Bi-objective Mixed-integer Programming Model Research Articles

Integrated optimization of transport capacity and train timetabling with time-dependent passenger demand

When facing a surge in passenger demand especially during holidays, dispatchers have to adjust train operation organization for busy high-speed railway corridors. This paper is devoted to optimizing transport capacity considering the capacity pool and flexible train composition with time-dependent passenger demand to generate new timetables for both regular and additional trains. A bi-objective mixed integer programming model is formulated to minimize the waiting time of passengers and operation costs for capacity utilization. A local search technique is hybridized into an elitist heuristic algorithm based on NSGA-II to generate high-quality solutions. Two sets of numerical experiments are carried out based on a small-scale example and real-world data from the Wuhan-Guangzhou high-speed railway corridor to verify the effectiveness of the proposed methodology. The results show that (1) when considering time-dependent passenger demand, the satisfaction rate exceeds 90%; (2) when optimizing transport capacity, satisfaction is guaranteed while bringing reduction in operation costs.

An integrated bi-objective optimization model accounting for the social acceptance of renewable fuel production networks

Renewable liquid fuels produced from biomass, hydrogen, and carbon dioxide play an important role in reaching climate neutrality in the transportation sector. For large-scale deployment, production facilities and corresponding logistics have to be established. However, the implementation of such a large-scale renewable fuel production network requires acceptance by citizens. To gain insights into the structure of efficient and socially accepted renewable fuel production networks, we propose a bi-objective mixed-integer programming model. In addition to an economic objective function, we consider social acceptance as a second objective function. We use results from a conjoint analysis study on the acceptance and preference of renewable fuel production networks, considering the regional topography, facility size, production pathway, and raw material transportation to model social acceptance. We find significant trade-offs between the economic and social acceptance objective. The most favorable solution from a social acceptance perspective is almost twice as expensive as the most efficient economical solution. However, it is possible to strongly increase acceptance at a moderate expense by carefully selecting sites with preferred regional topography.

Iterated-local-search-based chaotic differential evolution algorithm for hybrid-load part feeding scheduling optimization in mixed-model assembly lines

PurposeDriven by sustainable production, mobile robots are introduced as a new clean-energy material handling tool for mixed-model assembly lines (MMALs), which reduces energy consumption and lineside inventory of workstations (LSI). Nevertheless, the previous part feeding scheduling method was designed for conventional material handling tools without considering the flexible spatial layout of the robotic mobile fulfillment system (RMFS). To fill this gap, this paper focuses on a greening mobile robot part feeding scheduling problem with Just-In-Time (JIT) considerations, where the layout and number of pods can be adjusted.Design/methodology/approachA novel hybrid-load pod (HL-pod) and mobile robot are proposed to carry out part feeding tasks between material supermarkets and assembly lines. A bi-objective mixed-integer programming model is formulated to minimize both total energy consumption and LSI, aligning with environmental and sustainable JIT goals. Due to the NP-hard nature of the proposed problem, a chaotic differential evolution algorithm for multi-objective optimization based on iterated local search (CDEMIL) algorithm is presented. The effectiveness of the proposed algorithm is verified by dealing with the HL-pod-based greening part feeding scheduling problem in different problem scales and compared to two benchmark algorithms. Managerial insights analyses are conducted to implement the HL-pod strategy.FindingsThe CDEMIL algorithm's ability to produce Pareto fronts for different problem scales confirms its effectiveness and feasibility. Computational results show that the proposed algorithm outperforms the other two compared algorithms regarding solution quality and convergence speed. Additionally, the results indicate that the HL-pod performs better than adopting a single type of pod.Originality/valueThis study proposes an innovative solution to the scheduling problem for efficient JIT part feeding using RMFS and HL-pods in automobile MMALs. It considers both the layout and number of pods, ensuring a sustainable and environmental-friendly approach to production.

