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The optimization of investment portfolios is a topic of major importance in financial decision making, with many relevant models available in the relevant literature. The purpose of this paper is to perform a thorough comparative assessment of different bi-objective models as well as multi-objective one, in terms of the performance and robustness of the whole set of Pareto optimal portfolios.

In this study, three bi-objective models are considered (mean-variance (MV), mean absolute deviation, conditional value-at-risk (CVaR)), as well as a multi-objective model. An extensive comparison is performed using data from the Standard and Poor’s 500 index, over the period 2005–2016, through a rolling-window testing scheme. The results are analyzed using novel performance indicators representing the deviations between historical (estimated) efficient frontiers, actual out-of-sample efficient frontiers and realized out-of-sample portfolio results.

The obtained results indicate that the well-known MV model provides quite robust results compared to other bi-objective optimization models. On the other hand, the CVaR model appears to be the least robust model. The multi-objective approach offers results which are well balanced and quite competitive against simpler bi-objective models, in terms of out-of-sample performance.

This is the first comparative study of portfolio optimization models that examines the performance of the whole set of efficient portfolios, proposing analytical ways to assess their stability and robustness over time. Moreover, an extensive out-of-sample testing of a multi-objective portfolio optimization model is performed, through a rolling-window scheme, in contrast static results in prior works. The insights derived from the obtained results could be used to design improved and more robust portfolio optimization models, focusing on a multi-objective setting.

This study aims to reduce carbon emissions and costs in an automobile production plant by improving the operational management efficiency of a serial assembly line assisted by a feeding electric tow vehicle (ETV).

A multi-objective function is formulated to minimize the energy consumption of the ETV from which emissions and costs are measured. First, a mixed-integer linear programming model is used to solve the feeding problem for different sizes of the assembly line. Second, a bi-objective optimization (HBOO) model is used to simultaneously minimize the most eco-efficient objectives: the number of completed runs (tours) by the ETV along the assembly line, and the number of visits (stops) made by the ETV to deliver kits of components to workstations.

The most eco-efficient strategy is always the bi-objective optimal solution regardless of the size of the assembly line, whereas, for single objectives, the optimization strategy differs depending on the size of the assembly line.

Instances of the problem are randomly generated to reproduce real conditions of a particular automotive factory according to a previous case study. The optimization procedure allows managers to assess real scenarios improving the assembly line eco-efficiency. These results promote the implementation of automated control of feeding processes in green manufacturing.

The HBOO-model assesses the assembly line performance with a view to reducing the environmental impact effectively and contributes to reducing the existent gap in the literature. The optimization results define key strategies for manufacturing industries eager to integrate battery-operated motors or to address inefficient traffic of automated transport to curb the carbon footprint.

The purpose of this study is to understand the functional power of frequency from-to chart (FFTC) as an independent solution-key for generation optimal (exact) facilities sequences with an equal distance of straight-line flow patterns. The paper will propose a bi-objective function model based on the Torque Method then will turn it into a computer-based technique with a permutative manner using the full enumeration method. This model aims to figure out if there is a difference between the moment minimization and backtracking treatment. Furthermore, the proposed technique will measure the performance of related works from literature to numerically highlight their limitations.

The literature of related works provided two-principles assumed mastering material flow sequences. The researchers gathered and analyzed the three methods – used FFTC as an independent technique – mentioned in the literature then measured their performance with the proposed technique. The proposed technique is based on the computation of torque value using an enhancement of bi-objective function model then application a permutative approach with full enumeration methodology. The bi-objective function model used once to mimic the grand moment value of FFTC and again to study the reflection of minimizing the congestion of backtracking movements on the minimization of total transportation cost.

Based on the analysis of literature and comparative results of its three case studies using the proposed technique, it is found that: there are optimum facilities sequences with rich opportunities of exact pathway selection. Reduction methodology is an inefficient way to generate exact results. There is a gap between combining the minimization of the grand moment and the treatment of the backtracking problem.

This study is one of the first contributions that discusses the assumption of integration between optimization moment value and its relation to treatment backtracking problem. Also, the illness of reduction methodology to reach optimal solutions. The further direction of this research will highlight the conjecture of searching the exact results for small size problems, analyzing the given data and its logical dimensions, developing logical rules for solving and verifying large size problems based on the exact results (The conjecture of P = NP).

This paper provides a detailed numerical analysis of the most common problems generally faced facility layout problems through understanding the lack of integration between moment minimization and backtracking minimization. Also, the inefficiency of reliance on reduction methodology either in scores of frequencies between facilities with weak relation or the number of permutations. Based on those findings, further study will search the logical philosophy exactly optimizing FFTC manually or without having to deal with a permutative approach for large size problems – which considered non-deterministic polynomial-time problem.

