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Journal of Industrial and Management Optimization

November 2020 , Volume 16 , Issue 6

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Portfolio optimization with relaxation of stochastic second order dominance constraints via conditional value at risk
Meng Xue, Yun Shi and Hailin Sun
2020, 16(6): 2581-2602 doi: 10.3934/jimo.2019071 +[Abstract](2754) +[HTML](856) +[PDF](550.82KB)

A portfolio optimization model with relaxed second order stochastic dominance (SSD) constraints is presented. The proposed model uses Conditional Value at Risk (CVaR) constraints at probability level \begin{document}$ \beta\in(0,1) $\end{document} to relax SSD constraints. The relaxation is justified by theoretical convergence results based on sample average approximation (SAA) method when sample size \begin{document}$ N\to\infty $\end{document} and CVaR probability level \begin{document}$ \beta $\end{document} tends to 1. SAA method is used to reduce infinite number of inequalities of SSD constraints to finite ones and also to calculate the expectation value. The proposed relaxation on the SSD constraints in portfolio optimization problem is achieved when the probability level \begin{document}$ \beta $\end{document} of CVaR takes value less than but close to 1, and the model can then be solved by cutting plane method. The performance and characteristics of the portfolios constructed by solving the proposed model are tested empirically on three sets of market data, and the experimental results are analyzed and discussed. Furthermore, it is shown that with appropriate choices of CVaR probability level \begin{document}$ \beta $\end{document}, the constructed portfolios are sparse and outperform the portfolios constructed by solving portfolio optimization problems with SSD constraints, with either index portfolios or mean-variance (MV) portfolios as benchmarks.

Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level
Chao Xu, Yinghui Dong, Zhaolu Tian and Guojing Wang
2020, 16(6): 2603-2623 doi: 10.3934/jimo.2019072 +[Abstract](2318) +[HTML](792) +[PDF](480.26KB)

In this paper, we investigate the valuation of dynamic fund protections under the assumption that the market value of the basic fund and the protection level follow regime-switching processes with jumps. The price of the dynamic fund protection (DFP) is associated with the Laplace transform of the first passage time. We derive the explicit formula for the Laplace transform of the DFP under the regime-switching, hyper-exponential jump-diffusion process. By using the Gaver-Stehfest algorithm, we present some numerical results for the price of the DFP.

Admission control for finite capacity queueing model with general retrial times and state-dependent rates
Madhu Jain and Sudeep Singh Sanga
2020, 16(6): 2625-2649 doi: 10.3934/jimo.2019073 +[Abstract](2893) +[HTML](1055) +[PDF](3005.05KB)

The finite state dependent queueing model with \begin{document}$ F $\end{document}-policy is investigated by considering the general retrial attempts. On arrival in the system, if the job finds the server engaged, it is forced to enter into the retrial orbit. After a random period of time, the job from the retrial orbit re-attempts for the service. According to \begin{document}$ F $\end{document}-policy, as the system attains its full capacity, the arrivals are restricted to join the system until the number of jobs comes down to the prefixed threshold value '\begin{document}$ F $\end{document}'. The supplementary variable corresponding to the remaining retrial time is used to frame the governing equations which are solved by using Laplace-Stieltjes transform and then applying the recursive method. Special models for machine repair and time-sharing queue are deduced by setting the state dependent rates. Several system indices are obtained explicitly which are further used to facilitate the sensitivity analysis by considering a numerical illustration. A cost function is constructed and minimized for evaluating the optimal threshold parameter and optimal service rate.

Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty
Jutamas Kerdkaew and Rabian Wangkeeree
2020, 16(6): 2651-2673 doi: 10.3934/jimo.2019074 +[Abstract](2320) +[HTML](779) +[PDF](439.6KB)

We introduce robust weak sharp and robust sharp solution to a convex programming with the objective and constraint functions involved uncertainty. The characterizations of the sets of all the robust weak sharp solutions are obtained by means of subdiferentials of convex functions, DC fuctions, Fermat rule and the robust-type subdifferential constraint qualification, which was introduced in X.K. Sun, Z.Y. Peng and X. Le Guo, Some characterizations of robust optimal solutions for uncertain convex optimization problems, Optim Lett. 10. (2016), 1463-1478. In addition, some applications to the multi-objective case are presented.

