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Journal of Industrial and Management Optimization

July 2022 , Volume 18 , Issue 4

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Painlevé-Kuratowski convergences of the solution sets for vector optimization problems with free disposal sets
Nguyen Minh Tung and Mai Van Duy
2022, 18(4): 2255-2276 doi: 10.3934/jimo.2021066 +[Abstract](1426) +[HTML](537) +[PDF](500.99KB)
Abstract:

This paper aims to present results on the Painlev\begin{document}$ \mathrm{\acute{e}} $\end{document}-Kuratowski set-convergence of the sets of both infimal and minimal points of a sequence of perturbed vector optimization problems through free disposal sets. By assumptions of sequential compactness of the feasible sets or the uniform coerciveness of objective functions, this convergence is obtained both in the image and given spaces under the perturbations of objective functions and feasible sets. Besides, we also establish set-convergences of sequences of approximation solution sets. Applications to the stability of conic, quadratic and linear vector optimization problems are given. Some examples are provided to illustrate our results.

Approximation algorithm for spherical $ k $-means problem with penalty
Chenchen Wu, Wei Lv, Yujie Wang and Dachuan Xu
2022, 18(4): 2277-2287 doi: 10.3934/jimo.2021067 +[Abstract](1161) +[HTML](460) +[PDF](584.81KB)
Abstract:

The \begin{document}$ k $\end{document}-means problem is a classical combinatorial optimization problem which has lots of applications in many fields such as machine learning, data mining, etc. We consider a variant of \begin{document}$ k $\end{document}-means problem in the spherical space, that is, spherical \begin{document}$ k $\end{document}-means problem with penalties. In the problem, it is allowable that some nodes in the spherical space can not be clustered by paying some penalty costs. Based on local search scheme, we propose a \begin{document}$ \left(4 (11+4\sqrt{7})+ \epsilon\right) $\end{document}-approximation algorithm using singe-swap operation, where \begin{document}$ \epsilon $\end{document} is a positive constant.

Optimization of inventory system with defects, rework failure and two types of errors under crisp and fuzzy approach
Javad Taheri and Abolfazl Mirzazadeh
2022, 18(4): 2289-2318 doi: 10.3934/jimo.2021068 +[Abstract](1289) +[HTML](478) +[PDF](2911.25KB)
Abstract:

In this paper, a new approach was applied to a single-item single-source (\begin{document}$ SISS $\end{document}) system at the "\begin{document}$ EOQ-type $\end{document}" mode considering imperfect items and uncertainty environment. The mentioned method was intended to produce an optimum order/production quantity as well as taking care of imperfect processes. The imperfect proportion of the received lot size was described by an imperfect inspection process. That is, two-way inspection errors may be committed by the inspector as separate items. Thus, this survey was aimed to maximize the benefit in the traditional inventory systems. The incorporation of both defects and defective classifications (Type-\begin{document}$ I\&II $\end{document} errors) was illustrated, in a way that the defects were returned by the consumers. Moreover, this inventory model had an extra step in the scope of inspection; which occurred after the rework process with no inspection error. To get closer to the practical circumstances and to consider the uncertainty, the model was formulated in the fuzzy environment. The demand, rework, and inspection rates of the inventory system were considered as the triangular fuzzy numbers where the output factors of the inventory system were obtained via nonlinear parametric programming and Zadeh's extension principle. Finally, this scenario was illustrated through a mathematical model. The concavity of the objective function was also calculated and the total profit function was presented to clarify the solution procedure by numerical examples.

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering
Burcu Gürbüz
2022, 18(4): 2319-2334 doi: 10.3934/jimo.2021069 +[Abstract](1264) +[HTML](510) +[PDF](1518.93KB)
Abstract:

Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Besides, an error analysis of the approximate solutions is given. Accuracy of the method is shown by the results. Consequently, illustrative examples are considered and detailed analysis of the problem is acquired. Consequently, the future outlook is discussed in conclusion.

Design of probabilistic $ l_2-l_\infty $ filter for uncertain Markov jump systems with partial information of the transition probabilities
Liqiang Jin, Yanqing Liu, Yanyan Yin, Kok Lay Teo and Fei Liu
2022, 18(4): 2335-2349 doi: 10.3934/jimo.2021070 +[Abstract](1163) +[HTML](413) +[PDF](2027.4KB)
Abstract:

