A general space-time model for combinatorial optimization problems (and not only). (October 2020)

• Record Type: Journal Article
• Authors: Barbati, Maria; Corrente, Salvatore; Greco, Salvatore
• Is Part Of: Omega. Volume 96(2020)
• Publication Date: 2020-10
• Subjects: Portfolio decision analysis -- Multiple criteria decision aiding -- Dominance-based rough set approach -- Interactive multiobjective optimization; Management -- Periodicals; 658.4005
• DOI: 10.1016/j.omega.2019.05.003
• Languages: English
• ISSNs: 0305-0483

Abstract

Highlights: We present a model to select facilities, their location and their activation time. Our model integrates aspects of the most well-known operational research problems. Multiple criteria, plurality of stakeholders and uncertainty are considered. Our model supplies a dashboard that helps the interaction with the decision makers. Our model can be coupled with several multiobjective optimization methodologies. Abstract: We consider the problem of defining a strategy consisting of a set of facilities taking into account also the location where they have to be assigned and the time in which they have to be activated. The facilities are evaluated with respect to a set of criteria. The plan has to be devised respecting some constraints related to different aspects of the problem such as precedence restrictions due to the nature of the facilities. Among the constraints, there are some related to the available budget. We consider also the uncertainty related to the performances of the facilities with respect to considered criteria and plurality of stakeholders participating to the decision. The considered problem can be seen as the combination of some prototypical operations research problems: knapsack problem, location problem and project scheduling. Indeed, the basic brick of our model is a variable xilt which takes value 1 if facility i is activated in location l at time t, and 0 otherwise. Due to the conjoint consideration of a location and a time in the decision variables, what we propose can be seen as a general space-time model for operations research problems. We discuss how such a model permits to handle complex problems using several methodologies including multiple attribute value theory and multiobjective optimization. With respect to the latter point, without any loss of the generality, we consider the compromise programming and an interactive methodology based on the Dominance-based Rough Set Approach. We illustrate the application of our model with a simple didactic example.