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Journal of Industrial and Management Optimization

January 2022 , Volume 18 , Issue 1

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An efficient genetic algorithm for decentralized multi-project scheduling with resource transfers
Jingwen Zhang, Wanjun Liu and Wanlin Liu
2022, 18(1): 1-24 doi: 10.3934/jimo.2020140 +[Abstract](1997) +[HTML](982) +[PDF](1302.63KB)
Abstract:

This paper investigates the decentralized resource-constrained multi-project scheduling problem with transfer times (DRCMPSPTT) in which the transfer times of the global resources among different projects are assumed to be sequence-independent, while transfers of local resources take no time within a project. First, two decision variables (\begin{document}$ {y_{ijg}} $\end{document} and \begin{document}$ {w_{ijg}} $\end{document}) are adopted to express the transition state of global resources between projects. \begin{document}$ {y_{ijg}} $\end{document} (takes a value of 0 or 1) represents whether activity i transfers global resource g to activity j; accordingly, the transferred quantity is denoted as \begin{document}$ {w_{ijg}} $\end{document}. Then, we construct an integer linear model with the goal of minimizing the average project delay for the DRCMPSPTT. Second, an adaptive genetic algorithm (GA) is developed to solve the DRCMPSPTT. To gain the schedules for the DRCMPSPTT, the traditional serial and parallel scheduling generation schemes (SGSs) are modified to combine with different resource transfer rules and to design multiple decoding schemes. Third, the numerical experiments are implemented to analyse the effects of eight decoding schemes, and we found that the scheme comprising the parallel SGS and maxRS rule can make the GA work the best; furthermore, the effectiveness of the GA_maxRS (GA embedded with the best scheme) is demonstrated by solving some instances with different sizes.

Statistical mechanics approach for steady-state analysis in M/M/s queueing system with balking
Ikuo Arizono and Yasuhiko Takemoto
2022, 18(1): 25-44 doi: 10.3934/jimo.2020141 +[Abstract](1940) +[HTML](701) +[PDF](345.01KB)
Abstract:

Behavior that a customer who has just arrived at a crowded queueing system leaves without joining the queue is known as the phenomenon of balking. Queueing systems with balking have been studied continually as one of significant subjects. In this paper, the theoretical approach for the steady-state analysis of the Markovian queueing systems with balking is considered based on the concept of the statistical mechanics. Here, it can be easily seen that the strength of balking is not constant but various in each queueing systems. Note that the strength of balking means how degree a customer who has just arrived at a crowded queueing system leaves without joining the queue. In our approach, under considering the difference of the strength of balking for each queueing systems, we have proposed a statistical mechanics model for analyzing the M/M/\begin{document}$ s $\end{document} queueing system with balking by introducing a parameter influencing the strength of balking. Further, we define a procedure for estimating the model parameter influencing the strength of balking. In addition, we consider a method of improving the performance of the M/M/\begin{document}$ s $\end{document} queueing system with balking by utilizing the statistical mechanics approach.

The joint location-transportation model based on grey bi-level programming for early post-earthquake relief
Yufeng Zhou, Bin Zheng, Jiafu Su and Yufeng Li
2022, 18(1): 45-73 doi: 10.3934/jimo.2020142 +[Abstract](1922) +[HTML](655) +[PDF](819.82KB)
Abstract:

The initial period after the earthquake is the prime time for disaster relief. During this period, it is of great value to rationally locate the transfer facilities of relief materials and effectively arrange the transportation of relief materials. Considering the characteristics of the two-level emergency logistics system including uncertain demand, uncertain transportation time, multiple varieties of relief materials, shortage of supply, multi-transportation modes and different urgencies of relief material demand, the integrated issue with the concern of transfer facility location and relief material transportation is studied. Then, this problem is formulated as a grey mixed integer bi-level nonlinear programming in which the upper-level aims at the shortest relief material transportation time and the lower-level aims at the maximum fairness of relief material distribution. According to the characteristics of the model, a hybrid genetic algorithm is designed to solve the proposed model. Finally, a numerical simulation is carried out on the background of 5.12 Wenchuan Earthquake. In addition, the validation of the proposed model and algorithm is verified.

Optimal investment and proportional reinsurance strategy under the mean-reverting Ornstein-Uhlenbeck process and net profit condition
Yin Li, Xuerong Mao, Yazhi Song and Jian Tao
2022, 18(1): 75-93 doi: 10.3934/jimo.2020143 +[Abstract](1769) +[HTML](662) +[PDF](413.1KB)
Abstract:

In this study, under the criterion of maximizing the expected exponential utility of terminal wealth, the optimal proportional reinsurance and investment strategy for an insurer is examined with the compound Poisson claim process. To make the model more realistic, the price process of the risky asset is modelled by the Brownian motion risk model with dividends and transaction costs, where the instantaneous of investment return follows as a mean-reverting Ornstein-Uhlenbeck process. At the same time, the net profit condition and variance reinsurance premium principle are also considered. Using stochastic control theory, explicit expressions for the optimal policy and value function are derived, and various numerical examples are given to further demonstrate the effectiveness of the model.

