Project Evaluation and Selection with Task Failures

We consider a company that schedules the tasks of its projects to maximize their expected net present value (ENPV) when tasks may fail. The failure of any task terminates the project immediately. We show that for projects with certain decreasing failure rates, the ENPV optimization problem can be solved using a linear program. The main focus of our work is on how constant task failure rates contribute to decreasing project risk as tasks are completed. Under constant task failure rate, earlier completion of a task improves its probability of success and the risk profile of the project. However, it may also accelerate costs, which worsen discounted cash flow. We show the equivalence of cash flow discount rate and failure rate. Further, if task failures are independent, then the failure rates are additive. We develop a model that (a) recognizes the reduction in project risk when a task is completed, (b) implements this risk reduction into the ENPV calculation, and (c) permits optimization of the ENPV through sequencing and timing decisions for the tasks. We design an algorithm to solve the problem optimally. This enables us to validate the contributions of our work using two computational studies. The first study demonstrates a significant increase in maximum project ENPV from improved project scheduling. The second study demonstrates a significant increase in total project portfolio value as a result of better informed project selection. Our work motivates companies to develop more precise information about the failure risks of their project tasks.