Multi-objective Mathematical Programming Model Research Articles

Job rotations based on physical and psychological workloads: A proposal for the footwear industry

IntroductionThe aim of this study is to propose a model of job rotations in shoes (sandals and tennis shoes) production cells, aiming at reducing the risk exposure to work-related musculoskeletal disorders considering physical and psychological workloads. MethodsThe physical load was assessed by the Occupational Repetitive Actions method, and the psychological load by the Job Stress Scale. A total of 259 workers in the footwear industry participated in this study. These loads were incorporated into a multi-objective mathematical programming model, where the objective functions aimed to minimize the maximum work-related musculoskeletal disorders and the maximum total work demand, and to maximize the minimum work control and social support to which a worker might be exposed during a daily journey. To the best of our knowledge, this is the first time in the literature that physical and psychological aspects are considered when solving job rotation problems. To tackle the problem, we propose a matheuristic based on an epsilon-constraint framework. This method allows us to generate different solutions with respect to the specific objective functions. To assess the effectiveness of the solutions, we calculated the variance of the scores of the physical and psychological loads in the conditions without and with rotations. ResultsFive rotation solutions were reached for the sandal production cells and twelve for the tennis shoe production cells. There was a reduction in the variation of physical and psychological loads in all solutions for both cells when compared to the no rotation condition. However, for the sandal production cells, the reduction in variation between the physical loads of the conditions with and without rotations was not significant due to the similarity of the exposure indices. ConclusionsThe model reduces the risk of work-related musculoskeletal disorders, promoting variability in muscle recruitment and enrichment of work content, being applicable in other segments.

A Multi-Objective Mathematical Programming Model for Project-Scheduling Optimization Considering Customer Satisfaction in Construction Projects

The aim of this study was to develop a multi-objective mathematical programming model for the trade-off of time, cost, and quality in the project-scheduling problem (PSP) by taking priorities and resource constraints as well as activity preemption into account. First, a small-sized problem instance that was a sub-project of an oil and gas construction project was used for te validation of the proposed model and algorithm. Subsequently, considering the sensitivity, complexity, and importance of oil and gas projects, the proposed model was implemented in a large-sized oil and gas construction project. Considering the NP-hardness of this problem, the NSGA-II metaheuristic algorithm was used to deal with the time, cost, and quality trade-off problem. Finally, a sensitivity analysis was implemented on the three main parameters of time, cost, and quality to investigate the effects of changes on the results. The findings show that the proposed model is more sensitive to cost changes, so an increase in project costs leads to a drastic change in the values of other objective functions.

A Multi-Objective Mathematical Programming Model for Transit Network Design and Frequency Setting Problem

In this study, we propose a novel multi-objective nonlinear mixed-integer mathematical programming model for the transit network design and frequency setting problem that aims at designing the routes and determining the frequencies of the routes to satisfy passenger demand in a transit network. The proposed model incorporates the features of real-life transit network systems and reflects the views of both passengers and the transit agency by considering the in-vehicle travel time, transfers, waiting times at the boarding and transfer stops, overcrowding and under-utilization of vehicles, and vehicle fleet size. Unlike previous studies that simplify several aspects of the transit network design and frequency setting problem, the proposed model is the first to determine routes and their frequencies simultaneously from scratch, i.e., without using line and frequency pools while considering the aforementioned issues, such as transfers and waiting. We solve the proposed model using Gurobi. We provide the results of what-if analyses conducted using a real-world public bus transport network in the city of Kayseri in Türkiye. We also present the results of computational tests implemented to validate and verify the model using Mandl benchmark instances from the literature. The results indicate that the model produces better solutions than the state-of-the-art algorithms in the literature and that the model can be used by public transit planners as a decision aid.

