Multi-objective Mixed-integer Model Research Articles

Multi-objective home health care routing: a variable neighborhood search method.

Health and convenience are two indispensable indicators of the society promotion. Nowadays, to improve community health levels, the comfort of patients and those in need of health services has received much attention. Providing Home Health Care (HHC) services is one of the critical issues of health care to improve the patient convenience. However, manual nurse planning which is still performed in many HHC institutes results in a waste of time, cost, and ultimately lower efficiency. In this research, a multi-objective mixed-integer model is presented for home health care planning so that in addition to focusing on the financial goals of the institution, other objectives that can help increase productivity and quality of services are highlighted. Therefore, four different objectives of the total cost, environmental emission, workload balance, and service quality are addressed. Taking into account medical staff with different service levels, and the preferences of patients in selecting a service level, as well as different vehicle types, are other aspects discussed in this model. The epsilon-constraint method is implemented in CPLEX to solve small-size instances. Moreover, a Multi-Objective Variable Neighborhood Search (MOVNS) composed of nine local neighborhood moves is developed to solve the practical-size instances. The results of the MOVNS are compared with the epsilon-constraint method, and the strengths and weaknesses of the proposed algorithm are demonstrated by a comprehensive sensitivity analysis. To show the applicability of the algorithm, a real example is designed based on a case study, and the results of the algorithm over real data are evaluated.

Integrated district electricity system with anaerobic digestion and gasification for bioenergy production optimization and carbon reduction

Carbon reduction requirements while securing energy demand create a huge development opportunity for district energy systems (DESs) supported by renewable energy. In this study, a DES was fueled with kitchen waste (KW) feedstock for bioenergy production optimization and sector decarbonization. Inspired by the cascading principle, gasification and anaerobic digestion have been used to treat mixed KW for maximizing bioenergy recovery. Furthermore, a multi-objective mixed-integer model with time series was built to express complex processes such as technology deployment and mass and renewable electricity flows using mathematical language, achieving a trade-off between economic and environmental benefits. The KW treatment industry in Chongqing city was chosen as the location for a case study, in which two electricity trade scenarios were simulated by adjusting the associated parameters. The results show that a DES with surplus electricity feed-in mode helps avoid inevitable adverse events on the main grid, as it ensures that at least 9,457 kWh per day, and up to a maximum of 16,793 kWh, will not be lost by long-distance transmission. Therefore, the mode also contributes more to carbon reduction benefits, but the levelized carbon reduction cost is between 353 and 470 CNY/tone CO2, which is higher than the average carbon tax level published by the trading market.

A New School Bus Routing Problem Considering Gender Separation, Special Students and Mix Loading: A Genetic Algorithm Approach

In developing countries, whereas the urban bus network is a major part of public transportation system, it is necessary to try to find the best design and routing for bus network. Optimum design of school bus routes is very important. Non-optimal solutions for this problem may increase traveling time, fuel consumption, and depreciation rate of the fleet. A new bus routing problem is presented in this study. A multi-objective mixed integer model is proposed to handle the associated problem. Minimization of transportation cost as well as traveling time is the main objectives. The main contributions of this paper are considering gender separation as well as mixed-loading properties in the school bus routing problem. Moreover, special and handicapped students are considered in this problem. The proposed model is applied in a real case study including 4 schools in Tehran. The results indicate the efficiency of the proposed model in comparison with the existing system. This comparison shows that the students’ travelling time is reduced by 28% for Peyvand middle smart school, 24% for Tehran international school, 13% for Hemmat School and 21% for Nikan High school. A customized Genetic Algorithm (GA) is proposed to solve the model. Penalty functions are used to handle the several constraints of the problem in Genetic Algorithm. The results justify the applicability and efficacy of the both proposed model and solution approach.

Multi-objective Truck Scheduling in a Physical Internet Road-Road Cross-docking Hub

Abstract Aiming towards a sustainable supply chain, Physical Internet (PI) has been presented as a global logistics network with standardized PI-containers. PI-nodes, and more specifically PI-hubs, are one of the key elements of the Physical Internet concept. This paper focuses on optimising operations in the Road-Road PI-hub, which was not addressed in the Physical Internet literature. Road-Road PI-hubs are designed to transfer PI-containers between suppliers’ and customers’ trucks. The objective is to minimize both the inbound/outbound trucks delays and the energy consumption during the transferring of PI-containers using PI-conveyors. The problem is formulated as a multi-objective mixed integer model (MO-MIP) to find the optimal Pareto front. The mathematical model is tested on an illustrative instance to show the tradeoff between trucks’ delays and PI-containers routing energy consumption. The primary goal of this paper is to provide a prospect to start optimizing PI-hubs by suggesting a multi-objective mathematical model as a beginning for future researches on the Road-Road PI-hubs.

