A computational framework for project scheduling, analysis and optimization

Abstract: The ability to develop complex products is a feature commonly required from modern engineering. The increasing complexity and size of some projects requires a suitable tool to address the subject effectively. Some authors define “engineering” as the application of mathematical and scientific principles. In this context, the ability to propose, execute and improve complex planning schedules is of paramount importance. A basic schedule is a general guidance for preparing and releasing various types of technical plans. These documents include technical management plans (such as hardware development plans, software development plans, configuration and data management plans, and risk management plans), supporting technical plans (such as system safety plans, manufacturing plans, and system support plans) and test plans (such as system integration, test, and verification plans and hardware and software test plans), to cite some. Due the relevance of the theme when dealing with complex projects, in this paper a methodology for task planning, analysis and optimization is proposed. A draft planning containing task dependence, time duration and used resource may be provided by the manager. The proposed framework is able to import such information from commercially available management software. The schedule is then translated as an optimization problem, where the overall time is the objective to be minimized. Resource allocation and risk management are considered by means of weighting factors. Pareto framework is considered in order to provide visibility of alternative scenarios. The proposed formulation considers different task priorities of the optimal planning. As a result, relevant information about optimal scheduling and sensitivity of alternative scenarios is provided. Numerical results show the viability of the proposed methodology.


Nowadays, more than ever, companies want to deliver products and services better, faster, and cheaper. At the same time, in the high-technology environment of the twenty-first century, nearly all organizations have found themselves building increasingly complex products and services.

In this context, a single company usually does not develop all the components that compose a product or service. More commonly, some components are built in-house and some are acquired; then all the components are integrated into the final product or service. Organizations must be able to manage and control this complex development and maintenance process.

A key point to achieve better performance is the project planning.

According to Capability Maturity Model Integration for development (CMMI, 2006), at maturity level 2, the projects of the organization have ensured that processes are planned and executed in accordance with a given policy. The process discipline reflected by maturity level 2 helps to ensure that existing practices are retained during times of stress. At the last level, the maturity level 5, an organization continually improves its processes based on a quantitative understanding of the common causes of variation inherent in processes. Maturity level 5 focuses on continually improving process performance.

Quantitative process improvement objectives for the organization are established, continually revised to reflect changing business objectives, and used as criteria in managing process improvement.

It motivates the development of a tool for fast analysis of changes in planning. The current paper proposes a new formulation for optimization of an arbitrary planning project. Based on a linear programming model, the current purpose ensures the global optimality independent of the initial configuration. Low CPU time is another attractive feature of the current purpose.

The remainder of the paper is organized as follows. Section 2 reviews some works in this field and presents a widely adopted classification for planning and scheduling problems. Linear programming framework, multiple objective optimization and the proposed model to scheduling problems are presented in section 3. Section 4 analyses performance results of the proposed strategy. Concluding remarks and directions for future works are given in section 5.