Performance analysis and optimization research of multi-channel cognitive radio networks with a dynamic channel vacation scheme
Zhanyou Ma, Wenbo Wang, Wuyi Yue and Yutaka Takahashi
2022, 18(1): 95-110 doi: 10.3934/jimo.2020144 +[Abstract](1447) +[HTML](574) +[PDF](567.68KB)
Abstract:

In order to resolve the issues of channel scarcity and low channel utilization rates in cognitive radio networks (CRNs), some researchers have proposed the idea of "secondary utilization" for licensed channels. In "secondary utilization", secondary users (SUs) opportunistically take advantage of unused licensed channels, thus guaranteeing the transmission performance and quality of service (QoS) of the system. Based on the channel vacation scheme, we analyze a preemptive priority queueing system with multiple synchronization working vacations. Under this discipline, we build a three-dimensional Markov process for this queueing model. Through the analysis of performance measures, we obtain the average queueing length for the two types of users, the mean busy period and the channel utility. By analyzing several numerical experiments, we demonstrate the effect of the parameters on the performance measures. Finally, in order to optimize the system individually and socially, we establish utility functions and provide some optimization results for PUs and SUs.

Dynamic-programming-based heuristic for multi-objective operating theater planning
Ya Liu and Zhaojin Li
2022, 18(1): 111-135 doi: 10.3934/jimo.2020145 +[Abstract](2074) +[HTML](695) +[PDF](717.49KB)
Abstract:

This study focuses on the assignment of surgical operations to operating room (OR) blocks to minimize not only the utilization cost of the OR blocks but also the number of patterns generated. We propose a dynamic-programming-based heuristic to solve this problem. Using an iterative formulation, we separate the patterns individually. The computational results show that the proposed heuristic is efficient. Compared with "quasi-optimal" plans, the average cost gap ranges from 0.022 to 0.066 for various scenarios. A lower bound based on column generation procedure is developed. Results show that the average absolute difference of three scenarios are respectively 0.045, 0.081 and 0.115. According to evaluations based on performance indicators from the extant literature, the utilization ratio of the operating theater (OT) varies from 1% underutilization to 2% overutilization in the solutions yielded by the proposed heuristic. This study deals with a multi-objective optimization problem, the second objective of which plays a significant role in reducing the preparation cost, error probability, and staff fatigue in medical systems, where security and human issues are far more emphasized than in other sectors. To the best of our knowledge, our study is the first to investigate such a real-world multi-objective OT planning problem.

An alternative tree method for calibration of the local volatility
Wenxiu Gong and Zuoliang Xu
2022, 18(1): 137-156 doi: 10.3934/jimo.2020146 +[Abstract](1523) +[HTML](641) +[PDF](598.69KB)
Abstract:

In this paper, we combine the traditional binomial tree and trinomial tree to construct a new alternative tree pricing model, where the local volatility is a deterministic function of time. We then prove the convergence rates of the alternative tree method. The proposed model can price a wide range of derivatives efficiently and accurately. In addition, we research the optimization approach for the calibration of local volatility. The calibration problem can be transformed into a nonlinear unconstrained optimization problem by exterior penalty method. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S & P 500 index. Numerical results confirm the excellent performance of the alternative tree pricing model.

Modified spectral PRP conjugate gradient method for solving tensor eigenvalue complementarity problems
Ya Li, ShouQiang Du and YuanYuan Chen
2022, 18(1): 157-172 doi: 10.3934/jimo.2020147 +[Abstract](1448) +[HTML](680) +[PDF](645.6KB)
Abstract:

Tensor eigenvalue complementary problems, as a special class of complementary problems, are the generalization of matrix eigenvalue complementary problems in higher-order. In recent years, tensor eigenvalue complementarity problems have been studied extensively. The research fields of tensor eigenvalue complementarity problems mainly focus on analysis of the theory and algorithms. In this paper, we investigate the solution method for four kinds of tensor eigenvalue complementarity problems with different structures. By utilizing an equivalence relation to unconstrained optimization problems, we propose a modified spectral PRP conjugate gradient method to solve the tensor eigenvalue complementarity problems. Under mild conditions, the global convergence of the given method is also established. Finally, we give related numerical experiments and numerical results compared with inexact Levenberg-Marquardt method, numerical results show the efficiency of the proposed method and also verify our theoretical results.

