Bi-objective Optimization Approach Research Articles

Environmentally sustainable inventory control for perishable products: A bi-objective reorder-level policy

In order to improve sustainability and transparency in the decision making for inventory control, this paper presents a reorder-level model that considers product perishability. Conversely to most inventory control policies, the classical economic perspective is paired with an environmental one for a stochastic bi-objective optimization approach to reduce inventory logistics emissions and costs. In order to contrast stockouts, lost-sale costing and a service level constraint are integrated for a more comprehensive approach. Results show how the two objectives may be in contrast, and how Pareto-efficient solutions can help to analyze and select the proper trade-offs during decision making. Experiments indicate, for a case-study application, how the most relevant aspects affecting system performance are product shelf life and the possible need of temperature control during storage. Moreover, considering multiple sustainability perspectives in inventory management can help businesses consolidate and future-proof their operations, as well as meet environmental standards and customer demand for greener products and processes.

Solving the waste bin location problem with uncertain waste generation rate: A bi-objective robust optimization approach.

An efficient municipal solid waste (MSW) system is critical to modern cities in order to enhance sustainability and liveability of urban life. With this aim, the planning phase of the MSW system should be carefully addressed by decision makers. However, planning success is dependent on many sources of uncertainty that can affect key parameters of the system, for example, the waste generation rate in an urban area. With this in mind, this article contributes with a robust optimization model to design the network of collection points (i.e. location and storage capacity), which are the first points of contact with the MSW system. A central feature of the model is a bi-objective function that aims at simultaneously minimizing the network costs of collection points and the required collection frequency to gather the accumulated waste (as a proxy of the collection cost). The value of the model is demonstrated by comparing its solutions with those obtained from its deterministic counterpart over a set of realistic instances considering different scenarios defined by different waste generation rates. The results show that the robust model finds competitive solutions in almost all cases investigated. An additional benefit of the model is that it allows the user to explore trade-offs between the two objectives.

Optimizing industrial tunnel kiln operations for ceramic roof tile production: A bi-objective approach

The ceramic firing process constitutes a highly energy-intensive production step that significantly affects the quality and final properties of the ceramic product. This work presents a model-based, bi-objective optimization approach for an industrial-scale tunnel kiln used in ceramic roof tile production, focusing on the exploration of trade-offs between productivity and thermal energy consumption. Initially, sintering kinetics are established based on lab experiments and integrated within a novel physics-based tunnel kiln model, thus allowing sintering evolution to be considered for the derivation of the optimal kiln operation. Two bi-objective optimization studies are then conducted to explore trade-offs under steady-state and transient-state kiln operations, thus generating a set of non-dominated operating policies. The attained Pareto optimal solutions are then evaluated with respect to the values of Specific Energy Consumption (SEC), which is distinctly minimized. This results in optimal SEC values of 0.283 for the steady state and 0.277 kWh/kg for the transient state kiln operation.

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

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

Designing materials by laser powder bed fusion with machine learning-driven bi-objective optimization

To exploit the full industrial potential of additive manufacturing (AM) beyond prototyping, the resource-consuming identification of the optimal processing conditions needs to be minimized. This task becomes more challenging when multiple properties of the part shall be simultaneously optimized. We utilize machine learning (ML) methods in a case study on laser powder bed fusion (LPBF) of a Zr-based glass-forming alloy. Our experiments show that processing parameters affect density and amorphicity opposingly, demonstrating the efficacy of our ML-based approach. We employ multi-objective optimization using Gaussian Process Regression to model and predict target properties and their uncertainties of parts fabricated by LPBF – a widely used metal AM technology. With density and amorphicity as target parameters, we optimize models using the Pareto front facilitated by the Non-Dominated Sorting Genetic Algorithm II. Despite deviations in the amorphicity data, we demonstrate this method to identify the high-performance region of the process parameters and its ability to be iteratively enhanced with additional experimental data. This bi-objective optimization approach provides a robust toolset for navigating LPBF processing. It can be easily extended to a larger set of target properties and transferred to further AM technologies.

