(370d) A Holistic Approach for Portfolio Selection and Resource-Constrained Scheduling of Multi-Task Projects

Globalization and resulting competition necessitate companies to invest continually on technological upgrades and projects for their sustained economic growth. These projects invariably compete with each other for limited resources such as budget, time, workforce, materials, facilities, and equipment. Complex interactions among projects arising due to limited resources and the desire to reduce the time to market make it extremely difficult for the decision-makers to select the best portfolio of projects, and to schedule their activities optimally. In order to achieve an optimal mix and schedule of various project activities at various times, firms need more sophisticated methods to manage their project portfolio and to allocate resources by considering the complex trade-offs and interrelationships among projects. In this talk, we present a holistic approach for portfolio selection and task scheduling with the objective of maximizing the net present value (NPV) of the portfolio.

We model project as a set of interrelated tasks and suitable work units. Resources required for the project tasks can be either renewable or non-renewable. A resource is renewable, if its use does not destroy it. Once released by one task, it becomes available for reuse by another task. Typical examples of renewable resources are labor and machinery. Non-renewable resources are those that are not replenished after use. Once a part of it is used, that part is not available for use any longer. Capital budget is a typical non-renewable resource. The resource availability and usage restrictions may vary with time. In addition to these resource constraints, we consider several realistic features such as outsourcing options, penalties for delayed completion, and other inter-project considerations.

Most often, an industrial project may not yield any revenue before it is completed, so it is natural to consider that each project generates some cash on its completion. However, in some projects, completion of certain tasks may also generate revenues. Therefore, we allow revenue generation at the end of each task. The objective is to select the portfolio of projects, and to schedule all their tasks such that we get the maximum NPV.

In this presentation, we address the above important problem of simultaneous selection and resource-constrained scheduling of general multi-task projects (both process- and product-related) and present a holistic approach based on discrete-time mixed integer linear programming (MILP). We illustrate the performance of our model using a few benchmark problems adopted from the literature. Finally, we compare the performance of our model with two existing continuous-time models. The above numerical study shows that our model can successfully solve, within reasonable times, a variety of test problems involving as many as 78 tasks, three categories of renewable resources, one category of non-renewable resource, and piecewise linear delay penalties.

Keywords: Project selection; Scheduling; Portfolio optimization, Project management