Effect of reliability on varying demand and holding cost on inventory system incorporating probabilistic deterioration
Sudip Adak and G. S. Mahapatra
2022, 18(1): 173-193 doi: 10.3934/jimo.2020148 +[Abstract](1776) +[HTML](854) +[PDF](446.69KB)
Abstract:

This paper presents a mathematical framework to derive an inventory model for time, reliability, and advertisement dependent demand. This paper considers the demand rate is high initially, and then the demand rate reduces later stage, which reflects the situation related to cash in hand. The uncertain deterioration of the product presents through Uniform, Triangular, and Double Triangular probability distributions. The holding cost of the proposed inventory system is dependent on the reliability of the item to make this study a more realistic one. This proposed inventory system allows the situation of shortage and partially backlogged at a fixed rate. Numerical examples, along with managerial implications and sensitivity analysis of the inventory parameters, discuss to examine the effect of changes on the optimal total inventory cost.

Integration of cuckoo search and fuzzy support vector machine for intelligent diagnosis of production process quality
Huiqin Zhang, JinChun Wang, Meng Wang and Xudong Chen
2022, 18(1): 195-217 doi: 10.3934/jimo.2020150 +[Abstract](1402) +[HTML](543) +[PDF](1228.99KB)
Abstract:

The quality of High-tech products usually influenced by numerous cross-correlation quality characteristics in production process. However, traditional quality control method is difficult to satisfy the requirement of monitoring and diagnosing multiple related quality characteristics. Scholars found that the diagnosis effect of support vector machine method is better than others. But, constructing fuzzy support vector machine for diagnosis by calculating the sample membership degree from the sample point to the class center is vulnerable to the influence of sample noise points because it will lead to low accuracy rate. Therefore, this paper focus on exploring the issue about the abnormal pattern and intelligent diagnosis of interrelated multivariable process quality, by taking the multivariable quality characteristics of capacitor as research object. Using multivariate exponentially weighted moving average (MEWMA) control chart to joint monitor the multiple quality characteristics. Constructing a fuzzy support vector machine (FSVM) based on cloud calculative model and cuckoo search (CS) for intelligent diagnosis on abnormal pattern. The result showed that the diagnostic accuracy rate for sample data is 97.42%. In instance analysis, the average diagnosis accuracy rate is 95.60%. It verifies the CS-FSVM model has a good diagnosis performance.

A hierarchic framework for the propagating impacts of the China-U.S. trade war on volume of Chinese containerized exports
Bin Yu, Mengyan Hao, Yonglei Jiang and Lianjie Jin
2022, 18(1): 219-238 doi: 10.3934/jimo.2020151 +[Abstract](1630) +[HTML](709) +[PDF](1000.54KB)
Abstract:

The China-U.S. trade war between the world's two largest economies has received increasing attention. Due to the existing interdependencies within economic sectors, the trade war could bring about ripple effects and cause more damaging impacts than intuitive thoughts. By integrating Inoperability Input-output Model (IIM) and Partial Least Squares Regression (PLSR), we developed a hierarchic IIM-PLSR framework in this study to unravel the ripple effects of the China-U.S. trade war on volume of Chinese containerized exports. The results show that the China-U.S. trade war will affect the operability and output value of not only the tariff-targeted industries but the other interdependent industries. Contrary to expectations, the results show that the China-U.S. Trade War have an insignificant influence on the volume of containerized exports. Even in the worst scenario, the reduction percentage of containerized exports due to China-U.S. trade war is only 0.335%. This study brings fresh insights to stakeholders in the port industry for the implementation of rational port planning policies.

A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications
Timilehin Opeyemi Alakoya, Lateef Olakunle Jolaoso and Oluwatosin Temitope Mewomo
2022, 18(1): 239-265 doi: 10.3934/jimo.2020152 +[Abstract](2107) +[HTML](1371) +[PDF](483.33KB)
Abstract:

We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.

Analysis of dynamic service system between regular and retrial queues with impatient customers
Balasubramanian Krishna Kumar, Ramachandran Navaneetha Krishnan, Rathinam Sankar and Ramasamy Rukmani
2022, 18(1): 267-295 doi: 10.3934/jimo.2020153 +[Abstract](1388) +[HTML](738) +[PDF](1167.82KB)
Abstract:

In this article, we propose a dynamic operating of a single server service system between conventional and retrial queues with impatient customers. Necessary and sufficient conditions for the stability, and an explicit expression for the joint steady-state probability distribution are obtained. We have derived some interesting and important performance measures for the service system under consideration. The first-passage time problems are also investigated. Finally, we have presented extensive numerical examples to demonstrate the effects of the system parameters on the performance measures.