Countries Classification According to Covid-19 Data, Based on Aged-65 and Older, Using Multi-Objective Mathematical Goal Programming Model

Countries Classification According to Covid-19 Data, Based on Aged-65 and Older, Using Multi-Objective Mathematical Goal Programming Model

A food bank network design examining food nutritional value and freshness: A multi objective robust fuzzy model

One main reason for food scarcity is its improper and uneven distribution amongst those who require aid. To overcome this issue, charities and food banks serve as the connection between beneficiaries and donors. They are mostly nonprofit organizations but they incur operational costs for storage and delivery of the donated food items. The donated food items are either canned and cold, or hot meals from over production of businesses; and therefore their freshness, inventory and shelf-life bring about additional operational challenges in distribution and logistics. The uncertainty of demand and supply is another challenge to overcome, which necessitates a robust plan. This article proposes a multi-objective mathematical programming model for a food bank network design to optimize the cost, food freshness and its nutritional value. A robust fuzzy counterpart of the model is developed together with three solution methods including ϵ-constraint, MOGWO and NSGA II. The MOGWO algorithm shows a better performance in our numerical experiment with large instances. Its application on a case study resulted in a supply network with lower cost, smaller fleet size and higher food quality, although less fresh distributed foods compared to the benchmark network. The trade-off between the cost and freshness of food is depicted here by examining shelf-life of products and vehicle capacity. The long lasting products incur less transportation cost due to compactness of packaging, and similarly, higher capacity vehicles lead to more cost efficient dispatch with longer routes which decrease the freshness of food. According to our numerical results, higher uncertainty rate in the network increases total cost, but also overall nutritional value of the distributed food over the network due to greater supply of food.

Based on the multi-objective programming model, this paper explores the purchasing and transshipment schemes of enterprises

When an enterprise is producing, the production cost directly affects the overall economic benefit. If the production plan can be made in advance according to historical data, the production benefit of the enterprise can be greatly improved. For this reason, according to the historical data provided by a building and decorative board manufacturer, the TOPSIS method is used to evaluate suppliers, considering the minimum number of suppliers required for enterprise production, and trying to pursue the minimum purchasing cost and the minimum transportation loss, a multi-objective mathematical programming model is established, which is solved by sequential algorithm and target weighting method respectively, and the minimum number of suppliers, the ordering scheme and transportation scheme in the next 24 weeks are obtained.

RETRACTED: Selecting and balancing market portfolio using artificial intelligence and fuzzy multiobjective decision-making model

Most enterprises focus on product portfolio management (PPM) and exclude market portfolio management, and individual markets are selected solely based on financial performance which may not be appropriate because other factors may dictate the outcome of the market selection. This study proposes a market portfolio model that considers market share, market growth, market competition, market risk, and market cost to maximize overall profit. A three-stage approach is proposed to identify potential product markets using an AI algorithm. A set of the most promising market is then determined based on the results of Stage 1 using a fuzzy multi-objective mathematical programming model by concurrently maximizing the total market share and market growth, and minimizing the market competition and market risk. A single-objective mathematical programming model is then used to determine a market portfolio to maximize the total profit using the results for Stage 2. The single-objective model is tested using two sets of threshold constraints. The balance of the market portfolio is discussed and the results are compared. The novelty of the article: (1) the first study involves a product market portfolio, (2) the decision of market selection is scientific (using AI instead of personal judgment), holistic (factors include market share, growth, competition, risk, cost, and profit) and optimized (using mathematical optimization), and (3) the market portfolio maximizes total profit. (4) the proposed method produces a portfolio with a higher profit than the TOPSIS method.

Trust and personalized individual semantics based fusion method for heterogeneous multi-criteria group decision making and application to live streaming commerce

This paper develops a new trust and personalized individual semantics (PISs) based fusion method for heterogeneous multi-criteria group decision making (HMCGDM) and applies to the selection of live streaming commerce plan. Firstly, a consistency-driven optimization model is built to determine the PIS of linguistic terms in linguistic preference relation of criteria given by the trustor and recommenders. Secondly, this paper defines a harmony degree to reflect the degree of difference in the evaluation information of different recommenders in HMCGDM problem. Then, considering the trust relationship between trustor and recommenders and between the recommenders themselves, two multi-objective mathematical programming models are constructed. One purpose is to produce values to positions that are not assigned, and the other purpose is to fuse the evaluation information of recommenders. In addition, combining the preference information of criteria given by trustor and Shannon entropy based on the collective evaluation information, the subjective and objective weights of criteria can be determined respectively. The comprehensive criteria’s weights are acquired by an optimization model which aims at minimizing the Jenson-Shannon divergence between the subjective and objective weights. Finally, an example of selection of influencer or celebrity in live streaming commerce for promoting new products sales is offered to verify the effectiveness of the proposed method.

