Unit Commitment with Identical Units: Successive Subproblem Solving Method Based on Lagrangian Relaxation

Zhai,; Guan,; Cui,

doi:10.1109/mper.2002.4312580

Cited by 37 publications

(58 citation statements)

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“…Motivated by a method developed for power system optimization [35], penalty terms for the violation of coupling constraints are added to the objective function (9) to improve algorithm convergence and schedule quality through the reduction of constraint violation. As the penalty terms are not additive, a surrogate optimization framework [37] is used to overcome the limitations of standard Lagrangian relaxation approaches requiring separable formulations [4].…”

Section: A Overviewmentioning

confidence: 99%

An Optimization-Based Approach for Design Project Scheduling

Luh

Moser³

2008

IEEE Trans. Automat. Sci. Eng.

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Abstract-Concurrent engineering has been widely used in managing design projects to speed up the design process by concurrently performing multiple tasks. Since the progress of a design task often depends on the knowledge about other tasks and requires effective communication, tasks and communication activities need to be properly coordinated to avoid delays caused by waiting for information or the need for rework. This paper presents a novel formulation for design project scheduling with explicit modeling of task dependencies and the associated communication activities. General dependencies are modeled as combinations of three basic types representing sequential, concurrent, and independent processes. Communication activities are also modeled as tasks, and their interactions with design tasks are described by sets of intertask constraints. The objective is to achieve timely project completion with limited resources. To improve algorithm convergence and schedule quality, penalties on the violation of constraints coupling design tasks are added to the objective function. A solution methodology that combines Lagrangian relaxation, dynamic programming, and heuristic is developed to schedule design and communication tasks, and a surrogate optimization framework is used to overcome the "inseperability" caused by nonadditive penalties. A heuristic procedure is then developed to obtain scheduling policies from optimization results and to dynamically construct schedules. Numerical results show that the approach is effective to handle various task dependencies and the associated communication activities to provide high-quality schedules.Note to Practitioners-A short product design cycle is critical for manufacturers to succeed in the era of time-based competition. To speed up the design process, concurrent engineering has been widely used where multiple design tasks are concurrently performed. As a design task can be performed with preliminary or partial information on other tasks and the information may be updated, effective communication is required. If design and communication activities are not properly coordinated, the project may be significantly delayed by waiting for information or by the need for rework. This paper presents a novel formulation for design project scheduling by appropriately modeling task dependencies and the associated communication activities. A solution methodology based on decomposition and coordination is developed to schedule both design and communication tasks to achieve timely project completion. Numerical results show that the approach is effective to handle various task dependencies and the associated communication activities to provide high-quality schedules.

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Section: A Overviewmentioning

confidence: 99%

An Optimization-Based Approach for Design Project Scheduling

Luh

Moser³

2008

IEEE Trans. Automat. Sci. Eng.

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“…To improve algorithm convergence and schedule quality, additional terms to penalize coupling constraint violations are introduced motivated by a method developed for power systems [26] as shown in (18) at the bottom of the next page, where is the weight for penalties for coupling constraint violation. The overall problem is to minimize (18) subject to constraints within organizations, including operation processing requirements (1) and (5), arrival time constraints (4), operation precedence constraints (6), expected machine capacity constraints (3) and (7); and cross-organization constraints, including expected precedence constraints (10) and (11), and expected inventory level constraints (16) with given machine capacities and initial inventory levels .…”

Section: E the Objective Functionmentioning

confidence: 99%

“…Assuming the existence of a coordinator, the high level dual problem is to find an optimal set of multipliers to maximize the following dual function, i.e., (26) where is in (19) evaluated at optimal beginning times obtained from subproblem solutions, and the optimization is subject to nonnegativity of multipliers. To solve (26), the surrogate subgradient (SSG, [27]) method is used.…”

Section: E Solving the High Level Dual Problemmentioning

confidence: 99%

“…To solve (26), the surrogate subgradient (SSG, [27]) method is used. The key idea is that a proper search direction can be obtained under certain conditions without solving optimally all the subproblems.…”

Section: E Solving the High Level Dual Problemmentioning

confidence: 99%

“…In view of the size and the complexity of the problem, the standard LR-based method may converge slowly, and solutions may contain significant levels of constraint violation. To improve algorithm convergence and schedule quality, additional terms to penalize coupling constraint violation are introduced to the objective function motivated by a method developed for power systems [26]. In view that the penalty terms are not additive, the resulting objective function is inseparable, and this presents challenges to direct application of the Lagrangian Relaxation technique.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Lagrangian Relaxation Based Approach to Schedule Asset Overhaul and Repair Services

Luh

Soorapanth

et al. 2005

IEEE Trans. Automat. Sci. Eng.

