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Journal of Industrial & Management Optimization

November 2021 , Volume 17 , Issue 6

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A dynamical system method for solving the split convex feasibility problem
Zeng-Zhen Tan, Rong Hu, Ming Zhu and Ya-Ping Fang
2021, 17(6): 2989-3011 doi: 10.3934/jimo.2020104 +[Abstract](1305) +[HTML](577) +[PDF](1059.88KB)
Abstract:

In this paper a dynamical system model is proposed for solving the split convex feasibility problem. Under mild conditions, it is shown that the proposed dynamical system globally converges to a solution of the split convex feasibility problem. An exponential convergence is obtained provided that the bounded linear regularity property is satisfied. The validity and transient behavior of the dynamical system is demonstrated by several numerical examples. The method proposed in this paper can be regarded as not only a continuous version but also an interior version of the known \begin{document}$ CQ $\end{document}-method for solving the split convex feasibility problem.

Robust observer-based control for discrete-time semi-Markov jump systems with actuator saturation
Yueyuan Zhang, Yanyan Yin and Fei Liu
2021, 17(6): 3013-3026 doi: 10.3934/jimo.2020105 +[Abstract](1278) +[HTML](535) +[PDF](391.12KB)
Abstract:

This paper investigates the control synthesis for discrete-time semi-Markov jump systems with nonlinear input. Observer-based controllers are designed in this paper to achieve a better performance and robustness. The nonlinear input caused by actuator saturation is considered as a group of linear controllers in the convex hull. Moreover, the elapse time and mode dependent Lyapunov functions are investigated and sufficient conditions are derived to guarantee the \begin{document}$ H_\infty $\end{document} performance index. The largest domain of attraction is estimated as the existing saturation in the system. Finally, a numerical example is utilized to verify the effectiveness and feasibility of the developed strategy.

Equilibrium strategies in a supply chain with capital constrained suppliers: The impact of external financing
Qiang Yan, Mingqiao Luan, Yu Lin and Fangyu Ye
2021, 17(6): 3027-3047 doi: 10.3934/jimo.2020106 +[Abstract](1287) +[HTML](645) +[PDF](894.37KB)
Abstract:

In this study, we consider a two-echelon supply chain, where two capital constrained suppliers compete to sell their products through a common retailer. The retailer may provide advance payment to one or two suppliers. We show that whether the retailer considers merging with only one supplier depends upon the revenue sharing ratio and the additional administrative costs of the revenue sharing contract. Meanwhile, the supplier who drops out of the market may adopt a hybrid financing scheme by combining bank credit with equity financing to return to the market. We find that the deselected supplier can be allowed to participate in the market when the bank loans ratio is below a certain threshold. We further investigate the impact of the bank loans ratio and competition intensity on the players' decisions and profits. In addition, we find that there exists an optimal bank loans ratio for the deselected supplier. Specifically, it is optimal for the deselected supplier to adopt pure bank credit if the production cost is sufficiently low.

Quality choice and capacity rationing in advance selling
Taofeng Ye and Yan Zhao
2021, 17(6): 3049-3084 doi: 10.3934/jimo.2020107 +[Abstract](958) +[HTML](544) +[PDF](1496.06KB)
Abstract:

This study considers a seller who sells a single product to strategic consumers sensitive to both price and quality over two periods: advance and spot. Customers' valuations are uncertain in the first period and revealed over time. The seller's decisions include whether to offer the product and, if so, the quality of the product, the prices in both periods, and whether to ration capacity in the advance period. The analysis is separated into two cases: unlimited capacity and limited capacity. The first case acts as a benchmark for the latter. It is found that in each case, the seller's decisions on product offering and quality choice are fully determined by a single parameter, namely the cost coefficient of quality. The optimal rationing policy and its determinants, however, are distinct in these different settings. And the optimal rationing policy is contingent on whether the high- or low-quality product is offered. Further, our numerical studies show that the seller can benefit from capacity rationing and flexibility on quality choice. Specifically, the value of rationing is not evident, whereas the value of flexibility on quality choice is considerably significant.