The production scheduling problem employing non-identical parallel machines with due dates considering carbon emissions and multiple types of energy sources

This paper addresses the production scheduling problem with non-identical parallel machines in a high-mix, low-volume production environment with due dates, considering carbon emissions savings and diverse types of energy sources for machine operation. To this end, we present a bi-objective mixed-integer programming model that minimizes both the total production-related cost and the total carbon emissions in the production process to determine the optimal production strategy. For each machine, we consider various types of energy sources with different electricity generation costs and different amounts of carbon emissions. The proposed model is validated with an application to a manufacturer in Ulsan, the industrial capital of the Republic of Korea. Our results showcase the potential use of non-identical parallel machines to minimize the total cost and carbon emissions in green manufacturing. Furthermore, the results identify the trade-off between different energy sources and the total cost under different carbon emissions limits. Generally, as the carbon emissions limit increases, our proposed model tends to replace natural gas with coal to minimize the total cost. Also, we perform sensitivity analyses with respect to the energy price of different types of energy sources combined with nuclear and renewable energy sources. We find that coal provides more stability than natural gas in terms of the total cost, particularly when there are fluctuations in the price for coal and natural gas. Additionally, we determine the optimal combination of energy sources for various carbon emissions limits, aiming to minimize the total cost while simultaneously satisfying all production-related and environmental constraints.

Capital-constrained maintenance scheduling for road networks considering traffic dynamics

Road network maintenance scheduling mainly considers budget limits in the previous studies and largely ignores the capital constraints. This study proposes a bi-objective mixed integer programming model, in which the net present value (NPV) is maximized and the increased total system travel time (ITSTT) due to maintenance activities under the capital constraints is minimized. Since the road network flows cannot reach an equilibrium state overnight due to the variation of network capacity, a link-based day-to-day dynamics model is developed to simulate the transient fluctuation in the traffic flows and calculate the total system travel time of each day. The bi-objective model is solved by the nondominated sorting genetic algorithm-II (NSGA-II) that generates a set of optimal Pareto solutions. The TOPSIS method is then adopted to determine the best compromise solution. Finally, a case study is conducted to demonstrate the effects of key parameters on the values of the two objectives.

Sustainable and Resilient Capacity Expansion Planning for Chemical Processing Industry: A Bi-Objective Approach

According to United Nations reports, the worldwide population is expected to reach around 9.6 billion by 2050. This forecast emphasizes the critical role of energy and raw materials that are needed to meet the tremendous demand for goods. Consequently, firms feel pressured to establish sustainable and resilient strategic plans to acquire new process technologies and expand their capacity on time. These decisions are made at the highest management level, supported by a set of capacity expansion portfolios, to improve their competitiveness, especially in capital-intensive industries such as chemical processing. This paper investigates the sustainable and resilient capacity expansion problem for such industries within a long-term horizon. The main objective is to develop a holistic capacity expansion planning framework that fits the chemical processing industries and can be used to generate resilient scenarios while enhancing their sustainability measures. To this end, a bi-objective mixed-integer programming model was developed to solve the sustainability–resilience–profitability dilemma. The results showed a controversial relationship between the profitability of capacity expansion investments and a company’s commitment to sustainability and resilience. Furthermore, capacity expansion decisions were shown to primarily depend on the importance assigned to maximize profit as a managerial choice. However, there is no clear trend in sustainability preferences based on the sustainability weighting choice.

Automated generation of stacking plans for prefabricated panels transported by A-frame trailers

Prefabrication is a sustainable construction method that improves productivity and reduces environmental footprints. Prefabricated panel is one typical type of components widely used in practice. When designing panel stacking plans for transportation, practitioners should consider numerous practical factors, e.g., panel stability and reshufflings. However, in current practice, stacking plans are made on the basis of planners’ intuition and experience. A scientific method that can yield satisfactory panel stacking plans is thus required. Motivated by this real need, this paper aims to address a practical problem for practitioners: how to stack prefabricated panels transported by A-frame trailers with high stability and little reshuffling. This paper extends the literature by innovatively formulating a bi-objective mixed-integer programming model that incorporates all the aforementioned factors and objectives. A non-dominated sorting genetic algorithm is designed to approximate the Pareto optimal solutions. We conduct extensive numerical experiments to validate the effectiveness, efficiency, and applicability of our proposed model and algorithm. The developed model and algorithm are capable of automatically performing calculations and effectively generating vertical stacking plans of high quality for planners in real-world settings within seconds. Future research may be devoted to the optimization of stacking plans for other types of prefabricated components or the horizontal stacking plans for components transported by flat-bed trailers.