Modelling and computation of optimal multiple investment timing in multi-stage capacity expansion infrastructure projects
Jinghuan Li, Shuhua Zhang and Yu Li
2022, 18(1): 297-314 doi: 10.3934/jimo.2020154 +[Abstract](1276) +[HTML](543) +[PDF](865.66KB)
Abstract:

So far, the optimal investment timing to maximize the total profit of multi-stage capacity expansion infrastructure projects is not clear. In the case of uncertain demands, the optimal multiple stopping time theory is adopted to model the optimal decision-making of investment timing for multi-stage expansion infrastructure projects in a finite time horizon. In this context, the first-stage of the project involves a dedicated asset investment for later expansion, and the capacity of the project at each stage is constrained, which makes the cash flow of the project exhibit the characteristic of bull call spread. The upwind finite difference method and multi-least squares Monte Carlo simulation are combined to solve the project value and determine the optimal exercise boundaries at all stages described by a sequence of demand thresholds. A multi-stage power plant project is taken as an example to validate the model. Through the example, the optimal investment strategies and the value of the multi-stage project are provided; the effects of the dedicated asset and capacity constraint are illustrated. This study novelly reveals the effect of the capacity constraints on the project value using the bull call spread theory.

Preannouncement strategy of platform-type new product for competing platforms: Technical or marketing information
Ye Jiang and Tiaojun Xiao
2022, 18(1): 315-339 doi: 10.3934/jimo.2020155 +[Abstract](1743) +[HTML](785) +[PDF](1056.19KB)
Abstract:

What message should be released to consumers and developers is an important part of the preannouncement strategy of platforms' new product. From the perspectives of consumers and developers' information perceptions, we develop a game model of two-sided market, which can better describe the impacts of information preannouncement on consumers, developers, and platforms behavior in a competitive environment. There are two preannouncement strategies: Technical or marketing information. Our studies reveal that (i) when the development capabilities are heterogeneous enough, both platforms release technical information; (ii) both platforms preannounce marketing information when the heterogeneity of development capability is sufficiently small, even if it decreases total social welfare; (iii) the platform lacking competitive advantage is more inclined to adopt a strategy different from the competitive advantage platform, and competitive advantage platform is likely to change the preannouncement strategy constantly; (iv) the heterogeneity of platforms is the prerequisite for the asymmetric equilibrium, even if it may decrease the overall social welfare.

Portfolio optimization for jump-diffusion risky assets with regime switching: A time-consistent approach
Caibin Zhang, Zhibin Liang and Kam Chuen Yuen
2022, 18(1): 341-366 doi: 10.3934/jimo.2020156 +[Abstract](1384) +[HTML](641) +[PDF](473.6KB)
Abstract:

In this paper, an optimal portfolio selection problem with mean-variance utility is considered for a financial market consisting of one risk-free asset and two risky assets, whose price processes are modulated by jump-diffusion model, the two jump number processes are correlated through a common shock, and the Brownian motions are supposed to be dependent. Moreover, it is assumed that not only the risk aversion coefficient but also the market parameters such as the appreciation and volatility rates as well as the jump amplitude depend on a Markov chain with finite states. In addition, short selling is supposed to be prohibited. Using the technique of stochastic control theory and the corresponding extended Hamilton-Jacobi-Bellman equation, the explicit expressions of the optimal strategies and value function are obtained within a game theoretic framework, and the existence and uniqueness of the solutions are proved as well. In the end, some numerical examples are presented to show the impact of the parameters on the optimal strategies, and some further discussions on the case of \begin{document}$ n\geq 3 $\end{document} risky assets are given to demonstrate the important effect of the correlation coefficient of the Brownian motions on the optimal results.

Optimality results for a specific fractional problem
Nazih Abderrazzak Gadhi and Khadija Hamdaoui
2022, 18(1): 367-373 doi: 10.3934/jimo.2020157 +[Abstract](1150) +[HTML](503) +[PDF](350.06KB)
Abstract:

In this paper, one minimizes a fractional function over a compact set. Using an exact separation theorem, one gives necessary optimality conditions for strict optimal solutions in terms of Fréchet subdifferentials. All data are assumed locally Lipschitz.

A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project
Reza Lotfi, Zahra Yadegari, Seyed Hossein Hosseini, Amir Hossein Khameneh, Erfan Babaee Tirkolaee and Gerhard-Wilhelm Weber
2022, 18(1): 375-396 doi: 10.3934/jimo.2020158 +[Abstract](4853) +[HTML](1008) +[PDF](1160.45KB)
Abstract:

Sustainable development requires scheduling and implementation of projects by considering cost, environment, energy, and quality factors. Using a robust approach, this study investigates the time-cost-quality-energy-environment problem in executing projects and practically indicates its implementation capability in the form of a case study of a bridge construction project in Tehran, Iran. This study aims to take into account the sustainability pillars in scheduling projects and uncertainties in modeling them. To model the study problem, robust nonlinear programming (NLP) involving the objectives of cost, quality, energy, and pollution level is applied with resource-constrained. According to the results, as time diminished, the cost, energy, and pollution initially decreased and then increased, witha reduction in quality. To make the model close to the real world by considering uncertainties, the cost and quality tangibly improved, and pollution and energy consumption declined. We applied the augmented \begin{document}$ \varepsilon $\end{document}-constraint method to solve the proposed model. According to the result of the research, with regard to the time-cost, time-quality, time-energy, and time-pollution charts, as uncertainty increases, the cost and quality will improve, and pollution and energy will decrease.