Hadamard directional differentiability of the optimal value of a linear second-order conic programming problem
Qingsong Duan, Mengwei Xu, Liwei Zhang and Sainan Zhang
2021, 17(6): 3085-3098 doi: 10.3934/jimo.2020108 +[Abstract](1143) +[HTML](522) +[PDF](424.1KB)
Abstract:

In this paper, we consider perturbation properties of a linear second-order conic optimization problem and its Lagrange dual in which all parameters in the problem are perturbed. We prove the upper semi-continuity of solution mappings for the pertured problem and its Lagrange dual problem. We demonstrate that the optimal value function can be expressed as a min-max optimization problem over two compact convex sets, and it is proven as a Lipschitz continuous function and Hadamard directionally differentiable.

Optimal ordering and pricing models of a two-echelon supply chain under multipletimes ordering
Zhenkai Lou, Fujun Hou and Xuming Lou
2021, 17(6): 3099-3111 doi: 10.3934/jimo.2020109 +[Abstract](1167) +[HTML](504) +[PDF](345.8KB)
Abstract:

This paper studies ordering and pricing issues under multiple times ordering. A manufacturer and a retailer are involved in our discussion. The definition of a reasonable price is given based on the practical requirement. First, we construct a Stackelberg model in which the manufacturer and the retailer make their decisions respectively. During the process of derivation, both ordering time-points and optimal prices are expressed as functions of number of times of ordering. By solving a quadratic programming model with an undetermined parameter, we demonstrate that the optimal ordering time-points of the retailer are equidistant time points on the given selling period. Second, a cooperative model is developed in which the manufacturer and the retailer jointly make decisions. It is shown that the optimal retail price is lower and the number of times of ordering is more in the cooperative situation than the noncooperative one. Further, an allocation method based on revenue proportions is proposed.

Pricing and lot-sizing decisions for perishable products when demand changes by freshness
Onur Kaya and Halit Bayer
2021, 17(6): 3113-3129 doi: 10.3934/jimo.2020110 +[Abstract](1837) +[HTML](558) +[PDF](353.94KB)
Abstract:

Perishable products like dairy products, vegetables, fruits, pharmaceuticals, etc. lose their freshness over time and become completely obsolete after a certain period. Customers generally prefer the fresh products over aged ones, leading the perishable products to have a decreasing demand function with respect to their age. We analyze the inventory management and pricing decisions for these products, considering an age-and-price-dependent stochastic demand function. A stochastic dynamic programming model is developed in order to decide when and how much inventory to order and how to price these products considering their freshness over time. We prove the characteristics of the optimal solution of the developed model and extract managerial insights regarding the optimal inventory and pricing strategies. The numerical studies show that dynamic pricing can lead to significant savings over static pricing under certain parameter settings. In addition, longer replenishment cycles are seen under dynamic pricing compared to static pricing, even though similar quantities are ordered in each replenishment.

Two-period pricing and ordering decisions of perishable products with a learning period for demand disruption
Kebing Chen, Haijie Zhou and Dong Lei
2021, 17(6): 3131-3163 doi: 10.3934/jimo.2020111 +[Abstract](1148) +[HTML](519) +[PDF](839.94KB)
Abstract:

In this paper, we develop a two-period inventory model of perishable products with considering the random demand disruption. Faced with the random demand disruption, the firm has two order opportunities: the initial order at the beginning of selling season (i.e., Period 1) is intended to learn the real information of the disrupted demand. When the information of disruption is realized, the firm places the second order, and also decides how many unsold units should be carried into the rest of selling season (i.e., Period 2). The firm may offer two products of different perceived quality in Period 2, and therefore it must trade-off between the quantity of carry-over units and the quantity of young units when the carry-over units cannibalize the sales of young units. Meanwhile, there is both price competition and substitutability between young and old units. We find that the quantity of young units ordered in Period 2 decreases with the quality of units ordered in Period 1, while the pricing of young units is independent of the quality level of old units. However, both the surplus inventory level and the pricing of old units monotonically increase with their quality. We also investigate the influence of two demand disruption scenarios on the optimal order quantity and the optimal pricing when considering different quality situations. We find that in the continuous random disruption scenario, the information value of disruption to the firm is only related to the disruption mean, while in the discrete random disruption scenario, it is related to both unit purchase cost of young units and the disruption levels.

