Master Problem Research Articles

On Optimizing Ensemble Models using Column Generation

AbstractIn recent years, an interest appeared in integrating various optimization algorithms in machine learning. We study the potential of ensemble learning in classification tasks and how to efficiently decompose the underlying optimization problem. Ensemble learning has become popular for machine learning applications and it is particularly interesting from an optimization perspective due to its resemblance to column generation. The challenge for learning is not only to obtain a good fit for the training data set, but also good generalization, such that the classifier is generally applicable. Deep networks have the drawback that they require a lot of computational effort to get to an accurate classification. Ensemble learning can combine various weak learners, which individually require less computational time. We consider binary classification problems studying a three-phase algorithm. After initializing a set of base learners refined by a bootstrapping approach, base learners are generated using the solution of an linear programming (LP) master problem and then solving a machine learning sub-problem regarding a reduced data set, which can be viewed as a so-called pricing problem. We theoretically show that the algorithm computes an optimal ensemble model in the convex hull of a given model space. The implementation of the algorithm is part of an ensemble learning framework called decolearn. Numerical experiments with CIFAR-10 data set show that the base learners are diverse and that both the training and generalization error are reduced after several iterations.

A branch-and-price-and-cut algorithm for the unmanned aerial vehicle delivery with battery swapping

In the UAV-based urban delivery setting, the battery capacity serves as one of the key factors affecting the delivery range of drones. For a typical multi-rotor unmanned aerial vehicle (UAV), the maximum effective working range of a lithium battery for a single flight leg is approximately 20 km. In practice, the lithium battery is replaced each time the UAV completes a delivery, even though the remaining power of the replaced lithium battery is still capable of supporting the following flight legs. Therefore, the one-order-one-swapping strategy significantly brings down the battery utilisation as well as the efficiency of the delivery system. In the present paper, the UAV-based delivery problem with battery swapping decision is considered, where multiple en route pickup and deliveries are allowed. To obtain optimal decisions in terms of flight route, time and location of each battery swapping, a branch-and-price-and-cut algorithm is introduced. First we formulate this problem as a mixed integer linear programming (MILP) model, and then decompose it into a master problem and a pricing sub-problem, where the master problem is considered as a set covering model, and the sub-problem as an elementary shortest path problem with resource constraints (ESPPRC). To speed up the process of column generation, efficient heuristics are also integrated to provide basic feasible solutions. In the pricing sub-problem, a combination of heuristic algorithm and dynamic programming is implemented to improve the computational efficiency. In the numerical experiments, the proposed algorithm is tested on various scales of UAV-based urban delivery instances, the performance of which is analysed and compared with the off-the-shelf commercial solver.

New Exact Algorithm for the integrated train timetabling and rolling stock circulation planning problem with stochastic demand

This paper studies an integrated train timetabling and rolling stock circulation planning problem with stochastic demand and flexible train composition (TRSF). A novel stochastic integer programming model, which is formulated on a space-time underlying network to simultaneously optimize the train timetable and rolling stock circulation plan with flexible train composition, is proposed by explicitly considering the random feature of passenger distribution on an urban rail transit line. To solve this problem efficiently, the proposed model is decomposed into a master problem and a series of sub-problems regarding different stochastic scenarios. We further prove that each sub-problem model is equivalent to its linear programming relaxation problem, by proving that the coefficient matrix of each linear programming relaxation model is totally unimodular. Then, the classical Benders decomposition algorithm is applied to the studied problem. Based on the model characteristics, both single-cut and multi-cut methods with some speed-up techniques are developed to solve the proposed model in a novel and effective way. Numerical experiments are conducted on small-scale cases and large-scale cases derived from Shanghai Metro Line 17, and the results show that solving the stochastic problem can extract gains in efficiency and the value of stochastic solution tends to be high.

