A stochastic dynamic multiobjective model for sustainable decision making
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A stochastic dynamic multiobjective model for sustainable decision making Fouad Ben Abdelaziz1 · Cinzia Colapinto2,3 · Davide La Torre4,5 · Danilo Liuzzi5
© Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract The complexity of reality can be better represented by models able to involve uncertainty and time patterns. We present a general formulation of a stochastic dynamic multiobjective optimization model and we provide different solution concepts based on its transformation into different deterministic equivalent models. We provide two applications to sustainable decision making in portfolio management and optimal workforce allocation. Keywords Stochastic optimization · Multiobjective optimization · Dynamic optimization · Sustainability
1 Introduction Many current decisions are complex, based on many objectives and no certain information. A relevant example is sustainability which plays an important role in today’s world. Any decision or investment cannot be merely based on profit maximization or cost reduction but
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Fouad Ben Abdelaziz [email protected] Cinzia Colapinto [email protected]; [email protected] Davide La Torre [email protected]; [email protected] Danilo Liuzzi [email protected]
1
Neoma Business School, Rouen Campus, Mont-Saint-Aignan, France
2
Graduate School of Business, Nazarbayev University, Astana, Kazakhstan
3
Department of Management, Ca’ Foscari University of Venice, Venice, Italy
4
Dubai Business School, University of Dubai, Dubai, UAE
5
Department of Economics, Management and Quantitative Methods, University of Milan, Milan, Italy
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it has to involve other factors such as pollution control, land preservation, water usage, and so on. Any suitable mathematical model used to describe a sustainable decision making context needs to have the following characteristics: it is subject to uncertainty because there is a huge number of random exogenous factors; it is dynamic because it usually involves mid-term or long-term horizon; and it involves multiple objectives describing a variety of different criteria to be considered into the decision making process. In this paper we model the effect of uncertainty by using a classical probabilistic approach: we suppose that there is an underlying space of possible scenarios with associated probabilities. Each scenario will affect the objectives and thus the decision making process. To simplify the problem later on we will present some notions of deterministic equivalent problem and show how to transform a stochastic model into a deterministic one. The objective function is a vector-valued map which models the presence of several conflicting criteria: the notion of Pareto optimal solution is introduced as well as two practical techniques to reduce the problem to a scalar one. These techniques are scalarization and goal programming, respectively. After taking the scalarization of the deterministic equaivalent problem, the optimization program is reduced to a calcu
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