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This chapter presents selected multiobjective methods for multiperiod portfolio optimization problem. Portfolio models are formulated as multicriteria mixed integer programs. Reference point method together with weighting approach is proposed. The portfolio selection problem considered is based on a multiperiod model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to allocate the wealth on different securities to optimize the portfolio expected return, the probability that the return is not less than a required level. Multiobjective methods were used to find tradeoffs between risk, return, and the number of securities in the portfolio. In computational experiments the data set of daily quotations from the Warsaw Stock Exchange were used.

This chapter presents two multicriteria optimization models with bi and triple objectives solved with weighted-sum approach. Solved problems are allocation of personnel in a health care institution. To deal with these problems, mixed integer programming formulation has been applied. Results have shown the impact of problem parameter change for importance of the different objectives. Presented problems have been solved using AMPL programming language with solver CPLEX v9.1, with the use of branch and bound method.

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.

The paper formulates a bi-objective mixed-integer nonlinear programming model, aimed at minimizing the total labor hours and the workload unfairness for the multi-skilled worker assignment problem in Seru production system (SPS).

Three approaches, namely epsilon-constraint method, non-dominated sorting genetic algorithm 2 (NSGA-II) and improved strength Pareto evolutionary algorithm (SPEA2), are designed for solving the problem.

Numerous experiments are performed to assess the applicability of the proposed model and evaluate the performance of algorithms. The merged Pareto-fronts obtained from both NSGA-II and SPEA2 were proposed as final solutions to provide useful information for decision-makers.

SPS has the flexibility to respond to the changing demand for small amount production of multiple varieties products. Assigning cross-trained workers to obtain flexibility has emerged as a major concern for the implementation of SPS. Most enterprises focus solely on measures of production efficiency, such as minimizing the total throughput time. Solutions based on optimizing efficiency measures alone can be unacceptable by workers who have high proficiency levels when they are achieved at the expense of the workers taking more workload. Therefore, study the tradeoff between production efficiency and fairness in the multi-skilled worker assignment problem is very important for SPS.

The study investigates a new mixed-integer programming model to optimize worker-to-seru assignment, batch-to-seru assignment and task-to-worker assignment in SPS. In order to solve the proposed problem, three problem-specific solution approaches are proposed.

This paper proposes a two-level supply chain including suppliers and manufacturers. The purpose of this paper is to design a resilient fuzzy risk-averse supply portfolio selection approach with lead-time sensitive manufacturers under partial and complete supply facility disruption in addition to the operational risk of imprecise demand to minimize the mean-risk costs. This problem is analyzed for a risk-averse decision maker, and the authors use the conditional value-at-risk (CVaR) as a risk measure, which has particular applications in financial engineering.

The methodology of the current research includes two phases of conceptual model and mathematical model. In the conceptual model phase, a new supply portfolio selection problem is presented under disruption and operational risks for lead-time sensitive manufacturers and considers resilience strategies for risk-averse decision makers. In the mathematical model phase, the stages of risk-averse two-stage fuzzy-stochastic programming model are formulated according to the above conceptual model, which minimizes the mean-CVaR costs.

In this paper, several computational experiments were conducted with sensitivity analysis by GAMS (General algebraic modeling system) software to determine the efficiency and significance of the developed model. Results show that the sensitivity of manufacturers to the lead time as well as the occurrence of disruption and operational risks, significantly affect the structure of the supply portfolio selection; hence, manufacturers should be taken into account in the design of this problem.

The study proposes a new two-stage fuzzy-stochastic scenario-based mathematical programming model for the resilient supply portfolio selection for risk-averse decision-makers under disruption and operational risks. This model assumes that the manufacturers are sensitive to lead time, so the demand of manufacturers depends on the suppliers who provide them with services. To manage risks, this model also considers proactive (supplier fortification, pre-positioned emergency inventory) and reactive (revision of allocation decisions) resilience strategies.

The proposed model aims to consider the flying hours as a criterion to initiate maintenance operation. Based on this condition, aircraft must be checked before flying hours threshold is met. After receiving maintenance service, the model ignores previous flying hours and the aircraft can keep on flying until the threshold value is reached again. Moreover, the model considers aircraft age and efficiency to assign them to flights.

The aircraft maintenance routing problem (AMRP), as one of the most important problems in the aviation industry, determines the optimal route for each aircraft along with meeting maintenance requirements. This paper presents a bi-objective mixed-integer programming model for AMRP in which several criteria such as aircraft efficiency and ferrying flights are considered.

As the solution approaches, epsilon-constraint method and a non-dominated sorting genetic algorithm (NSGA-II), including a new initializing algorithm, are used. To verify the efficiency of NSGA-II, 31 test problems in different scales are solved using NSGA-II and GAMS. The results show that the optimality gap in NSGA-II is less than 0.06%. Finally, the model was solved based on real data of American Eagle Airlines extracted from Kaggle datasets.

The authors confirm that it is an original paper, has not been published elsewhere and is not currently under consideration of any other journal.

The purpose of this paper is to improve the relief procurement process as one of the most important elements of humanitarian logistics. For doing so, a novel two-round decision model is developed to capture the dynamic nature of the relief procurement process by allowing demand updating. The model accounts for the supply priority of items at response phase as well.

A mixed procurement/supply policy is developed through a mathematical model, which includes spot market procurement and a novel procurement auction mechanism combining the concepts of multi-attribute and combinatorial reverse auctions. The model is of bi-objective mixed-integer non-linear programming type, which is solved through the weighted augmented e-constraint method. A case study is also provided to illustrate the applicability of the model.