Data-Driven Distributionally Robust Optimization for Railway Timetabling Problem

Unpredictable disturbances that occur when the train is running often make the actual timetable deviate from the planned timetable and deteriorate service quality for passengers. To provide a robust planned timetable that is reliable in operation, this paper presents a two-stage distributionally robust railway timetabling (DRRT) model, where the decisions in the first and second stages are the planned and actual timetables, respectively. To deal with the uncertain travel time, the proposed DRRT model assumes the true distribution belongs to a Wasserstein ambiguity set centered at the empirical distribution constructed from finite samples and aims to minimize the sum of the total idle time, travel time, and worst-case expected delay over the ambiguity set. To solve this model, we design a decomposition algorithm with provable convergence, which iteratively solves a master problem and a set of subproblems. To enhance the algorithm efficiency, a blend of two popular decomposition methods is proposed to integrate their advantages, and the solution of the subproblems is accelerated by using an uncapacitated minimum-cost flow interpretation of the second-stage optimization problem. Experiments on real-world instances demonstrate the effectiveness of these enhancements. The results also show that our model prominently outperforms the sample average approximation model in terms of the out-of-sample performance, especially when only a small sample set is available. Moreover, at the expense of equal traffic efficiency, our model is more robust than those models that do not utilize distribution information. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of using finite historical data to provide a robust planned railway timetable, aiming at minimizing the traffic efficiency losses and expected delays under the worst-case distribution. Existing studies on dealing with the uncertain travel time usually assumed that the distribution is exactly known, or the distribution is completely unknown but the travel time belongs to an uncertainty set. However, in practice, the exact distribution is hard to know but can only be coarsely estimated from data. This paper proposes a data-driven two-stage model by assuming that the true distribution belongs to a 1-Wasserstein ball centered at the empirical distribution with a bounded support set, which is a middle ground between the above two distribution assumptions. To solve this problem efficiently, we propose a customized algorithm with provable convergence and then enhance it by exploiting problem-specific properties. This distributionally robust model can be easily shifted to other timetabling problems, and the algorithm enhancement techniques can also be applied to efficiently solve other two-stage recourse models with similar properties.

Transient Stability-Constrained Unit Commitment Using Input Convex Neural Network.

This article proposes a transient stability-constrained unit commitment (TSC-UC) model using input convex neural networks (ICNNs). An ICNN is trained to learn the transient function that maps prefault operation conditions (e.g., generator power output) to the transient stability index (TSI), which can be further utilized to identify the transient status (e.g., stable or unstable). Transient stability evaluation is conducted using the learned ICNN, without discretizing differential-algebraic equations (DAEs) or interacting with the time-domain simulation tools. Based on the convexity of ICNNs, the trained ICNN is exactly encoded as a linear programming (LP) model and integrated into conventional UC models to form a TSC-UC model. To impose transient stability constraints and expedite the solution process, the proposed TSC-UC model is decomposed into a UC master problem and two subproblems (i.e., network feasibility check subproblems and transient stability check subproblems). The decomposed problem is then iteratively solved using the Benders decomposition. Simulation tests are conducted in the New England 39-bus test system and IEEE 118-bus test system to verify the validity of the proposed approach.

Robust Optimization of Large-Scale Wind–Solar Storage Renewable Energy Systems Considering Hybrid Storage Multi-Energy Synergy

With the rapid integration of renewable energy sources, such as wind and solar, multiple types of energy storage technologies have been widely used to improve renewable energy generation and promote the development of sustainable energy systems. Energy storage can provide fast response and regulation capabilities, but multiple types of energy storage involve different energy conversion relationships. How to fully utilize the advantages of multiple energy storage and coordinate the multi-energy complementarity of multiple energy storage is the key to maintaining a stable operation of the power system. To this end, this paper proposes a robust optimization method for large-scale wind–solar storage systems considering hybrid storage multi-energy synergy. Firstly, the robust operation model of large-scale wind–solar storage systems considering hybrid energy storage is built. Secondly, the column constraint generation (CCG) algorithm is adopted to transform the original problem into a two-stage master problem and sub-problem for solving to obtain the optimal strategy of system operation with robustness. Finally, the validity of the proposed method is verified through case tests. The results show that the proposed method can effectively coordinate the multi-energy complementary and coordinated operation of multiple hybrid energy storage, and the obtained operation strategy of large-scale wind–solar storage systems can well balance the economy and robustness of the system.

Distributionally robust optimization model considering deep peak shaving and uncertainty of renewable energy

In order to achieve the goal of carbon neutrality, the capacity of renewable power generation is continuously expanding while thermal power units are transitioning from main power source to auxiliary power source. To alleviate the peak shaving burden of thermal power units under the uncertainty of renewable energy and improve the absorption level of renewable energy, a two-stage distributionally robust optimization (DRO) model considering deep peak shaving and the uncertainty of renewable energy is proposed. The day-ahead unit commitment solutions are determined in the first stage, and the detailed scheduling strategies are obtained in the second stage. Column-and-constraint generation (C&CG) algorithm is applied to solve the model, and the master problem and subproblem are reformulated as duality-free mixed integer linear programming problems. The results show that the scheduling strategy obtained based on the model can alleviate the peak shaving burden brought by the uncertainty of renewable energy and reduce the abandonment rate of wind resources and solar resources, and the proposed DRO model provides a good trade-off between economy and robustness compared to stochastic optimization (SO) and robust optimization (RO).

