Bi-objective Model Research Articles

Searching for alternatives to the closest targets: Identifying new directions for improvement while controlling additional efforts

Setting the closest targets is an appropriate approach for planning. Closest targets minimize the gap between actual performances and best practices, so they are the ones that require the least effort from organizations for their achievement. However, this paper shows that, in practice, we can find alternative targets, which do not require significant additional efforts (with respect to those involved in the achievement of the closest ones) and define directions for improvement that might be more aligned with management. For this reason, we propose here to complement that approach with the search of alternative targets controlling additional efforts. In order to do so, a search algorithm based on some bi-objective Data Envelopment Analysis benchmarking models is developed, which allows us to explore the strong efficient frontier of the production possibility set while keeping the distance within some limits. Decision making is the core of planning, and involves the selection of a future course of action from alternatives for the purpose of improving performance. The proposed approach is thus consistent with those principles of planning, as it relies on the availability of alternatives, so that decision makers can make a choice through an ex post evaluation of potential ways for improvement.

A bi-objective supplier location, supplier selection and order allocation problem with green constraints: scenario-based approach

In this study, There is a mixed-integer nonlinear program (MINLP) for a two-echelon supply chain that focuses on supplier location, supplier selection and order allocation with green constraints. This bi-objective model is designed and modeled with the aim of coordinating inventory and transportation among suppliers and warehouses and tries to simultaneously meet the targets of minimizing total costs and carbon dioxide emissions of polluting gas in transportation. Since some of the important parameters in this model are considered uncertain, the scenario-based analysis is proposed to deal with uncertainty. Thirty numerical examples with different values and various sizes are solved by applying two methods of MODM, LP metrics, and Multi-choice goal programming with utility functions (MCGP-U) and their results are compared with one of the soft computing methods, Genetic algorithm. TOPSIS, Coefficient of Variation (CV) and One-way analysis of variance (ANOVA) methods are employed for the comprehensive comparison of these numerical examples. Finally, the sensitivity analysis method and Tornado diagram are applied to analyze the effect of variations of the model’s inputs on the results of the model.

Sustainable smart waste classification and collection system: A bi-objective modeling and optimization approach

In the context of the “smart city”, information and communication technologies (ICT) have become indispensable in the planning and design of modern municipal solid waste management. Due to more waste varieties, there are urgent calls to implement waste classification worldwide, which promotes resource recycling to achieve sustainable development. In this paper, we present an ICT-based smart waste classification and collection system (SWCCS) that is abstracted as a bi-objective mathematical programming model to optimize the waste collection problem. To implement the proposed SWCCS effectively, we design a novel multi-objective hybrid algorithm based on the whale optimization and genetic algorithms (MOGWOA) with an improved convergence factor and a fast, non-dominated sorting method. A comparison of our algorithm with two classical multi-objective algorithms on generated test instances and on a real-world case shows that the proposed MOGWOA is more effective for optimizing the established model. This paper demonstrates how the ICT-based SWCCS works and how it can help sanitation companies improve waste collection both economically and environmentally.

The Biobjective Bike-Sharing Rebalancing Problem with Balance Intervals: A Multistart Multiobjective Particle Swarm Optimization Algorithm

The bike-sharing system (BSS), as a sustainable way to deal with the “last mile” problem of mass transit systems, is increasingly popular in recent years. Despite its success, the BSS tends to suffer from the mismatch of bike supply and user demand. BSS operators have to transfer bikes from surplus stations to deficit stations to redistribute them among stations by means of trucks. In this paper, we deal with the bike-sharing rebalancing problem with balance intervals (BRP-BIs), which is a variant of the static bike-sharing rebalancing problem. In this problem, the equilibrium of station is characterized by a balance interval instead of a balance point in the literature. We formulate the BRP-BI as a biobjective mixed-integer programming model with the aim of determining both the minimum cost route for a single capacitated vehicle and the maximum average rebalance utility, an index for the balanced degree of station. Then, a multistart multiobjective particle swarm optimization (MS-MOPSO) algorithm is proposed to solve the model such that the Pareto optimal solutions can be derived. The proposed algorithm is extended with crossover operator and variable neighbourhood search to enhance its exploratory capability. Compared with Hybrid NSGA-II and MOPSO, the computational experimental results demonstrate that our MS-MOPSO can obtain Pareto optimal solutions with higher quality.