A hybrid collaborative framework for integrated production scheduling and vehicle routing problem with batch manufacturing and soft time windows

This paper studies a new integrated production scheduling and vehicle routing problem where the production of customer orders is performed under a batch manufacturing environment and order deliveries are made by multi-trip heterogeneous vehicles in soft time windows. A bi-objective mixed-integer programming model with maximizing total profits and minimizing total weighted earliness and tardiness has been established. We develop a hybrid collaborative framework to solve this problem, which nests the collaborative mechanism in an optimization mode based on the hybrid algorithm. In the collaborative mechanism, a property on the ideal optimal departure time of the tour is first proposed, based on which an exact strategy is developed to simultaneously coordinate batch manufacturing and tour departure schedules. High-quality integrated solutions are provided by simultaneously making both production scheduling and vehicle routing decisions. Then, in order to get the best integrated solution, we adopt a multi-objective evolutionary algorithm improved by an adaptive large neighborhood search strategy based on the specific problem and coding form to realize the optimization mode. Computational experiments are performed on a dataset containing 30 instances of various scales. The results show that the proposed hybrid collaborative framework performs well in cardinality, convergence, distribution and spread, which is a very competitive method to solve this problem.

A robust optimization approach for platooning of automated ground vehicles in port hinterland corridors

Modern ports face significant challenges as strategic nodes of global supply chains, being responsible for the coordination of inbound and outbound flows at deep-sea and in hinterland transport corridors. Digitization and the adoption of disruptive technologies can help ports to tide over operational challenges. Automated Ground Vehicles (AGVs) are an integral part of operations at many modern ports, especially inside container terminals. With the shift to automated transport outside of the terminal areas, these AGVs may form platoons to establish an efficient port hinterland transport corridor. In this work, we propose a new robust optimization approach to assess the time and cost-efficiency of applying such AGV platoons in a container pickup and delivery problem. We develop a bi-objective mixed-integer programming model, which simultaneously minimizes time and cost elements, and also considers emissions. Each transportation task can be carried out by AGVs or conventional trucks, while the number of available vehicles for each mode is uncertain (as they are used to connect different modalities of container transport). The robust optimization model is based on an ellipsoidal uncertainty set to handle this uncertainty and an augmented epsilon constraint method to obtain Pareto-optimal solutions for this multi-objective problem. The developed framework is evaluated in two case studies: the Port of Rotterdam in The Netherlands and the Port of Valparaíso in Chile, with different traveling distances in corridors to a dry port (200 km) and a pre-terminal (11 km), respectively. The results indicate that the new direct delivery scheme by AGV platoons is significantly more cost- and time-efficient than the benchmark and provides a low-carbon emission transportation mode. While the benefits of decreased dwell times (56% on average) and carbon emissions (on average by 10%) are similar for short and long traveling distances, the savings in cost increase (from 4.9% to 8%) with the increased distance in the Rotterdam case.

Designing a resilient retail supply network for fresh products under disruption risks.

The retail sector supplies the daily fresh products and increasingly plays a key role in the stability and livability of cities. However, public health events such as COVID-19 have caused frequent product shortages in recent years. The risk of fresh product shortages not only causes retailers to lose profits, but also affects the normal life of residents. In this paper, we address the problem of designing a resilient retail supply network for fresh products under the supply disruption risks and propose a bi-objective mixed-integer programming model. This model can help retailers to select suppliers, distribution centers and transportation routes under different scenarios and implement three resilience strategies, namely, priority supply, multiple sourcing and lateral transshipment. We use the ε -constraint method to transform the multi-objective problem into a single objective model and develop a Lagrangian relaxation algorithm to solve the different scale instances. This model is solved for a real-life case of a supermarket to obtain managerial insights. In the case study, this paper shows the set of Pareto fronts with different inventory periods, maximum allowed decay and decay rate. We calculate the expected total cost under targeted disruption scenarios and evaluate the effectiveness of these resilience strategies when implemented concurrently or separately. Our results identify the most critical suppliers and distribution centers that should be fortified. We elaborate that more resilience strategies are not always better and managers need to take appropriate resilience strategies according to their own problems.

