Mixed Integer Linear Programming Model Research Articles

Matheuristic and learning-oriented multi-objective artificial bee colony algorithm for energy-aware flexible assembly job shop scheduling problem

With the increase of mass customization, flexible job shop scheduling problem considering assembly stage has widely existed in many manufacturing industries, such as die-casting mould factories. This problem is to find a reasonable machine assignment and operation sequence both in fabrication and assembly stages and simultaneously maximize production efficiency. In reality, energy shortages and environmental pollution have given an impetus to the development of energy-aware production scheduling problems. In this study, we address an energy-aware flexible assembly job shop scheduling problem (EFAJSP) with the objectives of minimizing flow time and energy consumption and first develop a mixed-integer linear programming (MILP) model to solve EFAJSP problem. Then, the model-specific characteristics are extracted and applied to a matheuristic decoding method for exploring the Pareto optimal solution. Due to the complexity of EFAJSP problem, a matheuristic and learning-oriented multi-objective artificial bee colony algorithm (MLABC), which combines the advantages of mathematical programming, reinforcement learning and meta-heuristic algorithm, is proposed. In addition, an initialization, destruction/construction operator and population update operator are proposed and work together to improve the exploration and exploitation performance of the proposed MLABC. Finally, numerical experimental results demonstrate the effectiveness of the proposed MILP model and the superiority of the MLABC over other algorithms in the literature.

Q-learning based scheduling method for continuous pickling process of titanium strips

This article addresses the energy consumption optimization problems of the pickling process for titanium strip manufacturing. The hybrid flow shop scheduling schemes for the pickling process of titanium strips are designed, and a novel shop scheduling method based on reinforcement learning is proposed for the pickling process of titanium strips. In the scheduling scheme, the pickling chemical treatment process of titanium strips are described as an asymmetric hybrid flow shop scheduling problem (AHFSP), and a mathematical model containing a temperature structure is established with the optimization objectives of minimizing pickling time and energy consumption. Based on the proposed scheduling scheme, a novel shop scheduling method based on reinforcement learning for the titanium strip pickling process is proposed. First, a mixed integer linear programing model for the mixed flow shop scheduling problem is established. Second, the flow shop scheduling problem with sequential energy consumption decisions is approximated as an asymmetric traveling sales-man problem (ATSP). Finally, the ATSP is described as a Markov decision processes (MDP), and a Q-learning based scheduling method for titanium strip pickling shops is proposed. Finally, the effectiveness of the proposed method is verified by examples, and the scheduling scheme can reduce the energy consumption by 16.61% on average while maintaining the schedule, which improves the productivity and economic efficiency.

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.

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.

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.

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 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.

Optimization of elective patient admissions during pandemics: case of COVID-19

With advent of the Covid pandemic, hospitals grappled with how to manage the sudden surge in demand while still treating those in need of service for other reasons. This study aims to provide an adaptive elective admission scheduling policy that maximizes throughput during a pandemic while maintaining the ability of a hospital to empty a specified number of beds over a short warning period (e.g. 5 days). This ability we call nimbleness. We propose a heuristic method based on two mixed-integer linear programming models (MILP) and a simulation model. The first MILP creates the initial schedule for patient admissions over the planning horizon while maximizing patient throughput. The second MILP considers the uncertainty of the emergency arrivals (including pandemic induced) and the patients’ length of stay and maximizes the number of scheduled patients admitted while ensuring the hospital’s nimbleness. A simulation model is built to create daily random arrivals and discharges. The models connect through an automated feedback loop until the heuristic approach converges on a solution. Numerical results demonstrate the ability of the approach to maintain high throughput while still responding to pandemic surges.

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 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.

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.