An adaptively regularized sequential quadratic programming method for equality constrained optimization
Songqiang Qiu and Zhongwen Chen
2020, 16(6): 2675-2701 doi: 10.3934/jimo.2019075 +[Abstract](2416) +[HTML](806) +[PDF](555.93KB)

In this paper, we devise an adaptively regularized SQP method for equality constrained optimization problem that is resilient to constraint degeneracy, with a relatively small departure from classical SQP method. The main feature of our method is an adaptively choice of regularization parameter, embedded in a trust-funnel-like algorithmic scheme. Unlike general regularized methods, which update regularization parameter after a regularized problem is approximately solved, our method updates the regularization parameter at each iteration according to the infeasibility measure and the promised improvements achieved by the trial step. The sequence of regularization parameters is not necessarily monotonically decreasing. The whole algorithm is globalized by a trust-funnel-like strategy, in which neither a penalty function nor a filter is needed. We present global and fast local convergence under weak assumptions. Preliminary numerical results on a collection of degenerate problems are reported, which are encouraging.

How's the performance of the optimized portfolios by safety-first rules: Theory with empirical comparisons
Yuanyao Ding and Zudi Lu
2020, 16(6): 2703-2721 doi: 10.3934/jimo.2019076 +[Abstract](1947) +[HTML](837) +[PDF](559.48KB)

Safety-first (SF) rules have been increasingly useful in particular for construction of optimal portfolios related to pension and other social insurance funds. How's the performance of the optimal portfolios constructed by different SF rules is an interesting practical question but yet less investigated theoretically. In this paper, we therefore analytically investigate the properties of the risky portfolios constructed by the three popular SF rules, denoted by the RSF, TSF and KSF, which are suggested and developed by A. D. Roy, L. G. Telser and S. Kataoka, respectively. Using Sharpe ratio as a measure of portfolio performance, we theoretically derive that the performance of an optimal portfolio constructed by the KSF approach depends on an acceptable level of extreme risk tolerance. The unique solution where the performance of the KSF portfolio is the same as that of the other two SF portfolios is found. By this we interestingly find that except this special case, under the finite optimal portfolios existent, the KSF portfolio always dominates the TSF portfolio in terms of the Sharpe ratio. In addition, in some market scenarios, even when the RSF and TSF portfolios do not exist in finite forms, the KSF rule can still apply to get a finite optimal portfolio. Moreover, in comparison with the RSF rule, a series of finite KSF portfolios can be interestingly constructed with their Sharpe ratios approaching to the maximum Sharpe ratio, which however cannot be reached by any corresponding finite RSF portfolio. Numerical comparisons of these rules by using a set of real data are further empirically demonstrated.

Bargaining equilibrium in a two-echelon supply chain with a capital-constrained retailer
Honglin Yang, Qiang Yan, Hong Wan and Wenyan Zhuo
2020, 16(6): 2723-2741 doi: 10.3934/jimo.2019077 +[Abstract](2525) +[HTML](1057) +[PDF](1324.62KB)

We investigate the bargaining equilibrium in a two-echelon supply chain consisting of a supplier and a capital-constrained retailer. The newsvendor-like retailer can borrow from a bank or use the supplier's trade credit to fund his business. In the presence of bankruptcy risk for both the supplier and retailer, with a wholesale price contract, we model the player's strategic interactions under the Nash and Rubinstein bargaining games. In both financing schemes, the Nash bargaining game overcomes the double marginalization effect under the Stackelberg game and achieves supply chain coordination. The Rubinstein bargaining game realizes the Pareto improvement of the supply chain. The player with stronger bargaining power always prefers to initially offer a contract under the Rubinstein bargaining game to obtain greater expected profit. Furthermore, we characterize the conditions under which bargaining power and discount factor affect the bargaining equilibrium. We numerically verify our theoretical results.

