Mixed Integer Linear Programming Research Articles

Peak shaving and self-consumption maximization in home energy management systems: A combined integer programming and reinforcement learning approach

This paper proposes a novel framework for Home Energy Management System based on the combination of integer programming and Reinforcement Learning (RL) for achieving efficient home-based Demand Response (DR). In particular, RL is exploited to manage the charge and discharge of Battery Energy Storage System (BESS), and Mixed Integer Linear Programming is exploited for load scheduling. The idea is to focus the RL specifically on BESS management, as its behavior is stochastic and is mainly affected by Photovoltaic (PV) production and user behavior changes. The scheduling decisions of household appliances, Electric Vehicles (EVs), and charging/discharging batteries can be subsequently obtained through the newly developed framework, of which the objective is dual, i.e., to minimize the electricity bill as well as the DR-induced dissatisfaction. Simulations are performed on a residential house level with multiple home appliances, an EV, PV panels, and electric storage. The test results demonstrate the effectiveness of the proposed home energy management framework under the application of different demand-side flexibility strategies.

Operation estimation on multiple public transport timetables integrated with vehicle scheduling in practice

ABSTRACT Even-headway and even-load timetables have been in practice for the past 50 years. The former stipulates constant departures to cultivate users’ habits accordingly, whereas the latter is oriented from demand regulations aiming to further reduce waiting times. However, striking the balance between operation reliability (derived from even-headway timetabling) and an on-demand response to passenger fluctuation (referring to even-load timetabling) requires addressing major challenges presented by peak or alternatively off-peak demands. Our work addresses this imbalance by comparable estimation. The focused problem involves timetabling, vehicle scheduling, fleet size, and operation reliability based on an identical modeling framework simultaneously involving the three models. Nonetheless, their compatibility warrants a unified measure estimation. Hence, a mixed integer linear programming model is built. Finally, multiple timetabling performance comparisons are observed by the Auckland public transport system yielding sensitivity analysis.

Model and heuristics for the multi-manned assembly line worker integration and balancing problem

This paper examines the balancing of assembly lines with multi-manned stations and a heterogeneous workforce. Both topics received considerable attention in the literature, but not in an integrated fashion. Combining these two characteristics gives rise to a highly combinatorial Multi-manned Assembly Line Worker Integration and Balancing Problem. When considering multi-manned stations, the already coupled decisions on assigning tasks to heterogeneous workers and workers to stations must be further linked with task scheduling assessments. We propose a Mixed-Integer Linear Programming model and develop two heuristic solution procedures, which tackle the problem with a hierarchical decomposition approach. Computational tests on a large dataset indicate that the proposed method can obtain good primal bounds in short computational times. We demonstrate that these results can be applied to the monolithic model either as a warm start or in a proximity search procedure to obtain synergistic gains with statistically significant differences. From a managerial perspective, we show that multi-manned stations can reduce the assembly line's length even in the presence of a heterogeneous workforce, which is crucial for many industries manufacturing large-size products.

Accurate and robust linear representation for containership stability conditions with ballast water

Stowage planning involves optimizing the placement of cargo on a ship while ensuring the ship's stability conditions are met. This optimization problem is typically formulated as a mixed-integer linear programming problem. However, a challenge arises in representing stability conditions as linear constraints since these conditions have non-linear relationships to the decision variables. Although there are methods for linearizing these stability conditions, they lack a systematic modeling approach and numerical verification of accuracy and reliability. In particular, the complex and diverse nature of ballast water contributes to significant non-linearity, posing a considerable challenge in developing an accurate linear approximation. This study proposes linear prediction methods that incorporate ballast water to address major stability conditions such as trim, drafts, shear force, bending moment, torsion, and transverse metacentric height. We introduce a comprehensive training and testing methodology for prediction, and validate the proposed method by comparing it with true values on two ships of different capacities, demonstrating its accuracy and scalability.

UAV-rider coordinated dispatching for the on-demand delivery service provider

Fast response is critical to the success of the on-demand delivery service providers. Recently, more and more on-demand delivery service providers have started trying to use UAVs/drones to cope with the increasing challenges due to delivery service-sensitive demand. In this study, we propose a novel UAV-rider coordinated on-demand delivery model from the perspective of the on-demand delivery service provider. The objective aims to provide cost-effective delivery solutions by introducing the UAV/drone fleets into the current rider-only on-demand delivery system. A mixed integer linear programming (MILP) model is formulated to solve the problem, which is verified by the solver Cplex. To further analyze the impacts of the integration of UAVs on the riders’ deployment in practice, we develop a modified adaptive large neighborhood search (ALNS) algorithm to solve real business large-scale instances. The mechanism of how to improve the operational efficiency of the delivery service provider by integrating UAVs and the best-coordinated mode between UAVs and riders is discussed by conducting real-data-based numerical experiments. The results show that, for the case with a small number of orders in a dispatch cycle, the pure UAV model is best for the on-demand delivery service provider. When there are a large number of orders received in one dispatch cycle, the UAV-rider coordinated model is the best one to achieve cost-effective solutions. Some useful managerial insights are obtained through extensive experiments.

