The Project Scheduling Problem with Non-Deterministic Activities Duration: A Literature Review

Purpose: The goal of this article is to provide an extensive literature review of the models and solution procedures proposed by many researchers interested on the Project Scheduling Problem with nondeterministic activities duration. Design/methodology/approach: This paper presents an exhaustive literature review, identifying the existing models where the activities duration were taken as uncertain or random parameters. In order to get published articles since 1996, was employed the Scopus database. The articles were selected on the basis of reviews of abstracts, methodologies, and conclusions. The results were classified according to following characteristics: year of publication, mathematical representation of the activities duration, solution techniques applied, and type of problem solved. Findings: Genetic Algorithms (GA) was pointed out as the main solution technique employed by researchers, and the Resource-Constrained Project Scheduling Problem (RCPSP) as the most studied type of problem. On the other hand, the application of new solution techniques, and the possibility of incorporating traditional methods into new PSP variants was presented as research trends. Originality/value: This literature review contents not only a descriptive analysis of the published articles but also a statistical information section in order to examine the state of the research activity carried out in relation to the Project Scheduling Problem with non-deterministic activities duration.Peer Reviewe

Stochastic multi-period multi-product multi-objective Aggregate Production Planning model in multi-echelon supply chain

In this paper a multi-period multi-product multi-objective aggregate production planning (APP) model is proposed for an uncertain multi-echelon supply chain considering financial risk, customer satisfaction, and human resource training. Three conflictive objective functions and several sets of real constraints are considered concurrently in the proposed APP model. Some parameters of the proposed model are assumed to be uncertain and handled through a two-stage stochastic programming (TSSP) approach. The proposed TSSP is solved using three multi-objective solution procedures, i.e., the goal attainment technique, the modified ε-constraint method, and STEM method. The whole procedure is applied in an automotive resin and oil supply chain as a real case study wherein the efficacy and applicability of the proposed approaches are illustrated in comparison with existing experimental production planning method

Military and Security Applications: Cybersecurity (Encyclopedia of Optimization, Third Edition)

The domain of cybersecurity is growing as part of broader military and security applications, and the capabilities and processes in this realm have qualities and characteristics that warrant using solution methods in mathematical optimization. Problems of interest may involve continuous or discrete variables, a convex or non-convex decision space, differing levels of uncertainty, and constrained or unconstrained frameworks. Cyberattacks, for example, can be modeled using hierarchical threat structures and may involve decision strategies from both an organization or individual and the adversary. Network traffic flow, intrusion detection and prevention systems, interconnected human-machine interfaces, and automated systems – these all require higher levels of complexity in mathematical optimization modeling and analysis. Attributes such as cyber resiliency, network adaptability, security capability, and information technology flexibility – these require the measurement of multiple characteristics, many of which may involve both quantitative and qualitative interpretations. And for nearly every organization that is invested in some cybersecurity practice, decisions must be made that involve the competing objectives of cost, risk, and performance. As such, mathematical optimization has been widely used and accepted to model important and complex decision problems, providing analytical evidence for helping drive decision outcomes in cybersecurity applications. In the paragraphs that follow, this chapter highlights some of the recent mathematical optimization research in the body of knowledge applied to the cybersecurity space. The subsequent literature discussed fits within a broader cybersecurity domain taxonomy considering the categories of analyze, collect and operate, investigate, operate and maintain, oversee and govern, protect and defend, and securely provision. Further, the paragraphs are structured around generalized mathematical optimization categories to provide a lens to summarize the existing literature, including uncertainty (stochastic programming, robust optimization, etc.), discrete (integer programming, multiobjective, etc.), continuous-unconstrained (nonlinear least squares, etc.), continuous-constrained (global optimization, etc.), and continuous-constrained (nonlinear programming, network optimization, linear programming, etc.). At the conclusion of this chapter, research implications and extensions are offered to the reader that desires to pursue further mathematical optimization research for cybersecurity within a broader military and security applications context