Bi-objective Mixed Integer Linear Programming Research Articles

A novel bi-objective model for sustainable and efficient airport logistics management: A case study on Copenhagen airport

Due to the growing volume of air transportation and the scarcity of airport resources, aviation planners are paying more attention to the efficiency of airport resource management. Optimizing the assignment and scheduling of ground facilities plays an important role in reducing ground congestion, flight delays, and passenger dissatisfaction. To prevent any collisions among aircraft on the apron, taxi network, and runways, safety considerations should be strictly followed by traffic controllers. Minimizing taxi time is another matter of importance in airport logistics management that helps mitigate environmental concerns (e.g., fuel consumption, tire abrasion, and noise pollution). In this study, a bi-objective mixed-integer linear programming model is developed to optimize the ground resource scheduling problem, taking into account the challenges of gate assignment, taxi planning, and runway scheduling. The model is developed in a way that includes safety and sustainability considerations. The validation of the proposed model is investigated through several examples based on Copenhagen airport using the augmented ε-constraint method. Since the simultaneous scheduling of multiple resources is an NP-hard problem, two multi-objective metaheuristic algorithms are employed to deal with the large-scale problems. The performance of the algorithms is then compared in terms of coverage and convergence rates. Additionally, the results are discussed in detail to provide managerial implications for airport authorities.

A new mathematical model and meta-heuristic algorithm for order batching, depot selection, and assignment problem with multiple depots and pickers

The ‘order picking problem’ involves the efficient and organized retrieval of items from shelves to fulfill customer orders. In this study, we consider a new configuration of warehouse system with multiple pickers and depots (m-pickers & n-depots) for manually operated ‘picker-to-parts’ warehouses. The efficiency of the process is measured based on two metrics: i- total order picking distance of each picker ii- total number of pickers assigned to each of depots. The handled problem is called as ‘Order Batching, Depot Selection and Assignment Problem with Multiple Depots and Multiple Pickers (OBDSAPMDMP)11OBDSAPMDMP = Order Batching, Depot Selection, and Assignment Problem with Multiple Depots and Multiple Pickers.’. To solve this complex problem, a new bi-objective Mixed-Integer Linear Programming (MILP) formulation for small-sized problems and a meta-heuristic called ‘Dependent Harmony Search (DHS)22DHS = Dependent Harmony Search.’ for large-sized problems are proposed. The performance of DHS algorithm is evaluated by comparing the optimal results attained by MILP model. For the problem size of 10 orders, the average gap (%) in distance between the solution of DHS and MILP is 4.22%, although in some experiments DHS can find the optimal solution in a very short time. Also, in related analysis, it is seen that constructing multiple depots instead of one left-most located depot decreases total order picking distance by 7.11% on average.

Design of a reverse logistics network for medical waste considering location and routing decisions

Medical waste generated in healthcare facilities is categorized as hazardous due to its infectious, toxic, or radioactive properties, posing substantial risks to human health and the environment. This research proposes a bi-objective Mixed-Integer Linear Programming model for designing reverse logistics networks that enable both economical and safe medical waste management. Said model determines optimal quantity, depot locations, and routes for transporting waste from its generating points (hospitals) to the treatment and disposal sites (depots).This research addresses a bi-objective location routing problem, with multiple depots, time windows, capacity constraints, and variated waste types, across a multi-period horizon. It is innovative because no previous works have successfully dealt with such a combination of pragmatic features. The Location Routing Problem is an already well-known NP-Hard problem, with the additional aforementioned features further adding to its complexity. Thus, a genetic algorithm to solve large-sized realistic instances within reasonable computing times had been developed.Numerical experiments considered 20 random instances contrasting exact and approximate solution approaches. Also, a medical waste collection case study of a public hospital network in Atlántico Department, Colombia, delivering a Pareto frontier solution set, was introduced. The results demonstrated the efficacy of the proposed genetic algorithm in successfully addressing small instances of the problem, delivering outcomes comparable to the Mixed-Integer Linear Programming model. Furthermore, it yields good-quality solutions in a reduced computational time for larger instances deemed unfeasible for the Mixed-Integer Linear Programming model.This article contributes to both scientific literature and practitioners by presenting a decision-making tool designed to address the medical waste reverse logistics challenge under realistic scenarios. It approaches the issue from a bi-objective standpoint, jointly considering economic factors and biomedical safety. Additionally, the article introduces realistic and pertinent assumptions that have not been explored in previous literature.

