Search results

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

This study aims to evaluate the performance of the most popular multi-objective programming scalarization methods in the literature for the aircraft sequencing and scheduling problem (ASSP). These methods are the weighted sum method, weighted goal programming, the ε-constraint method, the elastic constraint method, weighted Tchebycheff and augmented weighted Tchebycheff.

First, the ASSP for a single runway case was modeled using mixed-integer programming considering the safety and operational constraints and the objectives of the minimization of total delay and total flight time for a sample airport. The objectives were then combined by using the multi-objective programming scalarization methods and various expected times of arrival–departure samples were run for the mathematical models. Finally, the methods were evaluated in terms of the number of nondominated solutions, superior nondominated solution and the average solution time using the Measurement of Alternatives and Ranking according to Compromise Solution method, which is a popular multi-criteria decision-making method.

Augmented Weighted Tchebycheff was found to be the most effective approach to ASSP in terms of the evaluation criteria followed by Weighted Tchebycheff and then weighted sum method.

The methodology presented in this study could provide more efficient air traffic management in terminal maneuvering areas when multiple objectives need to be optimized.

Although there are studies including the comparison of several scalarization methods for other problems, the comparison of the methods for ASSP has not yet been handled in the literature. As there are several stakeholders in the air traffic system, ASSP includes several objectives, and as a result, this problem can benefit from analyses using this comparison.

Globalization of markets and pace of technological change have caused the growing importance of paying attention to supplier selection problem. Therefore, this study aims to choose the best suppliers by providing a mathematical model for the supplier selection problem considering the green factors and stochastic parameters. This paper aims to propose a multi-objective model to identify optimal suppliers for a green supply chain network under uncertainty.

The objective of this model is to select suppliers considering total cost, total quality parts and total greenhouse gas emissions. Also, uncertainty is tackled by stochastic programming, and the multi-objective model is solved as a single-objective model by the LP-metric method.

Twelve numerical examples are provided, and a sensitivity analysis is conducted to demonstrate the effectiveness of the developed mathematical model. Results indicate that with increasing market numbers and final product numbers, the total objective function value and run time increase. In case that decision-makers are willing to deal with uncertainty with higher reliability, they should consider whole environmental conditions as input parameters. Therefore, when the number of scenarios increases, the total objective function value increases. Besides, the trade-off between cost function and other objective functions is studied. Also, the benefit of the stochastic programming approach is proved. To show the applicability of the proposed model, different modes are defined and compared with the proposed model, and the results demonstrate that the increasing use of recyclable parts and application of the recycling strategy yield more economic savings and less costs.

This paper aims to present a more comprehensive model based on real-world conditions for the supplier selection problem in green supply chain under uncertainty. In addition to economic issue, environmental issue is considered from different aspects such as selecting the environment-friendly suppliers, purchasing from them and taking the probability of defective finished products and goods from suppliers into account.

The purpose of this study is to develop a holistic optimization model for an integrated sustainable fleet planning and closed-loop supply chain (CLSC) network design problem under uncertainty.

A novel mixed-integer programming model that is able to consider interactions between vehicle fleet planning and CLSC network design problems is first developed. Uncertainties of the product demand and return fractions of the end-of-life products are handled by a chance-constrained stochastic program. Several Pareto optimal solutions are generated for the conflicting sustainability objectives via compromise and fuzzy goal programming (FGP) approaches.

The proposed model is tested on a real-life lead/acid battery recovery system. By using the proposed model, sustainable fleet plans that provide a smaller fleet size, fewer empty vehicle repositions, minimal CO₂ emissions, maximal vehicle safety ratings and minimal injury/illness incidence rate of transport accidents are generated. Furthermore, an environmentally and socially conscious CLSC network with maximal job creation in the less developed regions, minimal lost days resulting from the work's damages during manufacturing/recycling operations and maximal collection/recovery of end-of-life products is also designed.

Unlike the classical network design models, vehicle fleet planning decisions such as fleet sizing/composition, fleet assignment, vehicle inventory control, empty repositioning, etc. are also considered while designing a sustainable CLSC network. In addition to sustainability indicators in the network design, sustainability factors in fleet management are also handled. To the best of the authors' knowledge, there is no similar paper in the literature that proposes such a holistic optimization model for integrated sustainable fleet planning and CLSC network design.

The purpose of this study is to provide conflict-free operations in terminal manoeuvre areas (TMA) using the point merge system (PMS), airspeed reduction (ASR) and ground holding (GH) techniques. The objective is to minimize both total aircraft delay (TD) and the total number of the conflict resolution manoeuvres (CRM).

The mixed integer linear programming (MILP) is used for both single and multi-objective optimization approaches to solve aircraft sequencing and scheduling problem (ASSP). Compromise criterion and ε-constraint methods were included in the methodology. The results of the single objective optimization approach results were compared with baseline results, which were obtained using the first come first serve approach, in terms of the total number of the CRM, TD, the number of aircraft using PMS manoeuvres, ASR manoeuvres, GH manoeuvres, departure time updates and on-time performance.

The proposed single-objective optimization approach reduced both the CRM and TD considerably. For the traffic flow rates of 15, 20 and 25 aircraft, the improvement of CRM was 53.08%, 41.12% and 32.6%, the enhancement of TD was 54.2%, 48.8% and 31.06% and the average number of Pareto-optimal solutions were 1.26, 2.22 and 3.87, respectively. The multi-objective optimization approach also exposed the relationship between the TD and the total number of CRM.

The proposed mathematical model can be implemented considering the objectives of air traffic controllers and airlines operators. Also, the mathematical model is able to create conflict-free TMA operations and, therefore, it brings an opportunity for air traffic controllers to reduce frequency occupancy time.