Towards a collective opinion generation approach with multiple objectives for evaluating rail transit station accessibility in urban areas

Urban rail transit can alleviate traffic congestion if sufficient ridership is achieved. The accessibility to rail transit stations largely determines public willingness to utilize urban rail transit. The current studies on the accessibility to rail transit stations tend to concentrate solely on individual rail transit lines or stations, neglecting the impact of the external macro-environment. Consequently, the outcomes of these measurements cannot accurately reflect the overall accessibility level of the region, nor do they furnish decision-makers with references for devising plans for rail transit development. This study introduces a novel approach for evaluating the accessibility to urban rail transit stations from a macro-level standpoint, utilizing expert knowledge. The present study conducts an analysis of the impact of political, economic, social, and technological factors on the accessibility to rail transit stations in urban areas. Subsequently, a comprehensive evaluation indicator system is developed based on the aforementioned analysis. Then, experts are summoned to provide their subjective evaluations for every indicator, which are depicted as probability distribution functions. The collective evaluation is derived through the aggregation of individual evaluations utilizing a bi-objective optimization approach that factors in both the collective fairness utility and the confidence level. Finally, the quantile average method is employed to consolidate the collective assessment outcomes of individual indicators, thereby deriving the level of accessibility to rail transit stations in urban areas. We design a small-scale application experiment and attempt to evaluate the accessibility to rail transit stations in Wuchang District, Wuhan with the proposed approach in order to demonstrate the feasibility of the approach.

Integrated System Design for Post-Disaster Management: Multi-Facility, Multi-Period, and Bi-Objective Optimization Approach

Disaster management requires efficient allocation of essential facilities with consideration of various objectives. During the response and recovery phase of disaster management (RRDM), various types of missions occur in multiple periods, and each of them needs different support from facilities. In this study, a bi-objective mathematical model was derived to support multi-period RRDM by optimal allocation of required facilities such as drone stations, shelters, emergency medical facilities, and warehouses according to the mission life cycle. Connectivity between facilities was considered to ensure inter-facility complementarity. For efficient derivation of Pareto solutions, a modified epsilon-constraint algorithm for bi-objective optimization was developed. The algorithm was tested with a realistic disaster simulation scenario using HAZUS 4.0 as a demonstration of the benefits of the proposed approach. With the simulation experiments, the proposed approach was expected to provide efficient operational plans and guidelines to decision makers for the bi-objective optimization problem in RRDM systems. In addition, the consideration of inter-facility connectivity can play an important role in the RRDM, especially for robustness and readiness.

Locating Senior-Friendly Restaurants in a Community: A Bi-Objective Optimization Approach for Enhanced Equality and Convenience

Senior-friendly restaurants are dining establishments that cater specifically to the needs and preferences of older adults in a community. As the physical capabilities of seniors progressively decline and their activity spaces contract over time, determining optimal locations for such restaurants to ensure their accessibility becomes crucial. Nevertheless, the criteria for the location selection of senior-friendly restaurants are multifaceted, necessitating the consideration of both equality and convenience. First, these restaurants often receive government funding, which means that equitable access should be guaranteed for all community residents. Second, the daily activity patterns of seniors should be accounted for. Therefore, these restaurants should be situated in close proximity to other essential facilities utilized by seniors, such as recreational facilities that accommodate routine postmeal activities. Despite the long-standing application of spatial optimization approaches to facility location issues, no existing models directly address the location selection of senior-friendly restaurants. This study introduces a bi-objective optimization model, the Community Senior-Friendly Restaurants Location Problem (CSRLP), designed to determine optimal locations for senior-friendly restaurants, taking into consideration both service coverage and proximity to recreational facilities simultaneously. We formulated the CSRLP as an integer linear programming model. Simulation tests indicate that the CSRLP can be solved both effectively and efficiently. Applying the CSRLP model to two communities in Dongcheng District, Beijing, China, we explored Pareto optimal solutions, facilitating the selection of senior-friendly restaurant locations under diverse scenarios. The results highlight the significant value of spatial optimization in aiding senior-friendly restaurant location planning and underscore key policy implications.

A bi-objective optimization approach for carbon capture and storage supply chain network combining with pricing policies: Economic and social aspects

