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

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 x ilt 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.

A Framework for Valuation and Portfolio Optimization of Venture Capital Deals with Contractual Terms

“…Operation research problems usually answer only one of the "what," "where," and "when" questions [22]. This paper aims to address the combination of these questions for the VCs portfolio.…”

A portfolio approach for the selection and the timing of urban planning projects

“…We also point out that uncertainty in the performances of urban projects with respect to the considered criteria can be taken into account. If we are dealing with quantitative information we could adopt the same approach followed by [37] in which the expected value of the evaluation in a given period is computed using the probability of different states of nature. For the qualitative evaluations, different methods in the literature have been proposed to calculate a cardinal probabilistic evaluation of each project (see e.g., [38]).…”