In this paper, the problem of \begin{document}$ l_2-l_\infty $\end{document} probabilistic filtering for uncertain Markov jump systems with partial information of the transition probabilities is studied, where the uncertainties are caused by randomly changing interior parameters. Combining the original system and the filtering system, an augmented error system is proposed. Some concepts of probability theory are introduced to handle the uncertainties. Due to the complicated structure of real practical systems, only partial information on the transition probabilities are available. In this paper, by using Lyapunov functional method and probability theory, linear matrix inequalities (LMIs) type of sufficient conditions are derived. Based on these sufficient conditions, a probability filter is constructed such that the augmented error system with partial information of the transition probabilities is stochastically stable with a given confidence level and satisfying an \begin{document}$ l_2-l_\infty $\end{document} performance index. Furthermore, the gain matrices of the filter are obtained through the introduction of slack matrices. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Evolution of revenue preference for competing firms with nonlinear inverse demand
Caichun Chai, Tiaojun Xiao and Zhangwei Feng
2022, 18(4): 2351-2367 doi: 10.3934/jimo.2021071 +[Abstract](1483) +[HTML](545) +[PDF](597.18KB)
Abstract:

This paper studies evolutionarily stable preferences of competing firms across independent markets. Two models are considered according to whether firms' preferences are discrete or continuous. When preferences are discrete, firms have two marketing strategies: profit maximization and revenue maximization. We find that, whether pure and mixed strategies are evolutionarily stable depends on the spectrum of pricing capability. When the pricing capability is moderate, the mixed strategy is an evolutionarily stable strategy. Revenue maximization is evolutionarily stable under relatively high pricing capability, whereas, in case of low pricing capability, firms opt to maximize their profits. Further, the stability of revenue preference is also examined under continuous preferences. We derive the conditions, under which a unique evolutionarily stable revenue preference appears as well as it is continuously stable. Our main results still hold when we extend our model to a general framework.

Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering
Wei Wang, Yang Shen, Linyi Qian and Zhixin Yang
2022, 18(4): 2369-2399 doi: 10.3934/jimo.2021072 +[Abstract](1301) +[HTML](448) +[PDF](632.26KB)
Abstract:

This paper studies the hedging problem of unit-linked life insurance contracts in an incomplete market presence of self-exciting (clustering) effect, which is described by a Hawkes process. Applying the local risk-minimization method, we manage to obtain closed-form expressions of the locally risk-minimizing hedging strategies for both pure endowment and term insurance contracts. Besides, we demonstrate the existence of the minimal martingale measure and perform numerical analyses. Our numerical results indicate that jump clustering has a significant impact on the optimal hedging strategies.

Uncertain spring vibration equation
Lifen Jia and Wei Dai
2022, 18(4): 2401-2414 doi: 10.3934/jimo.2021073 +[Abstract](1260) +[HTML](429) +[PDF](327.07KB)
Abstract:

The spring vibration equation is to model the behavior of a spring which has a time varying force acting on it. The stochastic spring vibration equation was proposed for modeling spring vibration phenomena with noise described by Wiener process. However, there exists a paradox in some cases. Thus, as a counterpart, this paper proposes uncertain spring vibration equation driven by Liu process to describe the noise. Moreover, the analytic solution of uncertain spring vibration equation is derived and the inverse uncertainty distribution of solution is proved. At last, this paper presents a paradox of stochastic spring vibration equation.

Open-loop solvability for mean-field stochastic linear quadratic optimal control problems of Markov regime-switching system
Kehan Si, Zhenda Xu, Ka Fai Cedric Yiu and Xun Li
2022, 18(4): 2415-2433 doi: 10.3934/jimo.2021074 +[Abstract](1256) +[HTML](557) +[PDF](521.35KB)
Abstract:

This paper investigates the mean-field stochastic linear quadratic optimal control problem of Markov regime switching system (M-MF-SLQ, for short). The representation of the cost functional for the M-MF-SLQ is derived using the technique of operators. It is shown that the convexity of the cost functional is necessary for the finiteness of the M-MF-SLQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. We demonstrate with a few examples that our results can be employed for tackling some financial problems such as mean-variance portfolio selection problem.

Optimal $ Z $-eigenvalue inclusion intervals of tensors and their applications
Caili Sang and Zhen Chen
2022, 18(4): 2435-2468 doi: 10.3934/jimo.2021075 +[Abstract](1042) +[HTML](511) +[PDF](623.63KB)
Abstract:

Firstly, a weakness of Theorem 3.2 in [Journal of Industrial and Management Optimization, 17(2) (2021) 687-693] is pointed out. Secondly, a new Geršgorin-type \begin{document}$ Z $\end{document}-eigenvalue inclusion interval for tensors is given. Subsequently, another Geršgorin-type \begin{document}$ Z $\end{document}-eigenvalue inclusion interval with parameters for even order tensors is presented. Thirdly, by selecting appropriate parameters some optimal intervals are provided and proved to be tighter than some existing results. Finally, as an application, some sufficient conditions for the positive definiteness of homogeneous polynomial forms as well as the asymptotically stability of time-invariant polynomial systems are obtained. As another application, bounds of \begin{document}$ Z $\end{document}-spectral radius of weakly symmetric nonnegative tensors are presented, which are used to estimate the convergence rate of the greedy rank-one update algorithm and derive bounds of the geometric measure of entanglement of symmetric pure state with nonnegative amplitudes.