Bi-objective speed-scaling robotic cell scheduling with peak power consumption constraint

This article studies the speed-scaling robotic cell scheduling problem with constrained peak power consumption. The objective is to minimize cycle time and peak power consumption simultaneously. First, we formulate a bi-objective mixed integer programming model for the problem and propose a strategy to preprocess overlapping time windows. Then, we analyze the structural properties of the proposed model and develop an iterative $ \varepsilon $-constraint method to generate its complete Pareto front. Numerical experiments demonstrate that the proposed method effectively solves the robotic cell scheduling problem and that appropriate scheduling of speed-scaling machines can make a trade-off between productivity and power consumption.

Bi-objective blood product scheduling under blood shortage and limited supply

Increased blood demand and limited blood supply make blood shortages a significant problem in the blood supply chain, which may cause immeasurable losses. The objective of this paper is to develop the scheduling scheme of blood products during blood shortages, considering limited blood supply. For this purpose, a bi-objective mixed-integer programming model is proposed, in which one objective minimises the maximum blood shortage of hospitals as well as the other one minimises the latest arrival time. To solve this model, a $ \varepsilon $-constraint-based hybrid algorithm called $ \varepsilon $-GA-VNS is presented, which benefits from exploration of the genetic algorithm (GA) and exploitation of the variable neighbourhood search (VNS) approaches. Then, a series of numerical experiments based on Solomon's benchmark were performed to evaluate the proposed model and algorithm. A performance comparison of $ \varepsilon $-GA-VNS and NSGA-II indicated that $ \varepsilon $-GA-VNS was superior to NSGA-II in both efficiency and effectiveness. Finally, sensitivity analyses of the uncertain and stochastic blood supply and demand impart several managerial insights.

A bi-objective hybrid vibration damping optimization model for synchronous flow shop scheduling problems

Flow shop scheduling deals with the determination of the optimal sequence of jobs processing on machines in a fixed order with the main objective consisting of minimizing the completion time of all jobs (makespan). This type of scheduling problem appears in many industrial and production planning applications. This study proposes a new bi-objective mixed-integer programming model for solving the synchronous flow shop scheduling problems with completion time. The objective functions are the total makespan and the sum of tardiness and earliness cost of blocks. At the same time, jobs are moved among machines through a synchronous transportation system with synchronized processing cycles. In each cycle, the existing jobs begin simultaneously, each on one of the machines, and after completion, wait until the last job is completed. Subsequently, all the jobs are moved concurrently to the next machine. Four algorithms, including non-dominated sorting genetic algorithm (NSGA II), multi-objective simulated annealing (MOSA), multi-objective particle swarm optimization (MOPSO), and multi-objective hybrid vibration-damping optimization (MOHVDO), are used to find a near-optimal solution for this NP-hard problem. In particular, the proposed hybrid VDO algorithm is based on the imperialist competitive algorithm (ICA) and the integration of a neighborhood creation technique. MOHVDO and MOSA show the best performance among the other algorithms regarding objective functions and CPU Time, respectively. Thus, the results from running small-scale and medium-scale problems in MOHVDO and MOSA are compared with the solutions obtained from the epsilon-constraint method. In particular, the error percentage of MOHVDO’s objective functions is less than 2% compared to the epsilon-constraint method for all solved problems. Besides the specific results obtained in terms of performance and, hence, practical applicability, the proposed approach fills a considerable gap in the literature. Indeed, even though variants of the aforementioned meta-heuristic algorithms have been largely introduced in multi-objective environments, a simultaneous implementation of these algorithms as well as a compared study of their performance when solving flow shop scheduling problems has been so far overlooked.

Robots’ picking efficiency and pickers’ energy expenditure: the item storage assignment policy in robotic mobile fulfillment system

The item storage assignment problem (ISAP) in a robotic mobile fulfillment system (RMFS) is addressed in the paper. Recently, most ISAP studies have concentrated on improving the robots’ picking efficiency while ignoring the fact that RMFS is a human-robot coordinated system. In ISAP, we also need to take human factors into account. This research investigates ISAP by considering both the robots’ picking efficiency and the pickers’ energy expenditure. The bi-objective mixed-integer programming model is developed to maximize the items’ similarities in the pods and minimize the pickers’ energy expenditure. The improved knee point-driven evolution algorithm (IKnEA) is proposed to solve the model. Experimental results demonstrate that IKnEA has superior distribution and convergence speed than NSGA-II and KnEA. IKnEA’s hypervolume (HV) indicator operates better than NSGA-II and KnEA in various warehouse scales. More layers of pods contribute to less travel distance for robots but more energy expenditure for pickers. Five Pareto solutions are presented to assist the decision-makers in selecting the optimal ISAP solutions given various preferences.

