Mixed-integer Programming Research Articles

A hierarchical multi-parametric programming approach for dynamic risk-based model predictive quality control

In this work, we present a hierarchical batch quality control strategy with real-time process safety management. It features a multi-time-scale decision-making framework augmenting: (i) Risk-aware model predictive controller for short-term set point tracking and dynamic risk control under disturbances; (ii) Control-aware optimizer for long-term quality and safety optimization over the entire batch operation; (iii) Intermediate surrogate model to bridge the timescale gap by readjusting the optimizer operating decisions for the controller. All of the above problems are solved via multi-parametric mixed-integer quadratic programming with a key advantage to generate offline explicit control/optimization laws as affine functions of process and risk variables. This allows for the design of a fit-for-purpose risk management plan prior to real-time implementation, while reducing the need for repetitive online dynamic optimization. A unified process model is used to underpin the consistency of hierarchical operational optimization. The proposed approach offers a flexible strategy to integrate distinct decision-making time scales which can be selected separately tailored to the process-specific need of control, fault prognosis, and end-batch quality control. A T2 batch reactor case study is presented to showcase this approach to systematically address the interactions and trade-offs of multiple decision layers toward improving process efficiency and safety.

Quadratic p-Median Problem: A Bender’s Decomposition and a Meta-Heuristic Local-Based Approach

In this paper, the quadratic p-median optimization problem is discussed, where the goal is to connect users to a selected group of facilities (emergency services, telecommunications servers, healthcare facilities) at the lowest possible cost. The problem is aimed at minimizing the cost of connecting these selected facilities. The costs are symmetric, meaning connecting two different points is the same in both directions. This problem extends the traditional p-median problem, a combinatorial problem used in various fields like facility location, network design, transportation, supply chain networks, emergency services, healthcare, and education planning. Surprisingly, the quadratic version has not been thoroughly considered in the literature. The paper highlights the formulation of two mixed-integer quadratic programming models to find optimal solutions to this problem. One model is a classic formulation, and the other is based on set cover theory. Linear versions and Bender’s decomposition formulations for each model are also derived. A Bender’s decomposition is solved using an algorithm that adds constraints during each iteration to improve the solution. Lazy constraints in the Gurobi solver’s branch and cut algorithm are dynamically added whenever a mixed-integer programming solution is found. Additionally, an efficient local search meta-heuristic is proposed that usually finds optimal solutions for tested instances. Challenging instances with up to 60 facilities and 2000 users are successfully solved. Our results show that Bender’s models with lazy constraints are the most effective for Euclidean and random test cases, achieving optimal solutions in less CPU time. The meta-heuristic also finds near-optimal solutions rapidly for these cases.

Multi-depot routing problem with van-based driverless vehicles

In order to strengthen the coordination between different delivery participants and means of transport, this work proposes one extension of multi-depot routing problems where vans and driverless vehicles are used in combination during the delivery. The operation process mainly includes two parts. One is that, vans carry several driverless vehicles and goods, and drop off or pick up driverless vehicles at stops. Another is that, driverless vehicles departing directly from depots and dropped off by vans deliver goods to customers in cooperation. During the delivery, vans and driverless vehicles are in close cooperation through the proposed multi-depot joint distribution and the proposed van-van joint distribution. By the two modes, one van can depart from one depot and return to another depot, and one driverless vehicle can be set off by one van at one stop and be picked up by another van at another stop. This multi-depot routing problem with van-based driverless vehicles is formulated as a mixed integer programming model which can be solved by a designed heuristic algorithm. The sensitivity analyses about the maximum number of driverless vehicles in one van and the maximum traveling time of driverless vehicles are also performed. The results reveal that they have limited effects on the delivery cost and the application of the two modes. In addition, the experimental results demonstrate that the application of the two modes is affected by the distribution of depots and stops.