A new gradient computational formula for optimal control problems with time-delay
Changjun Yu, Lei Yuan and Shuxuan Su
2022, 18(4): 2469-2482 doi: 10.3934/jimo.2021076 +[Abstract](1052) +[HTML](599) +[PDF](464.49KB)
Abstract:

In this paper, we consider a class of time-delay optimal control problem (TDOCP) with canonical equality and inequality constraints. By applying control parameterization method together with time-scaling transformation, a TDOCP can be readily solved by gradient-based optimization methods. The partial derivative of the cost as well as the constraint functions with respect to the decision variables are obtained by variational approach, which is inefficient when the discretization for the control function is relatively dense. For general optimal control problem without time-delay, co-state approach is an effective way to compute the gradients, however, when time-delay is involved in the dynamic system, the co-state system is not known. In this paper, we derive the co-state system for TDOCP to compute the gradients of the cost and constraints. Numerical results show that the computational efficiency is much higher when compared with the traditional variational approach.

A modification of Galerkin's method for option pricing
Mikhail Dokuchaev, Guanglu Zhou and Song Wang
2022, 18(4): 2483-2504 doi: 10.3934/jimo.2021077 +[Abstract](1168) +[HTML](494) +[PDF](491.46KB)
Abstract:

We present a novel method for solving a complicated form of a partial differential equation called the Black-Scholes equation arising from pricing European options. The novelty of this method is that we consider two terms of the equation, namely the volatility and dividend, as variables dependent on the state price. We develop a Galerkin finite element method to solve the problem. More specifically, we discretize the system along the state variable and build new basis functions which we use to approximate the solution. We establish convergence of the proposed method and numerical results are reported to show the proposed method is accurate and efficient.

Steady-state and first passage time distributions for waiting times in the MAP/M/s+G queueing model with generally distributed patience times
Omer Gursoy, Kamal Adli Mehr and Nail Akar
2022, 18(4): 2505-2532 doi: 10.3934/jimo.2021078 +[Abstract](1237) +[HTML](570) +[PDF](524.65KB)
Abstract:

We study the \begin{document}$ MAP/M/s+G $\end{document} queueing model that arises in various multi-server engineering problems including telephone call centers, under the assumption of MAP (Markovian Arrival Process) arrivals, exponentially distributed service times, infinite waiting room, and generally distributed patience times. Using sample-path arguments, we propose to obtain the steady-state distribution of the virtual waiting time and subsequently the other relevant performance metrics of interest via the steady-state solution of a certain Continuous Feedback Fluid Queue (CFFQ). The proposed method is exact when the patience time is a discrete random variable and is asymptotically exact when it is continuous/hybrid, for which case discretization of the patience time distribution is required giving rise to a computational complexity depending linearly on the number of discretization levels. Additionally, a novel method is proposed to accurately obtain the first passage time distributions for the virtual and actual waiting times again using CFFQs while approximating the deterministic time horizons by Erlang distributions or more efficient Concentrated Matrix Exponential (CME) distributions. Numerical results are presented to validate the effectiveness of the proposed numerical method.

Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case
Xue Qiao, Zheng Wang and Haoxun Chen
2022, 18(4): 2533-2552 doi: 10.3934/jimo.2021079 +[Abstract](1213) +[HTML](474) +[PDF](956.09KB)
Abstract:

In the real world, the demand cannot be depicted exactly because of customer behavior cannot be forecasted without error. In this paper, we study the effect of the error of the estimated price-demand parameters by analyzing the sensitivity of the optimal joint pricing and ordering policy on the price-demand parameters based on a periodic-review, multi-period and lost sale inventory model for perishable products with constant quantity decay rate and price-sensitive demand. Firstly, we formulate the joint pricing and inventory control problem and find the optimal ordering quantity and the optimal price for deterministic price-demand function. The optimal solutions show that the retailer tends to set a lower price in early periods of each ordering cycle in order to reduce the inventory holding costs. Furthermore, the sensitivity of the optimal joint pricing and inventory control system with respect to the price-demand parameters is examined analytically and evaluated numerically. The sensitivity analysis reveals that compared to the optimal ordering quantity, the optimal prices are less sensitive in the demand-price parameters. Finally, according to the findings of the sensitivity analysis, a heuristic method of regulating the estimated demand-price parameters is employed to improve the average profit. 185 words.