Designing a Sustainable Water Supply Strategy through Biobjective Mixed-Integer Linear Programming: A Case Study on Gaza

Designing a Sustainable Water Supply Strategy through Biobjective Mixed-Integer Linear Programming: A Case Study on Gaza

A new approach for reliability modeling in green closed-loop supply chain design under post-pandemic conditions: A case study

Climate change, pandemics, and economic crises have created complex challenges for supply chains. Managing such situations requires the development of reliable decision-making frameworks. In this paper, a multi-level, multi-product, and multi-period closed-loop supply chain is studied with environmental considerations. A bi-objective mixed-integer linear programming model is presented for facility location, flow allocation, and transportation mode determination. The objectives of the model are to minimize the total cost and maximize the reliability of suppliers to meet the needs of factories. In the area of reliability engineering, a new approach is defined for modeling the probability of supplier availability considering catastrophic failures caused by pandemics, economic sanctions, and other failure modes. Furthermore, the decision-maker can handle the emission of greenhouse gases by an upper-bound constraint. In order to face the simultaneous uncertainty of demand and the maximum CO2 emission allowed, a scenario-based two-stage stochastic programming approach is proposed. The improved version of the augmented ε-constraint method, known as AUGMECON2, is used to solve the proposed model. The efficiency of the model and the proposed solution approach are investigated through a real-world case study of a battery manufacturing company in Iran.

A Bi-objective location-routing model for the healthcare waste management in the era of logistics 4.0 under uncertainty

The purpose of this study is to apply Industry 4.0-based technologies to improve the management of infectious healthcare waste considering location-routing problem and population risk under uncertainty. To achieve this, a decision support system is developed and implemented utilizing a bi-objective mixed-integer linear programming (MILP) model. The bi-objective MILP model improves the performance of the healthcare waste management by applying Industry 4.0 technologies, including electric autonomous vehicles, information sharing system, internet of things (IoT), Global Navigation Satellite System (GNSS), and RFID-tagged waste bags. We develop a multi-objective solution approach by integrating the lexicographic and TH methods. The validity of the model has been established through its implementation in seven hospitals in the city of Karaj, Iran. The results denoted significant improvements in waste collection efficiency, route optimization, and the reduction of contamination risks.

Strategic flood impact mitigation in developing countries’ urban road networks: Application to Hanoi

Due to climate change, the frequency and scale of flood events worldwide are increasing dramatically. Flood impacts are especially acute in developing countries, where they often revert years of progress in sustainable development and poverty reduction. This paper introduces an optimization-based decision support tool for selecting cost-efficient flood mitigation investments in developing countries’ urban areas. The core of the tool is a scenario-based, multi-period, bi-objective Mixed Integer Linear Programming model which minimizes infrastructure damage and traffic congestion in urban road networks. The tool was developed in collaboration with Vietnamese stakeholders (e.g., local communities and government authorities), and integrates data and inputs from other disciplines, including social science, transport economics, climatology and hydrology. A metaheuristic, combining a Greedy Randomized Adaptive Search Procedure with a Variable Neighborhood Descent algorithm, is developed to solve large scale problem instances. An extensive computational campaign on randomly generated instances demonstrates the efficiency of the metaheuristic in solving realistic problems with hundreds of interdependent flood mitigation interventions. Finally, the applicability of the interdisciplinary approach is demonstrated on a real case study to generate a 20-year plan of mitigation investments for the urban area of Hanoi. Policy implications and impacts of the study are also discussed.

A novel adjusted real-time decision-making for dynamic distribution in the grocery supply chain