Corporate and personal credit scoring via fuzzy non-kernel SVM with fuzzy within-class scatter
Jian Luo, Xueqi Yang, Ye Tian and Wenwen Yu
2020, 16(6): 2743-2756 doi: 10.3934/jimo.2019078 +[Abstract](2273) +[HTML](801) +[PDF](360.03KB)

Nowadays, the effective credit scoring becomes a very crucial factor for gaining competitive advantages in credit market for both customers and corporations. In this paper, we propose a credit scoring method which combines the non-kernel fuzzy 2-norm quadratic surface SVM model, T-test feature weighting strategy and fuzzy within-class scatter together. It is worth pointing out that this new method not only saves computational time by avoiding choosing a kernel and corresponding parameters in the classical SVM models, but also addresses the "curse of dimensionality" issue and improves the robustness. Besides, we develop an efficient way to calculate the fuzzy membership of each training point by solving a linear programming problem. Finally, we conduct several numerical tests on two benchmark data sets of personal credit and one real-world data set of corporation credit. The numerical results strongly demonstrate that the proposed method outperforms eight state-of-the-art and commonly-used credit scoring methods in terms of accuracy and robustness.

An incremental nonsmooth optimization algorithm for clustering using $ L_1 $ and $ L_\infty $ norms
Burak Ordin, Adil Bagirov and Ehsan Mohebi
2020, 16(6): 2757-2779 doi: 10.3934/jimo.2019079 +[Abstract](1328) +[HTML](302) +[PDF](770.51KB)

An algorithm is developed for solving clustering problems with the similarity measure defined using the \begin{document}$ L_1 $\end{document} and \begin{document}$ L_\infty $\end{document} norms. It is based on an incremental approach and applies nonsmooth optimization methods to find cluster centers. Computational results on 12 data sets are reported and the proposed algorithm is compared with the \begin{document}$ X $\end{document}-means algorithm.

Optimal investment and reinsurance with premium control
Xin Jiang, Kam Chuen Yuen and Mi Chen
2020, 16(6): 2781-2797 doi: 10.3934/jimo.2019080 +[Abstract](2087) +[HTML](760) +[PDF](445.97KB)

This paper studies the optimal investment and reinsurance problem for a risk model with premium control. It is assumed that the insurance safety loading and the time-varying claim arrival rate are connected through a monotone decreasing function, and that the insurance and reinsurance safety loadings have a linear relationship. Applying stochastic control theory, we are able to derive the optimal strategy that maximizes the expected exponential utility of terminal wealth. We also provide a few numerical examples to illustrate the impact of the model parameters on the optimal strategy.

A robust reduced-order observers design approach for linear discrete periodic systems
Lingling Lv, Wei He, Xianxing Liu and Lei Zhang
2020, 16(6): 2799-2812 doi: 10.3934/jimo.2019081 +[Abstract](1833) +[HTML](797) +[PDF](366.14KB)

This paper investigates the problem of designing reduced-order observers for linear discrete-time periodic (LDP) systems. In case that the linear discrete-time periodic system is observable, an algebraic equivalent system is obtained by non-singular linear transformation, and the partial states to be observed are separated simultaneously. Then the considered problem is transformed into the problem of solving a class of periodic Sylvester matrix equation and an iterative algorithm for periodic reduced-order state observers design is derived. In addition, robust consideration based on periodic reduced-order state observers for LDP systems is also conducted. At last, one numerical example is worked out to illustrate the effectiveness of the proposed approaches.

Analysis of the queue lengths in a priority retrial queue with constant retrial policy
Arnaud Devos, Joris Walraevens, Tuan Phung-Duc and Herwig Bruneel
2020, 16(6): 2813-2842 doi: 10.3934/jimo.2019082 +[Abstract](2563) +[HTML](872) +[PDF](683.48KB)

In this paper, we analyze a priority queueing system with a regular queue and an orbit. Customers in the regular queue have priority over the customers in the orbit. Only the first customer in the orbit (if any) retries to get access to the server, if the queue and server are empty (constant retrial policy). In contrast with existing literature, we assume different service time distributions for the high- and low-priority customers. Closed-form expressions are obtained for the probability generating functions of the number of customers in the queue and orbit, in steady-state. Another contribution is the extensive singularity analysis of these probability generating functions to obtain the stationary (asymptotic) probability mass functions of the queue and orbit lengths. Influences of the service times and the retrial policy are illustrated by means of some numerical examples.