Optimizing the organization of the first mile in agri-food supply chains with a heterogeneous fleet using a mixed-integer linear model

Consumers are increasingly demanding high-quality food, which presents significant challenges for agricultural supply chains. While the majority of research in the agri-food sector has concentrated on optimizing logistics costs and meeting demand by focusing on minimizing the last mile, the complexity of the first mile in the agricultural supply chain has been less explored. Farmers must efficiently manage the harvesting process and the transportation of harvested produce to consolidation centers to ensure the delivery of high-quality products. This paper addresses this research gap by introducing a mixed-integer programming model that leverages vehicle routing problem concepts to optimize the logistics processes involved in transporting harvested products from various fields to a central depot. The primary objective is to minimize total logistics costs associated with visiting different fields during a pick-up round using multiple vehicles. The model has been applied to a case study involving an agricultural cooperative in Greece as part of the European BBTWINS project, which aims to enhance agri-food value chain digitalization for improved resource efficiency. The results demonstrate that organizing the first mile of the agri-food supply chain with a cooled vehicle for pick-up rounds can reduce logistics costs by up to 40% compared to the current practices.

Optimal allocation of wind-based distributed generators and STATCOMs using a hierarchical stochastic programming approach

Allocating static synchronous compensators (STATCOMs) to regulate given allotted wind-based distributed generators (W-DGs) during planning stages can provide high investment returns by maximizing the installed W-DGs. Amidst rising global warming concerns, commitments to adopt renewable energy gain international momentum to curb greenhouse emissions and meet environmental targets, reducing reliance on fossil-based resources. Renewable energy's intermittency complicates distribution planning, stressing voltage devices and increasing network losses. This paper presents a new hierarchical stochastic planning model that addresses uncertainties related to W-DGs and generic loads. The model optimizes allocation with voltage constraints and reactive power while incorporating a two-stage mixed-integer nonlinear program (MINLP), maximizing net profit, and adding an economic dimension to promote renewable energy investments. Improved wind power modeling with historical data and collective evaluation metrics for selecting the best-fitted probability distribution function (PDF) enhances the accuracy of wind power integration assessment. The hierarchical approach considers relaxed voltage constraints in Stage I to allow maximum allotment of W-DGs while introducing STATCOMs and DGs' reactive power in Stage II to address voltage violations. Verification on the Canadian 41-bus network demonstrates the advantage of the hierarchical approach in allocating more W-DGs and achieving higher profits than the simultaneous planning approach. These advances significantly enhance renewable energy integration in power systems.

Mixed-integer disciplined convex programming approach applied to the optimal energy supply of near-zero energy buildings

Energy needs in the buildings sector accounts for 40 % of global energy demand. Therefore, the implementation of several renewable energy sources is necessary to reduce this demand. The design stage of a decentralized generation project requires quantifying the power to be installed and the energy forecast for each source throughout the useful life of the building. This study develops a novel optimization algorithm for a long-term economic function based on mixed-integer disciplined convex programming (MIDCP) which guarantees the sustainability of the building and its energy systems. The robust algorithm integrates risk management of intermittent sources, technical and economic parameters of selected technologies, and life cycle analysis (LCA) of different energy systems, including storage. Furthermore, the penetration of green hydrogen into the distributed generation mix is evaluated as an important contribution. Meteorological and energy demand variables of two antagonistic scenarios were also used as inputs to the algorithm. As a result, the optimal energy supply sizing for tertiary buildings in the two defined locations was obtained. The results of the simulations have achieved an optimal convergence of 100 % in the proposed scenarios, with a resolution time of 14 s and using a memory of about 183 MB. The simulations suggest a higher penetration of green hydrogen in scenarios where supply and investment costs decrease to gray hydrogen supply levels, reaching up to 81 % coverage of the thermal demand of the building. Hybrid energy systems under favorable conditions show a penetration of about 92 % within the distributed generation mix. The developed tool could enable decision-makers to optimally plan distributed generation projects in buildings based on economic, policy, and geographic conditions.

Optimization Method of Mine Ventilation Network Regulation Based on Mixed-Integer Nonlinear Programming

Mine ventilation is crucial for ensuring safe production in mines, as it is integral to the entire underground mining process. This study addresses the issues of high energy consumption, regulation difficulties, and unreasonable regulation schemes in mine ventilation systems. To this end, we construct an optimization model for mine ventilation network regulation using mixed-integer nonlinear programming (MINLP), focusing on objectives such as minimizing energy consumption, optimal regulation locations and modes, and minimizing the number of regulators. We analyze the construction methods of the mathematical optimization model for both selected and unselected fans. To handle high-order terms in the MINLP model, we propose a variable discretization strategy that introduces 0-1 binary variables to discretize fan branches’ air quantity and frequency regulation ratios. This transformation converts high-order terms in the constraints of fan frequency regulation into quadratic terms, making the model suitable for solvers based on globally accurate algorithms. Example analysis demonstrate that the proposed method can find the optimal solution in all cases, confirming its effectiveness. Finally, we apply the optimization method of ventilation network regulation based on MINLP to a coal mine ventilation network. The results indicate that the power of the main fan after frequency regulation is 71.84 kW, achieving a significant energy savings rate of 65.60% compared to before optimization power levels. Notably, ventilation network can be regulated without adding new regulators, thereby reducing management and maintenance costs. This optimization method provides a solid foundation for the implementation of intelligent ventilation systems.