Congressional Apportionment: A Multiobjective Optimization Approach

Two events, with major implications for U.S. voters, occur after each decennial census. First, congressional “apportionment” takes place, followed by congressional “districting.” Apportionment determines how to allocate the 435 seats in the House of Representatives across the 50 states, whereas districting determines the geographic boundaries assigned to representatives within each state. Although districting and the practice of gerrymandering often receive great attention in the media and courts, the best way to apportion representatives across states has been debated for nearly 250 years. Historical methods (including the current method) each satisfy some desirable optimality criteria that the others are not guaranteed to satisfy. Moreover, none are guaranteed to optimize certain reasonable fairness measures (e.g., minimum range, minimum bias). To our knowledge, we are the first to formulate and analyze a multiobjective optimization approach to apportionment, allowing policymakers to identify Pareto-optimal allocations and quantify their trade-offs between several competing criteria. Some of these models can be formulated and solved as mixed-integer linear programs, whereas others require the solution of mixed-integer, nonconvex, quadratically constrained quadratic programs. We take advantage of recent software advances that allow one to solve these problems with optimality guarantees. Policy implications of our work include Pareto curves from historical censuses and simulations, which suggest opportunities for improvement in some objectives at little sacrifice to others. This paper was accepted by David Simchi-Levi, operations management. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.02472 .

Peer-to-peer multi-period energy market with flexible scheduling on a scalable and cost-effective blockchain

Peer-to-Peer (P2P) electricity trading is an emerging means for allowing communities to share local energy production and demand response through direct trading. It is projected to play an important role in the future energy market by increasing the incentive to own and operate distributed energy resources (DERs) and participate in demand response (DR). A common approach to implementing P2P trading is with blockchain, however, existing solutions feature limitations. Typically, concerns involve either scalability and high transaction costs or projects implementing a permissioned blockchain that does not provide the trust and decentralization desired. In addition, the majority of market designs are simplified and do not capture the distinct complexity of electricity markets. They do not consider the inter-temporal constraints of appliances and DERs that need to run for multiple periods. Complex market designs that address these issues have not been implemented in blockchain based systems due to the computational limitations of such systems. To improve these two aspects, this paper proposes a market formulation that supports products running multiple periods with flexible scheduling, modeled as a mixed integer linear programming problem that optimizes social welfare. The trading platform is then implemented as a side chain of Polkadot, a network of blockchains designed to be secure, scalable, and economically feasible to foster an ecosystem of application-specific sidechains. This design is demonstrated to improve social welfare and achieve scalability by benchmarking the number of transactions that can be included per second, based upon typical assumptions of the market size. The result is a decentralized and performant system that allows for complex market designs to be implemented in a blockchain environment. This approach simplifies the process for participants, allowing them to bid DER or DR devices, directly and easily, even when this requires constraints across periods.

The establishment of a performance evaluation model using education informatization to evaluate teacher morality construction in colleges and universities

Abstract To improve the effectiveness of the construction of teacher morality in colleges and universities, this article employs the performance evaluation model of education informatization to construct an evaluation system for the construction of teacher morality in colleges and universities. The evaluation of the construction effect of teacher morality is carried out through intelligent data analysis, and the significant error is used as the parameter of the teacher’s morality to make estimations. Moreover, a binary variable is introduced to judge whether the data have a significant error. Mixed integer linear and nonlinear programming methods are employed to detect significant errors. In addition, the idea of synchronizing teachers’ moral data is added. The effectiveness of the proposed method is verified by a simulation study using MATLAB 2017. The results show that it is necessary to establish and improve the talent flow mechanism that conforms to the requirements to promote the rational flow of teachers.