Air-Conditioner Group Power Control Optimization for PV integrated Micro-grid Peak-shaving
Mohammed Al-Azba, Zhaohui Cen, Yves Remond and Said Ahzi
2021, 17(6): 3165-3181 doi: 10.3934/jimo.2020112 +[Abstract](1193) +[HTML](540) +[PDF](1138.12KB)
Abstract:

Heating, Ventilation, and Air-Condition (HVAC) systems are considered to be one of the essential applications for modern human life comfort. Due to global warming and population growth, the demand for such HVAC applications will continue to increase, especially in arid areas countries like the Arabian Gulf region. HVAC systems' energy consumption is very high and accounts for up to 70% of the total load consumption in some rapidly growing GCC countries such as Qatar. Additionally, the local extremely hot weather conditions usually lead to typical power demand peak issues that require adequate mitigation measures to ensure grid stability. In this paper, a novel control scheme for a combined group of Air-Conditioners is proposed as a peak-shaving strategy to address high power demand issues for Photo-Voltaic(PV)-integrated micro-grid applications. Using the local daily ambient temperature as input, the AC group control optimization is formulated as a Mixed-Integer Quadratic Programming (MIQP) problem. Under an acceptable range of indoor temperatures, the units in the same AC group are coordinately controlled to generate desired power consumption performance that is capable of shaving load peaks for both power consumption and PV generation. Finally, various simulations are performed that demonstrate the effectiveness of the proposed control strategy.

Alliance strategy of construction and demolition waste recycling based on the modified shapley value under government regulation
Jun Huang, Ying Peng, Ruwen Tan and Chunxiang Guo
2021, 17(6): 3183-3207 doi: 10.3934/jimo.2020113 +[Abstract](1270) +[HTML](561) +[PDF](1508.85KB)
Abstract:

Construction and demolition waste (CDW) recycling enterprises have an imperfect operation system, which leads to low recovery rate and low production profits. A feasible method to improve this situation involves seeking a high-efficiency enterprise alliance strategy in the CDW recycling system composed of manufacturers, retailers and recyclers and designing a reasonable and effective coordination mechanism to enhance their enthusiasm for participa-tion. First, we constructed a Stackelberg game model of CDW recycling under government regulation and analyzed the optimal alliance strategy of CDW recycling enterprises under punishment or subsidy by the government as a game leader. In order to ensure the stable cooperation of the alliance, we used the Shapley value method to coordinate the distribution of the optimal alliance profit and improved the fairness and effectiveness of the coordination mechanism through modification of the unequal rights factor. Finally, based on the survey data of Chongqing, we further verified the conclusion through numerical simulation and an-alyzed changes in various parameters at different product costs. The results show that the alliance strategy and coordination mechanism can improve the CDW recovery rate, improve the recycling market status, and increase the production profits of enterprises.

Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem
Bhawna Kohli
2021, 17(6): 3209-3221 doi: 10.3934/jimo.2020114 +[Abstract](1077) +[HTML](468) +[PDF](304.15KB)
Abstract:

The main aim of this paper is to establish sufficient optimality conditions using an upper estimate of Clarke subdifferential of value function and the concept of convexifactor for optimistic bilevel programming problems with convex and non-convex lower-level problems. For this purpose, the notions of asymptotic pseudoconvexity and asymptotic quasiconvexity are defined in terms of the convexifactors.