Weakening convergence conditions of a potential reduction method for tensor complementarity problems
Xiaofei Liu and Yong Wang
2022, 18(4): 2553-2566 doi: 10.3934/jimo.2021080 +[Abstract](1039) +[HTML](441) +[PDF](414.74KB)
Abstract:

Recently, under the condition that the included tensor in the tensor complementarity problem is a diagonalizable and positive definite tensor, the convergence of a potential reduction method for tensor complementarity problems is verified in [a potential reduction method for tensor complementarity problems. Journal of Industrial and Management Optimization, 2019, 15(2): 429–443]. In this paper, we improve the convergence of this method in the sense that the condition we used is strictly weaker than the one used in the above reference. Preliminary numerical results indicate the effectiveness of the potential reduction method under the new condition.

Due-window assignment scheduling with learning and deterioration effects
Shan-Shan Lin
2022, 18(4): 2567-2578 doi: 10.3934/jimo.2021081 +[Abstract](1100) +[HTML](519) +[PDF](357.91KB)
Abstract:

This paper considers single machine due-window assignment scheduling problems with position-dependent weights. Under the learning and deterioration effects of jobs processing times, our goal is to minimize the weighted sum of earliness-tardiness, starting time of due-window, and due-window size, where the weights only depends on their position in a sequence (i.e., position-dependent weights). Under common due-window (CONW), slack due-window (SLKW) and different due-window (DIFW) assignments, we show that these problems remain polynomial-time solvable.

A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem
Xiaoni Chi, Zhongping Wan and Zijun Hao
2022, 18(4): 2579-2598 doi: 10.3934/jimo.2021082 +[Abstract](1200) +[HTML](587) +[PDF](633.83KB)
Abstract:

The weighted complementarity problem (wCP) can be applied to a large variety of equilibrium problems in science, economics and engineering. Since formulating an equilibrium problem as a wCP may lead to highly efficient algorithms for its numerical solution, wCP is a nontrivial generalization of the complementarity problem. In this paper we consider a special weighted linear complementarity problem (wLCP), which is the more general optimization of the Fisher market equilibrium problem. A full-modified-Newton infeasible interior-point method (IIPM) for the special wLCP is proposed. The algorithm reformulates the central path of the perturbed problem as an equivalent system of equations, and uses only full-Newton steps at each iteration, so-called a feasibility step (i.e., a full-modified-Newton step) and several usual centering steps. The polynomial complexity of the algorithm is as good as the best known iteration bound for these types of IIPMs in linear optimization.

Quantitative stability of the ERM formulation for a class of stochastic linear variational inequalities
Jianxun Liu, Shengjie Li and Yingrang Xu
2022, 18(4): 2599-2610 doi: 10.3934/jimo.2021083 +[Abstract](955) +[HTML](536) +[PDF](431.08KB)
Abstract:

This paper focuses on the quantitative stability analysis of the expected residual minimization (ERM) formulation for a class of stochastic linear variational inequalities. Firstly, the existence of solutions of the ERM formulation and its perturbed problem is discussed. Then, the quantitative stability of the ERM formulation is derived under suitable probability metrics. Finally, the sample average approximation (SAA) problem of the ERM formulation is studied, and the rates of convergence of optimal solution sets are obtained under different assumptions.

Variable metric proximal stochastic variance reduced gradient methods for nonconvex nonsmooth optimization
Tengteng Yu, Xin-Wei Liu, Yu-Hong Dai and Jie Sun
2022, 18(4): 2611-2631 doi: 10.3934/jimo.2021084 +[Abstract](1395) +[HTML](485) +[PDF](760.27KB)
Abstract:

We study the problem of minimizing the sum of two functions. The first function is the average of a large number of nonconvex component functions and the second function is a convex (possibly nonsmooth) function that admits a simple proximal mapping. With a diagonal Barzilai-Borwein stepsize for updating the metric, we propose a variable metric proximal stochastic variance reduced gradient method in the mini-batch setting, named VM-SVRG. It is proved that VM-SVRG converges sublinearly to a stationary point in expectation. We further suggest a variant of VM-SVRG to achieve linear convergence rate in expectation for nonconvex problems satisfying the proximal Polyak-Łojasiewicz inequality. The complexity of VM-SVRG is lower than that of the proximal gradient method and proximal stochastic gradient method, and is the same as the proximal stochastic variance reduced gradient method. Numerical experiments are conducted on standard data sets. Comparisons with other advanced proximal stochastic gradient methods show the efficiency of the proposed method.

The loss-averse newsvendor problem with quantity-oriented reference point under CVaR criterion
Wei Liu, Shiji Song, Ying Qiao, Han Zhao and Huachang Wang
2022, 18(4): 2633-2650 doi: 10.3934/jimo.2021085 +[Abstract](1082) +[HTML](523) +[PDF](538.99KB)
Abstract:

This paper studies a single-period inventory problem with quantity-oriented reference point, where the newsvendor has loss-averse preferences and conditional value-at-risk (CVaR) measure is introduced to hedge against his risk. It is shown there exists a unique optimal order quantity maximizing the CVaR of utility. Moreover, it is decreasing in loss aversion level, confidence level and target unit profit, respectively. Then we establish the sufficient conditions under which the newsvendor's optimal order quantity may be larger than, equal to or less than the classical newsvendor solution. In particular, when the target unit profit is a convex combination of the maximum and minimum, the optimal order quantity is independent of price and cost parameters. Numerical experiments are conducted to illustrate our results and present some managerial insights.

