Sample-path solutions for simulation optimization problems and stochastic variational inequalities

inequality;simulation;optimization

Applications of Semidefinite Optimization in Stochastic Project Scheduling

We propose a new method, based on semidefinite optimization, to find tight upper bounds on the expected project completion time and expected project tardiness in a stochastic project scheduling environment, when only limited information in the form of first and second (joint) moments of the durations of individual activities in the project is available. Our computational experiments suggest that the bounds provided by the new method are stronger and often significant compared to the bounds found by alternative methods.Singapore-MIT Alliance (SMA

Calculating Project Completion in Polynomial Processing Time

Technology-based organizations and knowledge organizations rely on large activity networks to manage Research & Development (R&D) projects. Avoiding optimistic completion times due to the characteristic Program Evaluation and Review Technique (PERT) assumptions is a problem that can grow exponentially in complexity with the number of activities. A recursive technique that solves the problem in a polynomial number of steps has been developed, assuming that all duration times follow beta distributions. It is important to notice that the only two 100% valid approaches to calculate the project completion time are simulation and the stochastic sum for each and every path in the network. Nevertheless, both require finding the shape parameters, and that is precisely the main contribution of this paper: a system of equations to calculate the shape parameters of each activity and the overall project

Measures of Risk on Variability with Application in Stochastic Activity Networks

We propose a simple measure of variability of some of the more commonly used distribution functions in the class of New-Better-than-Used in Expectation (NBUE). The measure result in a ranking of the distributions, and the methodology used is applicable to other distributions in NBUE class beside the one treated here. An application to stochastic activity networks is given to illustrate the idea and the applicability of the proposed measure. Keywords: Alternative Risk measure, Portfolio, Coefficient of Variation, Skewness, Project management,  Stochastic activity networks

Bounds on series-parallel slowdown

We use activity networks (task graphs) to model parallel programs and consider series-parallel extensions of these networks. Our motivation is two-fold: the benefits of series-parallel activity networks and the modelling of programming constructs, such as those imposed by current parallel computing environments. Series-parallelisation adds precedence constraints to an activity network, usually increasing its makespan (execution time). The slowdown ratio describes how additional constraints affect the makespan. We disprove an existing conjecture positing a bound of two on the slowdown when workload is not considered. Where workload is known, we conjecture that 4/3 slowdown is always achievable, and prove our conjecture for small networks using max-plus algebra. We analyse a polynomial-time algorithm showing that achieving 4/3 slowdown is in exp-APX. Finally, we discuss the implications of our results.Comment: 12 pages, 4 figure

Probabilistic combinatorial optimization: Moments, semidefinite programming, and asymptotic bounds

10.1137/S1052623403430610SIAM Journal on Optimization151185-20

Models for robust resource allocation in project scheduling.

The vast majority of resource-constrained project scheduling efforts assumes complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. In reality, however, project activities are subject to considerable uncertainty which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects the makespan of a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed robust resource allocation problem in exact and approximate formulations. The procedure relies on constraint propagation during its search. We report on computational results obtained on a set of benchmark problems.Model; Resource allocation; Scheduling;

Managing technology risk in R&D project planning: Optimal timing and parallelization of R&D activities.

An inherent characteristic of R&D projects is technological uncertainty, which may result in project failure, and time and resources spent without any tangible return. In pharmaceutical projects, for instance, stringent scientific procedures have to be followed to ensure patient safety and drug efficacy in pre-clinical and clinical tests before a medicine can be approved for production. A project consists of several stages, and may have to be terminated in any of these stages, with typically a low likelihood of success. In project planning and scheduling, this technological uncertainty has typically been ignored, and project plans are developed only for scenarios in which the project succeeds. In this paper, we examine how to schedule projects in order to maximize their expected net present value, when the project activities have a probability of failure, and where an activity's failure leads to overall project termination. We formulate the problem, show that it is NP-hard and develop a branchand- bound algorithm that allows to obtain optimal solutions. We also present polynomial-time algorithms for special cases, and present a number of managerial insights for R&D project and planning, including the advantages and disadvantages of parallelization of R&D activities in different settings.Applications; Branch-and-bound; Computational complexity; Exact algorithms programming; Integer; Pharmaceutical; Project management; Project scheduling; R&D projects analysis of algorithms; Risk industries;