Stochastic multi-objective models for network design problem

Goal programming approach to solving network design problem with multiple objectives and demand uncertainty

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.

The COVID-19 outbreak has forced people to stay at home to prevent the spread of the virus. In this case, social media platforms have become the main communication venue for people. Online sales platforms have also become the main field for people’s daily consumption. So, how to make full use of social media to carry out online advertising promotion, and then achieve better marketing, is one of the core issues that the marketing industry must pay attention to and solve. Therefore, this study takes the advertiser as the decision-maker, maximizes the number of full playing, likes, comments and forwarding, and minimizes the cost of advertising promotion as the decision-making goals, and Key Opinion Leader (KOL) selection as the decision vector. Based on this, a multi-objective uncertain programming model of advertising promotion is constructed. Among them, the chance-entropy constraint is proposed by combining the entropy constraint and the chance constraint. In addition, the multi-objective uncertain programming model is transformed into a clear single-objective model through mathematical derivation and linear weighting of the model. Finally, the practicability and effectiveness of the model are verified by numerical simulation, and decision-making suggestions for advertising promotion are put forward.

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.

In real-world decision-making, uncertainty plays a crucial role, especially when dealing with complex, multi-objective optimization problems. Traditional linear programming (LP) models often have the assumption that the data is precise and deterministic. However, this ‎assumption is often not realistic for many applications, as imprecision will always be present. This paper presents a fuzzy solution to ‎Z-Z-number-based multi-objective linear programming (ZMOLP) models. Z-numbers can combine fuzzy logic and Z-numbers to manage ‎uncertainty in (multi-objective) decision dilemmas. A Z-number consists of two parts: a fuzzy number for the uncertainty in the ‎data and a reliability score that indicates the degree of confidence in the data. The two aspects of Z-numbers make them ef‎fective for modeling imprecise data in multi-objective positioning. The effectiveness and overall computational efficiency of different ‎fuzzy membership functions (triangular, trapezoidal, Gaussian, etc.) were also explored to understand their impact on optimal solu‎tions. Z-numbers, through fuzzy numbers, provide a flexible and adaptable decision-making solution far superior to traditional methods ‎for managing imprecision that leads to a better representation of uncertainty related to objectives and constraints. To demonstrate the viability of Z-number-based approaches, practical applications were employed to illustrate their usage in healthcare decision-making and ‎engineering optimization‎.

Multiobjective linear programming model on injection oilfield recovery system

A multi-objective fuzzy linear programming model for optimization of natural gas supply chain through a greenhouse gas reduction approach

The vendor selection and order quantity allocation problem with fuzzy demand and price discount is formulated as a multi-objective mixed-integer fuzzy programming model. The proposed model has the following characteristics: deterministic and fuzz constraints, and the assumption of fuzzy demand and price discount are expressed by using constraint equations. According to the special features of the model, appropriate solution strategy is proposed. It involves three steps: (1) membership function for every fuzzy objective and constraint is set up; (2) by means of max-min operator, the multi-objective mixed-integer fuzzy programming model is converted into several equivalent single-objective linear programming model; (3) the optimal solution for order quantity allocation problem is derived based on two-phase approach. An application example was also given for testing the feasibility and effectiveness of the proposed method

In this paper, a general closed-loop supply chain (CLSC) network is configured which consists of multiple customers, parts, products, suppliers, remanufacturing subcontractors, and refurbishing sites. We propose a three-stage model including evaluation, network configuration, and selection and order allocation. In the first stage, suppliers, remanufacturing subcontractors, and refurbishing sites are evaluated based on a new quality function deployment (QFD) model. The proposed QFD model determines the relationship between customer requirements, part requirements, and process requirements. In addition, the fuzzy sets theory is utilised to overcome the uncertainty in the decision-making process. In the second stage, the closed-loop supply chain network is configured by a stochastic mixed-integer nonlinear programming model. It is supposed that demand is an uncertain parameter. Finally in the third stage, suppliers, remanufacturing subcontractors, and refurbishing sites are selected and order allocation is determined. To this end, a multi-objective mixed-integer linear programming model is presented. An illustrative example is conducted to show the process. The main novel innovation of the proposed model is to consider the CLSC network configuration and selection process simultaneously, under uncertain demand and in an uncertain decision-making environment.