This study demonstrates the ability of proposed approach to model post-disaster procurement which considers the dynamic environment of the relief logistics. The sensitivity analyses provide useful managerial insights for decision makers by studying the impacts of critical parameters on the solutions.

This paper proposes a novel reverse auction framework for relief procurement in the form of a multi-attribute combinatorial auction. Also, to deal with dynamic environment in the post-disaster procurement, a novel two-period programming model with demand updating is proposed. Finally, by considering the priority of relief items and model’s applicability in the setting of relief logistics, post-disaster horizon is divided into three periods and a mixed procurement strategy is developed to determine an appropriate supply policy for each period.

Supply chain is an important aspect for all the companies and can affect many aspects of companies. Especially the disruption in supply chain is causing huge impacts and consequences that are difficult to deal with. This chapter presents a review of selected multiple criteria problems used in supply chain optimization. Research analyzed the multiple criteria decision-making methods to tackle the problem of supplier evaluation and selection. It also focuses on the problem of supply chain when a disruption happens and presents strategies to deal with the issue of disruptions in supply chain and how to mitigate the impact of disruptions. Prevention, response, protection, and recovery strategies are explained. Practical part is focused in the risk-averse models to minimize expected worst-case scenario by single sourcing. Computational experiments for practical examples have been solved using CPLEX solver.

This paper aims to minimize the mean-risk cost of sustainable and resilient supplier selection, order allocation and production scheduling (SS,OA&PS) problem under uncertainty of disruptions. The authors use conditional value at risk (CVaR) as a risk measure in optimizing the combined objective function of the total expected value and CVaR cost. A sustainable supply chain can create significant competitive advantages for companies through social justice, human rights and environmental progress. To control disruptions, the authors applied (proactive and reactive) resilient strategies. In this study, the authors combine resilience and social responsibility issues that lead to synergy in supply chain activities.

The present paper proposes a risk-averse two-stage mixed-integer stochastic programming model for sustainable and resilient SS,OA&PS problem under supply disruptions. In this decision-making process, determining the primary supplier portfolio according to the minimum sustainable-resilient score establishes the first-stage decisions. The recourse or second-stage decisions are: determining the amount of order allocation and scheduling of parts by each supplier, determining the reactive risk management strategies, determining the amount of order allocation and scheduling by each of reaction strategies and determining the number of products and scheduling of products on the planning time horizon. Uncertain parameters of this study are the start time of disruption, remaining capacity rate of suppliers and lead times associated with each reactive strategy.

In this paper, several numerical examples along with different sensitivity analyses (on risk parameters, minimum sustainable-resilience score of suppliers and shortage costs) were presented to evaluate the applicability of the proposed model. The results showed that the two-stage risk-averse stochastic mixed-integer programming model for designing the SS,OA&PS problem by considering economic and social aspects and resilience strategies is an effective and flexible tool and leads to optimal decisions with the least cost. In addition, the managerial insights obtained from this study are extracted and stated in Section 4.6.

This work proposes a risk-averse stochastic programming approach for a new multi-product sustainable and resilient SS,OA&PS problem. The planning horizon includes three periods before the disruption, during the disruption period and the recovery period. Other contributions of this work are: selecting the main supply portfolio based on the minimum score of sustainable-resilient criteria of suppliers, allocating and scheduling suppliers orders before and after disruptions, considering the balance constraint in receiving parts and using proactive and reactive risk management strategies simultaneously. Also, the scheduling of reactive strategies in different investment modes is applied to this problem.

One of the main advantages of the proposed model is that it is flexible to generate n-day pairings simultaneously. It means that, despite previous researches, one-day to n-day pairings can be generated in a single model. The flexibility in generating parings causes that the proposed model leads to better solutions compared to existing models. Another advantage of the model is minimizing the risk of COVID-19 by limitation of daily flights as well as elapsed time minimization. As airports are among high risk places in COVID-19 pandemic, minimization of infection risk is considered in this model for the first time. Genetic algorithm is used as the solution approach, and its efficiency is compared to GAMS in small and medium-size problems.

One of the most complex issues in airlines is crew scheduling problem which is divided into two subproblems: crew pairing problem (CPP) and crew rostering problem (CRP). Generating crew pairings is a tremendous and exhausting task as millions of pairings may be generated for an airline. Moreover, crew cost has the largest share in total cost of airlines after fuel cost. As a result, crew scheduling with the aim of cost minimization is one of the most important issues in airlines. In this paper, a new bi-objective mixed integer programming model is proposed to generate pairings in such a way that deadhead cost, crew cost and the risk of COVID-19 are minimized.

The proposed model is applied for domestic flights of Iran Air airline. The results of the study indicate that genetic algorithm solutions have only 0.414 and 0.380 gap on average to optimum values of the first and the second objective functions, respectively. Due to the flexibility of the proposed model, it improves solutions resulted from existing models with fixed-duty pairings. Crew cost is decreased by 12.82, 24.72, 4.05 and 14.86% compared to one-duty to four-duty models. In detail, crew salary is improved by 12.85, 24.64, 4.07 and 14.91% and deadhead cost is decreased by 11.87, 26.98, 3.27, and 13.35% compared to one-duty to four-duty models, respectively.

The authors confirm that it is an original paper, has not been published elsewhere and is not currently under consideration of any other journal.