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Journal of Industrial & Management Optimization

March 2021 , Volume 17 , Issue 2

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Collaborative environmental management for transboundary air pollution problems: A differential levies game
David W. K. Yeung, Yingxuan Zhang, Hongtao Bai and Sardar M. N. Islam
2021, 17(2): 517-531 doi: 10.3934/jimo.2019121 +[Abstract](1400) +[HTML](540) +[PDF](357.14KB)

This paper develops a new cooperative dynamic time consistent model for studying regional air pollution management issues in a cooperative game framework for formulating pollution control policies and dynamically consistent compensation mechanisms. As air pollution is a transboundary issue, unilateral response on the part of one region is generally ineffective. Regional cooperation is essential to resolve serious environmental problems. In addition, the long-term environmental impacts are closely related to the building up existing air pollution stocks in Sulfur Dioxide (SO2), Nitrogen Dioxide (NO2), Respirable suspended particulates (RSP) and Ozone (O3). A cooperative dynamic game with different types of pollutants is developed. We characterize the non-cooperative outcomes, and examine the cooperative arrangements, group optimal actions, and individually rational imputations. In particular, an air pollution levy consisting of four components involving damage charges on emissions of sulfur dioxide, nitrogen dioxide, respirable suspended particulates and ozone depletion materials. Cooperative games offer the possibility of socially optimal and group efficient solutions to the lack of cooperation among different regions involving decision problems among strategic actors. This paper makes a valuable contribution to the literature as this is the first cooperative dynamic time consistent model for regional management of different types of air pollutants.

Hybrid social spider optimization algorithm with differential mutation operator for the job-shop scheduling problem
Guo Zhou, Yongquan Zhou and Ruxin Zhao
2021, 17(2): 533-548 doi: 10.3934/jimo.2019122 +[Abstract](1036) +[HTML](489) +[PDF](488.99KB)

The job-shop scheduling problem is one of the well-known hardest combinatorial optimization problems. The problem has captured the interest of a significant number of researchers, but no efficient solution algorithm has been found yet for solving it to optimality in polynomial time. In this paper, a hybrid social-spider optimization algorithm with differential mutation operator is presented to solve the job-shop scheduling problem. To improve the exploration capabilities of the social spider optimization algorithm (SSO), we incorporate the DM operator (a mutation operator taken from the deferential evolutionary (DE) algorithm) into the framework of the female cooperative operator. The experimental results show that the proposed method effectiveness in solving job-shop scheduling compared to other optimization algorithms in the literature.

Analysis of $GI^{[X]}/D$-$MSP/1/\infty$ queue using $RG$-factorization
Sujit Kumar Samanta and Rakesh Nandi
2021, 17(2): 549-573 doi: 10.3934/jimo.2019123 +[Abstract](895) +[HTML](491) +[PDF](482.73KB)

This paper analyzes an infinite-buffer single-server queueing system wherein customers arrive in batches of random size according to a discrete-time renewal process. The customers are served one at a time under discrete-time Markovian service process. Based on the censoring technique, the UL-type \begin{document}$ RG $\end{document}-factorization for the Toeplitz type block-structured Markov chain is used to obtain the prearrival epoch probabilities. The random epoch probabilities are obtained with the help of classical principle based on Markov renewal theory. The system-length distributions at outside observer's, intermediate and post-departure epochs are obtained by making relations among various time epochs. The analysis of waiting-time distribution measured in slots of an arbitrary customer in an arrival batch has also been investigated. In order to unify the results of both discrete-time and its continuous-time counterpart, we give a brief demonstration to get the continuous-time results from those of the discrete-time ones. A variety of numerical results are provided to illustrate the effect of model parameters on the performance measures.

