NONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY
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Project planning and scheduling when there are both resource constraints and uncertainty in task durations is an important and complex problem. There is a long history of work on deterministic resource-constrained project scheduling problems, but efforts directed at stochastic versions of that problem are fewer and more recent. Incorporating the ability to reallocate resources among tasks to change the characteristics of their duration probability distributions adds another important dimension to the problem, and enables integration of project planning and scheduling. Among the small number of previous works on this subject, there are two very different perspectives. Golenko-Ginzburg and Gonik (1997, 1998) have created a simulation-based approach that ?operates? the project through time and attempts to optimize locally regarding decisions on starting specific tasks at specific times. Turnquist and Nozick (2004) have formulated a nonlinear optimization model to plan resource allocations and schedule decisions a priori. This has the advantage of taking a global perspective on the project in making resource allocation decisions, but it is not adaptive to the experience with earlier tasks when making later decisions in the same way that the simulation approach is. Although the solution to their model produces a ?baseline schedule? (i.e., times when tasks are planned to start), the formulation puts much greater emphasis on resource allocation decisions. The paper by Turnquist and Nozick (2004) describes the problem formulation as a nonlinear optimization. For small problem instances (up to about 30 tasks), good solutions can be found using standard nonlinear programming packages(e.g., NPSOL). However, for larger problems, the standard packages often fail to find any solution in a reasonable amount of computational time. One major contribution of this dissertation is the development of a solution method that can solve larger problem instances efficiently and reliably. In this dissertation, we recommend using the partially augmented Lagrangian (PAL) method to solve the suggested nonlinear optimization. The test problems considered here include projects with up to 90 tasks, and solutions to the 90-task problems take about 2 minutes on a desktop PC. A second contribution of this dissertation is exploration of insights that can be gained through systematic variation of the basic parameters of the model formulation on a given problem. These insights have both computational and managerial implications for practical application of the model.