/6 to calculate the expected activity durations, and perform critical path analysis using the expected activity durations t. 3) The expected project completion time T is assumed to be the sum of the expected durations of activities on critical path. 4) The variance of project completion time ߪ ଶ ் is assumed to be the sum of the variances of activities on the critical path. 5) Probabilities regarding project completion time can be determined from standard normal tables. 5 Incorporating uncertainty in activity times