The impacts of retailers' regret aversion on a random multi-period supply chain network
Yan Zhou, Chi Kin Chan and Kar Hung Wong
2022, 18(4): 2651-2675 doi: 10.3934/jimo.2021086 +[Abstract](1099) +[HTML](613) +[PDF](739.67KB)
Abstract:

Most current studies on the equilibrium decision-makings of a supply chain network (SCN) consider only completely rational retailers who always try to maximize their expected profits under the situations that demands are random. However, many evidences show that a retailer wants to choose the decision-making involving random demand which provides him with minimum regret. In this paper, we consider the impacts of retailers' anticipated regret aversion and experiential regret aversion on the equilibrium decision-makings of a random SCN with multiple production periods. Due to the random demand, the decision-makings of retailers are influenced not only by their anticipated regret, but also by their experiential regret after they have encountered bad or good experiences during past periods. The equilibrium conditions of the model are established. A numerical example is solved to illustrate the benefit of retailers obtained by considering their regret-averse behaviors. Moreover, it is found that retailers should consider their anticipated regret aversion or experiential regret aversion according to different situations of the demand markets.
 
Correction: The third author's affiliation, previously "School of Computational and Applied Mathematics," is now called "School of Computer Science and Applied Mathematics."

Optimal return and rebate mechanism based on demand sensitivity to reference price
Junling Han, Nengmin Wang, Zhengwen He and Bin Jiang
2022, 18(4): 2677-2703 doi: 10.3934/jimo.2021087 +[Abstract](1493) +[HTML](576) +[PDF](602.35KB)
Abstract:

The acceleration of electronic products' upgrade affects consumers' purchase behaviour. How to encourage consumers to return old products in order to upgrade to new products and how to optimize such the closed-loop supply chain are important managerial topics. According to the theory of reference price, the closed-loop supply chain model with fixed rebate and variable rebate is established. The analysis results imply that, when consumers' willingness to return second-hand products depends on manufacturers' rebates and prices of new products, the profit of closed-loop supply chain decreases. In addition, when consumers are sensitive to price difference, enterprises can adopt low profit margin methods to increase new product demand. Furthermore, the profit of the manufacturer is closely related to whether consumers are loss-seeking or loss-averse. Finally, our analysis provides the insights of the relationship between the optimal return and rebate mechanism and the use time of the previous generation of products.

Generalized Clarke epiderivatives of the extremum multifunction to a multi-objective parametric discrete optimal control problem
Nguyen Thi Toan
2022, 18(4): 2705-2720 doi: 10.3934/jimo.2021088 +[Abstract](932) +[HTML](433) +[PDF](485.37KB)
Abstract:

This paper deals with the generalized Clarke epiderivative of the extremum multifunction of a multi-objective parametric convex discrete optimal control problem with linear state equations and control constraints. By establishing an abstract result on the generalized epiderivative of the extremum multifunction of a multi-objective parametric convex mathematical programming problem, we derive a formula for computing the generalized Clarke epiderivative of the extremum multifunction to a multi-objective parametric convex discrete optimal control problem. Examples are given to illustrate the obtained results.

Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products
Yanhua Feng, Xuhui Xia, Lei Wang and Zelin Zhang
2022, 18(4): 2721-2748 doi: 10.3934/jimo.2021089 +[Abstract](1186) +[HTML](509) +[PDF](712.9KB)
Abstract:

Considering the quality of recycled products, we develop a game model of a multi-level competitive recycling and remanufacturing supply chain with two manufacturers and multiple recyclers. Being focus on two mainstream game models, namely the manufacturer-recycler cooperation game model and the manufacturer-led Stackelberg game model, we explore the connection between optimal pricing decisions and performance levels of the supply chain members. Although researches indicate that the quality of recycled products will not affect the pricing decisions in the forward supply chain, it is positively related to the recycling price, the repurchase price, and the overall profit in the reverse supply chain, and the intensity of competition among manufacturers or recycled products will affect the pricing decisions and the performance levels of the two models. In the manufacturer-led Stackelberg game model, the supply chain does not reach the Pareto optimum, which uses the recycling cost sharing contract to achieve the coordination. Afterwards, the profits of the two manufacturers and multiple recyclers in the supply chain are increased, and the overall profit of the supply chain system is higher than that of the manufacturer-led Stackelberg game model. Finally, numerical analysis is conducted to verify the proposed coordination mechanism and its effectiveness.