Carbon capture and storage (CCS) technology and pricing policies are two mitigation strategies that attempt to tackle the carbon emission problem. Nonetheless, the uncertainty of public reaction to CCS infrastructure installation has been noted as a significant issue that may lead to either cancelations, delays, or influence the deployment cost of CCS infrastructure. Although these strategies are solutions to reduce carbon emissions, the entire supply chain itself needs to align with sustainability policy. While some previous studies have addressed mitigation strategies or the combination of social objective and CCS technology, the impact of social objectives on reservoir openness has not been explored. This article contributes to the literature by illustrating the effect of social objectives on reservoir openness and the total cost of the CCS supply chain. Through the development of a two-stage mixed-integer linear programming model, we optimize the supply chain network design. In the first stage, a single-objective model minimizes capture, transportation, and sequestration costs along with CO2 emission costs to the atmosphere, considering various carbon tax prices. In the second stage, a bi-objective model maximizes social acceptance towards CO2 injection wells (reservoirs) to analyze the impact of cultural dimensions. Our findings reveal that maximizing the social objective leads to increased costs compared to the economic optimum, and it significantly influences the openness of reservoirs based on cultural dimensions. Furthermore, we demonstrate that an increase in the CO2 tax enhances the amount of captured carbon and the complexity of the pipeline network in the supply chain. This insight has implications for governments and decision-makers who can encourage industries to adopt CCS technology by setting appropriate carbon tax prices. To validate the model, we apply it to a case study in the European Union cement industry, one of the major carbon emitters among all industries. Our results not only confirm the model's effectiveness but also show its potential for practical application. Overall, our study presents a comprehensive framework for designing a two-stage sustainable supply chain network for CCS technology that optimizes economic and social objectives while considering CO2 pricing.

Synchronization of train timetables in an urban rail network: A bi-objective optimization approach

As urban rail networks in big cities tend to expand, the synchronization of trains has become a key issue for improving the service quality of passengers because most urban rail transit systems in the world involve more than one connected line, and passengers must transfer between these lines. In contrast to most existing studies that focus on a single line, in this study, we focus on synchronized train timetable optimization in an urban rail transit network, considering the dynamic passenger demand with transfers as well as train loading capacity constraints. First, we propose a mixed-integer programming (MIP) formulation for the synchronization of training timetables, in which we consider the optimization of two objectives. The first objective is to minimize the total waiting time of passengers, involving arriving and transfer passengers. Our second objective is a synchronization quality indicator (SQI) with piecewise linear formulation, which we propose to evaluate the transfer convenience of passengers. Subsequently, we propose several linearization techniques to handle the nonlinear constraints in the MIP formulation, and we prove the tightness of our reformulations. To solve large-scale instances more efficiently, we also develop a hybrid adaptive large neighbor search algorithm that is compared with two benchmarks: the commercial solver CPLEX and a metaheuristic. Finally, we focus on a series of real-world instances based on historical data from the Beijing metro network. The results show that our algorithm outperforms both benchmarks, and the synchronized timetable generated by our approach reduces the average waiting time of passengers by 1.5% and improves the connection quality of the Beijing metro by 14.8%.

A Novel Design Concept of Cemented Paste Backfill (CPB) Materials: Biobjective Optimization Approach by Applying an Evolved Random Forest Model.

For cemented paste backfill (CPB), uniaxial compressive strength (UCS) is the key to ensuring the safety of stope construction, and its cost is an important part of the mining cost. However, there are a lack of design methods based on UCS and cost optimization. To address such issues, this study proposes a biobjective optimization approach by applying a novel evolved random forest (RF) model. First, the evolved RF model, based on the beetle search algorithm (BAS), was constructed to predict the UCS of CPB. The consistency between the predicted value and the actual value is high, which proves that the hybrid machine learning model has a good effect on the prediction of the UCS of CPB. Then, considering the linear relationship between the costs and the components of CPB, a mathematical model of the cost is constructed. Finally, based on the weighted sum method, the biobjective optimization process of the UCS and cost of CPB is conducted; the Pareto front optimal solutions of UCS and the cost of CPB can be obtained by the sort of solution set. When the UCS or the cost of CPB is constant, the Pareto front optimal solutions can always have a lower cost or a higher UCS compared with the actual dataset, which proves that the biobjective optimization approach has a good effect.

A hybrid bi-objective optimization approach for joint determination of safety stock and safety time buffers in multi-item single-stage industrial supply chains

In material requirements planning (MRP) systems, safety stock and safety time are two well-known inventory buffering strategies to protect against supply and demand uncertainties. While the role of safety stocks in coping with uncertainty is well studied, safety time has received only scarce attention in the supply chain management literature. Particularly, most previous operations research models have typically considered the use of such inventory buffers in a separate fashion, but not together. Here, we propose a decision support system (DSS) to address the problem of integrating optimal safety stock and safety time decisions at the component level, in multi-supplier multi-item single-stage industrial supply chains under dynamic demands and stochastic lead times. The DSS is based on a hybrid bi-objective optimization approach that simultaneously optimizes upstream inventory holding costs and β-service levels, suggesting multiple non-dominated Pareto-optimal solutions to decision-makers. We further explore a weighted closed-form analytical expression to select a single Pareto-optimal point from a set of non-dominated solutions, thereby enhancing the practical application of the proposed DSS. We describe the implementation of our approach in a major automotive electronics company operating under a myriad of components with dynamic demand, uncertain supply and requirements plans with different degrees of sparsity. We show the potential of our approach to improve β-service levels while minimizing inventory-related costs. The results suggest that, in certain cases, it appears to be more cost-effective to combine safety stock with safety time compared to considering each inventory buffer independently.