The proposed model can be employed for all industrial projects, including roads, construction, and manufacturing.

Research on cascading failure modes and attack strategies of multimodal transport network
Jingni Guo, Junxiang Xu, Zhenggang He and Wei Liao
2022, 18(1): 397-410 doi: 10.3934/jimo.2020159 +[Abstract](1319) +[HTML](602) +[PDF](741.67KB)
Abstract:

Cascading failure overall exists in practical network, which poses a risk of causing significant losses. Studying the effect of different cascading failure modes and attack strategies of the network is conducive to more effectively controlling the network. In the present study, the uniqueness of multimodal transport network is investigated by complying with the percolation theory, and a cascading failure model is built for the multimodal transport network by considering recovery mechanisms and dynamics. Under the three failure modes, i.e., node failure, edge failure and node-edge failure, nine attack strategies are formulated, consisting of random node attacking strategy (RNAS), high-degree attacking strategy (HDAS), high-closeness attacking strategy (HCAS), random edge attacking strategy (REAS), high-importance attacking strategy (HIAS1), high-importance attacking strategy (HIAS2), random node-edge attacking strategy (RN-EAS), high degree-importance1 attacking strategy (HD-I1AS), as well as high closeness-importance2 attacking strategy (HC-I2AS). The effect of network cascading failure is measured at the scale of the affected network that varies with the failure ratio and the network connectivity varying with the step. By conducting a simulation analysis, the results of the two indicators are compared; it is suggested that under the three failure modes, the attack strategies exhibiting high node closeness as the indicator always poses more effective damage to the network. Next, a sensitivity analysis is conducted, and it is concluded that HCAS is the most effective attack strategy. Accordingly, the subsequent study on the cascading failure of multimodal transport network should start with the nodes exhibiting high closeness to optimize the network.

The approximation algorithm based on seeding method for functional $ k $-means problem
Min Li, Yishui Wang, Dachuan Xu and Dongmei Zhang
2022, 18(1): 411-426 doi: 10.3934/jimo.2020160 +[Abstract](1226) +[HTML](568) +[PDF](328.91KB)
Abstract:

Different from the classical \begin{document}$ k $\end{document}-means problem, the functional \begin{document}$ k $\end{document}-means problem involves a kind of dynamic data, which is generated by continuous processes. In this paper, we mainly design an \begin{document}$ O(\ln\; k) $\end{document}-approximation algorithm based on the seeding method for functional \begin{document}$ k $\end{document}-means problem. Moreover, the numerical experiment presented shows that this algorithm is more efficient than the functional \begin{document}$ k $\end{document}-means clustering algorithm.

Stability for semivectorial bilevel programs
Gaoxi Li, Liping Tang, Yingquan Huang and Xinmin Yang
2022, 18(1): 427-438 doi: 10.3934/jimo.2020161 +[Abstract](1203) +[HTML](543) +[PDF](306.46KB)
Abstract:

This paper studies the stability for bilevel program where the lower-level program is a multiobjective programming problem. As we know, the weakly efficient solution mapping for parametric multiobjective program is not generally lower semicontinuous. We first obtain this semicontinuity under a suitable assumption. Then, a new condition for the lower semicontinuity of the efficient solution mapping of this problem is also obtained. Finally, we get the continuities of the value functions and the solution set mapping for the upper-level problem based on the semicontinuities of solution mappings for the lower-level parametric multiobjective program.

Solving fuzzy linear fractional set covering problem by a goal programming based solution approach
Ali Mahmoodirad, Harish Garg and Sadegh Niroomand
2022, 18(1): 439-456 doi: 10.3934/jimo.2020162 +[Abstract](1705) +[HTML](560) +[PDF](334.59KB)
Abstract:

In this paper, a fuzzy linear fractional set covering problem is solved. The non-linearity of the objective function of the problem as well as its fuzziness make it difficult and complex to be solved effectively. To overcome these difficulties, using the concepts of fuzzy theory and component-wise optimization, the problem is converted to a crisp multi-objective non-linear problem. In order to tackle the obtained multi-objective non-linear problem, a goal programming based solution approach is proposed for its Pareto-optimal solution. The non-linearity of the problem is linearized by applying some linearization techniques in the procedure of the goal programming approach. The obtained Pareto-optimal solution is also a solution of the initial fuzzy linear fractional set covering problem. As advantage, the proposed approach applies no ranking function of fuzzy numbers and its goal programming stage considers no preferences from decision maker. The computational experiments provided by some examples of the literature show the superiority of the proposed approach over the existing approaches of the literature.