PurposeThe current research has developed a novel method to update the decisions regarding real-time data, named the dynamic adjusted real-time decision-making (DARDEM), for updating the decisions of a grocery supply chain that avoids both frequent modifications of decisions and apathy. The DARDEM method is an integration of unsupervised machine learning and mathematical modeling. This study aims to propose a dynamic proposed a dynamic distribution structure and developed a bi-objective mixed-integer linear program to make distribution decisions along with supplier selection in the supply chain.Design/methodology/approachThe constantly changing environment of the grocery supply chains shows the necessity for dynamic distribution systems. In addition, new disruptive technologies of Industry 4.0, such as the Internet of Things, provide real-time data availability. Under such conditions, updating decisions has a crucial impact on the continued success of the supply chains. Optimization models have traditionally relied on estimated average input parameters, making it challenging to incorporate real-time data into their framework.FindingsThe proposed dynamic distribution and DARDEM method are studied in an e-grocery supply chain to minimize the total cost and complexity of the supply chain simultaneously. The proposed dynamic structure outperforms traditional distribution structures in a grocery supply chain, particularly when there is higher demand dispersion. The study showed that the DARDEM solution, the online solution, achieved an average difference of 1.54% compared to the offline solution, the optimal solution obtained in the presence of complete information. Moreover, the proposed method reduced the number of changes in downstream and upstream decisions by 30.32% and 40%, respectively, compared to the shortsighted approach.Originality/valueIntroducing a dynamic distribution structure in the supply chain that can effectively manage the challenges posed by real-time demand data, providing a balance between distribution stability and flexibility. The research develops a bi-objective mixed-integer linear program to make distribution decisions and supplier selections in the supply chain simultaneously. This model helps minimize the total cost and complexity of the e-grocery supply chain, providing valuable insights into decision-making processes. Developing a novel method to determine the status of the supply chain and online decision-making in the supply chain based on real-time data, enhancing the adaptability of the system to changing conditions. Implementing and analyzing the proposed MILP model and the developed real-time decision-making method in a case study in a grocery supply chain.

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.

A scenario-based game theory integrating with a location-allocation-routing problem in a pre- and post-disaster humanitarian logistics network under uncertainty

PurposePre-positioning and distributing relief items are important parts of disaster management as it simultaneously considers activities from both pre- and post-disaster stages. This study aims to address this problem with a novel mathematical model.Design/methodology/approachIn this research, a bi-objective mixed-integer linear programming model is developed to tackle pre-positioning and distributing relief items, and it is formulated as an integrated location-allocation-routing problem with uncertain parameters. The humanitarian supply chain consists of relief facilities (RFs) and demand points (DPs). Perishable and imperishable relief commodities (RCs), different types of vehicles, different transportation modes, a time window for delivering perishable commodities and the occurrence of unmet demand are considered. A scenario-based game theory is applied for purchasing RCs from different suppliers and an integrated best-worst method-technique for order of preference by similarity to ideal solution technique is implemented to determine the importance of DPs. The proposed model is used to solve several random test problems for verification, and to validate the model, Iran’s flood in 2019 is investigated as a case study for which useful managerial insights are provided.FindingsManagers can effectively adjust their preferences towards response time and total cost of the network and use sensitivity analysis results in their decisions.Originality/valueThe model locates RFs, allocates DPs to RFs in the pre-disaster stage, and determines the routing of RCs from RFs to DPs in the post-disaster stage with respect to minimizing total costs and response time of the humanitarian logistics network.

Efficient Humanitarian Logistics: Multi-Commodity Location–Inventory Model Incorporating Demand Probability and Consumption Coefficients

Background: A logistics network plan could be a major key issue due to its effect on supply chain effectiveness and responsiveness. This study aims to investigate the inventory location in the humanitarian logistics response stage using a three-level logistics network to integrate location–allocation problems such as warehouse location and shelter allocation to each facility, and then determine the inventory level in each warehouse. Methods: In this research, the center and its distribution, as well as the reduction in service-level costs due to inventory deficit, have been considered to increase the level of shelter services. In order to investigate the network, in this study, bi-objective mixed-integer linear programming (BOMILP) is presented. Results: The first objective is to reduce location costs and inventory costs that take into account probable demand, consumption factors, and transportation costs, and the second objective is to raise the level of services offered to victims in the model. The software programs GAMS win32, 25.1.2 and MATLAB have been utilized with numerical examples in various dimensions. Conclusions: To maximize the efficiency and quality of the service, first, the model was numerically solved, and then the location where the most commodities could be transported at the lowest possible cost was identified.

Logic-based Benders decomposition for bi-objective parallel machine selection and job scheduling with release dates and resource consumption

This work addresses a new bi-objective parallel machine selection and job scheduling problem with release dates and resource consumption. It consists in optimally selecting subcontractors (machines) from a set of geographically dispersed locations and scheduling the orders (jobs) to the selected subcontractors for processing while meeting the order release dates and resource consumption restrictions, so as to simultaneously minimize the maximum completion time, i.e., the makespan, and the total cost including machine usage cost and resource consumption cost. The problem is first formulated into a bi-objective mixed-integer linear program based on linear ordering (LO-MILP), and then valid inequalities are explored based on property analysis. To solve it, an ɛ-constraint method based on LO-MILP (ɛ-LO-MILP) is first proposed. To more efficiently solve it, we also develop a tailored logic-based Benders decomposition combined with ɛ-constraint method (ɛ-LBBD) where a novel method to obtain a tight lower bound of the identical parallel machine with machine-dependent release dates and some problem-specific cuts are proposed. Numerical experiments on an illustrative example are conducted to show the applicability of the model and algorithm and intuitively reveal the trade-off between production efficiency and cost. Experimental results on 200 instances with up to 100 orders demonstrate that ɛ-LBBD can reduce the computation time by about 28.92% compared to ɛ-LO-MILP and yields better Pareto solutions than ɛ-LO-MILP and the well-known non-dominated sorted genetic algorithm II do.

