Project Scheduling Tools

1. Sequencing There are four possible sequencing modes in MS Project. Suppose B follows A. FS: Finish Start – Start B after A is completed SS: Start Start – Start A and B at same time FF: Finish Finish – Finish A and B at same time SF: Start Finish – Start A after B is completed Lags are delays between work on activities

FS Sequence - Traditional B E.g. Sand and Paint A Lag B E.g. Sprinklers and Landscape

SS Sequence A E.g. Plant Lawn and Flowers A B A E.g. Drywall: Hang and Tape Lag B

FF Sequence A E.g. Olympics B A Lag E.g. Olympics B

SF Sequence A E.g. Not Practical B A B E.g. Ocean Cruise Lag

2. Activity Uncertainty PERT assumptions (Richard Schonberger and Ken Mac Crimmon Beta distribution assumption PERT approximation formula for mean and variance Estimates of a, m, and b Errors of above up to 30%, but tend to cancel Worse problem is merge event bias (probability near-critical path becomes critical) – estimates consistently optimistic

Example 2.1 B,2 A,1 D,1 C,3 Critical path is ACD but ABD is near critical. Criticality index: probability path critical.

Use Simulation or Monte Carlo Analysis Generate random numbers (electronic, formulas, tables, books) i.e. 28 • Convert to random probabilities i.e. .28 What is probability of probability? • Convert random probability to random variate. Follows distribution of say actual activity time.

Finding Random Variates, Problem 2.1 B C PMF CDF Mean – 1 1 2 .3 .3 Mean 2 3 .4 .7 Mean + 1 3 4 .2 .9 Mean + 2 4 5 .1 1.0 Random probability of .28 gives B random variate of 1; .46 gives C value of 3.

Simulation of Problem 2.1 RN B(2) RN C(3) Length Path .28 1 .46 3 5 ACD .97 4 .09 2 6 ABD .63 2 .33 3 5 ACD .53 2 .76 4 6 ACD .73 3 .00 5 7 ACD Expected length = 5.8 > 5 (merge event bias) Criticality index of ACD = 0.8 or 80%

Project Simulation Simulation includes GERT – Graphical Evaluation and Review Technique Crystal Ball – Copy comes with text Probabilistic branching from node – B may follow A Probabilistic times for activities – various distributions Flexibility in node realization – activity time can = 0 Looping permitted – rework Critique of Simulation – R. Schonberger recommends intensive critical path scrutiny

3. Limited Resource Scheduling Resources include labor, material, equipment, space, and money Money versus time tradeoffs Methods Crashing – How to shorten activities – cost penalties Resource loading – amount of resource needed per period. Resource leveling or balancing – evening out resource use, reacting to limited resources Simulation programs can help level