The purpose of this paper is to investigate the major factors influencing retailer’s optimal ordering strategy in a supply chain consisting of one supplier and one retailer, where the retailer is newsvendor-like and capital-constrained, and further explore the issue of supply chain coordination.

Based on bi-objective programming which is modeled under the mean-variance framework, the retailer’s optimal ordering strategy is derived. Furthermore, through comparative analysis between decentralized system and centralized system along with a numerical simulation, this study examines the theoretical conclusions about supply chain coordination.

This study shows that a poor retailer with a high Expected Terminal Wealth Target Threshold (ETWTT) would ignore bankruptcy risk and order more, whereas a rich retailer is relatively conservative. It also reveals that in some cases, the optimal order quantity and performance of decentralized system could be both improved. However, the centralized system can always get more profit than the decentralized one.

This study uses a bankruptcy threshold to describe retailer’s bankruptcy risk, and considers retailer’s wealth status to formulate the model as an innovative bi-objective programming. The type of retailer as rich or poor in terms of his wealth status and asset structure is distinguished. Moreover, the impacts of retailer’s type and ETWTT on ordering strategy are examined.

In this chapter, four bi-objective vehicle routing problems are considered. Weighted-sum approach optimization models are formulated with the use of mixed-integer programming. In presented optimization models, maximization of capacity of truck versus minimization of utilization of fuel, carbon emission, and production of noise are taken into account. The problems deal with real data for green logistics for routes crossing the Western Pyrenees in Navarre, Basque Country, and La Rioja, Spain.

Heterogeneous fleet of trucks is considered. Different types of trucks have not only different capacities, but also require different amounts of fuel for operations. Consequently, the amount of carbon emission and noise vary as well. Modern logistic companies planning delivery routes must consider the trade-off between the financial and environmental aspects of transportation. Efficiency of delivery routes is impacted by truck size and the possibility of dividing long delivery routes into smaller ones. The results of computational experiments modeled after real data from a Spanish food distribution company are reported. Computational results based on formulated optimization models show some balance between fleet size, truck types, and utilization of fuel, carbon emission, and production of noise. As a result, the company could consider a mixture of trucks sizes and divided routes for smaller trucks. Analyses of obtained results could help logistics managers lead the initiative in environmental conservation by saving fuel and consequently minimizing pollution. The computational experiments were performed using the AMPL programming language and the CPLEX solver.

Optimization of resources related to man, money, manpower and those related to organization is critical in context of after-sales supply chains. Many times, organizational objectives in terms of resource optimization and providing superior customer experience might be conflicting, however.

One such instance is when customers expect near 100% service level in which case the organizational costs to meet such high service level goes up significantly. To this end, in this research a novel bi-objective optimization model has been evolved for a typical after-sales service supply chain network constituted of the manufacturer, the retailer and the customer. The first objective function pertains to maximization of the manufacturer's and the retailer's profit. The second objective function is related to the minimization of tardiness of order fulfilment (by the retailer) for the customer.

Employing a small problem instance, the authors generate a number of findings related to service level and information asymmetry. In particular, the authors observe that achieving best possible manufacturer-retailer profit and at the same time 100% service level is a mathematical impossibility. Furthermore, reducing information asymmetry between the customer and the retailer (as opposed to reducing information asymmetry between the retailer and the manufacturer) actually yields higher profits for the manufacturer-retailer pair.

This research describes the mathematical structure of a three-tier after-sales supply chain wherein information quality and service level requirements are key constraints. Furthermore, the study evolves the bi-objective optimization model as a formulation that can drive the operational decisions of manufacturers and retailers who are part of such after-sales service supply chains.

This study aims to deal with a project portfolio selection problem aiming to maximize the net present value of the project portfolio and minimize the resource usage variation between successive time periods.

A bi-objective mixed integer programming model is presented under resource constraints. The parameters related to outlays and net cash flows of existing and new projects are considered to be uncertain. An augmented ε-constraint (AUGMECON) method is used to solve the proposed model, and a fuzzy approach is used to find the most preferred Pareto-optimal solutions among those generated by AUGMECON method. The effectiveness of the proposed solution method is compared with three other multi-objective optimization methods. Finally, some sensitivity analyses are performed to assess the effect of changing a number of parameters on the values of objective functions.

The proposed approach helps corporations make optimal decisions for rebalancing their project portfolio, through launching some new candidate projects and upgrading some of the existing projects.

