Multi-objective Mathematical Programming Research Articles

An integrated model of supply chain resilience considering supply and demand uncertainties

AbstractThe complexity of the global supply chain has increased dramatically over the past few decades as a result of uncertainty caused by various factors. This paper studies the optimal strategy for supply chain resilience models considering supply disruptions and demand fluctuations. We present two‐stage stochastic programming models based on different scenarios, including a risk‐neutral model that considers the expected total cost, a risk‐averse model that considers the conditional value‐at‐risk measure, and a responsiveness model that considers the service level. We also propose multiobjective mathematical programming that considers all three models simultaneously and suggests the solution approach. Finally, we present the results of computational experiments and demonstrate how to cope with uncertainty through flexibility and redundancy. We offer a set of nondominated solutions from the multiobjective model and derive managerial insights, which suggest a decision‐making strategy between the disruption risk, expected total cost, and service level.

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.

An integrated chance-constrained stochastic model for a preemptive multi-skilled multi-mode resource-constrained project scheduling problem: A case study of building a sports center

A multi-mode resource-constrained project scheduling problem (MRCPSP) with multiple skills is investigated in this paper. Unlike the traditional form of this problem, and considering the real-world project circumstances, project activities can be preempted. In this paper, a new multi-objective mixed-integer linear programming (MILP) model with three objective functions is extended. These objectives are: (1) minimizing the project makespan, (2) minimizing the total resource costs, and (3) minimizing the total project risk. Based on real-life projects, non-renewable resources are represented as an uncertain stochastic parameter. To cope with the uncertain environment, chance-constrained programming with a confidence level is considered. A real-world construction project of a sports center in Tehran is utilized to demonstrate the applicability of the presented formulation. A well-known lexicographic optimization method, namely AUGMECON2, is applied to solve the proposed formulation with three objectives. Ultimately, for the case study and two datasets J30 and MM50, the proposed lexicographic optimization algorithm is compared with an efficient multi-objective mathematical programming technique known as the AUGMECON method. The comparison is based on performance metrics (i.e., IGD and HV) commonly used in multi-objective optimization. The results show the relative dominance of the proposed lexicographic optimization algorithm over the AUGMECON method in all sizes of the problem instances.

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 time-varying stock portfolio selection model based on optimized PSO-BiLSTM and multi-objective mathematical programming under budget constraints

A time-varying stock portfolio selection model based on optimized PSO-BiLSTM and multi-objective mathematical programming under budget constraints

A Hybrid Model Based on Multi-Attribute Decision Making and Fuzzy Multi-Objective Mathematical Programming for Stock Portfolio Evaluation and Selection Using Z-Number Approach

A Hybrid Model Based on Multi-Attribute Decision Making and Fuzzy Multi-Objective Mathematical Programming for Stock Portfolio Evaluation and Selection Using Z-Number Approach

Duality for Multiobjective Programming Problems with Equilibrium Constraints on Hadamard Manifolds under Generalized Geodesic Convexity

This article is devoted to the study of a class of multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifolds (in short, (MPPEC)). We consider (MPPEC) as our primal problem and formulate two different kinds of dual models, namely, Wolfe and Mond-Weir type dual models related to (MPPEC). Further, we deduce the weak, strong as well as strict converse duality relations that relate (MPPEC) and the corresponding dual problems employing geodesic pseudoconvexity and geodesic quasiconvexity restrictions. Several suitable numerical examples are incorporated to demonstrate the significance of the deduced results. The results derived in this article generalize and extend several previously existing results in the literature.

Multiple criteria decision making and robust optimization to design a development plan for small and medium-sized enterprises in the east of Iran

This paper is based on a project of developing small and medium-sized enterprises in South Khorasan, Iran. A combination of multiple criteria decision making and robust multi-objective optimization is used for prioritizing industrial clusters and optimally assigning governmental funds. First, criteria for evaluating clusters are weighted using the best-worst method and clusters are prioritized using the VIKOR method. Second, governmental funding is assigned to the highest priority cluster using robust multi-objective mathematical programming. An innovative method is applied to identify the solution of the Pareto-front with the highest efficiency. In a case study from South Khorasan, computational results show that international market share attraction is the most important criterion and the age of the cluster is the least important criterion in the development of the industrial clusters. The cluster defined for barberry and jujube fruits is determined to be the first-ranked cluster. Most of the total available budget for the development of this cluster is assigned to action plans for marketing and trade development and for investment and financial planning. The proposed methodology thus successfully aided the decision makers to plan their work regarding funding of industrial clusters. We believe that the methodology can be applied as a general tool to help managers of industrial development to better assign governmental funding to develop industrial clusters.

Focusing on Important Problems

Research in Multiple Criteria Decision Making (MCDM) and its subfields (multi-attribute utility theory or Decision Analysis, AHP, Goal Programming, MCDA, multi-objective mathematical programming, EMO) is very active. However, our general feeling is that bright, young people do not focus their energies sufficiently on solving important problems despite many very important problems that deserve attention. Some of the problems are critical to the well-being of the world. The purpose of our essay is to identify these very important problems (or mega trends, as they are sometimes called) and briefly discuss how the research community could help solve or at least alleviate such problems. The reader could interpret our essay as suggestions for a research agenda or program. It does not matter whether we are AHP scholars, multi-objective optimizers, or decision analysts, everyone’s contribution is needed.

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.

Optimality Conditions for Multiobjective Mathematical Programming Problems with Equilibrium Constraints on Hadamard Manifolds

In this paper, we consider a class of multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifolds (in short, (MMPEC)). We introduce the generalized Guignard constraint qualification for (MMPEC) and employ it to derive Karush–Kuhn–Tucker (KKT)-type necessary optimality criteria. Further, we derive sufficient optimality criteria for (MMPEC) using geodesic convexity assumptions. The significance of the results deduced in the paper has been demonstrated by suitable non-trivial examples. The results deduced in this article generalize several well-known results in the literature to a more general space, that is, Hadamard manifolds, and extend them to a more general class of optimization problems. To the best of our knowledge, this is the first time that generalized Guignard constraint qualification and optimality conditions have been studied for (MMPEC) in manifold settings.

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.

A sustainability approach to vehicle modular platform design: A mathematical model

Today, sustainability and its economic, social, and environmental pillars are the main elements of new product market development. Therefore, manufacturers, considering all stages of a product life-cycle, consider it necessary to have a framework for producing sustainable products. Moreover, new product design and development processes especially sub-process of product definition and detailed design processes can play a very critical role in developing product sustainability. This paper considers the role that the car platform can play in creating a family of products and with regard to various data related to the environmental, economic, and social pillars of each of the 15 modules of a car platform and also, using the best–worst method technique and multi-objective mathematical programming with the augmented epsilon constraint method, we were able to achieve a set of platforms with maximum sustainability. The present study explores the possibility of determining the most efficient combinations of modules for every one of the 23 cars’ platforms to produce a collection of products. Through these methods, the 54 efficient solutions in the Pareto front were achieved, and out of this number, after considering all the factors and weights of the objective functions, solution no. 51 was selected as the most efficient. Subsequently, all the 15 module variants of the 23 platforms were determined for solution no. 51. Finally, these variants were ranked on the basis of the SAW technique, and finally, sensitivity analysis is done.

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.