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In this paper, we study how uncertainties weighing on the climate system impact the optimal technological pathways the world energy system should take to comply with stringent mitigation objectives. We use the TIAM-World model that relies on the TIMES modelling approach. Its climate module is inspired by the DICE model. Using robust optimization techniques, we assess the impact of the climate system parameter uncertainty on energy transition pathways under various climate constraints. Unlike other studies we consider all the climate system parameters which is of primary importance since: (i) parameters and outcomes of climate models are all inherently uncertain (parametric uncertainty); and (ii) the simplified models at stake summarize phenomena that are by nature complex and non-linear in a few, sometimes linear, equations so that structural uncertainty is also a major issue. The use of robust optimization allows us to identify economic energy transition pathways under climate constraints for which the outcome scenarios remain relevant for any realization of the climate parameters. In this sense, transition pathways are made robust. We find that the abatement strategies are quite different between the two temperature targets. The most stringent one is reached by investing massively in carbon removal technologies such as bioenergy with carbon capture and storage (BECCS) which have yields much lower than traditional fossil fuelled technologies.

More than half of the world’s population live in cities, and by 2050, it is expected that this proportion will reach almost 68%. These densely populated cities consume more than 75% of the world’s primary energy and are responsible for the emission of around 70% of anthropogenic carbon. Providing sustainable energy for the growing demand in cities requires multifaceted planning approach. In this study, we modeled the energy system of the Greater Montreal region to evaluate the impact of different environmental mitigation policies on the energy system of this region over a long-term period (2020–2050). In doing so, we have used the open-source optimization-based model called the Energy–Technology–Environment Model (ETEM). The ETEM is a long-term bottom–up energy model that provides insight into the best options for cities to procure energy, and satisfies useful demands while reducing carbon dioxide (CO2) emissions. Results show that, under a deep decarbonization scenario, the transportation, commercial, and residential sectors will contribute to emission reduction by 6.9, 1.6, and 1 million ton CO2-eq in 2050, respectively, compared with their 2020 levels. This is mainly achieved by (i) replacing fossil fuel cars with electric-based vehicles in private and public transportation sectors; (ii) replacing fossil fuel furnaces with electric heat pumps to satisfy heating demand in buildings; and (iii) improving the efficiency of buildings by isolating walls and roofs.

We consider the problem of optimal decision making under uncertainty but assume that the decision maker’s utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over other lotteries and being risk averse, S-shaped, or prudent. These criteria extend the ones used in the first- and second-order stochastic dominance framework. We then give tractable formulations for such decision-making problems. We formulate them as robust utility maximization problems, as optimization problems with stochastic dominance constraints, and as robust certainty equivalent maximization problems. We use a portfolio allocation problem to illustrate our results. This paper was accepted by Dimitris Bertsimas, optimization.

Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions, which depend on a randomization device producing uniformly distributed samples that are independent of all uncertain factors affecting the decision problem. We find that, in the absence of distributional ambiguity, deterministic decisions are optimal if both the risk measure and the feasible region are convex or alternatively, if the risk measure is mixture quasiconcave. We show that some risk measures, such as mean (semi-)deviation and mean (semi-)moment measures, fail to be mixture quasiconcave and can, therefore, give rise to problems in which the decision maker benefits from randomization. Under distributional ambiguity, however, we show that, for any ambiguity-averse risk measure satisfying a mild continuity property, we can construct a decision problem in which a randomized decision strictly outperforms all deterministic decisions. This paper was accepted by Teck Ho, optimization.

Robust optimization is a methodology that has gained a lot of attention in the recent years. This is mainly due to the simplicity of the modeling process and ease of resolution even for large scale models. Unfortunately, the second property is usually lost when the cost function that needs to be “robustified” is not concave (or linear) with respect to the perturbing parameters. In this paper we study robust optimization of sums of piecewise linear functions over polyhedral uncertainty set. Given that these problems are known to be intractable, we propose a new scheme for constructing conservative approximations based on the relaxation of an embedded mixed-integer linear program and relate this scheme to methods that are based on exploiting affine decision rules. Our new scheme gives rise to two tractable models that, respectively, take the shape of a linear program and a semidefinite program, with the latter having the potential to provide solutions of better quality than the former at the price of heavier computations. We present conditions under which our approximation models are exact. In particular, we are able to propose the first exact reformulations for a robust (and distributionally robust) multi-item newsvendor problem with budgeted uncertainty set and a reformulation for robust multiperiod inventory problems that is exact whether the uncertainty region reduces to a L 1 -norm ball or to a box. An extensive set of empirical results will illustrate the quality of the approximate solutions that are obtained using these two models on randomly generated instances of the latter problem.