The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain
Jian Liu, Xin Wu and Jiang-Ling Lei
2022, 18(4): 2749-2782 doi: 10.3934/jimo.2021090 +[Abstract](1250) +[HTML](608) +[PDF](3033.82KB)
Abstract:

Consumer green preference (CGP) and fairness concern have posed significant impact on supply chain, respectively. This paper study the combined impacts of CGP and fairness concern on the supply chain that consists of a manufacturer, a green retailer, and a traditional retailer. Specifically, the optimal decision-makings are solved in seven cases, fairness neutrality (FN), the green retailer and the traditional retailer has vertical fairness concern (VFC) respectively, the two retailers has horizontal fairness concern (HFC) respectively, both retailers have vertical fairness concern (BVFC), both retailers have horizontal fairness concern (BHFC). Our main results via numerical simulation follow. (1) The improvement of CGP benefits the supply chain members except the traditional retailer. (2) The green retailer's VFC benefits itself and the whole supply chain, whereas bad for the manufacturer and the traditional retailer. However, the green retailer's HFC bad for itself, while benefits the manufacturer and the traditional retailer. (3) The traditional retailer's profits are affected by both CGP and fairness concern. (4) The high level of BVFC benefits the two retailers, but bad for the manufacturer. Conversely, the high level of BHFC will intensify competition between retailers and thus bad for them, while the manufacturer can benefit from it.

An online-decision algorithm for the multi-period bank clearing problem
Zongwei Chen
2022, 18(4): 2783-2803 doi: 10.3934/jimo.2021091 +[Abstract](1265) +[HTML](494) +[PDF](613.36KB)
Abstract:

The bank clearing problem (BCP) refers to the problem of designing an optimal clearing algorithm for the interbank payment system. Due to the way in which for the payment system has evolved, the classical BCP model is insufficient for addressing this problem accurately. In particular, delayed settlements are allowed in the now popular high-frequency deferred net settlement (DNS) system. In practice, the characteristics of incoming payment instructions are heavily connected to the time of day, and can be predicted with reasonable precision based on historical data. In this paper, we study the multi-period bank clearing problem (MBCP) by introducing the time dimension and considering future instructions in the decision-making process. We design a new clearing algorithm for MBCP using a model predictive control (MPC) policy, which uses historical data to predict payment instructions in the future. We benchmark the designed algorithm's performance with the classical greedy algorithm on the basis of BCP. Given that the liquidity is regular or relatively low, the numerical results indicate that the designed algorithm significantly improves the quality of clearing decision-making and is robust with respect to forecasting errors and fluctuation of future transactions.
 
Correction: Instances of “sanitized data from CNAPS” have been corrected to “simulated data of CNAPS”. We apologize for any inconvenience this may cause.

Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites
Qian Zhao, Bitao Jiang, Xiaogang Yu and Yue Zhang
2022, 18(4): 2805-2826 doi: 10.3934/jimo.2021092 +[Abstract](1029) +[HTML](482) +[PDF](1615.86KB)
Abstract:

Multiple heterogeneous satellites mission optimization is a typical kind of non-deterministic polynomial-time hard (NP-hard) problem, and some complicated scenarios bring new challenges. A novel method of missing ship rapid search using multiple grouped heterogeneous satellites is introduced in this paper. The focus is on optimization of collaborative mission optimization for various satellites including low-earth orbit (LEO) satellite and geostationary orbit (GEO) satellites. A fast coverage of the wide sea area using imaging satellites with narrow coverage range has become the most important part to tackle this problem. However, due to different imaging mechanisms of heterogeneous satellites and other constraints, it brings a great challenge to construct the optimization model. A constrained optimization problem model considering the cooperation between LEO and GEO satellites is constructed. A solution strategy based on bi-level metaheuristic algorithm is designed. The time optimal solution of the collaborative task planning between LEO and GEO satellites can be obtained based on the optimal attitude maneuver path of GEO satellites. Thus, wide-area search for missing ships can be conducted in an effective way. The effectiveness of the proposed method is verified by an example.