Optimizing vehicle route, schedule, and platoon formation considering time-dependent traffic congestion

Vehicle platooning, a strategy where vehicles drive in close formations, has emerged as a promising approach to reduce fuel consumption. This study presents a comprehensive model of the time-dependent vehicle platooning problem, which synchronously considers routing, scheduling, and platoon formation to minimize total fuel costs in a network affected by time-dependent traffic congestion. We first propose a mixed integer linear programming model to address this problem. To solve the problem, we develop two solution methods: a tabu search method and a platoon clustering algorithm. Through numerical experiments, we demonstrate the effectiveness of our mathematical model and the efficiency of the proposed algorithms. Our findings provide insights into the operational aspects of platooning and reveal that time-dependent traffic congestion can reduce the fuel-saving effects of platooning. This study underscores the importance of considering time-dependent traffic congestion in route planning and scheduling to ensure the effectiveness of vehicle platooning.

Mixed-batch scheduling to minimize total tardiness using deep reinforcement learning

This study addresses the issue of scheduling batch machine to minimize total tardiness. Vacuum heat treatment allows multiple jobs to be processed as a batch, as long as they do not exceed the machine's weight and size limits; the weight and size of the jobs both impact the batch processing time. By considering the differences in the release time and due date for each job, a mixed-integer linear programming model is developed and validated using small-scale instances. To tackle large-scale scheduling problems, an intelligent algorithm based on deep reinforcement learning is proposed. Double deep Q-learning networks are designed, and the environmental state feature matrix is extracted as input parameters for the networks. Four job-sorting rules and three scheduling time windows are defined, resulting in twelve action rules within the action space. The most suitable action rule is dynamically selected based on the current batch's environmental status during the scheduling process. Through extensive comparison using large-scale random data, the proposed algorithm demonstrates significantly improved scheduling performance compared to the benchmark algorithms.

Assessing and Improving Automated Viewpoint Planning for Static Laser Scanning Using Optimization Methods

Abstract. The preparation of laser scanning missions is important for efficiency and data quality. Furthermore, it is a prerequisite for automated data acquisition, which has numerous applications in the built environment, including autonomous inspections and monitoring of construction progress and quality criteria. The scene and potential scanning locations can be discretized to facilitate the analysis of visibility and quality aspects. The remaining mathematical problem to generate an economic scan strategy is the Viewpoint Planning Problem (VPP), which asks for a minimum number of scanning locations within the given scene to cover the scene under pre-defined requirements. Solutions for this problem are most commonly found using heuristics. While these efficient methods scale well, they cannot generally return globally optimal solutions. This paper investigates the VPP based on a problem description that considers quality-constrained visibility in 3D scenes and suitable overlaps between individual viewpoints for targetless registration of acquired point clouds. The methodology includes the introduction of a preprocessing method designed to simplify the input data without losing information about the problem. The paper details various solution methods for the VPP, encompassing conventional heuristics and a mixed-integer linear programming formulation, which is solved using Benders decomposition. Experiments are carried out on two case study datasets, varying in specifications and sizes, to evaluate these methods. The results show the actual quality of the obtained solutions and their deviation from optimality (in terms of the estimated optimality gap) for instances where exact solutions can not be achieved.

A risk-averse distributionally robust optimisation approach for drone-supported relief facility location problem

Drone-supported last-mile humanitarian logistics applications play a crucial role in the rapid and efficient delivery of essential relief items, such as medicine, blood, and vaccines, during disaster and emergency situations. This paper explores a novel drone-supported relief facility location problem (DSRFLP) aimed at establishing an effective drone-supported last-mile humanitarian logistics system. The problem involves making joint decisions for both pre-disaster and post-disaster phases while considering the characteristics of drone-based delivery operations and uncertain demands. In the pre-disaster phase, we make the decisions regarding the locations of drone-supported relief facilities, inventory prepositioning of relief items, assignment of drones to the opened facilities, and allocation of drones to disaster demand sites. In the post-disaster phase, we make decisions related to delivery quantities. To tackle the challenge of incomplete demand distribution information in chaotic disaster environments, we establish a distributionally robust optimisation (DRO) model to handle the uncertainty of demands. This model adopts worst-case mean Conditional Value-at-Risk as the risk measurement, reflecting the risk-averse attitude of humanitarian organisers. In this paper, three ambiguity sets (box, ellipsoidal, and polyhedral) are considered to describe the ambiguity distributions of demands. To overcome the computational challenge, we reformulate the DRO model under three ambiguity sets into two mixed-integer linear programming models and one second-order cone programming model, which can be efficiently solved by off-the-shelf solvers. Furthermore, we validate our proposed DRO model through a small-scale example and a large-scale case study based on the Lushan earthquake in China. The computational outcomes underscore the superior performance of the proposed DRO model to mitigate the impact arising from incomplete probability distributions. We propose managerial implications and insights to support the decision-making of humanitarian organisations based on the experimental results. Finally, we propose two extended models to incorporate multiple relief items and equity constraints in priority settings and conduct numerical experiments to adapt to various real-world disaster scenarios.