A healthcare logistic network considering stochastic emission of contamination: Bi-objective model and solution algorithm

This paper presents a novel healthcare waste location-routing problem by concentrating on a new perspective in healthcare logistics networks. In this problem, there are healthcare, treatment, and disposal centers. Locations of healthcare centers are known, however, it is required to select appropriate locations for treatment, recycling, and disposal centers. Healthcare wastes are divided into infectious and non-infectious wastes. Since a great volume of healthcare wastes are infectious, the emission of contamination can have obnoxious impacts on the environment. The proposed problem considers a stochastic essence for the emission of contamination which depends on the transferring times. In this respect, transferring times between healthcare and treatment centers have been considered as normal random variables. As transferring time increases, it is more likely for the contamination to spread. Having visited a treatment center, infectious wastes are sterilized and they will no longer be harmful to the environment. This research develops a bi-objective mixed-integer mathematical formulation to tackle this problem. The objectives of this model are minimization of total costs and emission of contamination, simultaneously. Complexity of the proposed problem led the researchers to another contribution. This study also develops a Multi-Objective Water-Flow like Algorithm (MOWFA), which is a meta-heuristic, to solve the problem. This algorithm uses a procedure based on the Analytical Hierarchy Process (AHP) to rank the non-dominated solutions in the archive set. By means of a developed mating operator, the MOWFA utilizes the best ranked solutions of the archive in order to obtain high quality offspring. Two neighborhood operators have been designed for the MOWFA as the local search methods. Extensive computational experiments have been conducted to evaluate the effectiveness of the MOWFA on several test problems compared with other meta-heuristics, namely the Multi-Objective Imperialist Competitive Algorithm (MOICA) and Multi-Objective Simulated Annealing (MOSA). These experiments also include a real healthcare waste logistic network in Iran. The computational experiments demonstrate that our proposed algorithm prevails these algorithms in terms of some well-known performance evaluation measures.

Assessment of financial risk in the design and scheduling of multipurpose plants under demand uncertainty

ABSTRACT Industrial companies are seeking for highly flexible strategic and operational solutions to face the requirements of current dynamic markets. The aim of this work is to provide a decision support assessment for the design and scheduling of a multipurpose plant under demand uncertainty, allowing the assessment of alternative risk profile solutions. A general two-stage mixed-integer linear programming (MILP) model is proposed with the goal to maximise the annualised profit of the plant operation under a set of scenarios while minimising the associated financial risk. Considering the long-term investment perspective, the Conditional Value at Risk (CVaR) measure is used to evaluate the likelihood that a specific loss or gain will exceed a certain value at risk. A bi-objective model is formulated using the augmented ε-constraint method to generate an approximation to the Pareto-optimal curve, illustrating the trade-offs between plant profit (with the corresponding design and scheduling decisions) and the associated financial risk. Addressing a set of propositions regarding a case-study, the conclusions highlight the advantages of the risk measure integration in support of the decision-making process, discussing the managerial insights in the assessment of diverse financial outcomes for the solution optimisation.

Multi-mode resource constrained project scheduling problem along with contractor selection

In real-world environments, selecting the right contractor is an important issue which considerably influences completion time, total cost and quality of performing the project. This paper deals with the multi-mode resource constrained project scheduling problem (MRCPSP) and contractor selection (CS) in an integrated manner. In fact, each activity is assigned to a contractor, an execution mode is selected for each activity, and the start/finish times of activities are determined. This paper presents a bi-objective optimization model to deal with MRCPSP-CS, aiming to minimize the total cost and completion time of the project, simultaneously. Then, four multi-objective decision making (MODM) techniques are used to solve the proposed model. Since none of MODM techniques dominates other ones, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used to assess the performance of MODM techniques, confirming that MCGP-U outranks other ones. Finally, the augmented -Constraint method is used to solve some test problems, and perform sensitivity analysis on the number of contractors. Sensitivity analyses show that by increasing the number of available contractors, the Pareto front is significantly improved, and the Number of Pareto-optimal Solutions (NPS) increases. This helps decision maker(s) make appropriate decisions in a more flexible manner.

A bi-objective robust optimization model for hazardous hospital waste collection and disposal network design problem

The hazardous hospital waste (HHW) is one of the main problems in urban waste management, which requires the design and implementation of a special collection and disposal system. Hospital wastes were known as important hazardous waste to be efficiently disposed within a short operational time in order to prevent the spread of infections and diseases. In this research, a multi-objective robust optimization model was developed to design a collection and disposal network of HHW under uncertain condition. The objectives are to concurrently minimize the total cost including transportation and operations costs, and the total risk of transportation and operations. To solve the proposed bi-objective model, the augmented e-constraint method was employed. Moreover, the model validation is achieved using and solving several test problems in different sizes, and the analysis of the robust model was performed compared to the deterministic model. Finally, a real case study was conducted to demonstrate the applicability of the research’s methodology, which was done by determining Pareto front and performing a sensitivity analysis to evolve the managerial insights.