Optimizing of the Convertibility of Reconfigurable Manufacturing Systems

One of the most topical issues of sustainable development is extending the life cycle of production systems. Reconfigurable manufacturing system (RMS) aims to adapt efficiently to the rapidly changing market. One lever to extend the life cycle of RMS is the ability to quickly adapt to a new product (called convertibility). In this article, we present a model for the design of RMS, optimizing both its convertibility to prolongate its life cycle, and its cost to remain competitive. The convertibility is assessed on three axes: the choice of machines, the choice of transportation systems, and the physical configuration of the machines in the plant and their connection. We formalize this problem and model it by a bi-objective mixed-integer linear program. We illustrate our approach on an example.

Grid-based artificial bee colony algorithm for multi-objective job shop scheduling with manual loading and unloading tasks

This paper investigates a multi-objective job shop scheduling problem with manual loading and unloading tasks (MOJSSPLU) aiming to minimize makespan and total workload simultaneously. Taking human factors into consideration achieves a better balance between production efficiency and resource utilization. To address this problem, we first establish a bi-objective mixed-integer linear programming (MILP) model. Afterward, we combine the artificial bee colony algorithm with the grid technique to develop a grid-based artificial bee colony algorithm (GABC) for solving MOJSSPLU. The algorithm uses a decomposition approach with the earliest-shortest dispatching rule to reduce the complexity of MOJSSPLU. A grid coordinate system is constructed to divide the objective space into cells, facilitating individuals’ location and evaluation in the decision space. Moreover, we focus on improving the cooperation between the employed and onlooker bees and design a mathematical formula based on priority weights to generate onlooker bees to maximize information utilization and improve the exploration and exploitation capabilities of the algorithm. To ensure that the most promising individuals are retained and protected from being eliminated during the evolutionary, we propose an elitist non-dominated solutions reservation strategy for improving the diversity of the population. We further propose a dynamic adjustment of the grid-division method that focuses on improving the exploitation capacity of the algorithm in the objective space to enhance the diversity and convergence of the population. To test the performance of the GABC algorithm, we compare it to the MILP approach and other algorithms using modified benchmark instances. Furthermore, we conduct the Friedman and Wilcoxon nonparametric tests to validate the comparison results among the different algorithms. The computational results demonstrate that the algorithm GABC is efficient.

Optimizing worker productivity and the exposure to hand-arm vibration: a skill-based job rotation model

ABSTRACT Productivity and concerns regarding the well-being of workers exposed to vibrations stand as significant topics within labor-intensive sectors. In particular, this study contributes to the existing research by analyzing the problem with linkages among worker skill level, production rates, and vibration exposure. A bi-objective mixed integer linear programming model was employed to optimize both productivity and the exposure to hand-arm vibration in the manufacturing workplace. A sensitivity analysis was carried out to examine the impact of key parameters on the trade-off between productivity and vibration exposure. The results demonstrate the model’s effectiveness in determining the best job rotation schedules by achieving optimal productivity and vibration exposure for low and medium problem sizes. Moreover, the numerical case study points out that strengthening the workforce by adding more proficient skilled workers can maintain a good level of productivity with a decreased likelihood of excessive vibration exposure.