Route, speed, and bunkering optimization for LNG-fueled tramp ship with alternative bunkering ports

To reduce emissions, shipping companies are deploying eco-friendly ships, like those powered by LNG or methanol. Unlike traditional fuels, LNG bunkering is available at a limited number of ports. At the same time, tramp or bulk ships have fewer ports of call on their shipping lines, which may necessitate LNG-fueled ships sailing to alternative bunkering ports for refueling. The selection of bunkering ports impacts the operating costs of shipping lines due to differences in fuel prices and geographical locations. Moreover, it must factor in ship speed limits to meet loading and unloading schedules. To optimize the shipping route, speeds, and bunkering plan for LNG-fueled tramp ships, we develop an arc-based mixed-integer linear programming model with the objective of minimizing total operation costs. Subsequently, we propose a leg-based formulation based on the predetermined port call orders. Finally, case studies are conducted to demonstrate the effectiveness and efficiency of the models. Experimental results indicate that the bunkering mode with alternative bunkering ports effectively reduces total operating costs without altering the total voyage time, particularly with substantial differences in fuel prices between ports.

Combinatorial Benders decomposition for single machine scheduling in additive manufacturing with two-dimensional packing constraints

This paper addresses a single-machine scheduling problem in additive manufacturing (AM). We focus on the direct metal laser sintering (DMLS) technology of an AM process, where parts can be produced simultaneously in a batch. In this problem, we consider simultaneously the assignment of parts to batches and the packing of parts onto two-dimensional surfaces of the build chamber to minimize the makespan objective. To solve this problem, a mixed integer linear programming model is formulated, and an approximation algorithm is proposed, followed by an exact algorithm based on combinatorial Benders decomposition method with various Benders cuts and acceleration strategies (Algorithm CBD). Finally, we conduct a comprehensive computational study to verify the efficiency of our proposed Algorithm CBD. The computational results show that our proposed Algorithm CBD can effectively solve the test instances with different sizes.

Optimal dispatch of integrated electricity and heating systems considering the quality-quantity regulation of heating systems to promote renewable energy consumption

The integrated electricity and heating system (IEHS) can improve energy efficiency and promote renewable energy consumption. When quality-quantity regulation (QQR) is adopted, namely adjusting hydraulic and thermal conditions of heating system, the increase in operation flexibility is more remarkable. However, present IEHS dispatch models considering QQR overlook hydraulic characteristics of valves and variable frequency pumps resulting in inexecutable dispatch results easily and hindering IEHS’s flexibility potential. Furthermore, loop networks and the access of multiple heat sources in heating systems may lead to flow reversal, but current research adopts a fixed flow direction which suppresses the potential of flow reversal to improve flexibility. In this paper, we propose an IEHS dispatch model considering QQR to promote renewable energy consumption, which considers hydraulic characteristics of valves and variable frequency pumps, and flow reversal. Specifically, we introduce two binary flow direction labels for every branch in heating system model and then the IEHS dispatch model which can deal with flow reversal is established. A sequential solution process combining linear and nonlinear optimization is formulated to overcome the non-convex feature of IEHS dispatch model. Specifically, piecewise linearization and piecewise McCormick relaxation are combined to handle complex nonlinear terms in the dispatch model. Therefore, a mixed integer linear programming model is obtained and solved, of which results are used as initial values for nonlinear optimization. Results in the case study show that operation cost is decreased by 0.97% and renewable power consumption rate is increased from 83.31% to 84.42% after considering valve adjustment. Operation cost is further decreased by 6.06% and renewable power consumption rate is increased to 94.04% after considering flow reversal.

Transport capacity analysis for sharing-corridor metro lines under virtual coupling

In this study, a method is proposed to analyze the capacity improvement ability of using virtual coupling technology to the sharing-corridor metro lines for solving the problem of capacity bottleneck. A mixed integer linear programming model is developed to optimise the train timetable of sharing-corridor lines under the assumption of using the virtual coupling technology, considering the constraints related to train timetabling, virtual coupling technology, and passenger assignment, with the objective to improve the service quality. The model adopts the departure times, arrival times, and whether each train service is planned as virtually coupled, with its adjacent front one or the following one, as decision variables. Furthermore, a method is proposed to evaluate the capacity utilization referring to UIC 406 and considering the feature of virtual coupling technology. The experiments on Shanghai Metro Line 3 and Line 4 are implemented to verify the effectiveness on transport capacity and passenger service quality of the proposed method. The results show that using virtual coupling technology can launch eight more train services during morning peak hours and at most reduce passengers’ waiting time by 73.8 s.