Collaborative multicenter reverse logistics network design with dynamic customer demands

The vehicle routing problem for waste recycling has been created to improve resource utilization and reduce environmental pollution as a result of the rapid consumption of natural resources and the negative impact of waste on the environment. This study investigates a collaborative multicenter vehicle routing problem with time windows and dynamic customer demands. The collaboration among logistics facilities is an effective mechanism to reduce the number of vehicles and improve resource utilization in a multicenter reverse logistics network. A multi-objective mathematical programming model is proposed to coordinate static and dynamic customer demands while minimizing the total operating cost, the number of vehicles, and the total waiting time. A hybrid heuristic algorithm comprising an improved k-medoids clustering algorithm and an extended reference point-based non-dominated genetic algorithm- III, is designed to solve the multi-objective optimization model. The clustering algorithm is implemented to reduce the network complexity. The extended reference point-based non-dominated genetic algorithm- III with a dynamic insertion strategy is proposed to adjust service routes for dynamic customer demands and find the Pareto optimal solution for the multi-objective optimization model. The performance of the proposed algorithm is evaluated, and results suggest that the extended reference point-based non-dominated genetic algorithm- III has superior solutions in solving the collaborative multicenter vehicle routing problem with time windows and dynamic customer demands compared with other algorithms. The cost savings resulting from optimization are fairly distributed among participants in a collaborative alliance via the minimum cost remaining savings and principle of strictly monotonic path selection. The proposed methods are applied in a case study of a realistic reverse logistics network in Chongqing City, China. Different service periods and optimization strategies are discussed and compared to verify the effectiveness of the proposed solution methods. The optimization results indicate that the collaborative mechanism and dynamic insertion strategy can improve resource utilization and transportation efficiency and contribute to a sustainable urban logistics transportation system.

Designing an oil supply chain network considering sustainable development paradigm and uncertainty

This study proposes a multi-objective mathematical programming model to design an oil supply chain network at three levels: upstream, midstream and downstream. It includes oil wells, gas injection wells, production units, refineries, gas injection centers, distribution centers, export and import terminals. The proposed model optimizes all three economic, social and environmental goals at the same time. Drilling injection and production wells, transportation costs, production costs, gas injection center costs, as well as fixed and annual costs of refineries and distribution centers are all minimized in the economic dimension. The environmental dimension of sustainability reduces greenhouse gas emissions, while the social dimension of sustainability increases job opportunities. The optimization of associated petroleum gas injection operations into the reservoir is also taken into account in this study. The proposed model considers the uncertainty of critical parameters and employs a robust possibilistic hybrid approach to deal with it, as well as an interactive fuzzy approach to solve it. A case study in Iran is used to evaluate the suggested model's performance. In comparison to the single-objective economic model, the results of solving the model show that taking sustainability into account has reduced greenhouse gas emissions and increased job opportunities. The crude oil extraction potential increases in each period when gas injection optimization and reservoir pressure are taken into account. Furthermore, the cost of the supply chain grows as the amount of uncertainty in the suggested model rises. As a result, the uncertainty of system parameters must be considered.