Analysis of Markov-modulated fluid polling systems with gated discipline
Zsolt Saffer, Miklós Telek and Gábor Horváth
2021, 17(2): 575-599 doi: 10.3934/jimo.2019124 +[Abstract](816) +[HTML](464) +[PDF](543.53KB)

In this paper we present two different analytical descriptions of the fluid polling model with Markov modulated load and gated discipline. The fluid arrival to the stations is modulated by a common continuous-time Markov chain (the special case when the modulating Markov chains are independent is also included). The fluid is removed at the stations during the service period by a station dependent constant rate.

The first analytical description is based on the relationships of steady-state fluid levels at embedded server arrival and departure epochs. We derive the steady-state vector Laplace transform of the fluid levels at the stations at arbitrary epoch and its moments. The second analytical description applies the method of supplementary variables and results in differential equations, from which the joint density function of the fluid levels can be obtained.

We also propose computational methods for both analytical descriptions and provide numerical examples to illustrate the numeric computations.

Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours
Hongxia Sun, Yao Wan, Yu Li, Linlin Zhang and Zhen Zhou
2021, 17(2): 601-631 doi: 10.3934/jimo.2019125 +[Abstract](888) +[HTML](487) +[PDF](624.54KB)

We study competition in a dual-channel supply chain in which a single supplier sells a single product through its own direct channel and through two different duopolistic retailers. The two retailers have three competitive behaviour patterns: Cournot, Collusion and Stackelberg. Three models are respectively constructed for these patterns, and the optimal decisions for the three patterns are obtained. These optimal solutions are compared, and the effects of certain parameters on the optimal solutions are examined for the three patterns by considering two scenarios: a special case and a general case. In the special case, the equilibrium supply chain structures are analysed, and the optimal quantity and profit are compared for the three different competitive behaviours. Furthermore, both parametric and numerical analyses are presented, and some managerial insights are obtained. We find that in the special case, the Stackelberg game allows the supplier to earn the highest profit, the retailer playing the Collusion game makes the supplier earn the lowest profit, and the Stackelberg leader can gain a first-mover advantage as to the follower. In the general case, the supplier can achieve a higher profit by raising the maximum retail price or holding down the self-price sensitivity factor.

Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items
Musen Xue and Guowei Zhu
2021, 17(2): 633-648 doi: 10.3934/jimo.2019126 +[Abstract](865) +[HTML](550) +[PDF](316.28KB)

This paper studies a dynamic pricing and replenishment problem for perishable items considering the behavior of decision-maker (partially myopic or forward-looking) and the dynamic effects of cumulative sales. A dynamic optimization model is presented to maximize the total profit per unit time and solved on the basis of Pontryagin's maximum principle. The optimal pricing and replenishment strategies for partially myopic and forward-looking scenarios are obtained. By comparing the partially myopic and forward-looking strategies through numerical analysis, we find the main results: First, applying a skimming pricing strategy might be a good choice when the saturation effects are considered. Second, the decreasing rate of product sales, deterioration coefficient, and holding cost of perishable items per unit exhibit impact on the behavioral preference of decision-maker. Under certain conditions, partially myopic behavior can bring more profit than forward-looking behavior. These managerial implications provide useful guidelines for the decision-maker.

Supplier's investment in manufacturer's quality improvement with equity holding
Hong Fu, Mingwu Liu and Bo Chen
2021, 17(2): 649-668 doi: 10.3934/jimo.2019127 +[Abstract](917) +[HTML](614) +[PDF](505.34KB)

This paper considers a supply chain in which an upstream supplier sells a component to a downstream manufacturer facing a price and quality sensitive demand. The supplier has a chance to make investment in the manufacturer, which can not only enable the supplier to hold equity shares in the manufacturer and thus achieve profit sharing with the manufacturer, but also provide resources for the manufacturer to improve its product quality. Under any given investment strategy of the supplier, the equilibrium decisions of the two chain members on wholesale price and profit margin are characterized. Then, the supplier's optimal investment strategy is derived. The paper considers three competition models: supplier Stackelberg (SS), manufacturer Stackelberg (MS), and vertical Nash (VN) models, which correspond to different market power structures. The paper shows that the investment can always increase the market demand. Moreover, in both the SS and VN models, the value of the supplier's investment for the entire supply chain, comes from not only the quality improvement but also the profit sharing caused by equity holding; while in the MS model, the investment value comes only from the quality improvement.

