This paper addresses the optimal design and strategic planning of the integrated biofuel and petroleum supply chain system in the presence of pricing and quantity uncertainties. The drop-in properties of advanced hydr...
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This paper addresses the optimal design and strategic planning of the integrated biofuel and petroleum supply chain system in the presence of pricing and quantity uncertainties. The drop-in properties of advanced hydrocarbon biofuels pose considerable potential for biofuel supply chains to leverage the existing production and distribution infrastructures of petroleum supply chains, which may lead to significant capital savings. To achieve a higher modeling resolution and improve the overall economic performance, we explicitly model equipment units and material streams in the retrofitted petroleum processes and, propose a multi-period planning model to coordinate the various activities in the petroleum refineries. Furthermore, in order to develop an integrated supply chain that is reliable in the dynamic marketplace, we employ a stochastic programming approach to optimize the expectation under a number of scenarios associated with biomass availability, fuel demand, crude oil prices, and technology evolution. The integrated model is formulated as a stochastic mixed-integer linear program, which is illustrated by a case study involving 21 harvesting sites, 7 potential preconversion facilities, 6 potential integrated biorefineries, 2 petroleum refineries, and 39 demand zones. Results show the market share of biofuels increases gradually due to the increasing crude oil price and biomass availability.
We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous w...
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We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333-346, 2004). The SAAOA algorithm does internal sampling within a nonconvex outer-approximation algorithm where we iterate between a mixed-integer linear programming (MILP) master problem and a nonconvex nonlinear programming (NLP) subproblem. We prove that the optimal solutions and optimal value obtained by the SAAOA algorithm converge to the optimal solutions and the optimal value of the true SP problem as the sample size goes to infinity. The convergence rate is also given to estimate the sample size. Since the theoretical sample size estimate is too conservative in practice, we propose an SAAOA algorithm with confidence intervals for the upper bound and the lower bound at each iteration of the SAAOA algorithm. Two policies are proposed to update the sample sizes dynamically within the SAAOA algorithm with confidence intervals. The proposed algorithm works well for the special case of pure binary first stage variables and continuous stage two variables since in this case the nonconvex NLPs can be solved for each scenario independently. The proposed algorithm is tested with a stochastic pooling problem and is shown to outperform the external sampling approach where large scale MINLPs need to be solved.
We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and how to solve these equations using the St...
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We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and how to solve these equations using the stochastic Dual Dynamic programming algorithm. Finally, we consider a portfolio selection problem over an optimization period of random duration. For several instances of this problem, we show the gain obtained using a policy that takes the randomness of the number of stages into account over a policy built taking a fixed number of stages (namely the maximal possible number of stages).
In this paper, we introduce a compromise programming (CP) framework for solving a multi-objective two-stage stochastic unit commitment problem characterized by high penetration of wind power. The proposed framework ai...
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In this paper, we introduce a compromise programming (CP) framework for solving a multi-objective two-stage stochastic unit commitment problem characterized by high penetration of wind power. The proposed framework aims at finding best-compromise Pareto efficient on/off schedules, accounting for wind and power demand uncertainties: such solutions must trade off the three objectives of operating cost, CO2 emissions, and wind power curtailment in accordance to the decision maker preferences. To achieve this, we introduce a practical procedure to compute the ideal and Nadir points associated to the multi-objective two-stage stochastic unit commitment problem and propose a linearized l(1) norm-based compromise program to design best-compromise on/off schedules that correspondingly minimize and maximize their weighted distances to the ideal point and to the Nadir point, considering the preference weights assigned by the decision maker to each of the three objective functions. The proposed CP framework is applied to a case study related to the New England IEEE-39 bus test system. The results show that, compared to the schedule obtained through the traditional minimization of operating cost, the designed best-compromised schedules considerably improve CO2 emissions reduction and wind power curtailment performance by conservatively sacrificing operating cost performance.
Hub-and-spoke network (HSN) exploits economy of scale in transportation and reduces logistics operational cost through collaborations among nodes. Because of the uncertainty of origin-destination (OD) flows between no...
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This paper proposes a cloud computing framework in smart grid environment by creating small integrated energy hub supporting real time computing for handling huge storage of data. A stochastic programming approach mod...
