Multi-objective Mathematical Programming Research Articles

A Decision Support Framework for Resilient and Sustainable Service Design

AbstractResilient and sustainable service design is essential for ensuring the longevity and effectiveness of service systems. However, existing literature often neglects key aspects such as articulating resilience attributes and integrating sustainability dimensions. This study proposes a decision support model for a “resilient-sustainable service design” that merges service design principles with resilient system attributes and organizational sustainability goals. The framework incorporates a multi-objective mathematical programming model and a multi-phased Quality Function Deployment (QFD) approach to derive Pareto optimal solutions using the Brute Force algorithm. Applied in the m-health service sector in Bangladesh, the study reveals significant challenges, including limited awareness of services and logistical inefficiencies. To address these issues, flexible strategies such as demand planning and service innovation are implemented. The findings have direct implications for the improvement of service delivery processes and underscore the importance of considering both resilience and sustainability. While focusing on Bangladesh’s m-health sector, the insights gained have broader relevance globally. The integration of resilience and sustainability principles into service design is crucial for addressing complex challenges across sectors and regions. Future research could involve longitudinal studies to capture evolving resilience strategies and explore resilient-sustainable service systems from a broader perspective. This entails examining various factors such as technological advancements and socio-economic dynamics shaping resilient and sustainable service ecosystems.

Developing a Robust Multi-Skill, Multi-Mode Resource-Constrained Project Scheduling Model with Partial Preemption, Resource Leveling, and Time Windows

Real-world projects encounter numerous issues, challenges, and assumptions that lead to changes in scheduling. This exposure has prompted researchers to develop new scheduling models, such as those addressing constrained resources, multi-skill resources, and activity pre-emption. Constrained resources arise from competition among projects for limited access to renewable resources. This research presents a scheduling model with constrained multi-skill and multi-mode resources, where activity durations vary under different scenarios and allow for partial pre-emption due to resource shortages. The main innovation is the pre-emption of activities when resources are unavailable, with defined minimum and maximum delivery time windows. For this purpose, a multi-objective mathematical programming model is developed that considers Bertsimas and Sim’s robust model in uncertain conditions. The model aims to minimize resource consumption, idleness, and project duration. The proposed model was solved using a multi-objective genetic algorithm and finally, its validation was completed and confirmed. Analysis shows that limited renewable resources can lead to increased activity pre-emption and extended project timelines. Additionally, higher demand raises resource consumption, reducing availability and prolonging project duration. Increasing the upper time window extends project time while decreasing the lower bound pressures resources, leading to higher consumption and resource scarcity.

A multi-objective mathematical programming model for location-routing of COVID-19 healthcare waste in Tunisia

A multi-objective mathematical programming model for location-routing of COVID-19 healthcare waste in Tunisia

Constraint Qualifications and Optimality Conditions for Multiobjective Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds

In this paper, we investigate constraint qualifications and optimality conditions for multiobjective mathematical programming problems with vanishing constraints (MOMPVC) on Hadamard manifolds. The MOMPVC-tailored generalized Guignard constraint qualification (MOMPVC-GGCQ) for MOMPVC is introduced in the setting of Hadamard manifolds. By employing MOMPVC-GGCQ and the intrinsic properties of Hadamard manifolds, we establish Karush–Kuhn–Tucker (KKT)-type necessary Pareto efficiency criteria for MOMPVC. Moreover, we introduce several MOMPVC-tailored constraint qualifications and develop interrelations among them. In particular, we establish that the MOMPVC-tailored constraint qualifications introduced in this paper turn out to be sufficient conditions for MOMPVC-GGCQ. Suitable illustrative examples are furnished in the framework of well-known Hadamard manifolds to validate and demonstrate the importance and significance of the derived results. To the best of our knowledge, this is the first time that constraint qualifications, their interrelations, and optimality criteria for MOMPVC have been explored in the framework of Hadamard manifolds.

Constraint qualifications and optimality conditions for nonsmooth multiobjective mathematical programming problems with vanishing constraints on Hadamard manifolds via convexificators

In this paper, we introduce the notion of convexificators in the framework of Hadamard manifolds. We derive some calculus rules for convexificators on Hadamard manifolds and employ them to investigate nonsmooth multiobjective programming problems with vanishing constraints on Hadamard manifolds (abbreviated as, (NMPVC)). The Abadie constraint qualification (abbreviated as, (ACQ)), as well as the generalized (ACQ) (abbreviated as, (GACQ)), are introduced for (NMPVC) in terms of convexificators. Further, (GACQ) is employed to establish the well-known Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary Pareto efficiency criteria for (NMPVC). Moreover, we introduce several other constraint qualifications for (NMPVC) in the Hadamard manifold setting using convexificators and establish interrelations among them. We have furnished non-trivial examples in the framework of some well-known Hadamard manifolds to illustrate the significance of our results. As far as the best of our knowledge is concerned, constraint qualifications and optimality conditions for (NMPVC) have not yet been studied in the framework of Hadamard manifolds via convexificators.

Advancements in Multi-Objective Mathematical Programming Models and Solution Approaches for Sustainable Waste Management Practices in Vehicle Routing Problem: A Systematic Literature Review

In recent years, the integration of sustainable principles into the Vehicle Routing Problem (VRP) for efficient waste management has gained significant attention. This paper provides an overview of advancements in multi-objective mathematical programming (MP) models and the optimization techniques for sustainable waste management practices within the VRP framework. Sustainable waste management practices in the context of the VRP involve optimizing routes and schedules aim to reduce the environmental impact of waste collection. It investigates the integration of multi-objectives with sustainability criteria, including social, economic, and environmental considerations. Furthermore, it surveys various optimization methodologies applied in waste management to enhance efficiency and sustainability practices. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was employed as a formal systematic review guideline for data gathering. Data was obtained from studies conducted between 2017 and 2023. The analysis included a total of 18 papers from online sources and databases. Based on the literature review, it has been observed that the majority of the research focused on employing Mixed-Integer Linear Programming (MILP) models to tackle the optimization problem for waste management. The literature survey demonstrated significant contributions in computational performance, cost-effectiveness, operational efficiency, and utilization of real-world data by improving the solution approaches, aiming to prioritize economic, social, and environmentally friendly solutions. The paper aims to serve as a convenient reference for researchers and practitioners seeking information on using the MP model and solution approaches to optimize VRP for waste management.

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.