While Stackelberg leader-follower games and bilevelprogramming have become increasingly prevalent in game-theoretic modeling and optimization of decentralized supply chains, existing models can only handle linear pro...
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While Stackelberg leader-follower games and bilevelprogramming have become increasingly prevalent in game-theoretic modeling and optimization of decentralized supply chains, existing models can only handle linear programming or quadratic programming followers' problems. When discrete decisions are involved in the follower's problem, the resulting lower-level mixed-integer program prohibits direct transformation of the bilevel program into a single-level mathematical program using the MKT conditions. To address this challenge, we propose a mixed-integer bilevel programming (MIBP) modeling framework and solution algorithm for optimal supply chain design and operations, where the follower is allowed to have discrete decisions, e.g. facility location, technology selection, and opening/shutting-down of production lines. A reformulation-and-decomposition algorithm is developed for global optimization of the MIBP problems. A case study on an integrated forestry and biofuel supply chain is presented to demonstrate the application, along with comparisons to conventional centralized modeling and optimization methods. (C) 2016 Elsevier Ltd. All rights reserved.
This paper deals with the microgrid's bidding strategy (MGBS) problem in a day-ahead (DA) electricity market. To this end, the DA electricity prices, demand, and renewable energy uncertainties are modeled by diffe...
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This paper deals with the microgrid's bidding strategy (MGBS) problem in a day-ahead (DA) electricity market. To this end, the DA electricity prices, demand, and renewable energy uncertainties are modeled by different scenarios via generating several representative daily curves. However, the real-time (RT) electricity prices are modeled using robust optimization (RO) via predicting appropriate intervals. The existing paradigm to predict the RT intervals is to minimize the statistical errors, while this accuracy-oriented method may not necessarily yield the best MGBS plan against the actual realization of RT prices. The novelty of this research is to present a smart predict-and-optimize (SPO) methodology in which a cost-oriented prediction model replaces the existing accuracy-oriented methods. Trilevel mathematical programming is established to construct a cost-oriented model where the first level maximizes/minimizes the actual profit/cost by adjusting the predicted interval bounds of the RT prices. Knowing these trained interval bounds, the second level runs a scenario-based DA-MGBS. Then, a rescheduling problem is solved at the third level based on the actual realization of uncertainties. To solve this trilevel problem, a reformulation-and-decomposition (R&D) algorithm is utilized. The numerical experiment illustrates the advantages of the SPO method in terms of the microgrid (MG) cost.
In multi-parametric programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of stric...
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In multi-parametric programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-parametric quadratic programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integerbilevel optimization problems and the parametric solution of the dual of a convex problem.
作者：
Faghih, AliDahleh, Munther A.MIT
Dept Elect Engn & Comp Sci Cambridge MA 02139 USA MIT
Lab Informat & Decis Syst 77 Massachusetts Ave Cambridge MA 02139 USA MIT
Inst Data Syst & Soc 77 Massachusetts Ave Cambridge MA 02139 USA
The primary goal of this paper is to develop an optimization framework for studying the efficacy of transmission line reactance tweaking as a mechanism for post-disturbance control in a transmission network. We start ...
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The primary goal of this paper is to develop an optimization framework for studying the efficacy of transmission line reactance tweaking as a mechanism for post-disturbance control in a transmission network. We start by developing a mixed-integer linear programming (MILP) formulation for tracking the redistribution of direct current (DC) flows and the graph-theoretic evolution of a network topology over the course of cascading failures. Next, we propose a min-max setup for studying the impact of post-disturbance reactance tweaking on the resilience of the system to a worst-case disturbance. We devise a MILP reformulation scheme for the underlying bilevel non-convex mixed-integer nonlinear program to facilitate the computation of its globally optimal solution. We then develop a MILP framework for computing a tight upper bound (best-case scenario) on the efficacy of post-disturbance reactance tweaking for a given set of bus loads. Our numerical case study suggests that post-disturbance reactance tweaking, even on only a small number of lines, can be effective in reducing the amount of load shed in some scenarios in the tested system.
We study a service network design problem in which the network operator wishes to determine facility locations and sizes in order to satisfy the demand of the customers while balancing the cost of the system with a me...
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We study a service network design problem in which the network operator wishes to determine facility locations and sizes in order to satisfy the demand of the customers while balancing the cost of the system with a measure of quality-of-service faced by the customers. We assume customers choose the facilities that meet demand, in order to minimize their total cost, including costs associated with traveling and waiting. When having demand served at a facility, customers face a service delay that depends on the total usage (congestion) of the facility. The total cost of meeting a customer's demand at a facility includes a facility-specific unit travel cost and a function of the service delay. When customers all minimize their own costs, the resulting distribution of customer demand to facilities is modeled as an equilibrium. This problem is motivated by several applications, including supplier selection in supply chain planning, preventive healthcare services planning, and shelter location-allocation in disaster management. We model the problem as a mixed-integerbilevel program that can be reformulated as a nonconvex mixed-integer nonlinear program. The reformulated problem is difficult to solve by general-purpose solvers. Hence, we propose a Lagrangian relaxation approach that finds a candidate feasible solution along with a lower bound that can be used to validate the solution quality. The computational results indicate that the method can efficiently find feasible solutions, along with bounds on their optimality gap, even for large instances.
In this article, we elaborate on a budget constrained extension of the r-interdiction median problem with fortification (RIMF). The objective in the RIMF is to find the optimal allocation of protection resources to a ...
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In this article, we elaborate on a budget constrained extension of the r-interdiction median problem with fortification (RIMF). The objective in the RIMF is to find the optimal allocation of protection resources to a given service system consisting of p facilities so that the disruptive effects of r possible attacks to the system are minimized. The defender of the system needs to fortify q facilities of the present system to offset the worst-case loss of r non-fortified facilities due to an interdiction in which the attacker's objective is to cause the maximum possible disruption in the service level of the system. The defender-attacker relationship fits a bilevelintegerprogramming (BIP) formulation where the defender and attacker take on the respective roles of the leader and the follower. We adopt this BIP formulation and augment it with a budget constraint instead of a predetermined number of facilities to be fortified. In addition, we also assume that each facility has a flexible service capacity, which can be expanded at a unit cost to accommodate the demand of customers who were serviced by some other interdicted facility before the attack. First, we provide a discrete optimization model for this new facility protection planning scenario with a novel set of closest assignment constraints. Then, to tackle this BIP problem we use an implicit enumeration algorithm performed on a binary tree. For each node representing a different fortification scheme, the attacker's problem is solved to optimality using Cplex 11. We report computational results obtained on a test bed of 96 randomly generated instances. The article concludes with suggestions for future research.
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