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This paper proposes a cloud computing framework in smart grid environment by creating small integrated energy hub supporting real time computing for handling huge storage of data. A stochastic programming approach model is developed with cloud computing scheme for effective demand side management (DSM) in smart grid. Simulation results are obtained using GUI interface and Gurobi optimizer in Matlab in order to reduce the electricity demand by creating energy networks in a smart hub approach.
This study establishes a non-deterministic microgrid bidding strategy methodology participating in a day-ahead energy market. In this regard, a stochastic programming-based model is mathematically constructed, fully c...
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This study establishes a non-deterministic microgrid bidding strategy methodology participating in a day-ahead energy market. In this regard, a stochastic programming-based model is mathematically constructed, fully considering the uncertainty of day-ahead market prices, electricity demand, and renewable generation by creating several scenarios. The real-time electricity market is also considered, where the real-time price uncertainty is modeled using robust optimization. Even though robust optimization has already been employed to model real-time price uncertainty, the correlation among real-time prices at different hours is neglected. Thus, how real-time price correlation affects the optimal microgrid bidding strategy remains unclear. This study develops a novel mathematical model that captures real-time price correlations by constructing an ellipsoidal uncertainty set. In this context, unlike the current approaches in which the real-time price deviation ranges are modeled as constants at each hour, they are assumed to lie within a prespecified ellipsoidal uncertainty set. In doing so, a mixed-integer second-order cone programming problem is created, which existing solving methods can efficiently handle. The presented scheme is applied to a typical microgrid, and the efficiency and excellence of the presented framework are validated by comparing numerical results with traditional models.
Container shipping demands are usually classified into long-term contract demands from large shippers and ad hoc demands from spot shippers. Compared with stable long-term contract demands, spot container shipping dem...
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Container shipping demands are usually classified into long-term contract demands from large shippers and ad hoc demands from spot shippers. Compared with stable long-term contract demands, spot container shipping demands are often unstable due to their high frequent cancellations during the slot booking period and their uncertain arrivals even no-shows. This poses a challenge for shipping companies in making precise and profitable decisions on slot allocations for these spot demands, to avoid the loss of slot utilization and shipping profit. This paper thus focuses on a dynamic slot allocation problem for spot containers with consideration of their random arrivals and cancellations during the booking period to maximize the expected shipping profit, and formulates it as a Markov decision process (MDP) model. Due to the well-known curse of dimensionality of MDP models, this paper uses the approximate dynamic programming (ADP) approach to approximate our MDP model, and consequently develops a series of stochastic programming models, which can yield a near-optimal slot allocation policy. Numerical experiments are conducted to examine the effectiveness and superiority of our models obtained by the ADP approach. The computational results show that our dynamic slot allocation strategy can make shipping companies achieve a high slot utilization rate, up to 91.36 %. Furthermore, compared with various slot allocation policies commonly used by shipping companies in practice, the policy obtained by the approach used in this paper performs best in terms of profit, with an improvement of up to 33.26 %.
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexit...
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This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of sets defined by measurable multifunctions, which are in turn crucial for novel applications to stochastic and semi-infinite programming.
In the current context of growing electrification of the transport sector, offering rental and sharing programs for electric vehicles is considered one of the strategies to achieve decarbonization targets. Such progra...
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In the current context of growing electrification of the transport sector, offering rental and sharing programs for electric vehicles is considered one of the strategies to achieve decarbonization targets. Such programs should be supported by suitable optimization tools to manage the vehicle fleet, and make rental provision profitable for its operator. In this paper, we consider a rental system having a single station for electric vehicle pickup and delivery. For this system, we address the operational problem of simultaneously assigning rental requests to vehicles and determining the charging policies during inactivity intervals. The objective is to maximize the profit for the operator by minimizing the costs for electricity. The considered problem is complicated by uncertainty regarding the battery energy level when a vehicle returns to the station. This leads to a chance-constrained programming formulation, where the request-to-vehicle assignment and charging policies are determined by minimizing electricity costs while ensuring that the energy demand of the served requests is met with a prescribed high probability. Since the formulated mixed-integer problem with probabilistic constraints is hard to solve, a suboptimal approach is proposed, consisting of two sequential steps. In the first step, request-to-vehicle assignment is accomplished via a suitably designed heuristic procedure. Then, for a given assignment, the charging policy of each vehicle is determined by solving a relaxed chance-constrained problem. Numerical results are presented to assess the performance of both the assignment procedure and the optimization problem which determines the electric vehicle charging policies.
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