Bi-objective Mathematical Programming Model Research Articles

A New Biobjective Model to Optimize Integrated Redundancy Allocation and Reliability-Centered Maintenance Problems in a System Using Metaheuristics

A novel integrated model is proposed to optimize the redundancy allocation problem (RAP) and the reliability-centered maintenance (RCM) simultaneously. A system of both repairable and nonrepairable components has been considered. In this system, electronic components are nonrepairable while mechanical components are mostly repairable. For nonrepairable components, a redundancy allocation problem is dealt with to determine optimal redundancy strategy and number of redundant components to be implemented in each subsystem. In addition, a maintenance scheduling problem is considered for repairable components in order to identify the best maintenance policy and optimize system reliability. Both active and cold standby redundancy strategies have been taken into account for electronic components. Also, net present value of the secondary cost including operational and maintenance costs has been calculated. The problem is formulated as a biobjective mathematical programming model aiming to reach a tradeoff between system reliability and cost. Three metaheuristic algorithms are employed to solve the proposed model: Nondominated Sorting Genetic Algorithm (NSGA-II), Multiobjective Particle Swarm Optimization (MOPSO), and Multiobjective Firefly Algorithm (MOFA). Several test problems are solved using the mentioned algorithms to test efficiency and effectiveness of the solution approaches and obtained results are analyzed.

Multi-objective design of an organ transplant network under uncertainty

We propose a novel multi-period location–allocation model for the design of an organ transplant transportation network under uncertainty. The model consists of a bi-objective mathematical programming model that minimizes total cost and time, including waiting time in the queue for the transplant operation, while considering organs’ priorities. A fuzzy multi-objective programming based approach is presented to solve the small and medium size problems to optimality. For larger problems, we propose two meta-heuristics based algorithms. Lower bounds, and several numerical examples with managerial insights are discussed. A real case-study is provided, and the existing and the proposed optimal solutions are compared.

A fuzzy bi-objective mathematical model for optimum portfolio selection by considering inflation rate effects

Selecting and scheduling of project portfolios from a given set of investment proposals is one of the most important problems for which managers take several aspects into consideration. Inflation rate as one of these aspects is inherently uncertain, and because of this, various inflation rates can cause risky environments. Since risk can be decision driver for a proper selection, the purpose of this paper is fixed to minimize the risk and maximize the projects rate of return as two conflict objectives by considering inflation rate effects. A bi-objective mathematical programming model with fuzzy parameters is developed and well-known NSGA-II is applied to solve the developed model. Pareto plot of two conflict objectives helps decision maker (DM) to choose the best solution based on DM’s acceptable risk level. Moreover, the proposed model makes the project portfolio selection process more effective with developing a novel mathematical programming by sharing limited available budgets and resources. Finally, numerical results indicate the effectiveness of the proposed model with consideration the inflation rate effects on selecting project portfolios.

A new mixed-integer programming model for joint inventory-transportation problem in a social responsible supply chain

The role of corporate social responsibility (CSR) in supply chain management is an interesting subject that has attracted significant efforts of researchers and practitioners in recent years. This paper addresses the joint inventory-transportation problem in a three-echelon social responsible supply chain. A new bi-objective mixed-integer mathematical programming model is developed that its first objective function aims to minimise the total costs including transportation costs and inventory holding and shortage costs, while the second one maximises the social responsibility of the supply chain. To form the second objective function three credible CSR criteria are selected from the CSR measurement frameworks existed in the relevant literature. To show the performance and applicably of the proposed model an illustrative example is used. The illustrative example is solved by GAMS optimisation software and the corresponding results as well as some managerial implications are reported in the paper.

Robust possibilistic programming for socially responsible supply chain network design: A new approach

The importance of social responsibility of corporate and business units is increasingly emphasized by researchers and practitioners in recent years. Since supply chains play important roles in today's business environment, the issue of social responsibility should be considered carefully when designing and planning of supply chains to move towards sustainability. This paper addresses the problem of socially responsible supply chain network design under uncertain conditions. To this aim, first a bi-objective mathematical programming model is developed wherein its objective functions include minimizing the total cost and maximizing the supply chain social responsibility. Then, for coping with uncertain parameters effectively, a novel possibilistic programming approach, called robust possibilistic programming (RPP), is proposed. Several varieties of RPP models are developed and their differences, weaknesses, strengths and the most suitable conditions for being used are discussed. A real industrial case study is provided to illustrate the performance and applicability of the proposed RPP models in practice.

A biobjective model for the locational planning of hospitals and health centers

The aim of this paper is to propose a new location-allocation structure, in an effort to improve the operational shortcomings of the existing locations of primary health care centers. These shortcomings are mainly caused by the preference of patients to use local hospitals rather than health centers. The method is based on a biobjective mathematical programming model for locating hospitals and primary health care centers. Two objectives are considered: (1) minimization of distance between patients and facilities, (2) equitable distribution of the facilities among citizens. We formulate the model taking into consideration the interdependence of the locations i.e., the general hospitals and health centers. This approach enables us to introduce a new aspect to the location problem, namely public preferences and also to consider the decentralization of the health care system. In order to represent the available information we employ Geographic Information Systems (GIS). We apply this model in the area of Western Greece and then compare our results with the solution originally selected by planners. Demographic data concerning the major and minor population centers of the area were based on the latest census of 2001. The results confirm the necessity of applied scientific approaches for regulating the health care system in order to establish rational strategic planning and ensure the best use of the available resources.

Optimization of Multiobjective System Reliability Design Using FLC controlled GA

A practical optimal reliability design of a system required high system reliability could be formulated as an appropriate mathematical programming model, however, because in the real world, we should concern some kinds of decision criteria. Particularly, system reliability and construction cost are basically conflict each other, so that when taking both of them into consideration, the system reliability design model can be formulated as a bi-objective mathematical programming model. In this research, we consider a bi-criteria redundant system reliability design problem which is optimized by selecting and assigning system components among different valuable candidates for constructing a series-parallel redundant system. Such a problem is formulated as a bi-criteria nonlinear integer programming (bi-nIP) model. In the past decade, several researchers have developed many heuristic algorithms including genetic algorithms (GAs) for solving multi-criteria system reliability optimization problems and obtained acceptable and satisfactory results. Unfortunately, the Pareto solutions obtained by solving a multi-objective optimization problem using a GA cannot be guaranteed its quality, and the number of the Pareto solutions obtained is sometimes not so many. In order to overcome such problems, we propose a hybrid genetic algorithm combined with a Fuzzy Logic Controller (FLC) and a local search technique to obtain the Pareto solutions as many and good as possible. The efficiency of the proposed method is demonstrated through comparative numerical experiments.