Increasing the sustainability of a fresh vegetables supply chain through the optimization of funding programs: A multi-objective mathematical programming approach

Purpose: This research develops a model to improve the quality and freshness of sold vegetables through a funding program between farmers and retailers. Through this program, retailers who are interested in the distribution of first quality vegetables provide funds to farmers to increase their production this type of vegetables through the acquisition of new machinery, technology, or training.Design/methodology/approach: The problem is solved through a multi-objective mathematical programming model that simultaneously optimizes the supply chain profits, the waste of vegetables, the economic unfairness among farmers, the unfairness in the distribution of funds, and the freshness of sold vegetables. The ?-constraint method is used to obtain several non-dominated solutions to the problem after linearizing the non-lineal equations related to the unfairness objectives.Findings: Results show that it is possible to improve the indicators related to the vegetable waste, the economic unfairness, the unfairness in the distribution of funds and the freshness of vegetables while maintaining similar to optimal profits for the supply chain. Interesting trade-offs between the five objectives are identified, which can be used by supply chain members to select the most appropriate solution to be implemented in the real supply chain.Originality/value: This research models aspects relevant to the agri-food sector that have not been previously modelled for the problem under study. The main novelties of this paper are the consideration of the limited shelf life of the vegetables as well as the requirement of ensuring a minimum freshness at the moment of their sale, the price dependence on the quality and freshness of vegetables, the optimization of vegetable waste and the freshness of vegetables sold, as well as the joint optimization of the five previously defined objectives.

Coordinated routing system for fire detection by patrolling trucks with drones

Vehicle routing problem with drones (VRPD) is an extension of classical vehicle routing, which involves the usage of trucks and drones. Nowadays, bushfires are taken into account as a major global challenging subject. Indeed, forests are very vulnerable to fires, and the classical patrol systems cannot patrol all areas of the forest and pastures due to the difficult crossing of some routes.The literature survey demonstrated that the mathematical models are an efficient approach for planning forest and rangeland patrols. Drones and trucks are used in cooperation for forest monitoring in this study, with drones acting as an efficient and accurate means of monitoring routes that are impassable to ground vehicles. However, this novel approach deals with several substantial challenges, including limitation in the drone's battery and the routing problem in an integrated truck-drone system based on considering hard-to-reach areas and creating a trade-off between time and cost of the patrol process. These issues make significant differences between the proposed novel approach and the classical vehicle routing problem. Thus, it is essential to develop a comprehensive approach to resolve these crucial issues. The present study develops a multi-objective mathematical programming model as mixed-integer programming for simultaneous patrolling of trucks and drones. The augmented epsilon constraint (AEC) method has been considered to solve the two-objective mathematical programming model. Besides, Benders' decomposition (BD) algorithm has been employed to evaluate the achieved results in large-size problems. The performance of the BD algorithm has been confirmed in this study. The findings indicated that the proposed model efficiently protected the forest via monitoring all areas, including impassable areas where ground patrolling is impossible (e.g., the lack of roads due to dense vegetation). Also, it was proved that this system was a novel, cost-effective patrol, which prevents uncontrollable fires in the shortest possible time.

Multiobjective Mathematical Optimization Model for Municipal Solid Waste Management with Economic Analysis of Reuse/Recycling Recovered Waste Materials

Municipal solid waste management in developing countries like Nigeria did not consider benefits from reuse/recycling recovered waste materials during solid waste evacuation and disposal. The benefits from recovered waste materials mostly go to informal waste vendors and scavengers. This study developed a multiobjective mathematical programming model for waste evacuation and disposal, considering the benefits of reuse/recycling recovered waste materials. Data were collected from the Abuja environmental protection board (AEPB), personal interviews, and other stakeholders. The formulated model was solved using spreadsheet solver version 14.0. The study uses various daily budgetary provisions for solid waste evacuation and disposal at a 15% recovery level of solid waste materials to observe the responses of the model. The solution shows that at 71.5% recovery of reuse/recycling recovered waste material; no budgetary provision is required to evacuate and dispose of the waste at the collection centers. Benefits realized from recovered waste materials are sufficient to evacuate and dispose of the wastes. After a 71.5% level of recovery, the net benefit of $1,108.17 from recovered waste materials starts to accrue until the percentage recovery level reaches 100%. The volume of waste shifted to the disposal sites was reduced to 74.5 tons (i.e., unrecoverable waste material) which is 16.82% of the total waste generated per day, and 368.33 tons (83.18%) of waste materials were recovered. The study will give the policymakers viable information to aid proper planning while budgeting and controlling solid-waste-associated problems in the Abuja municipal area in particular and the country as large.