Transient analysis of N-policy queue with system disaster repair preventive maintenance re-service balking closedown and setup times
A. Azhagappan and T. Deepa
2020, 16(6): 2843-2856 doi: 10.3934/jimo.2019083 +[Abstract](2285) +[HTML](777) +[PDF](711.92KB)

This paper investigates the transient behavior of a \begin{document}$ M/M/1 $\end{document} queueing model with N-policy, system disaster, repair, preventive maintenance, balking, re-service, closedown and setup times. The server stays dormant (off state) until N customers accumulate in the queue and then starts an exhaustive service (on state). After the service, each customer may either leave the system or get immediate re-service. When the system becomes empty, the server resumes closedown work and then undergoes preventive maintenance. After that, it comes to the idle state and waits N accumulate for service. When the \begin{document}$ N^{th} $\end{document} one enters the queue, the server commences the setup work and then starts the service. Meanwhile, the system suffers disastrous breakdown during busy period. It forced the system to the failure state and all the customers get eliminated. After that, the server gets repaired and moves to the idle state. The customers may either join the queue or balk when the size of the system is less than N. The probabilities of the proposed model are derived by the method of generating function for the transient case. Some system performance indices and numerical simulations are also presented.

Multi-period optimal investment choice post-retirement with inter-temporal restrictions in a defined contribution pension plan
Huiling Wu, Xiuguo Wang, Yuanyuan Liu and Li Zeng
2020, 16(6): 2857-2890 doi: 10.3934/jimo.2019084 +[Abstract](2274) +[HTML](855) +[PDF](540.78KB)

This paper studies a multi-period portfolio selection problem during the post-retirement phase of a defined contribution pension plan. The retiree is allowed to defer the purchase of the annuity until the time of compulsory annuitization. A series of investment targets over time are set, and restrictions on the inter-temporal expected values of the portfolio are considered. We aim to minimize the accumulated variances from the time of retirement to the time of compulsory annuitization. Using the Lagrange multiplier technique and dynamic programming, we study in detail the existence of the optimal strategy and derive its closed-form expression. For comparison purposes, the explicit solution of the classical target-based model is also provided. The properties of the optimal investment strategy, the probabilities of achieving a worse or better pension at the time of compulsory annuitization and the bankruptcy probability are compared in detail under two models. The comparison shows that our model can greatly decrease the probability of achieving a worse pension at the compulsory time and can significantly increase the probability of achieving a better pension.

A two-priority single server retrial queue with additional items
Dhanya Shajin, A. N. Dudin, Olga Dudina and A. Krishnamoorthy
2020, 16(6): 2891-2912 doi: 10.3934/jimo.2019085 +[Abstract](2711) +[HTML](1104) +[PDF](541.77KB)

In this paper, we study a priority queueing-inventory problem with two types of customers. Arrival of customers follows Marked Markovian arrival process and service times have phase-type distribution with parameters depending on the type of customer in service. For service of each type of customer, a certain number of additional items are needed. High priority customers do not have waiting space and so leave the system when on their arrival a priority 1 customer is in service or the number of available additional items is less than the required threshold. Preemptive priority is assumed. Type 2 customers, encountering a busy server or idle with the number of available additional items less than a threshold, go to an orbit of infinite capacity to retry for service. The customers in orbit are non-persistent: if on retrial the server is found to be busy/idle with the number of additional items less than the threshold, this customer abandons the system with certain probability. Such a system represents an accurate enough model of many real-world systems, including wireless sensor networks and system of cognitive radio with energy harvesting and healthcare systems. The probability distribution of the system states is computed, using which several of the characteristics are derived. A detailed numerical study of the system, including the analysis of the influence of the threshold, is performed.

A zero-forcing beamforming based time switching protocol for wireless powered internet of things system
Hanyu Cao, Meiying Zhang, Huanxi Cai, Wei Gong, Min Su and Bin Li
2020, 16(6): 2913-2922 doi: 10.3934/jimo.2019086 +[Abstract](2367) +[HTML](834) +[PDF](373.03KB)

In this paper, a time switching (TS) protocol for the wireless powered communications system with per-antenna power constraints is considered. To eliminate the multi-user interference, we adopt the zero-forcing beamforming scheme to maximize the sum rate performance. A two-step algorithm is proposed to solve the sum rate maximization problem with per-antenna power constraints. More specifically, golden section search method is used to find optimal time switching factor in the first step. For each given TS factor, the sub-problem in the second step is convex, which can be efficiently solved by standard software package. Numerical results are provided to demonstrate the effectiveness of the proposed methods, and some interesting results are also observed.