Scheduling deferrable electric appliances in smart homes: a bi-objective stochastic optimization approach.

In the last decades, cities have increased the number of activities and services that depends on an efficient and reliable electricity service. In particular, households have had a sustained increase of electricity consumption to perform many residential activities. Thus, providing efficient methods to enhance the decision making processes in demand-side management is crucial for achieving a more sustainable usage of the available resources. In this line of work, this article presents an optimization model to schedule deferrable appliances in households, which simultaneously optimize two conflicting objectives: the minimization of the cost of electricity bill and the maximization of users satisfaction with the consumed energy. Since users satisfaction is based on human preferences, it is subjected to a great variability and, thus, stochastic resolution methods have to be applied to solve the proposed model. In turn, a maximum allowable power consumption value is included as constraint, to account for the maximum power contracted for each household or building. Two different algorithms are proposed: a simulation-optimization approach and a greedy heuristic. Both methods are evaluated over problem instances based on real-world data, accounting for different household types. The obtained results show the competitiveness of the proposed approach, which are able to compute different compromising solutions accounting for the trade-off between these two conflicting optimization criteria in reasonable computing times. The simulation-optimization obtains better solutions, outperforming and dominating the greedy heuristic in all considered scenarios.

A Bi-Objective Optimization Approach for a Parallel Machine Scheduling Problem Minimizing Total Quality Loss and Total Tardiness

A Bi-Objective Optimization Approach for a Parallel Machine Scheduling Problem Minimizing Total Quality Loss and Total Tardiness

A bi-objective optimization approach based on Lp-metric method in broiler production network: a case study

In this work, we analyse the chicken production in a poultry network composed of a set of farms that serves a slaughterhouse in the city of Tlemcen. Each farm has a chicken house dedicated to breeding, and each chicken house has three breeding modes: manual breeding, semi-automatic breeding, and automatic breeding. And each mode consumes an appropriate energy level depending on the degree of automation used, which directly affects the quality of the chicken. The objective of this study is to determine the best energy adaptation within the farm to obtain good quality chickens. The problem of this activity is the choice of the right energy level of breeding, which consumes a minimum energy value, and gives a good quality of chickens. Knowing that the quality improves with the increase of energy, this study serves to develop mathematical modelling of two objectives: minimization of energy consumption and maximization of the chicken quality produced. The two objectives are optimized independently, and then they are joined by adapting the LP-metric method to help the breeders choose the optimal energy level to obtain good quality chickens.

Crop Planning in Synchronized Crop-Demand Scenarios: A Biobjective Optimization Formulation

Crop planning problems have been extensively studied from different perspectives (profit maximization, optimizing available water use, sustainability, etc.). In this paper, a new approach is proposed that considers new forms of customer-producer relationship, involving long-term cooperation agreements where the product volumes are agreed, and the demand is guaranteed in advance. In this context, typical of manufacturing production systems, crop planning must guarantee a given production level on specific dates, thus becoming deterministic in nature. In that context, this paper introduces a lexicographic biobjective optimization approach that, in addition to cost minimization, aims at minimizing the risk of not meeting the agreed demands. The latter is done by maximizing the geographic dispersion of the crops so that weather risk is mitigated. A number of experiments have been carried out to test the proposed approach, showing the high complexity of the solution and opening the door to new solution procedures for a problem that results from interest given to the new type of relationships in the food logistics chain.

Robust Bi-Objective Operating Rooms Scheduling Problem Regarding the Shared Resources

In recent years, many efforts have been made to provide different strategies for enhancing the scheduling and planning of the operating rooms. The efficient planning and scheduling of ORs is a complex task since it has to account for the availability of human resources, medical equipment, and medication required for each surgery but that are often shared between different ORs. This paper proposes a mathematical approach to enhance the management of OR resources. It presents a bi-objective robust optimization approach for scheduling the surgeries in the ORs and recovery room, regarding the uncertainty of the surgery time, uncertainty of hospitalization time in the recovery room, and shared resources. The first objective function aims to minimize the maximum completion time of the surgeries and the second one minimizes the sum of the earliness-tardiness of the surgical operations. The suggested approach utilizes the multi-choice goal programming approach with utility function to solve the proposed model. The proposed approach is applied to a real case in the Shahid Beheshti hospital, Babol, Iran. The obtained results show that the suggested bi-objective robust optimization approach can enhance OR scheduling and should be designed into a decision support system for OR management.