A clustering-based extended genetic algorithm for the multidepot vehicle routing problem with time windows and three-dimensional loading constraints

Since the multidepot vehicle routing problem with time windows and three-dimensional loading constraints (MDVRPTW-TDLC) is a multiconstraint and combinatorial optimization problem, this study proposes a resource sharing scheme on the basis of customer clustering to achieve a balance of spatial resource spatial distributions, thereby reducing the operating costs in a collaborative multidepot logistics network. Moreover, this study proposes a vehicle compartment partition strategy based on cargo characteristics such as type and sizes to increase vehicle loading rates, after which the proposed MDVRPTW-TDLC is formulated as a bi-objective mixed-integer programming model to minimize the total operating costs while maximizing the average loading rate of vehicles. Subsequently, a two-stage hybrid algorithm combining a three-dimensional (3D) k-harmonic means clustering algorithm and extended nondominated sorting genetic algorithm-II (ENSGA-II) is developed to find the Pareto optimal solutions and solve the MDVRPTW-TDLC optimization model, followed by an introduction of the 3D k-harmonic means clustering algorithm to cluster customers, thereby reducing computational complexity. The proposed ENSGA-II, integrating the improved Clarke–Wright savings algorithm and NSGA-II is then used to obtain the final optimal solutions, followed by the application of a selective exchange mechanism between the clustering algorithm and ENSGA-II to enhance the global and local optimization capability, enabling fast and efficient computation of optimal solutions. Based on our investigations revealed through an algorithm comparison using the multiobjective harmony search algorithm, multiobjective evolution algorithm, multiobjective particle swarm optimization, monarch butterfly optimization, Runge Kutta optimizer, and Harris hawks optimization, ENSGA-II demonstrates better performance in reaching high-quality objective function values. Finally, a real-world case study of Chongqing City, China is employed to verify the efficiency of the proposed model and optimization algorithm, after which a comparison of the optimization results among different vehicle compartment partition strategies demonstrates the efficiency of the proposed method. We also discuss 16 scenarios with and without the vehicle compartment partition strategy with computational results showing an improved vehicle loading rate and reduced logistics operating costs with the adopted vehicle compartment partition strategy. Therefore, our results confirm that the proposed MDVRPTW-TDLC can facilitate the sustainable development of logistics operations, and providing decision support for constructing intelligent logistics systems smart cities.

A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy

Motivated by the call of the International Maritime Organization to meet the emission targets of 2030, this study considers two important practical aspects of quay crane scheduling: efficiency and energy consumption. More precisely, we introduce the bi-objective quay crane scheduling problem where the objective is to minimize the vessel’s completion time and the crane’s energy consumption. This is done by formulating a bi-objective mixed-integer programming model. A branch-and-bound algorithm was developed as the exact solution approach to find the full set of Pareto-optimal solutions. We consider (i) various lower bounds for both objectives, (ii) specific upper bounds, (iii) additional branching criteria, and (iv) fathoming criteria to detect Pareto-optimal solutions. Numerical experiments on benchmark instances show that the branch-and-bound algorithm can efficiently solve small- and medium-sized problems.

Sustainable Urban Logistics Distribution Network Planning with Carbon Tax

Global warming caused by excessive carbon dioxide emissions is threatening the sustainable development of human society. Considering the upcoming carbon tax policy in China, this paper studies the planning of dual-level urban logistics distribution network in the context of carbon emissions. Based on reasonable assumptions, a bi-objective mixed-integer programming model considering logistics operating costs and carbon emission costs is constructed. Given the problem size, an improved genetic algorithm is designed. Based on a numerical example, the optimization results of the improved genetic algorithm and the GLPK optimization suite are compared to verify the effectiveness of the proposed model and algorithm. Under different carbon tax rates, by adjusting the logistics distribution network along, the logistics operators can achieve a maximum cost savings of 19.4%, while carbon emissions can be reduced by up to 47.8%. The major conclusions include: carbon tax will bring about huge cost burdens for urban logistics operators; the reconfiguration of urban logistics network is a powerful measure to reduce carbon emission with the least extra costs; with problem size rises quickly, the intelligent algorithm as proposed in this article can always find near optimal solutions with acceptable time costs.