Minimization of Energy Consumption in TDMA-Based Wireless-Powered Multi-Access Edge Computing Networks

Many nodes in Internet of Things (IoT) rely on batteries for power. Additionally, the demand for executing compute-intensive and latency-sensitive tasks is increasing for IoT nodes. In some practical scenarios, the computation tasks of WDs have the non-separable characteristic, that is, binary offloading strategies should be used. In this paper, we focus on the design of an efficient binary offloading algorithm that minimizes system energy consumption (EC) for TDMA-based wireless-powered multi-access edge computing networks, where WDs either compute tasks locally or offload them to hybrid access points (H-APs). We formulate the EC minimization problem which is a non-convex problem and decompose it into a master problem optimizing binary offloading decision and a subproblem optimizing WPT duration and task offloading transmission durations. For the master problem, a DRL based method is applied to obtain the near-optimal offloading decision. For the subproblem, we firstly consider the scenario where the nodes do not have completion time constraints and obtain the optimal analytical solution. Then we consider the scenario with the constraints. By jointly using the Golden Section Method and bisection method, the optimal solution can be obtained due to the convexity of the constraint function. Simulation results show that the proposed offloading algorithm based on DRL can achieve the near-minimal EC.

A Decomposition Method for the Group-Based Quay Crane Scheduling Problem

This study addresses the quay crane scheduling problem (QCSP), which involves scheduling a fixed number of quay cranes to load and unload containers from ships in a maritime container terminal. The objective is to minimize the completion time while adhering to precedence, safety margin, and noncrossing constraints. Efficient scheduling of quay cranes plays a crucial role in reducing the time vessels spend at terminals. To solve the QCSP, we explore different schedule directions for the quay cranes. Specifically, we consider three directions: unidirectional, where the quay cranes maintain a consistent movement direction from upper to lower bays or vice versa after initial repositioning; bidirectional, allowing the cranes to change direction once during operations; and multidirectional, permitting freely changing movement direction during operations. For the bidirectional QCSP, we propose a new compact mathematical formulation. To obtain valid lower bounds on the optimal completion time, we derive various relaxations of this new formulation based on the different schedule directions. Our solution framework employs logic-based Benders decomposition, decomposing the problem into an assignment master problem and operation-sequence slave subproblems. Extensive computational experiments using benchmark instances from existing literature and newly generated instances validate the efficiency and effectiveness of the lower bounds and the exact solution approach. History: Accepted by Andrea Lodi, Area Editor for Design &amp; Analysis of Algorithms–Discrete. Funding: This work was supported by the Major Program of the National Natural Science Foundation of China [Grants 72192830 and 72192831], the National Natural Science Foundation of China [Grant 72102034], and the 111 Project [Grant B16009]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0298

Integrated optimization of container allocation and yard cranes dispatched under delayed transshipment

Due to variations in carrying capacity and visiting periods of vessels calling at terminals, certain transshipped containers may not be able to be transported immediately after arrival. Instead, they must be temporarily stored in the yard and scheduled for later transportation. Increased container storage time in the yard as a consequence of transit delays not only incurs additional costs for shipping companies, but also introduces new issues for terminal yard management. Therefore, this study investigates the daily storage yard management challenges that arise in marine container terminals that integrate space allocation and yard crane deployment decisions while considering the delayed transshipment of containers. A mixed-integer linear programming model is proposed to describe the problem, whose objectives are to minimize the transportation costs for container loading and discharge operations, penalty costs associated with the delayed transshipment of containers, transportation costs associated with containers not transshipped within the planning horizon, and yard crane inter-block movement costs. The Benders decomposition algorithm is applied to address this problem, and the traditional decomposition approach is improved by adding characteristics such as the development of strong optimality cuts and the generation of a powerful initial solution to the master problem. Extensive experiments are performed to validate the effectiveness of the model and efficiency of the proposed improved Benders decomposition algorithm.