Tabu search guided by reinforcement learning for the max-mean dispersion problem
Dieudonné Nijimbere, Songzheng Zhao, Xunhao Gu, Moses Olabhele Esangbedo and Nyiribakwe Dominique
2021, 17(6): 3223-3246 doi: 10.3934/jimo.2020115 +[Abstract](1315) +[HTML](554) +[PDF](508.17KB)
Abstract:

We present an effective hybrid metaheuristic of integrating reinforcement learning with a tabu-search (RLTS) algorithm for solving the max–mean dispersion problem. The innovative element is to design using a knowledge strategy from the \begin{document}$ Q $\end{document}-learning mechanism to locate promising regions when the tabu search is stuck in a local optimum. Computational experiments on extensive benchmarks show that the RLTS performs much better than state-of-the-art algorithms in the literature. From a total of 100 benchmark instances, in 60 of them, which ranged from 500 to 1, 000, our proposed algorithm matched the currently best lower bounds for all instances. For the remaining 40 instances, the algorithm matched or outperformed. Furthermore, additional support was applied to present the effectiveness of the combined RL technique. The analysis sheds light on the effectiveness of the proposed RLTS algorithm.

Channel leadership and recycling channel in closed-loop supply chain: The case of recycling price by the recycling party
Zhidan Wu, Xiaohu Qian, Min Huang, Wai-Ki Ching, Hanbin Kuang and Xingwei Wang
2021, 17(6): 3247-3268 doi: 10.3934/jimo.2020116 +[Abstract](1438) +[HTML](527) +[PDF](390.82KB)
Abstract:

Due to the fast growing of the waste electrical and electronic equipment (WEEE), the business values of closed-loop supply chains (CLSCs) have been well recognized. In this paper, we investigate the performance of the CLSCs under different combinations of the recycling channel and the channel leadership when the recycling price is determined by the recycling party. Specially, we consider a CLSC consisting of two channel members, i.e., a manufacturer and a retailer. Each member acting as the channel leader has three different channels to collect the used products, and they are (ⅰ) the manufacturer (M-channel), (ⅱ) the retailer (R-channel) and (ⅲ) the third-party (T-channel). Given the recycling party determines the recycling price, mathematical models are developed to investigate the performance of the CLSC under different combinations of the channel leadership and the recycling channel. Through a comparison analysis, we find that M-channel is the most effective recycling channel. Moreover, once the M-channel be adopted, the retailer-led structure is as good as manufacture-led structure. We find that the recycling channel structure could be more important than the channel leadership in the CLSC. Finally, we illustrate that the CLSC can be coordinated by a two-part tariff contract.

Order allocation model in logistics service supply chain with demand updating and inequity aversion: A perspective of two option contracts comparison
Weihua Liu, Xinran Shen, Di Wang and Jingkun Wang
2021, 17(6): 3269-3295 doi: 10.3934/jimo.2020118 +[Abstract](1156) +[HTML](552) +[PDF](610.94KB)
Abstract:

This paper considers an logistics service supply chain consisting of a logistics service integrator (LSI) and a number of functional logistics service providers (FLSPs). In the environment of demand updating, we focus on the inequity aversion among the FLSPs and introduce two option contracts (the reservation option contract and the option guarantee contract), build the multi-objective programming models, to explore effects of the inequity aversion behavior on the order allocation, and whether the two option contracts can mitigate the impact of inequity aversion on order allocation. Three important conclusions are obtained after two option contracts comparisons: first, there is an optimal update time, at which point, the order allocation results reach the optimal value and tend to be stable. Second, two option contracts both can not only increase the total performance of the supply chain, but also mitigate the impact of inequity aversion on the allocation under certain conditions. Third, when demand decreases, the reservation option contract is better than option guarantee contract, in contrast, when demand increases, option guarantee contract is better.

Fuzzy event-triggered disturbance rejection control of nonlinear systems
Peng Cheng, Yanqing Liu, Yanyan Yin, Song Wang and Feng Pan
2021, 17(6): 3297-3307 doi: 10.3934/jimo.2020119 +[Abstract](1069) +[HTML](487) +[PDF](326.91KB)
Abstract:

The problem of fuzzy based event-triggered disturbance rejection control for nonlinear systems is addressed in this paper. A new fuzzy event based anti rejection controller is designed and a fuzzy reduced disturbance observer is constructed. Sufficient conditions for the closed loop system to be asymptotically stable under an \begin{document}$ H_\infty $\end{document} performance index are derived. Based on these conditions, the design of a fuzzy event-triggered state feedback controller is formulated and solved. Numerical results are presented to demonstrate the correctness and effectiveness of our theoretical findings.