A novel bi-objective optimization model is proposed for designing a project portfolio problem under budget constraints and profit risk controls. Two types of projects including existing and new projects are considered in the problem. Minimization of resource usage variation between successive periods is considered in the model as one objective function. An AUGMECON method is used to solve the proposed bi-objective mathematical model. A fuzzy approach is applied to find the best Pareto-optimal solutions of AUGMECON method. Results of the proposed solution approach are compared with three other multi-objective decision-making methods in different numerical examples.

This paper aims to present a novel bi-objective mathematical model for a production-inventory system under uncertainty.

This paper addresses agile and lean manufacturing concepts alongside with green production methods to design an integrated capacitated lot sizing problem (CLSP). From a methodological perspective, the problem is solved in three phases. In the first step, an FM/M/C queuing system is used to minimize the number of customers waited to receive their orders. In the second step, an effective approach is applied to deal with the fuzzy bi-objective model and finally, a hybrid metaheuristic algorithm is used to solve the problem.

Some numerical test problems and sensitivity analyzes are conducted to measure the efficiency of the proposed model and the solution method. The results validate the model and the performance of the solution method compared to Gams results in small size test problems and prove the superiority of the hybrid algorithm in comparison with the other well-known metaheuristic algorithms in large size test problems.

This paper presents a novel bi-objective mathematical model for a CLSP under uncertainty. The proposed model is conducted on a practical case and several sensitivity analysis are conducted to assess the behavior of the model. Using a queue system, this problem aims to reduce the items waited in the queue to receive service. Two objective functions are considered to maximize the profit and minimize the negative environmental effects. In this regard, the second objective function aims to reduce the amount of emitted carbon.

The purpose of this paper is to develop a decision support tool for risk-based maintenance scheduling for a large heavily equipped gas sweetening unit in a Liquefied Natural Gas (LNG) plant. Two conflicting objectives, i.e., total maintenance cost and the reliability, are considered in the tool. The tool is tested with the real plant data and suggests several Pareto-optimal schedules for a decision maker to choose from. The financial impacts are assessed.

A bi-objective scheduling optimization model is developed for maintenance scheduling using a risk-based framework. The model is developed integrating genetic algorithm and simulation-based optimization to find Pareto-optimal schedules. The model delivered true Pareto front optimal solutions for given plant-specific data. The two conflicting objectives: the minimization of total expenditures incurred on maintenance-related activities and improving the total reliability are considered.

For large and complex processing facilities such as LNG plant, a shutdown of facility generates a significant financial impact, resulting in millions of dollars in production loss. The developed risk-based equipment selection strategy helps to minimize such an event of production loss by generating a thorough maintenance strategy for inspection, repair, overhaul or replacement schedule of the unit without initiating the shutdown. The proposed model has been successfully applied to obtain an optimize maintenance schedule for a gas sweetening unit.

A future work may consider the state-dependent models for various failure modes that will result in obtaining a better representation of the model. The proposed scheduling can further be extended to multi-criteria scheduling including availability, resource limitation and inflationary condition. A comparative analysis with other meta-heuristic techniques such as harmony search algorithm, tabu search, and simulated annealing will further help in confirming the schedule obtained from this application.

Maintenance scheduling using a conventional approach for special equipment generally does not consider the conflicting objectives. This research addresses this aspect using a bi-objective model. The usefulness of risk-based method is to assist in minimizing the financial and safety risk exposure to the operating companies, but some variation in results is expected due to varying risk matrix for different organizations.

Managing two objectives, i.e., minimizing the cost of maintenance-related activities, while at the same time maximizing the overall reliability dramatically, helps in mitigating adverse safety and financial risk due to fires, explosions, fatality and excessive maintenance cost.

Research develops a decision support tool for managing conflicting objectives for an LNG process. This research highlights the impact of utilizing the simulation-based approach coupled with risk-based equipment selection for complex processing unit or plant maintenance scheduling optimization.

This study aims to deal with the multi-mode resource-constrained project scheduling problem (MRCPSP) with the ability to transport resources among multiple sites, aiming to minimize the total completion time and the total cost of the project simultaneously.

To deal with the problem under consideration, a bi-objective optimization model is developed. All activities are interconnected by finish-start precedence relations, and pre-emption is not allowed. Then, the ɛ-constraint optimization method is used to solve 24 different-sized instances, ranging from 5 to 120 activities, and report the makespan, total cost and CPU time. A set of Pareto-optimal solutions are determined for some instances, and sensitivity analyses are performed to find the impact of changing parameters on objective values.

Results highlight the importance of resource transportability assumption on project completion time and cost, providing useful insights for decision makers and practitioners.

A novel bi-objective optimization model is proposed to deal with the multi-site MRCPSP, considering both the cost and time of resource transportation between multiple sites. To the best of the authors’ knowledge, none of the studies in the project scheduling area has yet addressed this problem.