Solving mathematical programming planning models subject to stochastic task success

Steven Joseph Honkomp, Purdue University

Abstract

This work considers the problem of resource constrained planning and scheduling arising in research and development project selection and execution. Applications of the type considered in this work are common to all of the chemical industries, where only a fraction of projects successfully make it to market, but are especially representative of the pharmaceutical and agricultural chemicals sectors where the development and approval processes are particularly rigorous. The key uncertainty considered in this work is the probability projects will be terminated during the R & D process as a result of failure to meet regulatory, economic, or other performance requirements. Typically there will be an extensive pool of projects, some of which will be in progress, and others which are under consideration for assignment. Each project requires different amounts of a number of shared resources, such as various categories of internal staff, contractors, and physical facilities. It is not unusual for each resource type to be simultaneously engaged in multiple tasks with different projects up to some maximum capacity. Each project involves a network of tasks that must be executed, for the most part, in a specified sequence. The specific timing of each task must be selected so as to balance the resource load and subject to resource constraints. Each project has assigned to it a relative importance weight and has a desired due date, which may be six or more quarters into the future. The solution approach proposed in this work is to formulate a mixed integer linear program which is based on the uniform time discretization model (UDM), but also, incorporates the mean task success probabilities and the possibility of concurrent assignment of tasks to resources. The resulting formulation allows resources to be effectively over-booked in order to account for the fact that most tasks in the sequence have a significant probability of resulting in an outcome that leads to termination of the project prior to its completion. Variations of the formulation are examined with a small example and industrially motivated cases. Finally, modifications are proposed which extend the utility of the formulation beyond the assumptions made during development.

Degree

Ph.D.

Advisors

Pekny, Purdue University.

Subject Area

Chemical engineering|Operations research

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