Strategic joining in a single-server retrial queue with batch service
Ke Sun, Jinting Wang and Zhe George Zhang
2021, 17(6): 3309-3332 doi: 10.3934/jimo.2020120 +[Abstract](933) +[HTML](473) +[PDF](905.88KB)
Abstract:

We consider a single-server retrial queue with batch service where potential customers arrive according to a Poisson process. The service process has two stages: busy period and admission period, which are corresponding to whether the server is in service or not, respectively. In such an alternate renewal process, if arrivals find busy period, they make join-or-balk decisions. Those joining ones will stay in the orbit and attempt to get into server at a constant rate. While, if arrivals find the server is in an admission period, they get into the server directly. At the end of each admission period, all customers in the server will be served together regardless of the size of the batch. The reward of each arrival after completion of service depends on the service size. Furthermore, customers in the orbit fail to get into the server before the end of each service cycle will be forced to leave the system. We study an observable scenario that customers are informed about the service period upon arrivals and an unobservable case without this information. The Nash equilibrium joining strategies are identified and the social- and profit- maximization problems are obtained, respectively. Finally, the optimal joining strategies in the observable queue and the comparison of social welfare between the two queues are illustrated by numerical examples.

Modeling and computation of mean field game with compound carbon abatement mechanisms
Shuhua Zhang, Junying Zhao, Ming Yan and Xinyu Wang
2021, 17(6): 3333-3347 doi: 10.3934/jimo.2020121 +[Abstract](997) +[HTML](519) +[PDF](895.72KB)
Abstract:

In this paper, we present a mean field game to model the impact of the coexistence mechanism of carbon tax and carbon trading (we call it compound carbon abatement mechanism) on the production behaviors for a large number of producers. The game's equilibrium can be presented by a system which is composed of a forward Kolmogorov equation and a backward Hamilton-Jacobi-Bellman (HJB) partial differential equation. An implicit and fractional step finite difference method is proposed to discretize the resulting partial differential equations, and a strictly positive solution is obtained for a non-negative initial data. The efficiency and the usefulness of this method are illustrated through the numerical experiments. The sensitivity analysis of the parameters is also carried out. The results show that an agent under concentrated carbon emissions tends to choose emission levels different from other agents, and the choices of agents with uniformly distributed emission level will be similar to their initial distribution. Finally, we find that for the compound carbon abatement mechanism carbon tax has a greater impact on the permitted emission rights than carbon trading price does, while carbon trading price has a greater impact on carbon emissions than carbon tax.

C-eigenvalue intervals for piezoelectric-type tensors via symmetric matrices
Xifu Liu, Shuheng Yin and Hanyu Li
2021, 17(6): 3349-3356 doi: 10.3934/jimo.2020122 +[Abstract](913) +[HTML](514) +[PDF](330.98KB)
Abstract:

C-eigenvalues of piezoelectric-type tensors play an crucial role in piezoelectric effect and converse piezoelectric effect. In this paper, by the partial symmetry property of piezoelectric-type tensors, we present three intervals to locate all C-eigenvalues of a given piezoelectric-type tensor. Numerical examples show that our results are better than the existing ones.

New inertial method for generalized split variational inclusion problems
Preeyanuch Chuasuk, Ferdinard Ogbuisi, Yekini Shehu and Prasit Cholamjiak
2021, 17(6): 3357-3371 doi: 10.3934/jimo.2020123 +[Abstract](1519) +[HTML](657) +[PDF](345.5KB)
Abstract:

The purpose of this paper is to introduce a new inertial iterative method for solving split variational inclusion problems in real Hilbert spaces. We prove that the generated sequence converges weakly to the solution of the considered problem under some mild conditions. The major contributions of our results are: (ⅰ) to increase the rate of convergence of the method for solving split variational inclusion problem through the inertial extrapolation step, (ⅱ) to relax the choice of the inertial factor and show the inertial factor can be chosen greater than 1/3 unlike what is previously known before for inertial proximal point method in the literature (ⅲ) to show the numerical efficiency and superiority of our proposed method through some test example.