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Abstract-Overhaul and repair services are important segments of the remanufacturing industry, and are characterized by complicated disassembly, repair and assembly process plans, stochastic operations, and the usage of rotable inventory. In view of today's time-based competition, effectively scheduling such services and managing rotable inventory and uncertainties are becoming imperative to achieve on-time deliveries and low overall costs. In this paper, a novel formulation for overhaul and repair services is presented where key characteristics, such as uncertain asset arrivals and operation processing times, and rotable parts are abstracted to model an overhaul center and multiple repair shops in a distributed framework to reflect organizational structures. Interactions between the overhaul center and repair shops are described by sets of coupling constraints across the organizations. Rotable inventory dynamics is formulated in terms of repair operation completion times and asset assembly beginning times to facilitate minimization of inventory holding costs through scheduling. A solution methodology combining Lagrangian relaxation, stochastic dynamic programming, and heuristics is developed to schedule operations in a coordinated manner to minimize total tardiness, earliness, and inventory holding costs. Additionally, penalty terms associated with coupling constraint violations are introduced to the objective function to improve algorithm convergence and schedule quality, and a surrogate optimization framework is used to overcome the inseparability difficulty caused by the penalty terms. Numerical testing results show that the new approach is computationally effective to handle rotable inventory and uncertainties, and provides high quality schedules with low overall costs for stochastic remanufacturing systems.Note to Practitioners-Overhaul and repair services for jet engines, helicopters, airplanes, are important segments of the remanufacturing industry, and are characterized by complicated disassembly, repair and assembly process plans, stochastic operations, and the usage of rotable inventory. In view of today's highly competitive business climate, effectively scheduling such services and managing rotable inventory and uncertainties are becoming critical to achieve on-time deliveries and low overall costs. In this paper, a novel formulation for overhaul and repair services is presented where key characteristics, such as uncertain asset

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Benders‐Decomposition‐Based Voltage‐Stability‐Constrained Unit‐Commitment Taking Reactive Power Limit into Account

Omi

Shirai

2022

IEEJ Transactions Elec Engng

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To determine economic-efficient and secure generation schedules, unit commitment (UC) with network and stability constraints will play an important role in the electricity market. We define a voltage-stability-constrained unit commitment problem taking reactive power limit into account (VSCUC-QLIM) since the decreasing of synchronous generators may threat the voltage stability of electricity systems. This VSCUC-QLIM problem is modeled as a mixed-integer nonlinear programming with equilibrium constraints, which is too complex to be solved directly. Therefore, we apply Benders decomposition to solve this complex problem: the master problem consists of the UC problem to determine the commitment states for generators, and the subproblem consists of the voltage-stability-constrained optimal power flow with complementarity constraints problem. However, the subproblem calculation may not converge depending on the commitment states due to the following reasons: (i) any power-flow solution cannot be obtained or (ii) the voltage stability requirement cannot be satisfied on the commitment state given by the master problem. To deal with these difficulties, two partial problems of the subproblem are added as a pre-subproblem and postsubproblem in the proposed method. The combination of these subproblems generate different types of Benders cut depending on the condition. The proposed method was implemented on MATPOWER, and evaluated for daily scheduling on an IEEE six-bus test system and IEEJ standard WEST10 system. The evaluation results validated the effectiveness of the proposed method from the perspective of economic efficiency and voltage stability.

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Unit Commitment with Identical Units: Successive Subproblem Solving Method Based on Lagrangian Relaxation

Cited by 37 publications

References 0 publications

An Optimization-Based Approach for Design Project Scheduling

An Optimization-Based Approach for Design Project Scheduling

A Lagrangian Relaxation Based Approach to Schedule Asset Overhaul and Repair Services

Benders‐Decomposition‐Based Voltage‐Stability‐Constrained Unit‐Commitment Taking Reactive Power Limit into Account

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