Avoiding sudden maritime risk: A new variable speed route planning model by integrating Spatio-temporal dimension

Variable speed route planning is important for ships to avoid large-scale and sudden risk. However, in the face of massive amounts of grid data, current algorithms are still unable to establish a mathematical model to effectively avoid such risk in a variable speed manner. Therefore, this paper proposes a variable speed maritime route planning model integrating spatial and temporal considerations. First, in the temporal dimension, a bi-objective mixed-integer linear programming model is developed considering the minimization of risk and residual action power, and selection and mutation operators in the genetic algorithm are improved to solve the programming model. Second, a segment parallel A*(SPA*) method is proposed to improve spatial planning capacity. SPA* successfully reduces runtime by designing a parallel computing structure and adaptive heuristic function to simultaneously handle several segments of the path considering variable speed and reduce the expansion of useless grids. Three rounds of simulation experiments are conducted on small and large datasets with sudden and continuous risk scenarios in the vicinity of the South China Sea and Indonesian Throughflow, respectively. These experiments involve comparative analyses of our algorithm with the uniform speed scheme and with three conventional algorithms. The results show that in the face of both sudden and continuous risks, the path of our model outperforms the uniform speed scheme in all cases, takes an average of only 13.11 s to plan a route on the large dataset and is more compliant with the norms of the International Maritime Organization (IMO). Numerically, it is approximately 6 times and 7 times lower than the best performing of the remaining algorithms in terms of runtime and the rate of violating IMO.

Timetable Rescheduling Using Skip-Stop Strategy for Sustainable Urban Rail Transit

Unanticipated events inevitably occur in daily urban rail transit operations, disturbing the scheduled timetable. Despite the mild delay, the busy operation system probably tends to worsen a larger disturbance and even lead to a knock-on disruption if no rescheduling is timely carried out. We propose a bi-objective mixed-integer linear programming model (MILP) that employs the skip-stop operation strategy to eliminate unscheduled delays. This model addresses two distinct, yet interconnected objectives. Firstly, it aims to minimize the difference between the plan and the actual operation. Secondly, it strives to minimize the number of left-behind passengers. In order to resolve this MILP problem, we devised a Pareto-based genetic algorithm (GA). Based on the case study, we certify the superior effectiveness with comparisons to the whale optimization algorithm and the epsilon constraint method. The outcomes affirm that our model has the potential to reduce the total delay time of the line by 44.52% at most compared with the traditional all-stop running adjustment model. The optimal scheme saved 6.08% of the total costs based on a trade-off between operators’ interests and passenger satisfaction.

Planning for pharma supply chain under uncertainty considering inventory optimization

In this paper, a bi-objective mixed-integer linear programming model is constructed to manage the pharmaceutical supply chain of a hospital. The proposed model aims to concurrently reduce the overall cost of obtaining drugs from several vendors and choose the best suitable source. The suggested model takes into account supplier distance, inventory management, and multi-product and multi-period. The major assumptions of the proposed model are product storage for future periods of decreased demand and supplier capacity. The results indicate that the ideal approach can minimize hospital supply and pharmaceutical planning expenses. The Best-Worst and TOPSIS methods determine which pharmaceutical supplier should be selected for future orders. The suggested model identifies human resource capability as an essential factor that might significantly affect the system’s total cost. The results of applying the model and the sensitivity analysis validate the efficacy and validity of the suggested mathematical model and solution strategy.

A robust chance-constrained programming approach for a bi-objective pre-emptive multi-mode resource-constrained project scheduling problem with time crashing

The presented study proposes a novel bi-objective mixed integer linear programming (MILP) framework for the multi-mode resource-constrained project scheduling problem (MRCPSP) with pre-emptive and non-preemptive activities splitting under uncertain conditions. Minimising the project makespan and resource costs are the considered objectives. Renewable and non-renewable resources along with different modes are taken into account for activities implementation. Additionally, some activities can be crashed by consuming additional renewable and non-renewable resources. Model uncertainty is efficiently addressed by utilising a fuzzy chance constrained programming (CPP) method as well as extending two robust possibilistic programming models. The capability of the presented mathematical framework is validated using problem instances from PSPLIB (j10, j14, j20, and j30) and MMLIB (MM50 and MM100). Finally, a detailed computational comparison is presented to assess the performance of the two robust possibilistic programming models.

A new fuzzy bi-objective mixed-integer linear programming for designing a medical waste management network in the Coronavirus epidemic: a case study

ABSTRACT The COVID-19 pandemic has increased medical assistance and service demand, necessitating the development of a comprehensive model for managing medical waste networks. Despite extensive research, there is a lack of models examining infectious and hazardous waste simultaneously. This paper presents a multi-layered bi-objective mixed-integer linear program model, dividing infectious and non-infectious waste into different categories. The model consists of several stages for safe recycling of medical waste. Fuzzy programming and an augmented-constraint approach are employed to tackle uncertainty in parameters. A real case study from Tehran is examined, and numerical and computational results are provided to prove the model’s efficiency. The results indicate that insufficient disposal centers may require increasing their capacity.