Application of Three Metaheuristic Algorithms to Time-Cost-Quality Trade-Off Project Scheduling Problem for Construction Projects Considering Time Value of Money

Time, cost, and quality have been known as the project iron triangles and substantial factors in construction projects. Several studies have been conducted on time-cost-quality trade-off problems so far, however, none of them has considered the time value of money. In this paper, a multi-objective mathematical programming model is developed for time-cost-quality trade-off scheduling problems in construction projects considering the time value of money, since the time value of money, which is decreased during a long period of time, is a very important matter. Three objective functions of time, cost, and quality are taken into consideration. The cost objective function includes holding cost and negative cash flows. In this model, the net present value (NPV) of negative cash flow is calculated considering the costs of non-renewable (consumable) and renewable resources in each time period of executing activities, which can be mentioned as the other contribution of this study. Then, three metaheuristic algorithms including multi-objective grey wolf optimizer (MOGWO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective particle swarm optimization (MOPSO) are applied, and their performance is evaluated using six metrics introduced in the literature. Finally, a bridge construction project is considered as a real case study. The findings show that considering the time value of money can prevent cost overrun in projects. Additionally, the results indicate that the MOGWO algorithm outperforms the NSGA-II and MOPSO algorithms.

Multi-objective Mathematical Programming Model for Optimum Stratification in Multivariate Stratified Sampling

Multi-objective Mathematical Programming Model for Optimum Stratification in Multivariate Stratified Sampling

An urban metro network-based method to evaluate carbon emission and distribution cost of express delivery

A novel green delivery method for express delivery based on the urban metro network, referred to as Green metro express delivery (GMED), is presented. A multi-objective mathematical programming model is first proposed to maximize the search for the best transportation costs and lowest carbon emissions. To solve the GMED model e-ciently, a two-layer coding method is used to encode the path and the non-dominated sorting genetic algorithm II (NSGA-II) is adopted. Finally, a numerical experiment was conducted with Ningbo Metro Network as a case to prove the effectiveness and stability of NSGA-II in solving the GMED model. The result shows that: (a) Compared with the vehicle express delivery method (VED), GMED has lower carbon emissions and vehicle mileage. (b) For the same quantity of express delivery, the transportation costs of GMED and VED have their own advantages over different transportation distances. (c) For delivery distances with the same transportation cost, the lager the quantity of express delivery, the lower the transportation cost of GMED compared to VED.

NSGA-II algorithm for hub location-allocation problem considering hub disruption and backup hub allocation

Purpose One of the practical issues in the area of location and allocation is the location of the hub. In recent years, exchange rates have fluctuated sharply for a number of reasons such as sanctions against the country. Natural disasters that have occurred in recent years caused delays in hub servicing. The purpose of this study is to develop a mathematical programming model to minimize costs, maximize social responsibility and minimize fuel consumption so that in the event of a disruption in the main hub, the flow of materials can be directed to its backup hub to prevent delays in flow between nodes and disruptions in hubs. Design/methodology/approach A multi-objective mathematical programming model is developed considering uncertainty in some parameters, especially cost as fuzzy numbers. In addition, backup hubs are selected for each primary hub to deal with disruption and natural disasters and prevent delays. Then, a robust possibilistic method is proposed to deal with uncertainty. As the hub location-allocation problem is considered as NP-Hard problems so that exact methods cannot solve them in large sizes, two metaheuristic algorithms including a non-dominated sorting genetic algorithm non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are applied to tackle the problem. Findings Numerical results show the proposed model is valid. Also, they demonstrate that the NSGA-II algorithm outperforms the MOPSO algorithm. Practical implications The proposed model was implemented in one of the largest food companies in Iran, which has numerous products manufactured in different cities, to seek the hub locations. Also, due to several reasons such as road traffic and route type the difference in the rate of fuel consumption between nodes, this model helps managers and decision-makers to choose the best locations to have the least fuel consumption. Moreover, as the hub set up increases the employment rate in that city and has social benefits as it requires hiring some staff. Originality/value This paper investigates the hub location problem considering backup hubs with multiple objective functions to deal with disruption and uncertainty. Also, this study examines how non-hub nodes are assigned to hub nodes.