An evaluation of three DoE-guided meta-heuristic-based solution methods for a three-echelon sustainable distribution network

This article evaluates the efficiency of three meta-heuristic optimiser (viz. MOGA-II, MOPSO and NSGA-II)-based solution methods for designing a sustainable three-echelon distribution network. The distribution network employs a bi-objective location-routing model. Due to the mathematically NP-hard nature of the model a multi-disciplinary optimisation commercial platform, modeFRONTIER®, is adopted to utilise the solution methods. The proposed Design of Experiment (DoE)-guided solution methods are of two phased that solve the NP-hard model to attain minimal total costs and total CO2 emission from transportation. Convergence of the optimisers are tested and compared. Ranking of the realistic results are examined using Pareto frontiers and the Technique for Order Preference by Similarity to Ideal Solution approach, followed by determination of the optimal transportation routes. A case of an Irish dairy processing industry’s three-echelon logistics network is considered to validate the solution methods. The results obtained through the proposed methods provide information on open/closed distribution centres (DCs), vehicle routing patterns connecting plants to DCs, open DCs to retailers and retailers to retailers, and number of trucks required in each route to transport the products. It is found that the DoE-guided NSGA-II optimiser based solution is more efficient when compared with the DoE-guided MOGA-II and MOPSO optimiser based solution methods in solving the bi-objective NP-hard three-echelon sustainable model. This efficient solution method enable managers to structure the physical distribution network on the demand side of a logistics network, minimising total cost and total CO2 emission from transportation while satisfying all operational constraints.

Integrated forward/reverse logistics thin-film photovoltaic power plant supply chain network design with uncertain data

Unique features of solar energy, such as the low cost of operation and low pollution, make photovoltaic power plants attractive. Despite the advantages of these power plants, such as low cost of operation and operating without pollution, their high establishment cost compared to that of the conventional fossil fuel-fired power plants prevents their rapid growth. Therefore, designing and optimizing an efficient supply chain network will help to develop the photovoltaic industry. This study proposes a bi-objective model to design and optimize a thin-film photovoltaic power plant supply chain network integrating reverse logistics. The first objective minimizes the costs of supply chain network design, which optimizes decisions from suppliers to disposal centers. The second objective maximizes the efficiency of the data envelopment analysis model to find suitable locations of facilities. As there is uncertainty in electricity demand prediction and perfect foresight is not possible, a fuzzy-robust programming approach is devised to cope with the uncertain parameters. The validity and practicality of the proposed approach are investigated by a case study based on real-world data. Finally, K-Means clustering is incorporated into the model to analyze the installed photovoltaic capacity of different cities in each period. The results show that using an optimistic approach to deal with uncertainty reduces the total cost by 20% in comparison with using a pessimistic approach. The results also provide helpful insights for decision-makers and policymakers in allocating and optimizing the operation of facilities by considering the real-world characteristics of the candidate locations.

A bi-objective model for redundancy allocation problem in designing server farms: mathematical formulation and solution approaches

Communication has a remarkable and strategic role for the success of every enterprise. Nowadays, computer networks can be used as efficient tools to create connections between departments of an organization and to communicate with customers. Therefore, it is crucial for companies with IT-based activities to use computer networks so as to increase their efficiencies. In this paper, a bi-objective mathematical formulation is proposed for server farms. A server farm is a cluster of computer systems connected together to provide services to an organization and its customers. This model optimizes reliability and cost of server farms, concurrently. This problem is called the redundancy allocation problem that belongs to the class of NP-hard problems. Therefore, three meta-heuristics namely non-dominated sorting genetic algorithm II, pareto envelope-based selection algorithm II, and strength pareto evolutionary algorithm II have been hired to obtain feasible solutions in a reasonable computation time. To evaluate the performances of meta-heuristic methods, the e-constraint method as an exact algorithm has also been used. The outputs demonstrate appropriate effectiveness of the employed algorithms.

Integrated routing optimization for post-disaster rapid-detailed need assessment

The post-disaster need assessment for the affected area is of significance for the effective distribution of relief supplies. This paper innovatively concentrates on the integrated routing optimization problem for the rapid need assessment stage and the detailed need assessment stage. A bi-objective model with consideration of the effects of site familiarity and route familiarity is proposed. The proposed nonlinear model is equivalently transformed into a mixed-integer linear programming. A tabu search algorithm is designed to solve the proposed model, and its solving accuracy is validated by comparing with the solution of CPLEX based on a small-scale problem. To demonstrate the efficiency of the proposed model and algorithm for large-scale problems, the case of Ya'an earthquake in China is investigated. The experimental results reveal that comparing to the separate routing optimization and the sequential routing optimization, the integrated routing optimization can achieve a better coordination between the decisions of two stages.