Markov decision processes are an effective tool in modeling decision making in uncertain dynamic environments. Because the parameters of these models typically are estimated from data or learned from experience, it is not surprising that the actual performance of a chosen strategy often differs significantly from the designer's initial expectations due to unavoidable modeling ambiguity. In this paper, we present a set of percentile criteria that are conceptually natural and representative of the trade-off between optimistic and pessimistic views of the question. We study the use of these criteria under different forms of uncertainty for both the rewards and the transitions. Some forms are shown to be efficiently solvable and others highly intractable. In each case, we outline solution concepts that take parametric uncertainty into account in the process of decision making.

Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix). We demonstrate that for a wide range of cost functions the associated distributionally robust (or min-max) stochastic program can be solved efficiently. Furthermore, by deriving a new confidence region for the mean and the covariance matrix of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. These arguments are confirmed in a practical example of portfolio selection, where our framework leads to better-performing policies on the \"true\" distribution underlying the daily returns of financial assets.

This article studies a capacitated fixed-charge multiperiod location–transportation problem in which, while the location and capacity of each facility must be determined immediately, the determination of the final production and distribution of products can be delayed until actual orders are received in each period. In contexts where little is known about future demand, robust optimization, namely using a budgeted uncertainty set, becomes a natural method for identifying meaningful decisions. Unfortunately, it is well known that these types of multiperiod robust decision problems are computationally intractable. To overcome this difficulty, we propose a set of tractable conservative approximations for the problem that each exploit to a different extent the idea of reducing the flexibility of the delayed decisions. While all of these approximation models outperform previous approximation models that have been proposed for this problem, each also has the potential to reach a different level of compromise between efficiency of resolution and quality of the solution. A row generation algorithm is also presented to address problem instances of realistic size. We also demonstrate that full flexibility is often unnecessary to reach nearly, or even exact, optimal robust locations and capacities for the facilities. Finally, we illustrate our findings with an extensive numerical study where we evaluate the effect of the amount of uncertainty on the performance and structure of each approximate solution that can be obtained. The online appendix is available at https://doi.org/10.1287/trsc.2016.0728 .

The problem of coordinating a fleet of vehicles so that all demand points on a territory are serviced and the workload is most evenly distributed among the vehicles is a hard one. For this reason, it is often an effective strategy to first divide the service region and impose that each vehicle is only responsible for its own subregion. This heuristic also has the practical advantage that over time, drivers become more effective at serving their territory and customers. In this paper, we assume that client locations are unknown at the time of partitioning the territory and that each of them will be drawn identically and independently according to a distribution that is actually also unknown . In practice, it might be impossible to identify precisely the distribution if, for instance, information about the demand is limited to historical data. Our approach suggests partitioning the region with respect to the worst-case distribution that satisfies first- and second-order moments information. As a side product, our analysis constructs for each subregion a closed-form expression for the worst-case density function, thus providing useful insights about what affects the completion time most heavily. The successful implementation of our approach relies on two branch-and-bound algorithms: whereas the first finds a globally optimal partition of a convex polygon into two convex subregions, the second finds a local optimum for the harder n -partitioning problem. Finally, simulations of a parcel delivery problem will demonstrate that our data-driven approach makes better use of historical data as it becomes available.

Since the financial crisis of 2007–2009, there has been a renewed interest in quantifying more appropriately the risks involved in financial positions. Popular risk measures such as variance and value-at-risk have been found inadequate because we now give more importance to properties such as monotonicity, convexity, translation invariance, positive homogeneity, and law invariance. Unfortunately, the challenge remains that it is unclear how to choose a risk measure that faithfully represents a decision maker’s true risk attitude. In this work, we show that one can account precisely for (neither more nor less than) what we know of the risk preferences of an investor/policy maker when comparing and optimizing financial positions. We assume that the decision maker can commit to a subset of the above properties (the use of a law invariant convex risk measure for example) and that he can provide a series of assessments comparing pairs of potential risky payoffs. Given this information, we propose to seek financial positions that perform best with respect to the most pessimistic estimation of the level of risk potentially perceived by the decision maker. We present how this preference robust risk minimization problem can be solved numerically by formulating convex optimization problems of reasonable size. Numerical experiments on a portfolio selection problem, where the problem reduces to a linear program, will illustrate the advantages of accounting for the fact that the choice of a risk measure is ambiguous. This paper was accepted by Yinyu Ye, optimization .