The mathematical model presents the total number of CRM as an objective function in the ASSP using the MILP approach. The mathematical model integrates air traffic controllers’ and airline operators’ perspective together with new objective functions.

Assembly lines are one of the places where energy consumption is intensive in manufacturing enterprises. The use of robots in assembly lines not only increases productivity but also increases energy consumption and carbon emissions. The purpose of this paper is to minimize the cycle time and total energy consumption simultaneously in parallel robotic assembly lines (PRAL).

Due to the NP-hardness of the problem, A Pareto hybrid discrete firefly algorithm based on probability attraction (PHDFA-PA) is developed. The algorithm parameters are optimized using the Taguchi method. To evaluate the results of the algorithm, a multi-objective programming model and a restarted simulated annealing (RSA) algorithm are used.

According to the comparative study, the PHDFA-PA has a competitive performance with the RSA. Thus, it is possible to achieve a sustainable PRAL through the proposed method by addressing the cycle time and total energy consumption simultaneously.

To the best knowledge of the authors, this is the first study addressing energy consumption in PRAL. The proposed method for PRAL is efficient in solving the multi-objective balancing problem.

This paper aims to introduce a novel structure for the physical internet (PI)–enabled sustainable supplier selection and inventory management problem under uncertain environments.

To address hybrid uncertainty both in the objective function and constraints, a novel interactive hybrid multi-objective optimization solution approach combining Me-based fuzzy possibilistic programming and interval programming approaches is tailored.

Various numerical experiments are introduced to validate the feasibility of the established model and the proposed solution method.

Due to its interconnectedness, the PI has the opportunity to support firms in addressing sustainability challenges and reducing initial impact. The sustainable supplier selection and inventory management have become critical operational challenges in PI-enabled supply chain problems. This is the first attempt on this issue, which uses the presented novel interactive possibilistic programming method.

The purpose of this paper is to present a four‐phase dynamic feedback model for supply partner selection in agile supply chains (ASCs). ASCs are commonly used as a response to increasingly dynamic markets. However, partner selection in ASCs is inherently more complex and difficult under conditions of uncertainty and ambiguity as supply chains form and re‐form.

The model draws on both quantitative and qualitative techniques, including the Dempster‐Shafer and optimisation theories, radial basis function artificial neural networks (RBF‐ANN), analytic network process‐mixed integer multi‐objective programming (ANP‐MIMOP), Kraljic's supplier classification matrix and principles of continuous improvement. It incorporates modern computer programming techniques to overcome the information processing difficulties inherent in selecting from amongst large numbers of potential suppliers against multiple criteria in conditions of uncertainty.

The model enables decision makers to make efficient and effective use of the vastly increased amount of data that is available in today's information‐driven society and it offers a comprehensive, systematic and rigorous approach to a complex problem.

The model has two main drawbacks. First, practitioners may find it difficult to match supplier evaluation criteria with the strategic objectives for an ASC. Second, they may perceive the model to be too complex for use when speed is of the essence.

The main contribution of this paper is that, for the first time, it draws together work from previous articles that have described each of the four stages of the model in detail to present a comprehensive overview of the model.

The paper seeks to provide academic researchers and practitioners with a better understanding about purchasing strategies through an integrated approach to supplier selection and purchasing decisions.

This paper views supplier selection as a multi‐criteria problem. Through the analytical hierarchy process (AHP), in consideration of both quantitative and qualitative criteria, a set of candidate suppliers is identified. A multi‐objective linear programming (MOLP) model, with multiple objectives and a set of system constraints, is then formulated and solved to allocate the optimum order quantities to the candidate suppliers.

The paper provides tradeoffs among different objectives, which are more consistent with the complexity and nature of the real‐world decision‐making environment. It also offers better information and solutions supporting effective purchasing decisions.

The main concept of the proposed approach can be applicable to any organization with a purchasing function. However, its implementation will be very specific to a particular organization of interest, as each individual organization must define its own subjective criteria and constraints. The area of decision support system development, which automates (or computerizes) the input process of the proposed models and integrates with other databases in a company, will provide great opportunities for future research.

The paper provides practitioners with flexibility and effectiveness in their supplier selection and purchasing decision process and with a better understanding about their future purchasing strategies. The results from the application of the proposed models to the supplier selection problem at a high‐technology firm in Taiwan show that the models are effective and applicable.

This paper takes an integrated approach to problem analysis (i.e. multi‐objectives with both quantitative and qualitative information), uses a sound scientific methodology in model development (i.e. integrating AHP with MOLP), and provides practical use of the models. It offers additional knowledge and value to both academics and practitioners.

The purpose of this paper is twofold. Initially, a multi-objective binary integer programming model is proposed for designing an appropriate supply chain that takes into consideration both responsiveness and efficiency. Then, a responsiveness-cost efficient frontier is generated for the supply chain design that can help organizations find the right balance between responsiveness and efficiency, and hence achieve a strategic fit between organizational strategy and supply chain capabilities.

The proposed SC design model used both cross-functional and logistical SC drivers to build a binary integer programming model. To this end, various alternative solutions that correspond to different SC design portfolios were generated and a responsiveness-cost efficient frontier was constructed.

Various alternative solutions that correspond to different SC designs were generated and a responsiveness-cost efficient frontier was constructed to help the decision makers to design SC portfolios to achieve a strategic fit between organizational strategy and SC capabilities.

The proposed methodology enables the decision makers to incorporate both qualitative and quantitative judgements in SC design. The methodology is easy to use and it can be readily implemented by a software.

The proposed methodology allows for subjective value judgements of the decision makers to be considered in SC design and the efficiency-responsiveness frontier generated by the methodology provides a trade-off to be used when choosing between speed and cost efficiency in SC design.