Risk minimization inventory model with a profit target and option contracts under spot price uncertainty
Nana Wan, Li Li, Xiaozhi Wu and Jianchang Fan
2022, 18(4): 2827-2845 doi: 10.3934/jimo.2021093 +[Abstract](1136) +[HTML](411) +[PDF](456.07KB)
Abstract:

This paper aims to analyze the inventory purchasing model for a manufacturer with an objective of minimizing risk and a constraint on profit target, where the manufacturer buys the components from the supplier or in the spot market and tailors them into the final products to meet a deterministic demand. This paper develops the mean-variance optimization models without and with option contracts, and conducts numerical examples to explore how the target profit level, the spot price uncertainty and option contracts affect the manufacturer's optimal solutions and the level of risk. It is shown that without and with option contracts the manufacturer's level of risk is non-decreasing in the target profit level. With (without) option contracts, the manufacturer suffers a zero risk from a higher spot price uncertainty if the profit target is low, whereas suffers a lower (higher) risk from a higher spot price uncertainty if the profit target is high. Finally, the level of risk faced by the manufacturer is not higher with option contracts than without them. This paper facilitates the application of option contracts in inventory purchasing management with a spot market for the risk minimization manufacturer with a profit target consideration. New insights are also provided for the manufacturer to set an appropriate profit target for an affordable level of risk, and establish the risk observation mechanism for hedging against the spot price volatility effectively.

A time-division distribution strategy for the two-echelon vehicle routing problem with demand blowout
Min Zhang, Guowen Xiong, Shanshan Bao and Chao Meng
2022, 18(4): 2847-2872 doi: 10.3934/jimo.2021094 +[Abstract](1055) +[HTML](506) +[PDF](772.46KB)
Abstract:

Based on the rapid development of e-commerce, major promotional events and holidays can lead to explosive growth in market demand and place significant pressure on distribution systems. In this study, we considered a distribution system in which products are first transported to transfer satellites from a central depot and then delivered to customers from the transfer satellites. We modeled this distribution problem as a two-echelon vehicle routing problem with demand blowout (2E-VRPDB). We adopt a time-division distribution strategy to address massive delivery demand in two phases by offering incentives to customers who accept flexible delivery dates. We propose a hybrid fireworks algorithm (HFWA) to solve the 2E-VRPDB model. This model fuses an optimal cutting algorithm with an improved fireworks algorithm. To demonstrate the effectiveness and efficiency of the proposed HFWA, we conducted comparative analysis on a genetic algorithm and ant colony algorithm using a VRP example set. Finally, we applied the proposed model and HFWA to solve a distribution problem for the Jingdong Mall in Chengdu, China. The computational results demonstrate that the proposed approach can effectively reduce logistical costs and maintain a high service level.

Inertial Tseng's extragradient method for solving variational inequality problems of pseudo-monotone and non-Lipschitz operators
Gang Cai, Yekini Shehu and Olaniyi S. Iyiola
2022, 18(4): 2873-2902 doi: 10.3934/jimo.2021095 +[Abstract](1495) +[HTML](464) +[PDF](1398.94KB)
Abstract:

In this paper, we propose a new inertial Tseng's extragradient iterative algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz operator in real Hilbert spaces. We prove that the sequence generated by proposed algorithm converges strongly to an element of solutions of variational inequality problem under some suitable assumptions imposed on the parameters. Finally, we give some numerical experiments for supporting our main results. The main results obtained in this paper extend and improve some related works in the literature.

Optimal decision in a Statistical Process Control with cubic loss
Vladimir Turetsky and Valery Y. Glizer
2022, 18(4): 2903-2926 doi: 10.3934/jimo.2021096 +[Abstract](938) +[HTML](474) +[PDF](1234.88KB)
Abstract:

We consider the problem of time-sampling optimization for a Statistical Process Control (SPC). The aim of this optimization is to minimize the expected loss, caused by a delay in the detection of an undesirable process change. The expected loss is chosen as a cubic polynomial function of this delay. Such a form of the expected loss is justified by some real-life problems. The SPC optimization problem is modeled by a nonlinear calculus of variations problem where the functional is minimized by a proper choice of the sampling time-interval. Theoretical results are illustrated by several academic and real-life examples.

In the previous works of the authors, the SPC optimization problem was solved for linear, pure quadratic and quadratic polynomial criteria.

Designing an annual leave scheduling policy: Case of a financial center
Gonca Yıldırım and Ayyuce Aydemir-Karadag
2022, 18(4): 2927-2958 doi: 10.3934/jimo.2021097 +[Abstract](1215) +[HTML](454) +[PDF](1204.3KB)
Abstract:

Providing annual leave entitlements for employees can help alleviate burnout since paid-time off work directly affects the health and productivity of workers as well as the quality of the service provided. In this paper, we develop realistic vacation scheduling policies and investigate how they compare from both the employer and the employees' perspectives. Among those policies, we consider one that is used in practice, another that we propose as a compromise which performs very well in most cases, and one that is similar to machine scheduling for benchmarking. Integer programming models are formulated and solved under various settings for workload distribution over time, substitution and unit of time for vacations. We use three performance measures for comparisons: penalty cost of unused vacation days, percent vacation granted and level of employee satisfaction. We provide a real-life case study at a bank's financial center. Numerical results suggest that an all-or-nothing type of vacation policy performs economically worse than the others. Attractive annual leave scheduling policies can be designed by administering vacation schedules daily rather than weekly, ensuring full cover for off-duty employees, and offering employees some degree of choice over vacation schedules.