A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure
Vadim Azhmyakov, Juan P. Fernández-Gutiérrez, Erik I. Verriest and Stefan W. Pickl
2021, 17(2): 669-686 doi: 10.3934/jimo.2019128 +[Abstract](1051) +[HTML](438) +[PDF](470.38KB)

This paper extends a newly developed computational optimization approach to a specific class of Maximal Covering Location Problems (MCLPs) with a switched dynamic structure. Most of the results obtained for the conventional MCLP address the "static" case where an optimal decision is determined on a fixed time-period. In our contribution we consider a dynamic MCLP based optimal decision making and propose an effective computational method for the numerical treatment of the switched-type Dynamic Maximal Covering Location Problem (DMCLP). A generic geometrical structure of the constraints under consideration makes it possible to separate the originally given dynamic optimization problem and reduce it to a specific family of relative simple auxiliary problems. The generalized Separation Method (SM) for the DMCLP with a switched structure finally leads to a computational solution scheme. The resulting numerical algorithm also includes the classic Lagrange relaxation. We present a rigorous formal analysis of the DMCLP optimization methodology and also discuss computational aspects. The proposed SM based algorithm is finally applied to a practically oriented example, namely, to an optimal design of a (dynamic) mobile network configuration.

Note on $ Z $-eigenvalue inclusion theorems for tensors
Chaoqian Li, Yajun Liu and Yaotang Li
2021, 17(2): 687-693 doi: 10.3934/jimo.2019129 +[Abstract](818) +[HTML](484) +[PDF](319.02KB)

Wang et al. gave four \begin{document}$ Z $\end{document}-eigenvalue inclusion intervals for tensors in [Discrete and Continuous Dynamical Systems Series B, 1 (2017), 187-198]. However, these intervals always include zero, and hence could not be used to identify the positive definiteness of a homogeneous polynomial form. In this note, we present a new \begin{document}$ Z $\end{document}-eigenvalue inclusion interval with parameters for even-order tensors, which not only overcomes the above shortcomings under certain conditions, but also provides a checkable sufficient condition for the positive definiteness of homogeneous polynomial forms, as well as the asymptotically stability of time-invariant polynomial systems.

Robust multi-period and multi-objective portfolio selection
Lin Jiang and Song Wang
2021, 17(2): 695-709 doi: 10.3934/jimo.2019130 +[Abstract](879) +[HTML](436) +[PDF](520.47KB)

In this paper, a multi-period multi-objective portfolio selection problem with uncertainty is studied. Under the assumption that the uncertainty set is ellipsoidal, the robust counterpart of the proposed problem can be transformed into a standard multi-objective optimization problem. A weighted-sum approach is then introduced to obtain Pareto front of the problem. Numerical examples will be presented to illustrate the proposed method and validate the effectiveness and efficiency of the model developed.

Loss-averse supply chain decisions with a capital constrained retailer
Wenyan Zhuo, Honglin Yang, Leopoldo Eduardo Cárdenas-Barrón and Hong Wan
2021, 17(2): 711-732 doi: 10.3934/jimo.2019131 +[Abstract](1116) +[HTML](493) +[PDF](538.51KB)

In real-world transactions, capital constraints restrict the rapid development of the enterprises in the supply chain. The loss aversion behaviors of enterprises directly affect the decision making. This paper investigates the optimal decisions of both the supplier and the capital constrained retailer being loss aversion decision makers under different financing strategies. The capital constrained retailer may borrow from a bank or use the supplier's trade credit to satisfy uncertain demand. With a wholesale price contract, we analytically solve the unique Stackelberg equilibrium under two financing schemes. We derive the critical wholesale price that determines the retailer's financing preference. We identify the impacts of the loss aversion coefficients and initial capital level on the operational and financing decisions. Numerical examples reveal that there exists a Pareto improvement zone regarding the retailer's loss aversion coefficient and initial capital level.

