Resource-constrained Project Scheduling And Control With Stochastic Activity Duration

In this research we study the project scheduling and schedule control problems when activity duration of the project is stochastic.Traditional project scheduling and schedule control methods presume that activity duration is deterministic,however,in the real word,projects are subject to considerable uncertainties.Due to these uncertain influence factors,activities may take longer than expected,thus rendering the schedule that based on deterministic activity duration infeasible in practice.In order to tackle this problem,we view the activity duration as a random variable,and develop project scheduling and schedule control methodologies.To be specific,we address the following three problems: how to schedule a resource-constrained project in order to minimize it's expected duration,how to schedule a project so as to maximize it's expected net present value,and how to control the schedule.In the three problems above all activity duration is stochastic.We examine the performance of 17 priority rule heuristics and the justification technique on the stochastic resource-constrained project scheduling problem(SRCPSP).Among the 17 priority rules,12 are selected from the literature that are addressing the deterministic resource-constrained project scheduling problem(RCPSP),and the other 5 are newly designed,based on stochastic information of the SRCPSP.We evaluate the efficiency of the 17 priority rules on the benchmark data set PSPLIB,and analyze the impact of the project characteristics that were used to create this data set.Our computational results on large size instances show that the best priority rule for the RCPSP does not perform best for the SRCPSP.The best priority rule for the SRCPSP performs as well as the best meta-heuristic when the variance of the activity duration is medium,and outperforms all existing algorithms when this variance is high.The validity of justification on the SRCPSP depends on the priority rule and the activity duration variance.The project characteristics network complexity and resource factor do not influence the choice of the best priority rule,but resource strength does.We address project scheduling with net-present-value objective and exponential activity duration,using a continuous-time Markov decision chain.Previous research on this problem does not consider the resource constraints.In this study we develop a stochastic dynamic program to maximize the expected net present value of the resource constrained project with stochastic activity duration.We give a new algorithm to generate next stage states based on the present stage states,this algorithm can make sure all the newly generated states satisfy the logical relationships between activities and resource constraints,at the same time can reduce the number of redundant states drastically.We find the relationship between the optimal value of different states that satisfy some certain relationship,for all those states we only need to calculate one's optimal value.This accelerates the procedure of the dynamic program.Experimental results on large-sized instances validate our algorithm,and the results show that the order strength of the project has an important impact on the efficiency of the algorithm: when the order strength is low,there are more states thus needs more time to figure out the optimal expected net present value.We propose a new schedule control method for projects with stochastic activity duration.In our new method,we view the EVM/ES based indicators as quality characteristics and deploy statistical process control(SPC)charts to monitor the progress of a project.The key of using SPC chart to control the schedule of a project is the control limits.In our method,we first define the efficiency,reliability,performance and overreaction of a tolerance limit,and then analyze how the change of a tolerance limit will influence the above four indicators,finally,we define the efficiency-reliability factor function and overreaction-performance factor function.Based on the two functions,an algorithm is proposed to optimize the tolerance limits.An extensive computational experiment is carried out to assess the performance of the proposed approach.Experimental results show that our approach has more discriminatory power compared with three other methods in the literature,and is less sensitive to the influence factors.