A hybrid intersection control strategy for CAVs under fluctuating traffic demands: A value approximation approach

Confronted with growing and fluctuating traffic demands, urban transportation system has been encountering mounting challenges in traffic congestion, especially at intersections. With enhanced traffic control precision enabled by the emerging Connected and Automated Vehicle (CAV) technologies, this study proposes a hybrid control strategy for connected and automated traffic at urban intersections, which enables the integration of diverse control schemes to harness their strengths and mitigate their weaknesses. With rolling horizon strategy, a nonlinear optimization model is developed to determine the optimal traffic control plans considering both current status and forthcoming vehicle arrivals. Vehicle delays are elaborately characterized without relying on any empirical assumptions. The original model is converted to a Mixed Integer Programming with Quadratic Constraints (MIP-QC) by employing appropriate linearization techniques, which could be solved by commercial solvers. For the acquisition of instant and reliable solutions, a multilayer feedforward network-based approximate algorithm is developed, referred as Value Approximation Control (VAC) algorithm. Theoretical derivation is provided to validate the capability of VAC algorithm in the precise approximations of the value function in the traffic plan optimization problem, and ultimately enabling to acquire global optimal solutions via specific network design and training techniques. Numerical experiments on both artificial and researcher-collected datasets demonstrate that our proposed VAC algorithm achieves performance nearly equivalent to the mathematical model. Significantly, it outperforms current state-of-art traffic control methods in terms of both intersection throughput and average vehicle delay. Moreover, sensitivity analysis reveals the robustness of the VAC algorithm against inaccuracy in vehicle arrival information, and the stable performance even in the presence of significant disturbances.

Integrated production and outbound distribution scheduling problem with multiple facilities/vehicles and perishable items

Integrated production and distribution operations are crucial and necessary for companies to outperform their competitors. In this paper, we study an integrated problem includes heterogeneous facilities and capacitated vehicles. Our goal is to produce and distribute products in batches that meet customer demands at the lowest possible cost. We first give the formal definition of the problem, then propose a Mixed Integer Programming (MIP) formulation and strengthen with several polynomial size valid inequalities. Furthermore, we develop Memetic Algorithm (MA) and finally present 2592 test instances to illustrate the efficiency of both MA and MIP formulation. The optimal or feasible solutions for 1283 of 2592 test instances are obtained by the proposed MIP formulation. MA finds optimal or near optimal solutions for all these instances. When comparing the best solutions obtained by MA with the solutions of the MIP formulation, MA produces a superior result. Besides that, the time to obtain for optimal solutions are approximately 9 min and for all test instances approximately 82 min using MIP formulation. The time needed to solve all test instances with MA is only 3 sec. These findings clearly demonstrate the speed and accuracy of MA in producing results. These results also demonstrate that, it is possible to achieve solutions that are either equal or very close to those found by the MIP formulation, in an extremely short computation time with MA.

The Multi-Objective Shortest Path Problem with Multimodal Transportation for Emergency Logistics

The optimization of emergency logistical transportation is crucial for the timely dispatch of aid and support to affected areas. By incorporating practical constraints into emergency logistics, this study establishes a multi-objective shortest path mixed-integer programming model based on a multimodal transportation network. To solve multi-objective shortest path problems with multimodal transportation, we design an ideal point method and propose a procedure for constructing the complete Pareto frontier based on the k-shortest path multi-objective algorithm. We use modified Dijkstra and Floyd multimodal transportation shortest path algorithms to build a k-shortest path multi-objective algorithm. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments carried out on test sets of different scales and a comparison of the runtime using a commercial solver. The results show that the modified Dijkstra algorithm has a runtime that is 100 times faster on average than the modified Floyd algorithm, which highlights its greater applicability in large-scale multimodal transportation networks, demonstrating that the proposed method both has practical significance and can generate satisfactory solutions to the multi-objective shortest path problem with multimodal transportation in the context of emergency logistics.

