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We consider the problem of defining a strategy consisting of a set offacilities taking into account also the location where they have to be assignedand the time in which they have to be activated. The facilities are evaluatedwith respect to a set of criteria. The plan has to be devised respecting someconstraints related to different aspects of the problem such as precedencerestrictions due to the nature of the facilities. Among the constraints, thereare some related to the available budget. We consider also the uncertaintyrelated to the performances of the facilities with respect to consideredcriteria, and plurality of stakeholders participating to the decision. Theconsidered problem can be seen as the combination of some prototypicaloperations research problems: knapsack problem, location problem and projectscheduling. Indeed, the basic brick of our model is a variable $x_{ilt}$ whichtakes 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 thedecision variables, what we propose can be seen as a general space-time modelfor operations research problems. We discuss how such a model permits to handlecomplex problems using several methodologies including multiple attribute valuetheory and multiobjective optimization. With respect to the latter point,without any loss of the generality, we consider the compromise programming andan interactive methodology based on the Dominance-based Rough Set Approach. Weillustrate the application of our model with a simple didactic example.

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