Finite horizon portfolio selection problems with stochastic borrowing constraints
Junkee Jeon
2021, 17(2): 733-763 doi: 10.3934/jimo.2019132 +[Abstract](840) +[HTML](429) +[PDF](611.19KB)

In this paper we investigate the optimal consumption and investment problem with stochastic borrowing constraints for a finitely lived agent. To be specific, she faces a credit limit which is a constant fraction of the present value of her stochastic labor income at each time. By using the martingale approach and transformation into an infinite series of optimal stopping problems which has the same characteristic as finding the optimal exercise time of an American option. We recover the value function by establishing a duality relationship and obtain the integral equation representation solution for the optimal consumption and portfolio strategies. Moreover, we provide some numerical illustrations for optimal consumption and investment policies.

Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model
Jiannan Zhang, Ping Chen, Zhuo Jin and Shuanming Li
2021, 17(2): 765-777 doi: 10.3934/jimo.2019133 +[Abstract](989) +[HTML](507) +[PDF](375.66KB)

This paper investigates a continuous-time mean-variance portfolio selection problem based on a log-return model. The financial market is composed of one risk-free asset and multiple risky assets whose prices are modelled by geometric Brownian motions. We derive a sufficient condition for open-loop equilibrium strategies via forward backward stochastic differential equations (FBSDEs). An equilibrium strategy is derived by solving the system. To illustrate our result, we consider a special case where the interest rate process is described by the Vasicek model. In this case, we also derive the closed-loop equilibrium strategy through the dynamic programming approach.

Simulated annealing and genetic algorithm based method for a bi-level seru loading problem with worker assignment in seru production systems
Lan Luo, Zhe Zhang and Yong Yin
2021, 17(2): 779-803 doi: 10.3934/jimo.2019134 +[Abstract](1141) +[HTML](559) +[PDF](1299.05KB)

Seru production is one of the latest manufacturing modes arising from Japanese production practice. Seru can achieve efficiency, flexibility, and responsiveness simultaneously. To accommodate the current business environment with volatile demands and fierce competitions, seru has attracted more and more attention both from researchers and practitioners. A new planning management system, just-in-time organization system (JIT-OS), is used to manage and control a seru production system. The JIT-OS contains two decisions: seru formation and seru loading. By seru formation, a seru system with one or multiple appropriate serus is configured; by seru loading, customer ordered products are allocated to serus to implement production plans. In the process of seru formation, workers have to be assigned to serus. In this paper, a seru loading problem with worker assignment is constructed as a bi-level programming model, and the worker assignment on the upper level is to minimize total idle time while the lower level is to minimize the makespan by finding out optimal product allocation. A product lot can be splitted and allocated to different serus. The problem of this paper is shown to be NP-hard. Therefore, a simulated annealing and genetic algorithm (SA-GA) is developed. The SA is for the upper level programming and the GA is for the lower level programming. The practicality and effectiveness of the model and algorithm are verified by two numerical examples, and the results show that the SA-GA algorithm has good scalability.

An alternating linearization bundle method for a class of nonconvex optimization problem with inexact information
Hui Gao, Jian Lv, Xiaoliang Wang and Liping Pang
2021, 17(2): 805-825 doi: 10.3934/jimo.2019135 +[Abstract](938) +[HTML](524) +[PDF](704.92KB)

We propose an alternating linearization bundle method for minimizing the sum of a nonconvex function and a convex function. The convex function is assumed to be "simple" in the sense that finding its proximal-like point is relatively easy. The nonconvex function is known through oracles which provide inexact information. The errors in function values and subgradient evaluations might be unknown, but are bounded by universal constants. We examine an alternating linearization bundle method in this setting and obtain reasonable convergence properties. Numerical results show the good performance of the method.