A novel differentiated coverage-based lifetime metric for wireless sensor networks

This paper delves into optimizing network lifetime (NL) subject to connected-coverage requirement, a pivotal issue for realistic wireless sensor network (WSN) design. A key challenge in designing WSNs consisting of energy-limited sensors is maximizing NL, the time a network remains functional by providing the desired service quality. To this end, we introduce a novel NL metric addressing target-specific coverage requirements that remedies the shortcomings imposed by conventional definitions like first node die (FND) and last node die (LND). In this context, while we want targets to be sensed by multiple sensors for a portion of the network lifetime, we let the periods, during which cells are monitored by at least one sensor, vary. We also allow the ratios of multiple and single tracking times to differ depending on the target and incorporate target-based prioritization in coverage. Moreover, we address role assignment to sensors and propose a selective target-sensor assignment strategy. As such, we aim to reduce redundant data transmissions and hence overall energy consumption in WSNs. We first propose a unique 0-1 mixed integer programming (MIP) model, to analyze the impact of our proposal on optimal WSN performance, precisely. Next, we present comprehensive comparative studies of WSN performance for alternative NL metrics regarding different coverage requirements and priorities across a wide range of parameters. Our test results reveal that by utilizing our novel NL metric total coverage time can be improved significantly, while facilitating more reliable sensing of the target region.

Optimal allocation of distributed generation on DC Networks

A consistent increase in the installation of distributed generation (DG) in response to rising energy cost and demand throughout the world, especially for the last two decades, primarily aims to obviate upgrading investments for transmission and distribution lines on the existing power grid while ensuring sustainable, resilient, and reliable service to end users. Random installation of DG, on the other hand, can invalidate the existing grid’s designated objectives, and operational boundaries due to the changes in network topology resulting in unforeseen load flow. Appropriate integration of DG units on DC networks should be remedy to high transmission/distribution losses in lines, instabilities in voltage profiles, issues in power quality parameters, and derogation in the protection schemes. Based on the behavior of load profiles, e.g., 24 h or longer period, operational and technical constraints, this study proposes a framework that minimizes transmission/distribution losses on a DC network, in which discrete variables stand for the location of DGs. Optimal power flow (OPF) problem formulation underpins the proposed optimization framework. Overall, this computationally challenging planning problem refers to a mixed-integer nonlinear program (MINLP) including discrete variables with non-convex power balance/flow representations. To deal with the non-convexities and discrete form of the formulation, a mixed-integer second-order cone programming (MISOCP) relaxation, and branch-and-bound search are assigned. The validation of the introduced approach is carried out on the IEEE modified benchmark systems. With the help of proposed method, optimal allocation of DG units on 9-bus, 14-bus, and 30-bus systems, respectively, lead up to 99.93%, 94.38%, and 79.09% total power losses reduction.

Hub production scheduling problem with mold availability constraints

This research delves into a scheduling challenge inherent in the wheel hub casting process, a critical stage in automotive wheel manufacturing. The process involves shaping molten metal into specific wheel hub designs using dedicated molds. Diverse customer demands necessitate a unique mold for each wheel hub design, posing a scheduling challenge due to the limited availability of these expensive and long-lasting molds. There are 2 machines available for casting. Each wheel hub design requires a specific mold. These molds are expensive, long-lasting, and need periodic maintenance. The objective function is to minimize the total time (makespan) to complete all casting jobs. Only one job requiring a specific mold can be processed at a time (due to mold limitations). Molds are unavailable during maintenance periods. The challenge lies in scheduling jobs considering both machine availability and mold constraints to minimize the overall production time. We formulate a mathematical model using mixed integer programming to precisely represent the problem and its constraints. Inspired by the Longest Processing Time (LPT) rule, we propose a heuristic named LRTPT to efficiently schedule jobs on the two machines. For large-scale problems, we employ a novel SIAIS algorithm to find near-optimal solutions effectively. We also present a dedicated branch and bound algorithm specifically tailored to solve smaller-sized instances of the problem. This algorithm leverages two lower bounds and several dominance properties to expedite the search for the optimal solution. To evaluate the effectiveness of our proposed approaches, we conduct a series of comprehensive experiments. The results demonstrate that the branch and bound algorithm significantly outperforms the widely used optimization solver CPLEX for smaller problems. Furthermore, the SIAIS algorithm proves to be more efficient than existing scheduling heuristics.

