Resource allocation in a university environment : a test of the Ruefli, Freeland, and Davis goal programming decomposition algorithms / BEBR No. 735

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Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen's inequality that extends the one for stochastic program. To solve this challenging problem, we present a variant of Benders decomposition method in bilinear form, which actually provides an easy-to-use algorithm framework for further improvements, along with a few enhancement strategies based on structural properties or Jensen's inequality. Computational study shows that the presented Benders decomposition method, jointly with appropriate enhancement techniques, outperforms a commercial solver by an order of magnitude on solving chance constrained program or detecting its infeasibility

Scheduling of EV Battery Swapping, I: Centralized Solution

We formulate an optimal scheduling problem for battery swapping that assigns to each electric vehicle (EV) a best battery station to swap its depleted battery based on its current location and state of charge. The schedule aims to minimize a weighted sum of EVs’ travel distance and electricity generation cost over both station assignments and power flow variables, subject to EV range constraints, grid operational constraints, and ac power flow equations. To deal with the nonconvexity of power flow equations and the binary nature of station assignments, we propose a solution based on second-order cone programming (SOCP) relaxation of optimal power flow and generalized Benders decomposition. When the SOCP relaxation is exact, this approach computes a global optimum. We evaluate the performance of the proposed algorithm through simulations. The algorithm requires global information and is suitable for cases where the distribution grid, battery stations, and EVs are managed centrally by the same operator. In Part II of this paper, we develop distributed solutions for cases where they are operated by different organizations that do not share private information

Optimisation of an integrated transport and distribution system

Imperial Users onl

Techno-economic assessment of energy storage systems in multi-energy microgrids utilizing decomposition methodology

Renewable resources and energy storage systems integrated into microgrids are crucial in attaining sustainable energy consumption and energy cost savings. This study conducts an in-depth analysis of diverse storage systems within multi-energy microgrids, including natural gas and electricity subsystems, with a comprehensive focus on techno-economic considerations. To achieve this objective, a methodology is developed, comprising an optimization model that facilitates the determination of optimal storage system locations within microgrids. The model considers various factors, such as operating and emission costs of both gas and electricity subsystems, and incorporates a sensitivity analysis to calculate the investment and maintenance costs associated with the storage systems. Due to the incorporation of voltage and current relations in the electricity subsystem as well as gas pressure and flow considerations in the natural gas subsystem, the developed model is classified as a mixed-integer nonlinear programming model. To address the inherent complexity in solving, a decomposition approach based on Outer Approximation/Equality Relaxation/Augmented Penalty is developed. This study offers scientific insights into the costs of energy storage systems, potential operational cost savings, and technical considerations of microgrid operation. The results of the developed decomposition approach demonstrate significant advantages, including reduced solving time and a decreased number of iterations

On orbital allotments for geostationary satellites

The following satellite synthesis problem is addressed: communication satellites are to be allotted positions on the geostationary arc so that interference does not exceed a given acceptable level by enforcing conservative pairwise satellite separation. A desired location is specified for each satellite, and the objective is to minimize the sum of the deviations between the satellites' prescribed and desired locations. Two mixed integer programming models for the satellite synthesis problem are presented. Four solution strategies, branch-and-bound, Benders' decomposition, linear programming with restricted basis entry, and a switching heuristic, are used to find solutions to example synthesis problems. Computational results indicate the switching algorithm yields solutions of good quality in reasonable execution times when compared to the other solution methods. It is demonstrated that the switching algorithm can be applied to synthesis problems with the objective of minimizing the largest deviation between a prescribed location and the corresponding desired location. Furthermore, it is shown that the switching heuristic can use no conservative, location-dependent satellite separations in order to satisfy interference criteria

Optimizing Strategic Planning With Long-term Sequential Decision Making Under Uncertainty: A Decomposition Approach

The operations research literature has seen decision-making methods at both strategic and operational levels, where high-level strategic plans are first devised, followed by long-term policies that guide future day-to-day operations under uncertainties. Current literature studies such problems on a case-by-case basis, without a unified approach. In this study, we investigate the joint optimization of strategic and operational decisions from a methodological perspective, by proposing a generic two-stage long-term strategic stochastic decision-making (LSSD) framework, in which the first stage models strategic decisions with linear programming (LP), and the second stage models operational decisions with Markov decision processes (MDP). The joint optimization model is formulated as a nonlinear programming (NLP) model, which is then reduced to an integer model through discretization. As expected, the LSSD framework is computationally expensive. Thus, we develop a novel solution algorithm for MDP, which exploit the Benders decomposition with the ``divide-and-conquer\u27\u27 strategy. We further prove mathematical properties to show that the proposed multi-cut L-shaped (MCLD) algorithm is an exact algorithm for MDP. We extend the MCLD algorithm to solve the LSSD framework by developing a two-step backward decomposition (TSBD) method. To evaluate algorithm performances, we adopt four benchmarking problems from the literature. Numerical experiments show that the MCLD algorithm and the TSBD method outperform conventional benchmarks by up to over 90\% and 80\% in algorithm runtime, respectively. The practicality of the LSSD framework is further validated on a real-world critical infrastructure systems (CISs) defense problem. In the past decades, ``attacks\u27\u27 on CIS facilities from deliberate attempts or natural disasters have caused disastrous consequences all over the globe. In this study, we strategically design CIS interconnections and allocate defense resources, to protect the CIS network from sequential, stochastic attacks. The LSSD framework is utilized to model the problem as an NLP model with an alternate integer formulation. We estimate model parameters using real-world CIS data collected from a middle-sized city in the U.S. Previously established algorithms are used to solve the problem with over 45% improvements in algorithm runtime. Sensitivity analyses are conducted to investigate model behaviors and provide insights to practitioners

Short term hydrothermal coordination problem considering environmental concerns

Solving the Short Term Hy- drothermal Coordination Problem considers the resolution of both the Unit Commitment and the Economic Dispatch for thermal and hydraulic units. This problem is solved for several time horizons between a day and a week with a one-hour step. The traditional short-term scheduling problem of hydrother- mal units, minimizing fuel cost during a time, does not include concerns due to emission pol- lution coming from the operation of thermal plants. In this work, environmental constraints are considered. Focusing on avoiding post- dispatch corrections, the transmission network is modeled with a high level of detail consid- ering an AC power ow. These facts lead to a very complex optimization problem which is solved by using a novel decomposition approach based on Generalized Benders Decomposition and traditional, well-known optimization tech- niques. The approach presented in this work allows the decomposition of the whole problem in a quadratic mixed integer master problem, and in a separable non-linear subproblem. The former de nes the state and the active power dispatched by each unit whereas the latter de- termines the reactive power to meet the electri- cal constraints through a modi ed AC optimal power ow. Di erent variations of the devel- oped methodology were evaluated in order to consider environmental constraints. These ap- proaches were applied to a 9-bus test case and to a 87-bus real system