A bi-objective aircraft maintenance routing problem based on flying hours to efficient use of available fleet

PurposeThe proposed model aims to consider the flying hours as a criterion to initiate maintenance operation. Based on this condition, aircraft must be checked before flying hours threshold is met. After receiving maintenance service, the model ignores previous flying hours and the aircraft can keep on flying until the threshold value is reached again. Moreover, the model considers aircraft age and efficiency to assign them to flights.Design/methodology/approachThe aircraft maintenance routing problem (AMRP), as one of the most important problems in the aviation industry, determines the optimal route for each aircraft along with meeting maintenance requirements. This paper presents a bi-objective mixed-integer programming model for AMRP in which several criteria such as aircraft efficiency and ferrying flights are considered.FindingsAs the solution approaches, epsilon-constraint method and a non-dominated sorting genetic algorithm (NSGA-II), including a new initializing algorithm, are used. To verify the efficiency of NSGA-II, 31 test problems in different scales are solved using NSGA-II and GAMS. The results show that the optimality gap in NSGA-II is less than 0.06%. Finally, the model was solved based on real data of American Eagle Airlines extracted from Kaggle datasets.Originality/valueThe authors confirm that it is an original paper, has not been published elsewhere and is not currently under consideration of any other journal.

A bi-objective optimization model for the medical supplies' simultaneous pickup and delivery with drones

In the COVID-19 pandemic, it is essential to transport medical supplies to specific locations accurately, safely, and promptly on time. The application of drones for medical supplies delivery can break ground traffic restrictions, shorten delivery time, and achieve the goal of contactless delivery to reduce the likelihood of contacting COVID-19 patients. However, the existing optimization model for drone delivery is cannot meet the requirements of medical supplies delivery in public health emergencies. Therefore, this paper proposes a bi-objective mixed integer programming model for the multi-trip drone location routing problem, which allows simultaneous pick-up and delivery, and shorten the time to deliver medical supplies in the right place. Then, a modified NSGA-II (Non-dominated Sorting Genetic Algorithm II) which includes double-layer coding, is designed to solve the model. This paper also conducts multiple sets of data experiments to verify the performance of modified NSGA-II. Comparing with separate pickup and delivery modes, this study demonstrates that the proposed optimization model with simultaneous pickup and delivery mode achieves a shorter time, is safer, and saves more resources. Finally, the sensitivity analysis is conducted by changing some parameters, and providing some reference suggestions for medical supplies delivery management via drones.

A new vocation queuing model to optimize truck appointments and yard handling-equipment use in dual transactions systems of container terminals

In a dual transaction at a marine terminal, an external truck drops off one container and picks up another on a single trip. To ensure a successful dual transaction operation and smooth external truck arrivals, a bi-objective mixed integer programming model is developed that optimizes the allocation of appointment quotas simultaneously with the deployment of (yard) cargo handling equipment. Our model addresses the challenges posed by the different types of truck movement in the terminal, i.e., delivery, pickup, and dual transaction. These require different handling equipment, various deadlines, and multiple priorities. To estimate the queuing length of external trucks in single or dual transactions (as well as that of internal trucks), a novel three-level vocation queuing model is set up. For the bi-objectives optimization, we propose a revised non-dominated genetic algorithm to obtain the approximate optimal solution. Experimental results prove the efficiency and effectiveness of the method. It shows that the newly built vocation queuing model can estimate the prioritized queuing process more effectively in three respects: a) the 3-level queuing; b) discrete truck arrivals in the queuing system; c) non-interruption of servers. Our quota optimization design improves the model’s applicability to real cases, especially in the case of dual transactions. It is demonstrated that the method proposed in the paper could help terminal operators allocate quotas and simultaneously match the capacity of yard handling, thus improving truck services and terminal profitability.