An Efficient Approach for Solving Integrated Production and Distribution Planning Problems

The increasing customer expectations for customized products of high quality in short delays and the worldwide competition in terms of quality and costs have pushed industries to implement new strategies to manage their supply chain decisions. In this context, the integrated planning is becoming the most dominant over the operational research field because of its efficiency and its ability to cover the different aspects of the problem. Production routing problem is one of the problems of the integrated planning that is of interest in optimizing simultaneously production, inventory, and distribution planning. This paper has the purpose of developing two mono-objective models for the production-routing problem; one of them minimizes the total costs, while the other one minimizes the energy consumed by the production system. Finally, a bi-objective model is proposed to combine the two objectives mentioned previously using the LP-metric method in the context of a sustainable supply chain. Experimental results are also presented and discussed through the different scenarios.

A chance constrained fuzzy goal programming approach for perishable pharmaceutical supply chain network design

In this paper, a bi-objective mixed-integer linear programming model is formulated for designing a perishable pharmaceutical supply chain network under demand uncertainty. The objectives of the proposed model are to simultaneously minimize the total cost of the network and lost demand amount. The proposed model is multi-product and multi-period and includes simultaneous facilities location, vehicle routing, and inventory management; hence, it is considered an operational-strategic model. Procurement discounts, the lifetime of products, storing products for future periods, lost demand, and soft and hard time windows are the main assumptions of the proposed model. A novel hybrid approach, based on fuzzy theory, chance constrained programming, and goal programming approach, is developed for solving the proposed bi-objective model. The validity of the proposed model and developed solution approach is evaluated using data from Avonex, a prefilled syringe distribution chain serving 11 health centers in Tehran. The proposed model indicates that some lost sales exist, and to overcome the lost sales, the case company needs to invest a little more in addition to the initial investment of around 2 billion tomans. The results obtained from implementing the model and the sensitivity analysis, using real-world data, confirm the efficiency and validity of the proposed mathematical model and solution approach.

Decomposition-based hyperheuristic approaches for the bi-objective cold chain considering environmental effects

This paper proposed a novel approach for a practical version of the cold chain, namely location-routing problem-based low-carbon cold chain (LRPLCCC). In the proposed bi-objective model, the first objective is the total logistics cost, including the fixed costs of the opened depots and leased vehicles, as well as the cost of fuel consumption and carbon emissions, and the second is to minimize the amount of quality degradation that aims at improving clients’ satisfaction and maintain product freshness. The cargos of clients are classified into three types: general, refrigerated, and frozen cargos. Since the presented problem is NP-hard, a novel multi-objective hyperheuristic (MOHH) was proposed to obtain the Pareto solutions. In this framework, three selection strategies were developed to improve the performance of MOHH, that is, random simple, choice function, and FRR-MAB (fitness rate rank based multi-armed bandit), and three acceptance criteria using the decomposition approaches in MOEA/D were also developed, namely penalty-based boundary intersection, Tchebycheff, and modified Tchebycheff approaches. Extensive experiments were provided to verify the efficiency of the proposed algorithms and assessed the effects of algorithm parameters on the Pareto front. The results showed that the efficiency of the proposed algorithm outperforms several existing well-known multi-objective evolutionary algorithms (MOEA).

بررسی زنجیره تأمین حلقه‌باز و حلقه‌بسته تحت شرایط عدم‌قطعیت (موردمطالعه: شرکت ایران ترانسفو)

One of the main components of competition in the current competitive environment is supply chain; therefore, organizations need to have a reliable supply chain to increase efficiency and effectiveness. Moreover, due to the increase in environmental pollution and the requirements imposed by the governments to harness polluting activities, organizations are obliged to follow green supply chain practices that account for environmental considerations along with economic aspects. hence, in this study, a bi-objective model for a green, closed-loop supply chain under demand uncertainty is proposed which takes into account environmental consideration and economic aspects. Another important aspect of the supply chain network design is the concept of uncertainty. Due to societal and political evolutions and the scarcity of raw materials in the decision-making horizon, uncertainty is a significant measure in the models of supply chain. Indeed, in this study, the model was developed for a supply chain under uncertainty so that more compatibility with real-world conditions would be achieved. The results show that considering uncertainties makes the model more flexible. The advancement of technology and unpredictable behaviors of customers in markets have created a very complex competitive atmosphere. To evaluate the performance of the developed model, the case study of the Iran Transfo Company is considered.