Distributionally robust chance constrained problems under general moments information
Ke-Wei Ding, Nan-Jing Huang and Yi-Bin Xiao
2020, 16(6): 2923-2942 doi: 10.3934/jimo.2019087 +[Abstract](2181) +[HTML](888) +[PDF](488.82KB)

In this paper, we focus on distributionally robust chance constrained problems (DRCCPs) under general moments information sets. By convex analysis, we obtain an equivalent convex programming form for DRCCP under assumptions that the first and second order moments belong to corresponding convex and compact sets respectively. We give some examples of support functions about matrix sets to show the tractability of the equivalent convex programming and obtain the closed form solution for the worst case VaR optimization problem. Then, we present an equivalent convex programming form for DRCCP under assumptions that the first order moment set and the support subsets are convex and compact. We also give an equivalent form for distributionally robust nonlinear chance constrained problem under assumptions that the first order moment set and the support set are convex and compact. Moreover, we provide illustrative examples to show our results.

An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility
Xuewen Huang, Xiaotong Zhang, Sardar M. N. Islam and Carlos A. Vega-Mejía
2020, 16(6): 2943-2969 doi: 10.3934/jimo.2019088 +[Abstract](3402) +[HTML](1035) +[PDF](862.16KB)

This paper considers the Flexible Job-shop Scheduling Problem with Operation and Processing flexibility (FJSP-OP) with the objective of minimizing the makespan. A Genetic Algorithm based approach is presented to solve the FJSP-OP. For the performance improvement, a new and concise Four-Tuple Scheme (FTS) is proposed for modeling a job with operation and processing flexibility. Then, with the FTS, an enhanced Genetic Algorithm employing a more efficient encoding strategy is developed. The use of this encoding strategy ensures that the classic genetic operators can be adopted to the utmost extent without generating infeasible offspring. Experiments have validated the proposed approach, and the results have shown the effectiveness and high performance of the proposed approach.

Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function
Tadeusz Antczak and Najeeb Abdulaleem
2020, 16(6): 2971-2989 doi: 10.3934/jimo.2019089 +[Abstract](2349) +[HTML](907) +[PDF](421.31KB)

In this paper, a nonconvex vector optimization problem with multiple interval-valued objective function and both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are \begin{document}$ E $\end{document}-differentiable. The so-called \begin{document}$ E $\end{document}-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered \begin{document}$ E $\end{document}-differentiable vector optimization problem with the multiple interval-valued objective function. Also the sufficient optimality conditions are derived for such interval-valued vector optimization problems under appropriate (generalized) \begin{document}$ E $\end{document}-convexity hypotheses.

Pairs trading with illiquidity and position limits
Menglu Feng, Mei Choi Chiu and Hoi Ying Wong
2020, 16(6): 2991-3009 doi: 10.3934/jimo.2019090 +[Abstract](3248) +[HTML](878) +[PDF](4074.92KB)

We investigate the optimal investment among the money market account, a liquid risky asset (e.g. stock index) and an illiquid risky asset (e.g. individual stock), where the two risky assets are cointegrated. The illiquid risky asset is subject to a proportional transaction cost and the portfolio of the three assets faces certain position limits. We develop the optimal investment strategy to maximize the gain function, which is realized through an expected sum of discounted utilities given transaction costs and position limits. The problem formulation uses a singular control framework with cointegration that determines optimal trading boundaries among holding, selling and no-trading regions. We conduct comprehensive numerical analysis on the optimal investment strategy and features of the optimal trading boundaries given various levels of position limits.

Numerical solution to an inverse problem on a determination of places and capacities of sources in the hyperbolic systems
Yegana Ashrafova and Kamil Aida-Zade
2020, 16(6): 3011-3033 doi: 10.3934/jimo.2019091 +[Abstract](2058) +[HTML](777) +[PDF](567.96KB)

In the work we investigate the numerical solution to a class of inverse problems with respect to the system of differential equations of hyperbolic type. The specialties of considered problems are: 1) the impulse impacts are present in the system and it is necessary to determine the capacities and the place of their location; 2) the differential equations of the system are only related to boundary values, and arbitrarily; 3) because of the long duration of the object functioning, the exact values of the initial conditions are not known, but a set of possible values is given. The inverse problem under consideration is reduced to the problem of parametric optimal control without initial conditions with non-separated boundary conditions. For the solution it is proposed to use first-order optimization methods. The results of numerical experiments are given on the example of the inverse problem of fluid transportation in the pipeline networks of complex structure. The problem is to determine the locations and the volume of leakage of raw materials based on the results of additional observations of the state of the transportation process at internal points or at the ends of sections of the pipeline network.