Design of reverse logistics network for the end-of-life automobiles based on sustainable development

From the point of view of sustainable development, a multi-objective mixed integer model to solve the problem of location and flow distribution of reverse logistics network of end-of-life automobiles. To reflect the various aspects of sustainable development, not only to minimize the objectives of economic cost and environmental cost, at the same time with the maximization of social benefits as the goal. Combined with the case, using the ideal point method by using lingo, it is concluded that the sustainable of scrapped automobile reverse logistics network optimization scheme. In addition, the impact of government subsidy on the sustainability of reverse logistics network is analyzed. In addition, the uncertainty of product recovery and the influence of government subsidy on the sustainable development of reverse logistics network are analyzed. The results show that end-of-life automobiles with more dismantled products have a greater impact on the sustainability of reverse logistics network, and government subsidies have an ideal interval to make the sustainability of reverse logistics network reach the best state.

A new multi-objective mathematical model for hazardous waste management considering social and environmental issues

Hazardous waste management incorporates collection, separation, treatment, recycling and disposal of hazardous wastes. In this paper, a new multi-objective mixed integer model is presented for hazardous waste collection problem. The model aims to minimize transportation and construction costs, and environmental and population risks in hazardous waste management systems. This model is applied in a case study of Iran in order to help decision makers to decide on the location of separation, treatment, recycle, disposal centers, and established technology in treatment center. Moreover, this paper specifies routes between different facilities in collection network. For addressing population and environmental impacts and economical costs, three objective functions including total costs, total population exposure risk, and environmental risks are considered. An augmented e-constraint method is used to generate Pareto optimal solution for these conflicting objectives. Finally, proposed model is utilized in our case study and numerical results and some managerial insights are provided.

A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels

In the supply chain management, configuration of supply chain is the most important decision in the long term and supplier selection and order allocation are the most important decision in the medium-term that are considered separately. Considering these together can overcome the sub-optimality. This paper deals with an integrated model that has two phases. In the first phase, we present a framework for supplier selection criteria in Closed Loop Supply Chain (CLSC). In addition, we define two performance levels for each supplier based on the quantity and capability of purchasing from it to be closer to real world problem. The output of this phase is the score of each supplier in each criterion in each level. In the second phase, we propose a nonlinear multi-objective mixed integer model that determines the number and location of all facilities (strategic decision), flow in each echelon of CLSC (tactical decision) and supplier selection and order allocation (hybrid decision). The objective functions maximize profit and scores of suppliers and minimize total pollution. To solve the model, we have created a transformation based on the piecewise linearization method. The mathematical programming model illustrated by a real numerical example.

On the potential balance among compulsory education outcomes through econometric and multiobjective programming analysis

This paper sheds new light on the relationship between inputs and outputs in the framework of the educational production function. In particular, it is geared at gaining a better understanding of which factors may be affected in order to achieve an optimal educational output level. With this objective in mind, we analyze teacher-based assessments (actual marks) in three different subjects using a multiobjective schema. For much of the analysis we use data from a recent (2010) Survey – ESOC10, linked with the results from an educational assessment program conducted among 11 and 15 year-old students and with the administrative records on teacher-based scores. Following the statistical and econometric analysis of these data, they are used to build a multiobjective mixed integer model. A reference point approach is used to determine the profile of, potentially, the most “successful and balanced” students in terms of educational outcomes. This kind of methodology in multiobjective programming allows generating “very balanced” solutions in terms of the objective values (subjects). Finally, a sensitivity analysis is used to determine policies that can be carried out in order to improve the performance levels of primary and secondary education students. Particularly, policy makers should be more concerned with the need to promote some cultural habits – such as reading –, from both the students’ and parents’ side. Additionally, policy efforts should be focused on making the vocational pathways available to Spanish youth more appealing, with the aim of taking advantage of the particular skills of students not succeeding in the academic track.

A comprehensive dynamic cell formation design: Benders’ decomposition approach

This paper is seeking to design a dynamic cellular manufacturing system (DCMS). Area of multi-objective optimization is attractive not only for offering new opportunities for defining problem, but it helps us to extend and solve the anonymous problem. So a new multi-objective mixed integer model is presented for DCMS. The proposed model considers some real-world critical conditions in lean production which are neglected in similar studies in the literature. This model solves the part and machine grouping simultaneously with labor assignment to minimize the cost of various terms like reassignment cost of human resource, over time cost of equipments and labors, and maximize utilization rate of human resource. The model is linearized and validated with GAMS 22.1⧹Cplex. Because the Benders’ decomposition approach has not been applied to solve multi-objective CMS problems so far, we use this method to solve our model. The results are presented at the end.