A three echelon supply chain model with stochastic demand dependent on price, quality and energy reduction
Chandan Pathak, Saswati Mukherjee, Santanu Kumar Ghosh and Sudhansu Khanra
2022, 18(4): 2959-2975 doi: 10.3934/jimo.2021098 +[Abstract](1007) +[HTML](559) +[PDF](514.57KB)
Abstract:

While developing supply chain models, many researchers have shown great interest on how to reduce the consumption of non-renewable sources of energy, as non-renewable sources of energy is limited. The purpose of this paper is to formulate a three echelon supply chain model when the demand of items is assumed to be stochastically dependent on price, quality and reduction of energy. In the centralized model, suppler, manufacturer and retailer are the three members of the supply chain. The model is solved analytically to obtain optimal values of order quantity, unit price, promotional effort and amount of energy consumption which maximizes the profit function of the supply chain. Two decentralized models namely MR-Nash and MS-Nash have also been considered in a separate section. These two models have also been solved analytically to obtain the optimal solution of the decision variables. Three proposed models have been illustrated with a numerical example by considering exponential distribution of customer's demand. The sensitivity of the optimal solution revealed the appropriate channel strategy in case of decentralized scenario. It is speculated that when the manufacturer and the supplier collaborates, the profit difference is reduced by \begin{document}$ 39 \% $\end{document} than that of the MR-Nash.

A novel quality prediction method based on feature selection considering high dimensional product quality data
Junying Hu, Xiaofei Qian, Jun Pei, Changchun Tan, Panos M. Pardalos and Xinbao Liu
2022, 18(4): 2977-3000 doi: 10.3934/jimo.2021099 +[Abstract](1331) +[HTML](728) +[PDF](1468.97KB)
Abstract:

Product quality is the lifeline of enterprise survival and development. With the rapid development of information technology, the semiconductor manufacturing process produces multitude of quality features. Due to the increasing quality features, the requirement on the training time and classification accuracy of quality prediction methods becomes increasingly higher. Aiming at realizing the quality prediction for semiconductor manufacturing process, this paper proposes a modified support vector machine (SVM) model based on feature selection, considering the high dimensional and nonlinear characteristics of data. The model first improves the Radial Basis Function (RBF) in SVM, and then combines the Duelist algorithm (DA) and variable neighborhood search algorithm (VNS) for feature selection and parameters optimization. Compared with some other SVM models that are based on DA, genetic algorithm (GA), and Information Gain algorithm (IG), the experiment results show that our DA-VNS-SVM can obtain higher classification accuracy rate with a smaller feature subset. In addition, we compare the DA-VNS-SVM with some common machine learning algorithms such as logistic regression, naive Bayes, decision tree, random forest, and artificial neural network. The results indicate that our model outperform these machine learning algorithms for the quality prediction of semiconductor.

Managing piracy: Dual-channel strategy for digital contents
Yan-Xin Chai, Steven Ji-Fan Ren and Jian-Qiang Zhang
2022, 18(4): 3001-3027 doi: 10.3934/jimo.2021100 +[Abstract](1340) +[HTML](441) +[PDF](611.94KB)
Abstract:

The Internet offers digital content disc producers the opportunities to design dual channels by introducing an online-direct store alongside traditional retail stores, but also leads related firms to suffer significant piracy problems. Using a game-theoretic framework, we explore dual-channel marketing optimality as a piracy-mitigating strategy for digital content sold in the physical disc format. We construct a price-setting game between a digital content producer and its independent retailer(s) in a pirated market by endogenizing the producer's copyright protection investments. We show that dual-channel marketing, a complement or a substitute for conventional copyright protection, can strategically mitigate the piracy level by increasing the equal-size retail sales volume. We also investigate how firms' pricing strategies and profits are influenced by the endogenous interaction of dual-channel marketing and copyright protection. We unexpectedly find that in a pirated market with insufficient copyright protection, dual-channel marketing can simultaneously raise firm pricing and sales volumes when the producer sells through a monopolistic retailer. We also identify the conditions under which dual-channel marketing can mitigate profit losses caused by piracy for the producer and the retailer(s). Unlike previous research which shows that dual-channel marketing benefits the producer and the monopolistic retailer because it mitigates double marginalization, in the pirated market, this win-win outcome occurs even if accompanied by aggravated double marginalization. Moreover, dual-channel marketing can mitigate all the firms' profit losses caused by piracy only when it can complement conventional copyright protection, i.e., when the producer sells through a monopolistic retailer or duopolistic retailers. In each situation, counter-intuitively, as copyright protection becomes increasingly costly, although the retailer(s) is (are) more willing to accept dual-channel marketing, the producer has a decreased incentive to design such sales channels.

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

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