PM5_24FEB10 - Chapter PlanningwithUncertainty 1...

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1 Chapter  Planning with Uncertainty
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    2 The Effects of Uncertainty The most obvious effect is that uncertainty in a task duration causes late  completion of that task. Depending on the criticality of that task, this may delay overall project completion. Effective planning can reduce uncertainty or mitigate its effects. The more uncertain a task when it is initiated, the more monitoring and control are  needed to ensure effective performance.
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    3 Uncertain Task Durations Pessimistic time, t j p Most likely time, t j m Optimistic time, t j o Completion time of task j Time Probability density function Expected time,  μ It is widely assumed that, in many projects, task durations  follow the beta distribution shown below
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    4 Standard Approximations for Task  Durations For each task, we need three estimates:   most optimistic time, most pessimistic time, most likely time, o t p t m t 6 4 duration Expected m p o t t t + + = μ 6 deviation Standard o p t t - = σ In practice,  how easy is it  to estimate  these? These formulas are designed to approximate (simply, but not very  accurately) the beta distribution.
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    5 Three Mechanisms by which Uncertainty  Creates Problems 1. Parkinson’s Law 2. Procratinasting Workers 3. Schonberger’s Hypothesis
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    6 Mechanism 1: Parkinson’s Law Consider a project with two tasks in series, where the duration of each task is described by a random variable with value T i , i = 1, 2 E(T 1 ) E(T 2 ) So the expected makespan is 24 16.0
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    7 Example of Parkinson’s Law “Work expands so as to fill the time available for  its completion” C.N. Parkinson (1957) Set a deadline D = 24 days So T(D) = project makespan (function of D) where E[T(D)] = E(T 1 ) + E(T 2 ) + E[max(0, D - T 1  - T 2 )]  Values of T 1 Prob Values of T 2 Prob Project Makespan Prob 7 0.3 14 0.5 24 0.15 7 0.3 18 0.5 25 0.15 8 0.4 14 0.5 24 0.2 8 0.4 18 0.5 26 0.2 9 0.3 14 0.5 24 0.15 9 0.3 18 0.5 27 0.15 E[T(D)] = 25 days * * * *makespan expanded to fit  deadline Values of T 1 Values of T 2
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  8 Mechanism 2: Procrastinating Workers Set a deadline D = 24 days E’[T(D)] = E(T 1 ) + E(T 2 ) + E{max[0, D - T 1  - E(T 2 )]}  Values of T 1 Prob E[Delay] = max[0, D - T 1 - E(T2)] E[Makespan] 7 0.3 1 24 8 0.4 0 24 9 0.3 0 25 8 0.3 24.30 We can show that E[T(D)] ≥ E’[T(D)] ≥ D. What are some possible solutions? Provide incentives for early completion, set tight deadlines However, unreasonably tight deadlines may have other negative  effects (stress, loss of quality, turnover,…) A procrastinating worker waits until the last possible time to start (given  the  expected  duration of their task). * * Delayed by 
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This note was uploaded on 12/20/2010 for the course IEOR E4510 taught by Professor Mosherosenwein during the Spring '10 term at Columbia.

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PM5_24FEB10 - Chapter PlanningwithUncertainty 1...

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