An adaptive dynamic programming method for torque ripple minimization of PMSM
Tengfei Yan, Qunying Liu, Bowen Dou, Qing Li and Bowen Li
2021, 17(2): 827-839 doi: 10.3934/jimo.2019136 +[Abstract](929) +[HTML](503) +[PDF](1583.2KB)

The imperfect sinusoidal flux distribution, cogging torque, and current measurement errors can cause periodic torque ripple in the permanent magnet synchronous motor (PMSM). These ripples are reflected in the periodic oscillation of the motor speed and torque, causing vibration at low speeds and noise at high speeds. As a high-precision tracking application, ripple degrades the application performance of PMSM. In this paper, an adaptive dynamic programming (ADP) scheme is proposed to reduce the periodic torque ripples. An optimal controller is designed by iterative control algorithm using robust adaptive dynamic programming theory and strategic iterative technique. ADP is combined with the existing Proportional-Integral (PI) current controller and generates compensated reference current iteratively from cycle to cycle so as to minimize the mean square torque error. As a result, an optimization problem is constructed and an optimal controller is obtained. The simulation results show that the robust adaptive dynamic programming achieves lower torque ripple and shorter dynamic adjustment time during steady-state operation, thus meeting the requirements of steady speed state and the dynamic performance of the regulation system.

Optimal stop-loss reinsurance with joint utility constraints
Nan Zhang, Linyi Qian, Zhuo Jin and Wei Wang
2021, 17(2): 841-868 doi: 10.3934/jimo.2020001 +[Abstract](792) +[HTML](406) +[PDF](594.95KB)

We investigate the optimal reinsurance problems in this paper, specifically, the stop-loss strategies that can bring mutual benefit to both the insurance company and the reinsurance company. The utility improvement constraints are adopted by both contracting parties to guarantee that a reinsurance contract will bring higher expected utilities of wealth to the two participants. We also introduce five risk criteria that reflect the interests of both parties. Under each optimality criterion, we obtain explicit expressions of optimal stop-loss retentions and the corresponding optimised value of objective functions. The upper and lower bounds of expected utility increments under the optimal stop-loss retentions are provided. In the numerical example, we analyse the expected utility improvements under the criterion of minimising total Value-at-Risk. Notable increases in the lower bound of total utility increments are observed after adopting the joint utility improvement constraints.

On the stability of solutions for the generalized vector quasi-equilibrium problems via free-disposal set
Jingjing Wang, Zaiyun Peng, Zhi Lin and Daqiong Zhou
2021, 17(2): 869-887 doi: 10.3934/jimo.2020002 +[Abstract](843) +[HTML](375) +[PDF](676.46KB)

In this paper, we mainly discuss the stability of generalized vector quasi-equilibrium problems (GVQEPs) where the ordering relations are defined by free-disposal set. Firstly, by virtue of the oriented distance function \begin{document}$ (\triangle) $\end{document}, gap functions for (GVQEPs) are given and some properties of them are studied. Then, under some types of continuity assumption, the sufficient conditions of the upper semicontinuity and the upper Painlevé-Kuratowski convergence of solutions for (GVQEPs) are talked about. Moreover, sufficient and necessary conditions of the lower semicontinuity and the lower Painlevé-Kuratowski convergence of solutions for (GVQEPs) are obtained in normed linear spaces. Some examples are given to illustrate the results, and our results are new and extend some known results in the literature.