An exact decomposition technique for the deadline-constrained discrete time/cost trade-off problem with discounted cash flows

This paper addresses the deadline-constrained discrete time/cost trade-off problem with discounted cash flows in project scheduling optimization. Our objective is to optimize the net present value (NPV) of cash flows by selecting execution modes for activities while considering project deadlines. To address this problem, we propose an adapted model that combines the activity-on-node representation of the project network with the milestone activity payment system commonly used in real-world scenarios. This enhanced model accurately depicts project dynamics, enabling improved decision-making in NPV optimization. To solve the problem, we employ the generalized benders decomposition technique, which provides an exact solution approach to handle the computational complexity of the problem. Our approach introduces three types of feasibility cuts. The first type eliminates infeasible solutions by analyzing subproblem infeasibility. The second type enhances the generation of high-quality optimality cuts by iteratively introducing constraints to the master problem, utilizing dominated paths in the project network graph. Lastly, the third type targets the elimination of inferior infeasible solutions. Additionally, we generate a comprehensive dataset encompassing various scenarios and parameter ranges from existing literature. This dataset serves as a valuable resource for further research, with online accessibility and the latest solutions available for approximately 32,400 generated instances. Through our research, we demonstrate the superiority of our proposed solution procedure compared to existing methods in the field. By considering the specific requirements of project scheduling with NPV optimization and project deadlines, our approach contributes to more effective project planning and decision-making in real-world contexts.

Risk-constrained probabilistic coordination in coupled transmission and distribution system

High penetration of renewable energy has instigated stochastic power injection at interconnection between transmission system (TS) and distribution system (DS). This paper delves into the intricate collaborative risk based stochastic dispatching challenges due to contingencies and the integration of renewable sources in the TS and DS. A framework of risk constrained probabilistic problem (RCPC) is presented, which is divided into Probabilistic coordination (PC) and risk-based stochastic security-constrained unit commitment (RSSCUC). The PC is a stochastic linear problem and RSSCUC is a stochastic mixed integer non-linear problem. Therefore, the probabilistic analytical target cascading along with polynomial chaos expansion (PCE) has been utilized for solving the PC problem for coupled TS and DS. Here, PCE has provided the proposed algorithm with the needed capability to present stochastic shared variables as coefficients for PC. Further, the benders decomposition algorithm has been utilized for solving RSSCUC, by dividing it into master problem and sub problem to generate feasibility cuts. The proposed technique reduces the computational burden on the system, as it requires single stochastic coordination problem for all scenarios as an alternative of each coordination problem for each scenario and polynomial coefficients instead of multiple scenarios for each shared variable between TS and DS. Different case studies have been performed utilizing the 6-bus system and IEEE 118-bus system as TSs, 7-bus, 9-bus, 85-bus and 69-bus systems as DSs. Results depict the efficacy of the proposed method.

Elasticity-integrated pricing and allocation heuristic for airline revenue management

Setting the right fares is a key lever for increasing operating profitability in the airline industry. It is crucial to design fares that are both appealing to passengers and contribute to an increase in airline revenue. Although airline revenue management techniques have evolved to capture customer-choice behavior, the pricing and allocation decisions continue to be taken independently. However, since they are linked, a single optimization model can address this shortcoming. This paper presents a joint optimization model (JOM) that considers product prices and their allocation quantities as decision variables. A sequential optimization technique that divides the model into two decision problems is adopted to cope with JOM’s complexity. The problem is divided into a master problem and a sub-problem, wherein product price changes are made in the master problem and, with these fixed prices, optimization is performed in the sub-problem. The sub-problem is solved by simplifying the non-linear JOM into a linear programming problem. The direction of product price changes in the master problem is identified using price elasticity of demand. A heuristic based on this concept is proposed and tested. The Elasticity-integrated Pricing and Allocation Heuristic (EPAH) is observed to produce a consistent increase in existing revenues.

Unmanned aerial vehicle service network design for urban monitoring

This study examines the multi-depot location-routing problems of unmanned aerial vehicles (UAVs) for urban monitoring (MDLRP-UM). MDLRP-UM arises in various practical applications, including daily police patrols in urban residential areas, forest fire patrols, urban infrastructure status monitoring and data collection, traffic flow monitoring at important intersections, and monitoring of urban temperature and humidity, among others. These diverse applications can be modeled as a general mixed-integer quadratically constrained problem (MIQCP), where we jointly plan the service routes of the UAVs, the frequency on each route, and the location of the depots to minimize the total cost. To solve the proposed problem, we decompose it into a master problem and sub-problems. We then propose an iterative algorithm (termed as “Frequency-Time-Frequency Strategy”) to solve the sub-problems, which is to find the optimal frequency and corresponding single service time for a given single route. The “Frequency-Time-Frequency Strategy” is further nested within a tailored adaptive large neighborhood search (ALNS) based heuristic algorithm to solve the master problem. The efficiency and effectiveness of the proposed solution method are demonstrated by a series of numerical studies.