A reactive scheduling method for disturbances in aircraft moving assembly line

Aircraft assembly requires a large number of materials from hundreds of suppliers, and the uncertainty in material delivery has a negative impact on the assembly schedule. Existing researches stop short of introducing how to reschedule assembly activities in this context, so this paper addresses a reactive scheduling problem of aircraft moving assembly line with uncertain material delivery, and a bi-objective model is established. To absorb the advantage of machine learning-based method, we present a SVDD-based reactive scheduling method (SVDD-RS). Firstly, the models under different settings of disturbances in material delivery are solved, and the obtained policies are used to train the SVDD classification model in the offline training phase. In the online reactive scheduling phase, the trained SVDD classification model is used to make a preliminary decision for unstarted activities, and exact start-times are further determined by the local forward-looking algorithm. Computational experiments are carried out over practical cases generated from an aircraft assembly line to evaluate the performance of SVDD-RS. The results show that the SVDD classification model can quickly select policies with reasonable accuracy, and SVDD-RS can guarantee a quick response to the disturbance and produce a high-quality solution, compared to other existing reactive scheduling methods.

New peer effect-based approach for service matching in Cloud Manufacturing under uncertain preferences

Cloud manufacturing is a kind of sharing manufacturing, and the supply–demand matching between manufacturing services and customers has become one of the most important issues for a platform. Because of the increasing complexity of customer personalization, the cognitive information from both sides becomes uncertain and fuzzy. Linguistics is used to describe uncertain preferences, especially in platforms. Also, the cloud model is adopted to convert the linguistics to reflect the randomness and fuzziness. Meanwhile, as the rapid development of communication techniques has strengthened the connections between different agents, the final matching results are affected by connections. Hence, the peer effect, which describes the mutual influences among individuals, is introduced in our study. In addition, considering the different strengths of the connections, the peer effect is improved by integrating grey relations, which are used to evaluate the diverse connections. Finally, the workload is introduced in the form of adjustment parameters. Consequently, we establish a bi-objective model that aims to maximize satisfaction and minimize the differences among individuals. To solve the mathematical model, an improved cuckoo algorithm is proposed. Additionally, the design of an air outlet grille for new-energy vehicles is taken as an example, and the effectiveness of the proposed method is verified.

Tactical and operational planning for socially responsible fresh agricultural supply chain

Addressing an integrated decision-making structure for planting and harvesting scheduling may lead to more realistic, accurate, and efficient decision in fresh product supply chain. This study aims to develop an integrated bi-objective tactical and operational planning model for producing and distributing fresh crops. The first objective of the model is to maximize total revenue of supply chain. Over the past few years, there has been a considerable shift in emphasis in social responsibility of supply chains. Therefore, a key purpose of this article is to plan a socially responsible fresh agricultural supply chain as the second objective function. The proposed bi-objective model seeks to make optimal decisions on planting, harvesting scheduling (harvesting pattern), selecting the transport fleet type, and products supply channel to the consumers. To conduct the analysis, numerical examples are provided based on a real case study and the true Pareto front is achieved with augmented e-constraint method. The results indicated the applicability of the proposed model and verified its validity. Moreover, comparison between total weighting and e-constraint method is provided to ensure the efficiency of Pareto solutions.

Bi-objective optimization algorithms for joint production and maintenance scheduling under a global resource constraint: Application to the permutation flow shop problem

Production scheduling and maintenance planning are two of the most important tasks that managers face before implementing their decisions on the shop floor. Another issue managers have to keep in mind is the proper allocation of various resources for production. These issues create difficulties in the planning process. In this paper, we propose a bi-objective model that integrates the three aforementioned issues and determines production scheduling, maintenance planning and resource supply rate decisions in order to minimize the make span and total production costs, which include total maintenance, resource consumption and resource inventory costs. Two meta heuristic methods were employed to find approximations of the Pareto optimal front in a permutation flow shop environment: The well-known non-dominated sorting genetic algorithm (NSGA-II) and a bi-objective adaptation of the particle swarm optimization (BOPSO). Additionally, a bi-objective randomized local search (BORLS) heuristic was developed in order to generate multiple non-dominated solutions along its search path. Two sets of computational experiments were conducted. In the first set, the performances of the two meta heuristics with purely random initial populations were compared, with results showing the superiority of BOPSO over NSGA-II. In the second set, the initial populations were enhanced with heuristically generated solutions from BORLS and the performances of BOPSO, NSGA-II and BORLS used as an independent search algorithm, were compared. In this instance, the algorithms performed evenly for large problems, with the BORLS method generating better solutions when total production cost is emphasized.