On correlated defaults and incomplete information
Wai-Ki Ching, Jia-Wen Gu and Harry Zheng
2021, 17(2): 889-908 doi: 10.3934/jimo.2020003 +[Abstract](663) +[HTML](375) +[PDF](315.61KB)

In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market participants includes the default time of each firm and the periodic asset value reports. In this situation, the default time of each firm becomes a totally inaccessible stopping time to the market participants. The original structural model is first transformed to a reduced-form model. Then the conditional distribution of the default time together with the asset value of each name are derived. We prove the existence of the intensity processes of default times and also give the explicit form of the intensity processes. Numerical studies on the intensities of the two correlated names are conducted for some special cases.

A non-zero-sum reinsurance-investment game with delay and asymmetric information
Zhongbao Zhou, Yanfei Bai, Helu Xiao and Xu Chen
2021, 17(2): 909-936 doi: 10.3934/jimo.2020004 +[Abstract](851) +[HTML](524) +[PDF](572.01KB)

In this paper, we investigate a non-zero-sum stochastic differential reinsurance-investment game problem between two insurers. Both insurers can purchase proportional reinsurance and invest in a financial market that contains a risk-free asset and a risky asset. We consider the insurers' wealth processes with delay to characterize the bounded memory feature. For considering the effect of asymmetric information, we assume the insurers have access to different levels of information in the financial market. Each insurer's objective is to maximize the expected utility of its performance relative to its competitor. We derive the Hamilton-Jacobi-Bellman (HJB) equations and the general Nash equilibrium strategies associated with the control problem by applying the dynamic programming principle. For constant absolute risk aversion (CARA) insurers, the explicit Nash equilibrium strategies and the value functions are obtained. Finally, we present some numerical studies to draw economic interpretations and find the following interesting results: (1) the insurer with less information completely ignores its own risk aversion factor, but imitates the investment strategy of its competitor who has more information on the financial market, which is a manifestation of the herd effect in economics; (2) the difference between the effects of different delay weights on the strategies is related to the length of the delay time in the framework of the non-zero-sum stochastic differential game, which illustrates that insurers should rationally estimate the correlation between historical performance and future performance based on their own risk tolerance, especially when decision makers consider historical performance over a long period of time.

Robust portfolio selection for individuals: Minimizing the probability of lifetime ruin
Bing Liu and Ming Zhou
2021, 17(2): 937-952 doi: 10.3934/jimo.2020005 +[Abstract](743) +[HTML](383) +[PDF](557.0KB)

Robust portfolio selection has become a popular problem in recent years. In this paper, we study the optimal investment problem for an individual who carries a constant consumption rate but worries about the model ambiguity of the financial market. Instead of using a conventional value function such as the utility of terminal wealth maximization, here, we focus on the purpose of risk control and seek to minimize the probability of lifetime ruin. This study is motivated by the work of [3], except that we use a standardized penalty for ambiguity aversion. The reason for taking a standardized penalty is to convert the penalty to units of the value function, which makes the difference meaningful in the definition of the value function. The advantage of taking a standardized penalty is that the closed-form solutions to both the robust investment policy and the value function can be obtained. More interestingly, we use the "Ambiguity Derived Ratio" to characterize the existence of model ambiguity which significantly affects the optimal investment policy. Finally, several numerical examples are given to illustrate our results.

Designing prorated lifetime warranty strategy for high-value and durable products under two-dimensional warranty
Tong Peng
2021, 17(2): 953-970 doi: 10.3934/jimo.2020006 +[Abstract](704) +[HTML](403) +[PDF](478.99KB)

This paper considers a prorated lifetime warranty strategy for high-value and durable products under two-dimensional warranty. Different from previous studies, the factor of capital time value is introduced into this study for a long-period lifetime warranty coverage. Besides, the mathematical model considers the warranty coverage into three situations and adopts minimal repair and complete/minimal maintenance strategy in the proposed model. To illustrate the proposed model, this paper analyzes the manufacturer cost, consumer cost, additional warranty service price and profit. The main goal of this paper is to provide a comprehensive warranty service to consumers. Through a numerical example, it is found that the proposed lifetime warranty strategy can provide consumers warranty service throughout product lifetime and reduce the expected cost expenditure to consumers. In addition, it can also provide additional profit sources to manufacturers and meet the realization of warranty objectives, while combined maintenance strategy is adopted in lifetime warranty coverage.