A New Mathematical Model for Redesigning the Reverse Supply Chain with Social Sustainability

The flow of goods in the supply chain is divided into two types of direct and reverse flows. Recently, more attention has been paid to the reverse supply chain because it can create benefit in waste products. In this paper, a nonlinear integer mixed integer multi-objective mathematical programming model for inverse and sustainable supply chain is presented. The objective functions of this model are economic, social and environmental goals. In addition, this model covers four levels including suppliers, collection centers, recycling centers and consumers. The purpose of this article is to assist managers in making decisions at strategic and tactical levels such as choosing a suitable location for the establishment of collection and recycling centers, selecting production technology, determining the amount of production in each recycling center and the use of available vehicles. To solve this mathematical model, a method based on linearization as well as foal planning is developed. Finally, in order to validate and evaluate the performance, the model is examined using a numerical example and sensitivity analysis is performed on its various parameters.

Optimal project portfolio selection with reinvestment strategy considering sustainability in an uncertain environment: a multi-objective optimization approach

PurposeThis study aims to develop a model for project portfolio selection considering organizational goals such as budgets, sustainability cash flow and reinvestment strategy under an uncertain environment.Design/methodology/approachA multi-objective mathematical programming model is proposed for project selection, which takes the social, environmental and financial aspects into account as the objectives of the project portfolio selection problem. The project evaluation and selection process in one of the large capitals in the Middle East with numerous urban construction projects was considered as a real case study, in which the subjects of environmental and social sustainability are of great importance. Then, the most significant criteria for project evaluation and selection based on sustainability were identified and ranked using the fuzzy best-worst method (BWM).FindingsThe criterion of “defining clear and real objectives” was ranked first, “project investment return period” was ranked second, “minimum changes in the predicted range” was ranked third, and the other ten sustainability indicators were ranked as well. Next, the presented mathematical programming model was solved using the augmented e-constraint method. The sensitivity analysis indicated that increasing the amount of investments in projects would increase their net present value. Also, increased investment had no effect on sustainability, while decreased investment caused sustainability to not being optimal.Originality/valueThis study focuses on the impact of the amount of investments on projects, and the associated costs of sustainable projects. Further to the authors' knowledge, there has been no relevant study taking uncertainty into account. Also, very few studies proposed a mathematical programming model for the project portfolio selection problem. Moreover, this research uses the brainstorming and Delphi method to identify the sustainability indicators influencing the organization and screens the evaluation indicators. Furthermore, the weights of the evaluation indicators are determined using the fuzzy BWM based on the consistency of opinions.

A multi-objective stochastic programming model for post-disaster management

This paper develops a mathematical model for post-disaster planning with human casualties, which can be considered as operational guidance for the proper use of emergency resources. For this purpose, a stochastic mixed-integer programming model is provided to formulate the problem. The objective functions of the model are (1) maximizing the survival probability of patients, (2) minimizing the maximum of completion time of treatment of all patients, and (3) minimizing the total cost of operations. The model is solved with the ϵ-constraint method. Due to the NP-hardness of the problem which is a significant challenge in the literature, two innovative meta-heuristic algorithms are proposed, i.e. a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective simulated annealing (MOSA). Finally, a comprehensive computational analysis is performed for evaluation purposes. Also, a case study is made on the earthquake in Iran, which illustrates the real-world application of the model. Highlights A stochastic multi-objective mathematical programming model to allocate patients to hospitals and treat them. NSGA-II and MOSA are proposed, in addition to ϵ-constraint method as solution methods. Performance of two meta-heuristic algorithms is measured with five evaluation metrics. The study showed that NSGA-II is more effective than MOSA. The model was implemented on a real-world case, Tabriz earthquake in Iran.