Some inequalities for the minimum M-eigenvalue of elasticity M-tensors
Jun He, Guangjun Xu and Yanmin Liu
2020, 16(6): 3035-3045 doi: 10.3934/jimo.2019092 +[Abstract](1857) +[HTML](735) +[PDF](316.25KB)

In this paper, we derive some lower bounds for the minimum M-eigenvalue of elasticity M-tensors, these bounds only depend on the elements of the elasticity M-tensors and they are easy to be verified. Comparison theorems for elasticity M-tensors are also given.

Parametric Smith iterative algorithms for discrete Lyapunov matrix equations
Ai-Guo Wu, Ying Zhang and Hui-Jie Sun
2020, 16(6): 3047-3063 doi: 10.3934/jimo.2019093 +[Abstract](1919) +[HTML](739) +[PDF](1004.25KB)

An iterative algorithm is established in this paper for solving the discrete Lyapunov matrix equations. The proposed algorithm contains a tunable parameter, and includes the Smith iteration as a special case, and thus is called the parametric Smith iterative algorithm. Some convergence conditions are developed for the proposed parametric Smith iterative algorithm. Moreover, the optimal parameter for the proposed algorithm to have the fastest convergence rate is also provided for a special case. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithm.

Mean-CVaR portfolio selection model with ambiguity in distribution and attitude
Zhilin Kang, Xingyi Li and Zhongfei Li
2020, 16(6): 3065-3081 doi: 10.3934/jimo.2019094 +[Abstract](2472) +[HTML](926) +[PDF](466.67KB)

In this paper, we develop \begin{document}$ \alpha $\end{document}-robust (maxmin) models, where the Conditional Value-at-Risk (CVaR) is to be optimized under ambiguity in distribution, mean returns, and covariance matrix. Our models allow the investor to distinguish ambiguity and ambiguity attitude with different levels of ambiguity aversion. For the case when there is a risk-free asset and short-selling is allowed, we obtain the analytic solution for the \begin{document}$ \alpha $\end{document}-robust CVaR optimization model subject to a minimum mean return constraint. Moreover, we also derive a closed-form portfolio rule for the \begin{document}$ \alpha $\end{document}-robust mean-CVaR optimization problem in a market without the risk-less asset. The results obtained from solving the numerical example show that if an investor is more ambiguity-averse, his investment strategy will always be more conservative.

Effect of disruption risk on a supply chain with price-dependent demand
Min Li, Jiahua Zhang, Yifan Xu and Wei Wang
2020, 16(6): 3083-3103 doi: 10.3934/jimo.2019095 +[Abstract](2673) +[HTML](846) +[PDF](1508.33KB)

Supply chain disruption management has been a hot issue for a long time. This paper studies a supply chain consisting of two suppliers and a retailer. The suppliers may have correlated disruption risks and they choose their respective wholesale price. The retailer's demand is selling price-dependent. In a scenario of ex-ante pricing scheme, i.e., the retailer chooses selling price before the suppliers' disruption is resolved, we find that the disruption correlation affects the supply chain members' profits in a nonmonotonic way. In a scenario of responsive pricing scheme, i.e., the retailer chooses selling price after the suppliers' disruption is resolved, we show that when the suppliers' disruption correlation becomes stronger, the suppliers' profit will decrease while the retailer's profit will increase. Moreover, the retailer always earns a higher profit under the responsive pricing scheme than under the ex-ante pricing scheme. In an extension, we show that the suppliers' disruption correlations affects the supply chain members' profits in a similar way if the supply chain has two competitive retailers. However, in this extension, if the suppliers' disruption correlation is low, the retailers' profit is higher under the responsive pricing scheme; otherwise, the retailers' profit is higher under the ex-ante pricing scheme.

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




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