The skewness for uncertain random variable and application to portfolio selection problem
Bo Li and Yadong Shu
2022, 18(1): 457-467 doi: 10.3934/jimo.2020163 +[Abstract](1295) +[HTML](586) +[PDF](344.89KB)
Abstract:

Uncertainty and randomness are two basic types of indeterminacy, where uncertain variable is used to represent quantities with human uncertainty and random variable is applied for modeling quantities with objective randomness. In many real systems, uncertainty and randomness often exist simultaneously. Then uncertain random variable and chance measure can be used to handle such cases. We know that the skewness is a measure of distributional asymmetry. However, the concept of skewness for uncertain random variable has not been clearly defined. In this paper, we first propose a concept of skewness for uncertain random variable and then present a formula for calculating the skewness via chance distribution. Applying the presented formula, the skewnesses of three special uncertain random variables are derived. Finally, a portfolio selection problem is carried out for showing the efficiency and applicability of skewness and presented formula.

Second-Order characterizations for set-valued equilibrium problems with variable ordering structures
Shasha Hu, Yihong Xu and Yuhan Zhang
2022, 18(1): 469-486 doi: 10.3934/jimo.2020164 +[Abstract](1345) +[HTML](537) +[PDF](302.95KB)
Abstract:

The concepts of weakly efficient solutions and globally efficient solutions are introduced for constrained set-valued equilibrium problems with variable ordering structures. By applying the second-order tangent epiderivative and a nonlinear functional, necessary optimality conditions for weakly efficient solutions and globally efficient solutions are established without any convexity assumption. Under the cone-convexity of the objective and constraint functions, sufficient optimality conditions are given. In addition, the tangent derivatives of objective and constraint functions are separated. Simultaneously, a unified necessary and sufficient optimality conditions for weakly efficient solutions is derived, and the same goes for globally efficient solutions. In particular, we give specific examples to illustrate the optimality conditions, respectively.

Coordination of a sustainable reverse supply chain with revenue sharing contract
Sushil Kumar Dey and Bibhas C. Giri
2022, 18(1): 487-510 doi: 10.3934/jimo.2020165 +[Abstract](2025) +[HTML](949) +[PDF](760.26KB)
Abstract:

In this article, a three-echelon closed-loop supply chain is considered under sustainability consideration through remanufacturing of waste materials. Depending upon quality, the collector collects the used products and forwards to the manufacturer for remanufacturing. The collector offers a reward or incentive to consumers to influence them to return the used items. The shortfall amount of collected used items, if any, is meet up by the supplier by supplying fresh raw materials. In three separate cases viz centralized, decentralized and revenue-sharing contract, optimal incentives for end-customers and optimal profits of supply chain members are determined. The revenue-sharing contract is implemented in two different settings - one including the supplier and the other one excluding the supplier. The win-win outcome for the supply chain members is investigated and a specific range of the sharing parameter for win-win outcome is obtained. Optimal results are supported by numerical analysis, and sensitivity of the optimal results with respect to key parameters is analyzed.

Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk
Haixiang Yao, Ping Chen, Miao Zhang and Xun Li
2022, 18(1): 511-540 doi: 10.3934/jimo.2020166 +[Abstract](1782) +[HTML](566) +[PDF](547.79KB)
Abstract:

This paper investigates a multi-period asset allocation problem for a defined contribution (DC) pension fund facing stochastic inflation under the Markowitz mean-variance criterion. The stochastic inflation rate is described by a discrete-time version of the Ornstein-Uhlenbeck process. To the best of our knowledge, the literature along the line of dynamic portfolio selection under inflation is dominated by continuous-time models. This paper is the first work to investigate the problem in a discrete-time setting. Using the techniques of state variable transformation, matrix theory, and dynamic programming, we derive the analytical expressions for the efficient investment strategy and the efficient frontier. Moreover, our model's exceptional cases are discussed, indicating that our theoretical results are consistent with the existing literature. Finally, the results established are tested through empirical studies based on Australia's data, where there is a typical DC pension system. The impacts of inflation, investment horizon, estimation error, and superannuation guarantee rate on the efficient frontier are illustrated.

Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain
Zonghong Cao and Jie Min
2022, 18(1): 541-560 doi: 10.3934/jimo.2020167 +[Abstract](1527) +[HTML](592) +[PDF](449.24KB)
Abstract:

Consider a supply chain consisting of one manufacturer and one retailer. The manufacturer may open direct channels through ex-ante or ex-post encroachment, and the retailer can provide consumers with ex-ante or ex-post service. We investigates the effects of encroachment and services on the optimal strategy for two members in three decision modes: MR mode (ex-ante encroachment), MRM mode (ex-post encroachment and ex-post service), and MRMR mode (ex-post encroachment and ex-ante service). The results show that in the MRM mode, both the wholesale and retail prices may become higher with encroachment. Improving the service efficiency may hurt the retailer, and increasing the operating cost for direct channels harms the retailer, while benefits the manufacturer. In addition, only in the MRM mode, the retailer maybe benefits from encroachment under certain conditions. We further study the equilibrium mode and the result shows as follows. The MR mode, widely adopted by the literature on manufacturer encroachment, always is worst for the manufacturer. Only when both the operating cost for direct channels and the service efficiency are low, the equilibrium decision mode is the MRMR mode, otherwise the MRM mode is the equilibrium decision mode.

Simultaneous optimal predictions under two seemingly unrelated linear random-effects models
Yongge Tian and Pengyang Xie
2022, 18(1): 561-573 doi: 10.3934/jimo.2020168 +[Abstract](1165) +[HTML](541) +[PDF](371.83KB)
Abstract:

This paper considers simultaneous optimal prediction and estimation problems in the context of linear random-effects models. Assume a pair of seemingly unrelated linear random-effects models (SULREMs) with the random-effects and the error terms correlated. Our aim is to find analytical formulas for calculating best linear unbiased predictors (BLUPs) of all unknown parameters in the two models by means of solving a constrained quadratic matrix optimization problem in the Löwner sense. We also present a variety of theoretical and statistical properties of the BLUPs under the two models.

On the convexity for the range set of two quadratic functions
Huu-Quang Nguyen, Ya-Chi Chu and Ruey-Lin Sheu
2022, 18(1): 575-592 doi: 10.3934/jimo.2020169 +[Abstract](1916) +[HTML](609) +[PDF](3632.03KB)
Abstract:

Given \begin{document}$ n\times n $\end{document} symmetric matrices \begin{document}$ A $\end{document} and \begin{document}$ B, $\end{document} Dines in 1941 proved that the joint range set \begin{document}$ \{(x^TAx, x^TBx)|\; x\in\mathbb{R}^n\} $\end{document} is always convex. Our paper is concerned with non-homogeneous extension of the Dines theorem for the range set \begin{document}$ \mathbf{R}(f, g) = \{\left(f(x), g(x)\right)|\; x \in \mathbb{R}^n \}, $\end{document} \begin{document}$ f(x) = x^T A x + 2a^T x + a_0 $\end{document} and \begin{document}$ g(x) = x^T B x + 2b^T x + b_0. $\end{document} We show that \begin{document}$ \mathbf{R}(f, g) $\end{document} is convex if, and only if, any pair of level sets, \begin{document}$ \{x\in\mathbb{R}^n|f(x) = \alpha\} $\end{document} and \begin{document}$ \{x\in\mathbb{R}^n|g(x) = \beta\} $\end{document}, do not separate each other. With the novel geometric concept about separation, we provide a polynomial-time procedure to practically check whether a given \begin{document}$ \mathbf{R}(f, g) $\end{document} is convex or not.

Cooperation in traffic network problems via evolutionary split variational inequalities
Shipra Singh, Aviv Gibali and Xiaolong Qin
2022, 18(1): 593-611 doi: 10.3934/jimo.2020170 +[Abstract](1460) +[HTML](508) +[PDF](420.73KB)
Abstract:

In this paper, we construct an evolutionary (time-dependent) split variational inequality problem and show how to reformulate equilibria of the dynamic traffic network models of two cities as such problem. We also establish existence result for the proposed model. Primary numerical results of equilibria illustrate the validity and applicability of our results.

ADMM-type methods for generalized multi-facility Weber problem
Shun Zhang, Jianlin Jiang, Su Zhang, Yibing Lv and Yuzhen Guo
2022, 18(1): 613-634 doi: 10.3934/jimo.2020171 +[Abstract](1695) +[HTML](622) +[PDF](431.42KB)
Abstract:

The well-known multi-facility Weber problem (MFWP) is one of fundamental models in facility location. With the aim of enhancing the practical applicability of MFWP, this paper considers a generalized multi-facility Weber problem (GMFWP), where the gauge is used to measure distances and the locational constraints are imposed to new facilities. This paper focuses on developing efficient numerical methods based on alternating direction method of multipliers (ADMM) to solve GMFWP. Specifically, GMFWP is equivalently reformulated into a minmax problem with special structure and then some ADMM-type methods are proposed for its primal problem. Global convergence of proposed methods for GMFWP is established under mild assumptions. Preliminary numerical results are reported to verify the effectiveness of proposed methods.

Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution
Feimin Zhong, Jinxing Xie and Yuwei Shen
2022, 18(1): 635-654 doi: 10.3934/jimo.2020172 +[Abstract](1508) +[HTML](517) +[PDF](499.29KB)
Abstract:

This paper studies a multi-echelon serial supply chain with negotiations over wholesale prices between successive echelons. Two types of bargaining systems with power structures are compared: one adopts the generalized Kalai-Smorodinsky (KS) solution and the other adopts the generalized Nash solution. Our analyses show that, for any KS bargaining system with a given bargaining power structure, there is a Nash bargaining system with another bargaining power structure, such that the two systems are the same. However under the same power structure, the generalized KS solution results in lower wholesale price and higher total supply chain profit than the Nash solution does. Finally, we characterize the necessary and sufficient condition of the bargaining power structure under which the KS bargaining system Pareto dominates the Nash bargaining system, and the set characterized by such condition does not shrink to an empty set as the number of echelons increases to infinity.

Impacts of horizontal mergers on dual-channel supply chain
Xi Zhao and Teng Niu
2022, 18(1): 655-680 doi: 10.3934/jimo.2020173 +[Abstract](1525) +[HTML](547) +[PDF](581.91KB)
Abstract:

This paper investigates the impacts of horizontal mergers on a dual-channel supply chain given the rapid development of e-commerce. Three types of horizontal mergers are considered in a dual-channel supply chain consisting of three firm types: suppliers, single-channel retailer, and dual-channel retailer. A comparison with a benchmark pre-merger scenario underscores the impacts of each horizontal merger on firms in the dual-channel supply chain. First, where horizontal mergers occur (i.e., at upstream or downstream tier) has an impact on firms in the dual-channel supply chain. Second, synergy costs trigger the domination of the synergy effect. Third, the degree of consumer preference for channels affects the trigger due to which the synergy effect outweighs the competitive effect. Although dual channels prevail in supply chain management, few studies pay attention to horizontal mergers in this context. Unlike literature on horizontal mergers in single-channel supply chains, we suggest that the impacts of horizontal mergers in dual-channel supply chains have unique features, and channel preference plays an important role in such impacts.

Parallel-machine scheduling in shared manufacturing
Min Ji, Xinna Ye, Fangyao Qian, T.C.E. Cheng and Yiwei Jiang
2022, 18(1): 681-691 doi: 10.3934/jimo.2020174 +[Abstract](1638) +[HTML](527) +[PDF](280.49KB)
Abstract:

We consider parallel-machine scheduling in the context of shared manufacturing where each job has a machine set to which it can be assigned for processing. Such a set is called the processing set. In the shared manufacturing setting, a job can be assigned not only to certain machines for processing, but can also be processed on the remaining machines at a certain cost. Compared with traditional scheduling with job rejection, the scheduling model under study embraces the notion of sustainable manufacturing. Showing that the problem is NP-hard, we develop a fully polynomial-time approximation scheme to solve the problem when the number of machines is fixed.

Parameter optimal identification and dynamic behavior analysis of nonlinear model for the solution purification process of zinc hydrometallurgy
Qianqian Wang, Minan Tang, Aimin An, Jiawei Lu and Yingying Zhao
2022, 18(1): 693-712 doi: 10.3934/jimo.2021159 +[Abstract](876) +[HTML](419) +[PDF](3515.31KB)
Abstract:

Impurity removal is a momentous part of zinc hydrometallurgy process, and the quality of products and the stability of the whole process are affected directly by its control effect. The application of dynamic model is of great significance to the prediction of key indexes and the optimization of process control. In this paper, considering the complex coupling relationship of stage II purification process, a hybrid modeling method of mechanism modeling and parameter identification modeling was proposed on the basis of not changing the actual production process of lead-zinc smeltery. Firstly, the overall nonlinear dynamic mechanism model was established, and then the deviation between the theoretical value and the actual detected outlet ion concentration was taken as the objective function to establish the parameter identification optimization model. Since the built model is nonlinear, it may pose implementation problems. On the premise of deriving the gradient vector and Hessian matrix of the objective function with respect to the parameter vector, an optimization algorithm based on the steepest descent method and Newton method is proposed. Finally, using the historical production data of a lead-zinc smeltery in China, the model parameters were accurately inversed. An intensive simulation validation and analysis of the dynamic characteristics about the whole model shows the accuracy and the potential of the model, also in the perspective of practical implementation, which provides the basis for the optimal control of system output and the guidance for the optimal control of zinc powder addition.

2021 Impact Factor: 1.411
5 Year Impact Factor: 1.441
2021 CiteScore: 2.1

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