A dynamic system optimal dedicated lane design for connected and autonomous vehicles in a heterogeneous urban transport network

Numerous contemporary studies have posited that connected and autonomous vehicles (CAVs) hold the potential to enhance traffic safety and augment efficiency substantially. One widely discussed approach to optimize CAV operations within urban traffic networks involves the implementation of dedicated lanes (DLs). This study aims to assist system planners in optimally deploying DLs within heterogeneous urban traffic networks of CAVs and Human-Driven Vehicles (HDVs). In pursuit of this objective, we have introduced a multi-class dynamic traffic assignment framework that enhances network performance and offers insights into traffic dynamics. Additionally, our methodology considers dynamic routing behaviour while devising DLs, formulating and approximating the problem as a mixed-integer linear program (MILP). The resulting strategy delineates the temporal and spatial aspects of the deployment of DLs for CAVs, specifying the quantity and locations of these lanes. Subsequently, we assessed our framework using test-bed networks of varying sizes and demand profiles, evaluating the solution’s quality and the model’s adaptability to diverse traffic conditions. Our findings indicate that implementing DLs for CAVs can bolster vehicular throughput across the network while neglecting dynamic capacity variation in mixed traffic may yield misleading outcomes.

A proactive transshipment model for prototype parts logistics in the automotive industry

AbstractIn the logistics of prototype parts in the automotive industry, unique parts are stored in warehouses and provided to assembly service providers to ensure a timely assembly of the associated prototype vehicles. As the allocation of the assembly orders to the assembly service providers may change before the start of the assembly, the shipments are planned at short notice. This article considers the short-term task of planning shipments of individual prototype parts from multiple warehouses to multiple assembly service providers. The current literature on planning shipments focuses mainly on parts available in batch sizes larger than one. However, as prototype parts are individual, storing them in adequate warehouses is crucial. A mixed-integer linear programming model for planning transshipments of parts between the warehouses and shipments to the assembly service providers to minimize overall costs is presented. The model enables the utilization of spare capacities of planned transports for a proactive transshipment of parts between warehouses. To this end, the future shipment costs of parts to assembly service providers are approximated to determine suitable warehouses. A numerical study shows that the proactive approach leads to a considerable cost reduction.

Smart home energy management and active power loss analysis of a residential community

As the demand for energy continues its upward trajectory, judiciously managing the global energy resources has become increasingly imperative. One effective strategy to accomplish this efficiency is by strategically scheduling intelligent household appliances, a process that considers dynamic pricing schemes and the availability of renewable energy sources. This paper presents a comprehensive study that delves into optimizing smart home appliance utilization, considering electric vehicles and a modest rooftop photovoltaic installation. The study seeks to ascertain their potential impact on both energy consumption and cost mitigation. The proposed scheduling approach is centered on the optimal scheduling of smart appliances, harnessing the power of real-time pricing schemes to curtail the overall energy expenditure. The scheduling conundrum is meticulously modelled using General Algebraic Modeling System software and subsequently tackled by the CPLEX solver, leveraging mixed-integer linear programming techniques. Results reveal a remarkable achievement, with the potential for up to an 80.6 % reduction in the overall cost compared to the base case under various scenarios considering different approaches. To validate the integrity of the study, outcomes are juxtaposed with those of the base paper, and the superiority of the proposed method is evident from the results. Furthermore, the paper considers the ramifications of optimized scheduling on the voltage profile and overall system losses nearly 7 % less compared to the base case within the context of the IEEE 33-bus system. Thus, the presented work successfully analyzes the effect of household energy scheduling on the community level and scales up to a microgrid level.

Modeling a robust 2-service community healthcare network design problem with central hospital congestion

We address a more realistic variant of the community healthcare network design problem, considering a 2-service network framework and hospital congestion structures. Our objective is to minimise the total expected cost through strategic location of central hospitals and allocation of community health stations. Notably, each community health station is allocated to exactly two central hospitals. We also account for uncertainties in resident medical demands, which are challenging to predict accurately due to their volatility. To tackle this, we propose an adaptive distributionally robust optimisation approach that confines uncertain variables to an ambiguity set reflecting demand distribution characteristics. To enhance tractability, we reformulate the distributionally robust model as a mixed-integer linear programme within the specified ambiguity set. Numerical experiments on a real case demonstrate the validity and superiority of the proposed model. Finally, the impact of uncertainty is discussed in depth and some managerial insights for healthcare managers are summarised.