An asynchronous parallel benders decomposition method for stochastic network design problems

Benders decomposition (BD) is one of the most popular solution algorithms for stochastic integer programs. The BD method decomposes stochastic problems into one master problem and multiple disjoint subproblems. It thus lends itself readily to parallelization. In almost all studies on the parallelization of this algorithm, the master problem remains idle until every subproblem is solved and vice versa. This can clearly result in an extremely inefficient parallel algorithm due to excessive idle times. On the other hand, relaxing the synchronization requirement can yield a nonconvergent or less efficient algorithm that may even underperform when compared to the sequential version. Addressing these issues, we introduce an asynchronous parallel BD method for stochastic network design problems. We show that the proposed algorithm converges to the global optimum and suggest various acceleration strategies to enhance its performance. We conduct an extensive numerical study on benchmark instances from a generic stochastic network design problem. The results indicate that using up to 20 processors, our asynchronous algorithm is on average 1.4 times faster than the conventional low-level parallel methods.

Scenario-Based Robust Optimization for Two-Stage Decision Making Under Binary Uncertainty

This paper addresses problems of two-stage optimization under binary uncertainty. We define a scenario-based robust optimization (ScRO) formulation that combines principles of stochastic optimization (by constructing probabilistic scenarios) and robust optimization (by protecting against adversarial perturbations within discrete uncertainty sets). To solve it, we develop a sparse row generation algorithm that iterates between a master problem (which provides a lower bound based on minimal uncertainty sets) and a history-based subproblem (which generates an upper bound and updates minimal uncertainty sets). We generate scenarios and uncertainty sets from element-wise probabilities using a deviation likelihood method or from historical samples using a sample clustering approach. Using public data sets, results suggest that (i) our ScRO formulation outperforms benchmarks based on deterministic, stochastic, and robust optimization; (ii) our deviation likelihood and sample clustering approaches outperform scenario generation baselines; and (iii) our sparse row generation algorithm outperforms off-the-shelf implementation and state-of-the-art cutting plane benchmarks. An application to a real-world ambulance dispatch case study suggests that the proposed modeling and algorithmic approach can reduce the number of late responses by more than 25%. Funding: K. Wang’s research was supported by the National Natural Science Foundation of China [Grants 72322002, 52221005, and 52220105001]

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Problem definition: Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter’s co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles and chains. Methodology/results: We develop the first decomposition method that is able to consider long cycles and long chains for projected large realistic instances. Particularly, we propose a branch-and-price framework in which the pricing problems are solved (for the first time in packing problems in a digraph) through multivalued decision diagrams. We present a new upper bound on the optimal value of the KEP, obtained via our master problem. Computational experiments show superior performance of our method over the state of the art by optimally solving almost all instances in the PrefLib library for multiple cycle and chain lengths. Managerial implications: Our algorithm also allows the prioritization of the solution composition, for example, chains over cycles or vice versa, and we conclude, similar to previous findings, that chains benefit the overall matching efficiency and highly sensitized patients. Funding: This work was supported by NSERC Discovery Grant (RGPIN-2021-02609). Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.0192 .

Capacity Value Assessment for a Combined Power Plant System of New Energy and Energy Storage Based on Robust Scheduling Rules