Integrating resilience and reliability in semiconductor supply chains during disruptions

The semiconductor industry, a cornerstone of modern technology, has been crucial in driving globalization and supporting various sectors, from consumer electronics to automotive industries. However, in recent years, the industry has faced substantial challenges threatening its ability to meet the surging demand for semiconductor chips. Disruptions at any point in the supply chain, from raw material sourcing to end-product delivery, can substantially influence the semiconductor ecosystem. The intricate nature of such SCs makes them highly vulnerable to various disruptions, emphasizing the critical need for building resilient and reliable supply chain strategies. This article presents comprehensive research aimed at addressing critical gaps in the understanding and management of resilience and reliability within the semiconductor supply chain (SSC). This study proposes a multi-objective mixed-integer non-linear programming (MO-MINLP) model to configure an SSC while considering reliability and resilience measures. It emphasizes and draws attention to the importance of resilience and reliability in managing SSC disruptions during a pandemic and potential future epidemic outbreak. Exploring the precise breakdown of batch transportation between two sites shows how disruption can affect product flow along the SC. The applicability of the proposed method is demonstrated through a numerical example of an SSC, solved using the LINGO solver. Finally, a sensitivity analysis is conducted on the model's parameters to assess the capability and effectiveness of the results from managerial viewpoints.

An enhanced energy management system for coordinated energy storage and exchange in grid-connected photovoltaic-based community microgrids

This paper introduces an enhanced coordinated community energy management system (CEMS) for a community microgrid. It is designed to optimize residential energy consumption and facilitate energy sharing among smart homes. The proposed solution integrates constrained mixed-integer programming (CMIP) approach along with advanced optimization technique and cooperative game theory-based pricing mechanism to address critical challenges in existing energy management strategies, including load scheduling and efficient peer-to-peer energy trading. The CEMS approach is adopted for grid-connected community power systems that incorporate local energy sources such as photovoltaic and battery storage systems. This solution is implemented under a time-of-use dynamic pricing model for energy transfer from the main grid to the community peers, a modified mid-market pricing mechanism for the P2P energy exchange, and feed-in tariff for energy transfer from the community peers to the main grid. Besides, seagull optimization algorithm is applied to relax the CMIP problem to get the optimal rational solution of the scheduling problem which is subjected to a rounding process to obtain the best feasible solution. The obtained results indicate a substantial reduction in electricity costs, achieving daily savings of 72.21 % and reducing grid dependency by 41.95 %. Moreover, 82.2 % of the community's energy demand was met through locally generated resources with 18.39 % enhancement of the overall CMG self-consumption ratio comparing to the reference operating scenario. Ultimately, the study demonstrates the effectiveness of the management system in improving load profiles, maximizing the use of local renewable energy sources, and reducing electricity expenses, thereby providing a sustainable and economically viable model for future smart grids.

A learning-driven multi-objective cooperative artificial bee colony algorithm for distributed flexible job shop scheduling problems with preventive maintenance and transportation operations

In recent years, distributed production scheduling problems receive much attention from both scholars and practicers. Nevertheless, existing research on such problems commonly ignores machine maintenance and job transportation operations. This work proposes a distributed flexible job shop scheduling problem with preventative maintenance and transportation operations in consideration of sequence-dependent setup time. First, a mixed integer programming model is formulated to minimize maximum completion time of jobs and maximum workload of factories. Second, a learning-driven multi-objective cooperative artificial bee colony algorithm is developed to deal with the model. A Q-learning-based cooperation strategy between population and obtained non-dominated individuals is devised to strengthen the exploration and exploitation performance. Furthermore, heuristic-based population initialization, crossover operations in employed bee phase and iterated local search methods in onlooker bee phase are specially developed considering the problem characteristics. Finally, the proposed method is compared against three well-known meta-heuristics from existing literature and an exact solver CPLEX by using a set of benchmark instances. The results confirm the competitive performance of the developed model and algorithm for addressing the studied problems.