A bi-objective robust optimization approach for the management of infectious wastes with demand uncertainty during a pandemic

The current global COVID-19 pandemic attracts public attention to the management of waste generated by health-care activities. Due to the hazardous nature, infectious waste requires the design of a multi-tiered system to provide cost-efficient and eco-friendly services of waste collection, transportation, treatment, and final disposal. However, the impact of uncertainties has not been well studied in the existing literature. Considering the presence of random waste generation during a pandemic, we aim to answer the following questions: 1) where to locate temporary transfer stations and temporary treatment centers; 2) how to plan collection tours among the small generation nodes and temporary transfer stations; 3) how to plan the direct transportation from large generation nodes to treatment centers; 4) how to transport waste from temporary transfer stations to treatment centers, and 5) how to transport wastes from treatment centers to disposal facilities. The relevant cost and associated risk are respectively formulated and assessed using a scenario-based bi-objective robust approach. The complexity of the resulting mathematical model motivated the adaption and comparison of three multi-objective optimization approaches, including the goal programming method, a lexicographic weighted Tchebycheff approach, and an augmented ϵ-constraint solution technique. A case study based on the real situation in Wuhan, China, during the COVID-19 outbreak is conducted to demonstrate the workability of the proposed model and provide managerial insights for infectious waste management. The computational results show that our proposed model can more than double the demand fulfillment rate at an approximately 40% lower cost when facing a distinctively high increment in the amount of infectious waste.

A Bi-Objective Simulation-Based Optimization Approach for Optimizing Price, Warranty, and Spare Part Production Decisions Under Imperfect Repair

This paper proposes an efficient methodology based on the Monte-Carlo simulation-based bi-objective optimization, to determine base-warranty (BW) and extended warranty (EW) parameters based on the product lifecycle. The first objective, which is from the manufacturer’s perspective, maximizes the profit while the second objective minimizes the expected number of failures that occurred during the out-of-warranty period. The manufacturer can rectify failed products via minimal repair, imperfect repair and perfect repair. The optimization model has decision variables including the product price, BW length, EW length, EW price, product failure rate, imperfect repair level, and spare part production rate in each time interval. The structure of the model admits the design of a hybrid method based on the multi-objective optimization search algorithm, Monte-Carlo simulation and an exact Out-Of-Kilter (OOK) algorithm. The nondominated sorting genetic algorithm (NSGA-II) and the multi-objective particle swarm optimization (MOPSO) algorithm are used as search algorithms. The proposed approach consists of three stages, where in the first stage, product price, BW length, EW length, EW price, product failure rate, imperfect repair level are set by NSGA-II/MOPSO. In the second stage, the number of failed products is calculated by the Monte-Carlo simulation and in the third stage, we show that the spare part inventory control sub problem can be transformed to a minimum cost network flow problem which is optimized by the OOK algorithm to attain a unified solution. A Taguchi approach is used to find the optimum level of parameters. The performance of algorithms is compared based on three different metrics. Results on a real-world problem demonstrate that the NSGA-II-OOK algorithm is more effective than the MOPSO-OOK algorithm. Through a sensitivity analysis, we analyze how various levels of planning horizon can affect Pareto-set which indicates valuable managerial insight.

Energy and spectral efficiency trade-off in OCDMA-PON assisted by non-linear programming methods

Two important metrics for performance evaluation in optical code division multiple access networks (OCDMA) are energy efficiency (EE) and spectral efficiency (SE). Both metrics are investigated in this work through the bi-objective optimization approach by analyzing the trade-off between SE and EE. We first formulate the SE–EE optimization as a bi-objective optimization (BOO) problem with minimum rate requirement constraints. Then, considering the non-convexity of the BOO problem, it is converted into a single-objective optimization (SOO) problem by utilizing weighted sum method. Nonlinear programming methods as sequential quadratic programming method (SQP) and majoration–minimization (MaMi) are applied to solve the BOO problem, with QoS guarantees for the OCDMA networks. Resource efficiency (RE) is able to explore the trade-off between EE and SE in OCDMA networks. The optimization methods were applied and their performance-complexity trade-offs are compared with the exhaustive search (ES) method. Numerical results were performed considering practical and realistic scenarios, including a wide range of nodes, while the solutions obtained by the methods are represented in the Pareto front.