Agri-food supply chain optimization through a decentralized production process in the olive oil industry

A tactical/operational model is proposed to assist decision-making in harvest planning and olive oil production planning of the different producers in the rural sector, considering allocation and transportation decisions of the kilograms of olives to the production plant with temporary relocation decisions of the mobile olive oil mills through decentralized production activities in the agri-food supply chain. A Mixed Integer Linear Programming model is presented that maximizes the profit of small farmers in the production process of single-varietal extra virgin olive oil. The decisions are based on the geographical dispersion of the different olive growers and the oil concentration of the olive varieties in a certain period, which depends on the climatic conditions of each sector where the olives are cultivated. The mathematical programming model is applied in Coquimbo, Chile, using actual data collected from previous harvest seasons. The computational results of the optimization model indicate that transportation decisions impact olive harvesting and oil production decisions. It is concluded that cooperatives of small producers in the rural sector increase overall profits and reduce transportation costs and the number of kilometers traveled by at least 41% through a decentralized production process with mobile production plants.

An iterated greedy algorithm with acceleration of job allocation probability for distributed heterogeneous permutation flowshop scheduling problem

Distributed manufacturing paradigm is becoming one of the dominant manufacturing models today. Heterogeneities between factories exist in fact due to the differences in process flexibility and machine performance. Most research focuses on identical distributed factories and overlooks the influence of heterogeneous factories on the subproblem of job allocation. This paper investigates a distributed heterogeneous permutation flowshop scheduling problem (DHPFSP) to minimize the makespan, and a mixed-integer linear programming (MILP) model is established. Building upon a special phenomenon of job assignment to a specific heterogeneous factory in DHPFSP, an iterated greedy algorithm with acceleration of job allocation probability (IGP) is proposed. To utilize this phenomenon, a job allocation probability matrix is introduced to describe the trend of job allocation, and a fast pass strategy with job allocation probability is suggested to speed up the algorithm search process. Furthermore, to generate a high-quality initial solution quickly for IGP, an NEH-based heuristic framework for distributed heterogeneous factory environment (NEHDHF) is proposed. In NEHDHF, several distinct initial job sequence generation strategies and a new first-f job allocation strategy are proposed for obtain a better initial solution. In computational experiments, there are 720 test instances designed and publicized. The IGP achieves 535 best solutions out of 720 instances. Statistically sound results demonstrate the effectiveness of the presented algorithms for the considered problem.

An efficient bi-objective optimization approach for the optimal design of omnichannel supply chain distribution networks with sustainability

ABSTRACT This article studies a bi-objective omnichannel supply chain network design (SCND) problem, while simultaneously minimizing the overall supply chain (SC) cost and associated environmental emissions. A novel bi-objective mixed integer linear programming model is formulated, then an efficient optimization approach is proposed for the problem. Experimental studies on a case study and 210 random testing instances were conducted to evaluate the performance of the proposed model and approach. For the case study, 10 Pareto-optimal solutions were obtained within 1.9 s. For the random testing instances, the average number of Pareto-optimal solutions and computational time were 10.19 and 18.85 s, respectively. The overall results show that the proposed method is efficient and outperforms the adapted non-dominated sorting genetic algorithm II on test instances. Computational results indicate that this approach could assist decision makers in making good decisions, with considerable SC cost saving and carbon emission reductions in different situations.

Designing function-specific minimal microbiomes from large microbial communities

Microorganisms exist in large communities of diverse species, exhibiting various functionalities. The mammalian gut microbiome, for instance, has the functionality of digesting dietary fibre and producing different short-chain fatty acids. Not all microbes present in a community contribute to a given functionality; it is possible to find a minimal microbiome, which is a subset of the large microbiome, that is capable of performing the functionality while maintaining other community properties such as growth rate and metabolite production. Such a minimal microbiome will also contain keystone species for SCFA production in that community. In this work, we present a systematic constraint-based approach to identify a minimal microbiome from a large community for a user-proposed function. We employ a top-down approach with sequential deletion followed by solving a mixed-integer linear programming problem with the objective of minimising the L1-norm of the membership vector. Notably, we consider quantitative measures of community growth rate and metabolite production rates. We demonstrate the utility of our algorithm by identifying the minimal microbiomes corresponding to three model communities of the gut, and discuss their validity based on the presence of the keystone species in the community. Our approach is generic, flexible and finds application in studying a variety of microbial communities. The algorithm is available from https://github.com/RamanLab/minMicrobiome.