With the rapid increase in new energy penetration, the uncertainty of the power system increases sharply. We can smooth out fluctuations and promote the more grid-friendly integration of new energy by combining it with energy storage. This paper proposes an evaluation method for assessing the value of a combined power plant system of new energy and energy storage using robust scheduling rules. Firstly, the k-means clustering algorithm is improved by using the elbow method in order to generate typical scenarios that can be used for the operation optimization of the combined power plant system of new energy and energy storage. Then, a two-stage robust optimization model of the combined power plant system of new energy and energy storage with a min–max–min structure is constructed according to the uncertainty of new energy. In this model, the operation constraints and coordinated control of wind–solar–thermal–storage units are considered. By constructing the uncertainty set of the new energy output, the overall operating cost of the system is minimized and uncertainty adjustment parameters are introduced to flexibly adjust the conservatism of the scheduling rules. Furthermore, based on the column and constraint generation algorithm and strong duality theory, the original problem can be decomposed into a master problem and subproblems with mixed integer linear characteristics for an alternating solution, so as to obtain the optimal solution of the original problem, and finally obtain the robust scheduling rule with the lowest operating cost under the worst scenario. Finally, based on the wind and solar power output curves and the output of each unit under the robust scheduling rules, combined with the value estimation method of the combined power plant system of new energy and energy storage, the value of the combined power plant system of new energy and energy storage is evaluated. Through the establishment of models and example analysis, it is proven that raising the quantity of the grid-connected power generated with new energy will cause an increase in the volatility of the power system; it will also bring considerable benefits to new energy plants, and the energy storage can improve the stability of the system. The above can provide references for the subsequent energy storage configuration in the planning of a combined power plant system of new energy and energy storage.

Two-stage robust optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage hybrid energy system

The hybrid energy system of hydro-powers, pumped storages and renewable energies has become a new topic direction in modern power system developments. Consequently, it is essential to realize a rational and efficient allocation of different energy source capacities. Nevertheless, there is still a gap between the available studies and the requirement for further hybrid energy system development. This paper focuses on the optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage power system. In this direction, a bi-level programming model for the optimal capacity configuration of wind, photovoltaic, hydropower, pumped storage power system is derived. To model the operating mode of a pumped storage power station, two 0-1 variables are introduced. To handle the nonlinear and nonconvex lower level programing problem caused by the two 0-1 variables, it is proposed that the 0-1 variables are treated as some uncertain parameters. Also, by treating the 0-1 variables as some uncertain parameters, a two-stage robust optimization problem to decompose the original bi-level programing one into a master problem and a subproblem is finally introduced. The Karush-Kuhn-Tucker (KKT) conditions are then applied to simplify and linearize the min-max problem and nonlinear terms in the master problem. This results in both the master problem and the subproblem being formulated as mixed integer linear programming (MILP) problems. By utilizing the powerful Column-and-Constraint Generation (C&amp;amp;CG) algorithm, the two-stage robust optimization model is decomposed into an iterative procedure of solving the master problem and the subproblem sequentially. This approach eliminates the need for intricate optimization algorithms as commonly used in existing bi-level planning problems in hybrid energy systems. Finally, the effectiveness and advantages of the proposed model is verified by the numerical results on a case study.

Robust optimization for the integrated berth allocation and quay crane assignment problem

AbstractThis paper studies the berth allocation and quay crane assignment problem (denoted by BACAP) under uncertainty. We assume that the ships' arrival and operation time is uncertain in this problem. We merge the proactive and reactive strategies to address the two‐stage robust optimization (denoted by RO) model for the BACAP to obtain a complete schedule with robustness. We obtain the berth allocation and quay crane assignment with a proactive strategy in the first stage. In the second stage, we formulate a rescheduling model with a reactive strategy considering the sensitivity towards the change in the complete schedule. The second stage model is based on the prospect theory, a quantitative way to describe the stakeholders' perception, including the port managers and shipowners, of the deviation from the baseline plan. The two stages are iterated until a favorable schedule with high robustness is found. To illustrate the superiority of the two‐stage robust optimization model with the prospect theory for the complete schedule, we give an intuitive example to compare the performance among the related models. The two‐stage RO model with the prospect theory for the complete schedule can generate a lower cost and higher robustness schedule. As for the solution methods, the column and constraint generation (denoted by C&amp;CG) algorithm is applied to obtain the exact solution for the two‐stage RO model. Moreover, we propose the scenario‐constrained C&amp;CG (denoted by SC) algorithm, which can reduce constraints and variables for the master problem to accelerate the solving process of the two‐stage RO model. In addition, the optimality of the SC algorithm is verified by analyzing the pattern of the occurrence of the worst‐case scenarios. Besides, to tackle the large‐scale instances, we propose the schedule‐fixed (denoted by SF) algorithm, in which the results of the previous iterations are treated as fixed. The SF algorithm can increase computing efficiency with a small gap compared to the optimal solution value. Furthermore, extensive numerical experiments are conducted on both real‐life instances and randomly generated instances to verify the superiority and generality of our model and algorithms.