Modelling and optimization for integrated scheduling problem considering spare parts production, batch transportation and equipment operation

Existing production scheduling research has made great effort to integrate multiple production-related actives to achieve efficient product supply, such as the integration of production and transportation, and the integration of production and equipment operation and maintenance (O&M). However, rare studies are executed to investigate the integration of production, transportation and O&M, which may lead to inefficient supply plans. Encouraged by this, we consider a novel integrated scheduling problem, in which two-stage hybrid flow shop scheduling for spare parts manufacturing, transportation scheduling of the third-party logistics (3PL) and operational strategies of complex equipment are considered simultaneously. To tackle it, a mixed-integer linear programming model is constructed to minimize total production costs, minimize transportation costs and maximize operational utility of the equipment. Furthermore, a two-stage memetic algorithm (TSMA) is designed for addressing the problem. It employs a five-layer encoding method for chromosome representation and three well-tailored initialization methods to generate a high-quality initial population. In the first optimization stage, some problem-specific operators, including three crossovers, two mutations, and an entity-oriented local search operator, are proposed to improve its search capability. Two cost-saving strategies devised in the second optimization stage are designed to further optimize the optimal Pareto solutions generated in the previous stage. Extensive experiments demonstrate the superiority of the proposed designs and TSMA in addressing the considered problem. In addition, the necessity of integrating production, transportation and equipment operation is verified through a set of comparison experiments. The study enriches integrated production scheduling theory, and provides methodological support for improving operational utility of complex equipment.

An effective multi-restart iterated greedy algorithm for multi-AGVs dispatching problem in the matrix manufacturing workshop

An excellent automated guided vehicle (AGV) scheduling scheme can effectively improve the productivity of automated manufacturing factories and reduce costs, so the AGV dispatching problem (AGVDP) has become a research hotspot. This paper studies AGVDP with AGV capacity and the latest delivery time to reduce the cost of the total objective consisting of AGV cost, travel cost, and penalty cost. To this end, a mixed-integer linear programming model and a multi-restart iterated greedy (MRIG) algorithm are proposed. According to the characteristics of the problem, an improved nearest neighbor-based heuristic algorithm (INNH) is proposed to generate an initial solution. INNH includes a balanced two-factor selection strategy and a multiple-try insertion strategy. In the MRIG, the destruction stage has been improved to have an adaptive parameter. To enhance the quality of the initial solution and the depth of the evolution, two improved reference local searches are proposed. Furthermore, a multi-restart strategy with a checking mechanism and five restart methods is designed to avoid MRIG falling into the local optimum. The results of sufficient statistical experiments show that the MRIG is obviously superior to the existing algorithms when solving AGVDP.

Application of IoT technology for enhancing the consumer willingness to return E-waste for achieving circular economy: A Lagrangian relaxation approach

Poor management of waste electronic and electrical equipment (e-waste) has resulted in serious challenges to the environment and, consequently, to living organisms. Increasing consumer willingness to return household e-waste is a practical solution for better e-waste management. In this paper, for the first time, a circular supply chain network is structured by applying internet of things (IoT) technology to increase consumer willingness to return household e-waste and to manage the network more effectively. For this purpose, we formulate a mixed-integer linear programming model whose objective is to minimize strategic costs (setup costs and IoT deployment costs) and operational costs (transportation costs, costs associated with IoT, and processing costs in centers), simultaneously. In addition, we developed a heuristic algorithm based on Lagrangian relaxation to solve the proposed MILP model. The performance of the proposed algorithm is evaluated by comparing its results with GAMS results using eight small-sized simulated problems. Furthermore, eight large-size problems are simulated and solved by the proposed algorithm. Finally, the data of an Iranian knowledge-based company is employed to validate the presented mathematical model and algorithm, and the sensitivity analysis process is used to examine the accuracy of the obtained results.