A modelling and solution approach for wind-affected drone-truck routing problem under uncertainty

In the field of logistics and transportation, drones and trucks effectively enhance each other’s capabilities by offering complementary benefits in terms of speed, cargo capacity, and charging frequency. Thus, efficient management of their collaboration is an important task. Although there is a vast literature addressing different aspects of drone-truck combined operations (DTCO), only a few studies incorporate the energy consumption of drones into the optimization model, and the existing ones have made simplified assumptions. This paper proposes an optimization model for DTCO by incorporating a comprehensive energy function affected by the drone speed, cargo weight, wind speed, and wind direction, paying attention to environmental viewpoints. Due to this energy function, the problem is formulated as a mixed-integer nonlinear programming (MINLP) model. To enhance tractability and efficiency, we provide a linear approximation for the MINLP model. Given the stochastic nature of wind conditions throughout the day, we extend the deterministic model as a scenario-based stochastic one. Incorporating uncertainty makes the model more complex and hence, we adopt a modified progressive hedging algorithm (PHA) to efficiently solve the model. Computational results over a variety of instances confirm the effectiveness of the proposed approach.

Environmental challenge of vehicle dispatching in marine container drayage

AbstractIn marine container drayage (CD), which refers to the transport of goods over a short distance, empty containers (ECs) are required to be transported long distances between a terminal and a shipper/consignee by conventional transportation. This causes truck traffic congestion in harbor districts that increases CO2 emissions (CO2EM). This study addresses the vehicle dispatch problem with respect to the environmental impact of marine CD, considering the tractor dwell time is long at the customer site due to cumbersome container loading/unloading (L/U). We model this problem as an extended version of the vehicle routing problem with precedence constraints to minimize the total CO2 weighted travel distance. To improve CD operation in long L/U time, we propose a new practice for CD operations. Additionally, we develop a mixed integer programing model (MIP) for the new practice representation, and propose a Simulated Annealing (SA) based heuristic approach to solving the new practice instance. By implementing our proposed new operation, in a long L/U time, the CO2EM, EC move and number of tractors required can also be reduced by allowing uncoupled tractor move.

Efficient routing in robotic movable fulfillment systems with integer programming: A rolling horizon and heuristic approach

This paper addresses an integrated rack assignment and robot routing problem arising in robotic movable fulfillment systems (RMFS). This NP-hard planning task goes beyond current literature by simultaneously optimizing movable rack selection and multi-agent collision-free path finding, rather than decomposing them. A mixed integer programming (MIP) model with a new level-space-time network representation is proposed, jointly considering reusable racks, robot-rack pairings, storage repositioning, and collision avoidance. To improve computational efficiency, a fast rolling horizon heuristic and greedy algorithm are developed. Extensive experiments demonstrate that the integrated method's solutions can improve by 30 % upon conventional decomposed approaches. Intriguing test cases reveal the model, suggesting non-intuitive robot carryover policies that are unfound by separate selection and routing methods. This indicates potential optimization benefits from explicitly coordinating task assignment, scheduling, and routing decisions in complex automated warehousing systems. The rolling horizon heuristic solutions approach optimality with much greater efficiency than directly solving one large MIP, validating its practical value. This research provides useful integrated modeling insights, efficient solution algorithms, and decision support for efficiently controlling next-generation robotic movable fulfillment systems.

Matheuristic algorithm for dock planning problems considering tandem and parallel methods in the shipbuilding industry

Docks are crucial production resources that significantly impact shipyard productivity. This study addresses a real-world dock planning problem (DPP) focused on ship production scheduling within docks. Unlike traditional scheduling issues, the DPP involves managing multiple concurrent tasks due to the use of tandem and parallel methods common in the shipbuilding industry. This distinctive feature introduces unique considerations and opportunities for optimizing production processes within shipyards. Despite its importance, research on DPPs is limited, with dock planning typically depending on the expertise of planners. This study formally defines a DPP as a mixed-integer programming (MIP) model, incorporating tandem and parallel methods. It also introduces MathLNS, a matheuristic algorithm that combines MIP-based large neighborhood search with heuristic methods, as an efficient solution approach to this problem. The effectiveness of the proposed model and algorithm is evaluated using real-world data from one of the largest shipbuilders globally. The results demonstrate significant improvements over the planner-driven approach. Notably, the developed algorithm has been integrated into the company’s production planning system, resulting in improved dock planning efficiency. Furthermore, the proposed approach offers potential benefits for other shipbuilding companies, enhancing operational efficiency in dock planning.