This paper aims to provide a state-of-the-art review of the transport network design problem (NDP) under uncertainty and to present some new developments on a bi-objective-reliable NDP (BORNDP) model that explicitly optimizes the capacity reliability and travel time reliability under demand uncertainty. Both are useful performance measures that can describe the supply-side reliability and demand-side reliability of a road network. A simulation-based multi-objective genetic algorithm solution procedure, which consists of a traffic assignment algorithm, a genetic algorithm, a Pareto filter, and a Monte-Carlo simulation, is developed to solve the proposed BORNDP model. A numerical example based on the capacity enhancement problem is presented to demonstrate the tradeoff between capacity reliability and travel time reliability in the NDP.

In an increasingly competitive global environment, more and more engineering designers are aware of the importance of facility layout on the entire manufacturing system. With the diversification of products, the proportion of multi-species and one-piece small batch production systems increase, this study focuses on small and medium enterprises as the main target, and researches its facility layout of manufacturing system and design of optimization model. In this paper, we discuss the layout of manufacturing system according to the characteristics of small and medium enterprises, and give a framework process for the layout design. Then learning from the existing planning model, we establish an optimization model for multi-objective non-linear programming to reflect the true environment of layout. By improving the original multi-objective non-linear programming model, we make this multi-objective non-linear programming model more consistent with requirements of facility layout

Whole blood or apheresis donations? A multi-objective stochastic optimization approach

Sustainable supply chain networks have attracted considerable attention in recent years as a means of dealing with a broad range of environmental and social issues. This paper reports a multi-objective mixed-integer linear programming (MILP) model for use in the design of a sustainable closed loop supply chain network under uncertain conditions. The proposed model aims to minimize total cost, optimize environmental impacts of establishment of facilities, processing and transportation between each level as well as social impacts including customer satisfaction. Due to changes in business environment the uncertainty existed in the research problem, in this paper the chance constrained fuzzy programming approach applied to cope with uncertainties in parameter of the proposed model. Then the proposed multi-objective model solves as single-objective model using LP-metric method.

In the initial stage of emergency rescue for major railway emergencies, there may be insufficient emergency resources. In order to ensure that all the emergency demand points can be effectively and fairly rescued, considering the fuzzy properties of the parameters, such as the resource demand quantity, the dispatching time and the satisfaction degree, the railway emergency resources dispatching optimization model is studied, with multi- demand point, multi-depot, and multi-resource. Based on railway rescue features, it was proposed that the couple number of relief point - emergency point is the key to affect railway rescue cost and efficiency. Under the premise of the maximum satisfaction degree of quantity demanded at all emergency points, a multi-objective programming model is established by maximizing the satisfaction degree of dispatching time and the satisfaction degree of the couple number of relief point - emergency point. Combined with the ideal point method, a restrictive parameter interval method for optimal solution was designed, which can realize the quick seek of Pareto optimal solution. Furthermore, an example is given to verify the feasibility and effectiveness of the method.

Purpose This study introduces a multi-vaccine multi-echelon supply chain (MVMS) framework designed to ensure sustainable vaccine distribution during outbreaks. The framework aims to minimize the total costs of vaccine distribution and reduce greenhouse gas (GHG) emissions to mitigate environmental impacts while maximizing job opportunities within the network. Design/methodology/approach Our proposed appraoch employs a multi-objective mixed-integer linear programming model. Findings The findings indicate that incorporating uncertainties related to demand and inspection errors significantly facilitates timely responses to unexpected shortages, fulfills the requirements of healthcare facilities, and enhances the supply chain’s resilience against future uncertainties. This study also explores managerial implications and suggests avenues for future research to further advance this field. Originality/value Existing literature on MVMS often relies on simplifying assumptions of perfect vaccines and primarily focuses on demand uncertainty. However, real-world supply chains are typically marked by imperfections, disruptions, and a variety of uncertainties beyond demand. In this work, we address several sources of parameter uncertainty, including demand variability, inspection errors, vaccine waste, and defective treatments rates to enhance the robustness of our model.