An efficient low complexity algorithm for box-constrained weighted maximin dispersion problem
Zi Xu, Siwen Wang and Jinjin Huang
2021, 17(2): 971-979 doi: 10.3934/jimo.2020007 +[Abstract](815) +[HTML](376) +[PDF](420.68KB)

The box-constrained weighted maximin dispersion problem is to find a point in an \begin{document}$ n $\end{document}-dimensional box such that the minimum of the weighted Euclidean distance from given \begin{document}$ m $\end{document} points is maximized. In this paper, we first propose a two-phase method to solve it. In the first phase, we adopt a block successive upper bound minimization (BSUM) algorithm framework and choose a special piecewise linear upper bound function for the weighted maximin dispersion problem. The per-iteration complexity of our algorithm is very low, since the subproblem is a one-dimensional piecewise linear minimax problem over the box constraints, or eqivalently, a two-dimensional linear programming problem which can be solved in at most \begin{document}$ O(m) $\end{document} time by existing algorithms. In the second phase, a useful rounding is employed to enhance the solution. Moreover, we propose another strengthened two-phase algorithm, which employs a maximum improvement successive upper-bound minimization (MISUM) algorithm instead of BSUM algorithm in the first phase. At each step, only the block that provides the maximum improvement of the upper bound function is updated. Then, it can be proved that every limit point of the iterate generated by this strengthened algorithm is a stationary point. Numerical results show that the proposed algorithms are efficient.

Optimal reinsurance-investment and dividends problem with fixed transaction costs
Xin Zhang, Jie Xiong and Shuaiqi Zhang
2021, 17(2): 981-999 doi: 10.3934/jimo.2020008 +[Abstract](796) +[HTML](401) +[PDF](478.42KB)

In this paper, we consider the dividend optimization problem for a financial corporation with fixed transaction costs. Besides the dividend control, the financial corporation takes proportional reinsurance to reduce risk and invests its reserve in a financial market consisting of a risk-free asset (bond) and a risky asset (stock). Because of the presence of the fixed transaction costs, the problem becomes a mixed classical-impulse stochastic control problem. We solve this problem explicitly and construct the value function together with the optimal policy.

Non-dominated sorting methods for multi-objective optimization: Review and numerical comparison
Qiang Long, Xue Wu and Changzhi Wu
2021, 17(2): 1001-1023 doi: 10.3934/jimo.2020009 +[Abstract](1068) +[HTML](461) +[PDF](1320.13KB)

In multi-objective evolutionary algorithms (MOEAs), non-domina-ted sorting is one of the critical steps to locate efficient solutions. A large percentage of computational cost of MOEAs is on non-dominated sorting for it involves numerous comparisons. By now, there are more than ten different non-dominated sorting algorithms, but their numerical performance comparing with each other is not clear yet. It is necessary to investigate the advantage and disadvantage of these algorithms and consequently give suggestions to specific users and algorithm designers. Therefore, a comprehensively numerical study of non-dominated sorting algorithms is presented in this paper. Firstly, we design a population generator. This generator can generate populations with specific features, such as population size, number of Pareto fronts and number of points in each Pareto front. Then non-dominated sorting algorithms were tested using populations generated in certain structures, and results were compared with respect to number of comparisons and time consumption. Furthermore, In order to compare the performance of sorting algorithms in MOEAs, we embed them into a specific MOEA, dynamic sorting genetic algorithm (DSGA), and use these variations of DSGA to solve some multi-objective benchmarks. Results show that dominance degree sorting outperforms the other methods, fast non-dominance sorting performs the worst and the other sorting algorithms performs equally.

2019  Impact Factor: 1.366




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