On the $ BMAP_1, BMAP_2/PH/g, c $ retrial queueing system
Yi Peng and Jinbiao Wu
2021, 17(6): 3373-3391 doi: 10.3934/jimo.2020124 +[Abstract](1032) +[HTML](489) +[PDF](432.33KB)
Abstract:

In this paper, we consider the BMAP/PH/c retrial queue with two types of customers where the rate of individual repeated attempts from the orbit is modulated according to a Markov Modulated Poisson Process. Using the theory of multi-dimensional asymptotically quasi-Toeplitz Markov chain, we obtain the algorithm for calculating the stationary distribution of the system. Main performance measures are presented. Furthermore, we investigate some optimization problems. The algorithm for determining the optimal number of guard servers and total servers is elaborated. Finally, this queueing system is applied to the cellular wireless network. Numerical results to illustrate the optimization problems and the impact of retrial on performance measures are provided. We find that the performance measures are mainly affected by the two types of customers' arrivals and service patterns, but the retrial rate plays a less crucial role.

Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort
Wenying Xie, Bin Chen, Fuyou Huang and Juan He
2021, 17(6): 3393-3415 doi: 10.3934/jimo.2020125 +[Abstract](1168) +[HTML](544) +[PDF](397.6KB)
Abstract:

This paper deals with a one-period two-stage supply chain, in which a loss-averse retailer facing stochastic demand orders products from a risk-neutral supplier subject to yield uncertainty. Marketing effort exerted by the retailer is employed to enhance the final market demand. We first establish a performance benchmark, and show that the wholesale price contract fails to coordinate the supply chain due to the effects of double marginalization and loss aversion. Then we propose a revenue-cost-sharing contract in order to achieve supply chain coordination. It is verified that a properly designed revenue-cost-sharing contract can achieve perfect coordination and a win-win outcome synchronously. Our results reveal that it is simple to implement and arbitrarily allocate the total channel profit between the retailer and the supplier. In addition, we examine the effect of the retailer's loss aversion degree on contract parameters and profit allocation, and we show that both the retailer and the supplier can benefit from marketing effort.

Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning
Qingguo Bai, Jianteng Xu, Fanwen Meng and Niu Yu
2021, 17(6): 3417-3444 doi: 10.3934/jimo.2020126 +[Abstract](1250) +[HTML](549) +[PDF](487.79KB)
Abstract:

This paper incorporates carbon emission regulation and cost learning effects to examine a manufacturer-retailer supply chain for deteriorating items over a multi-period planning horizon. We investigate their impacts on supply chain coordination under the assumption that the product demand is affected by the selling price, promotional effort and inventory level. We first propose two algorithms for determining optimal solutions of the centralized and decentralized models. We show that the decentralized system can be coordinated perfectly with a two-part tariff contract. Further, we study necessary conditions under which members of the supply chain can accept this contract. At last, we conduct numerical experiment to illustrate the obtained theoretical results in impact analysis and the robustness of the coordinated model.

Bayesian decision making in determining optimal leased term and preventive maintenance scheme for leased facilities
Chih-Chiang Fang
2021, 17(6): 3445-3473 doi: 10.3934/jimo.2020127 +[Abstract](1852) +[HTML](627) +[PDF](923.53KB)
Abstract:

Under a business competitive environment, quite a few enterprises choose capital leasing to reduce tax payment and investment risk instead of buying facilities. Since the durability and service life of leased facilities will be longer, the breakdowns and deterioration of leased facilities are inevitable during lease period. Accordingly, in order to reduce the related costs and keep the facility's health during lease period, preventive maintenances are required to perform to reduce the cost of free-repair warranty and maintain customers' satisfaction. However, performing preventive maintenance is not easy to scheme due to the scarcity of historical failure data. Accordingly, the study integrates lease and maintenance decisions into a synthetic strategy, and it can be applied under the situation of only expert's evaluation and/or scare historical failure data by employing Bayesian analyses. In this study, the mathematical models and corresponding algorithms are developed to determine the best preventive maintenance scheme and the optimal term of contract for leased facilities to maximize the expected profit. Moreover, the computerized architecture is also proposed, and it can help the lessor to solve the issue in practice. Finally, numerical examples and the sensitive analyses are provided to illustrate the managerial strategies under different leased period and the preventive maintenance policies.

Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models
Mahdi Roozbeh, Saman Babaie–Kafaki and Zohre Aminifard
2021, 17(6): 3475-3491 doi: 10.3934/jimo.2020128 +[Abstract](1022) +[HTML](465) +[PDF](591.64KB)
Abstract:

In classical regression analysis, the ordinary least–squares estimation is the best strategy when the essential assumptions such as normality and independency to the error terms as well as ignorable multicollinearity in the covariates are met. However, if one of these assumptions is violated, then the results may be misleading. Especially, outliers violate the assumption of normally distributed residuals in the least–squares regression. In this situation, robust estimators are widely used because of their lack of sensitivity to outlying data points. Multicollinearity is another common problem in multiple regression models with inappropriate effects on the least–squares estimators. So, it is of great importance to use the estimation methods provided to tackle the mentioned problems. As known, robust regressions are among the popular methods for analyzing the data that are contaminated with outliers. In this guideline, here we suggest two mixed–integer nonlinear optimization models which their solutions can be considered as appropriate estimators when the outliers and multicollinearity simultaneously appear in the data set. Capable to be effectively solved by metaheuristic algorithms, the models are designed based on penalization schemes with the ability of down–weighting or ignoring unusual data and multicollinearity effects. We establish that our models are computationally advantageous in the perspective of the flop count. We also deal with a robust ridge methodology. Finally, three real data sets are analyzed to examine performance of the proposed methods.

A polyhedral conic functions based classification method for noisy data
Müge Acar and Refail Kasimbeyli
2021, 17(6): 3493-3508 doi: 10.3934/jimo.2020129 +[Abstract](1121) +[HTML](474) +[PDF](519.45KB)
Abstract:

This paper presents a robust binary classification method, which is an extended version of the Modified Polyhedral Conic Functions (M-PCF) algorithm, earlier developed by Gasimov and Ozturk. The new version presented in this paper, has new features in comparison to the original algorithm. The mathematical model used in the new version, is relaxed by allowing some inaccuracies in an optimal way. By this way, it is aimed to reduce the overfitting and improve the generalization property. In the original version, the sublevel set of a separating function generated at every iteration, does not contain any element of the other set. This is changed in the new version, where the sublevel sets of separating functions generated by the new algorithm, are allowed to contain some elements from other set. On the other hand, the new algorithm uses a tolerance parameter which prevents generating "less productive separating functions". In the original version, the algorithm continues till all points of the "first" set are separated from the second one, where a separating function is generated if there still exist unseparated elements regardless the number of such elements. In the new version, the tolerance parameter is used to terminate iterations if there are only a few unseparated elements. By this way, it is aimed to improve the generalization property of the algorithm, and therefore the new version is called Parameterized Polyhedral Conic Functions (P-PCF) method. The performance and efficiency of the proposed algorithm is demonstrated on well-known datasets from the literature and on noisy data.

Quantum-inspired satin bowerbird algorithm with Bloch spherical search for constrained structural optimization
Sen Zhang, Guo Zhou, Yongquan Zhou and Qifang Luo
2021, 17(6): 3509-3523 doi: 10.3934/jimo.2020130 +[Abstract](1315) +[HTML](511) +[PDF](472.5KB)
Abstract:

To enhance the optimization ability of the satin bowerbird optimization (SBO) algorithm, in this paper, a novel quantum-inspired SBO with Bloch spherical search is proposed. In this algorithm, satin bowerbirds are encoded using qubits described on the Bloch sphere, each satin bowerbird occupies three locations in the search space and each location represents an optimization solution. Using the search method of general SBO to adjust the two parameters of the qubit, qubit rotation is performed on the Bloch sphere, which simultaneously updates the three locations occupied by a qubit and quickly approaches the global optimal solution. Finally, the experimental results of five examples of structural engineering design show that the proposed algorithm is superior to other state-of-the-art metaheuristic algorithms in terms of the performance measures.

Continuity, differentiability and semismoothness of generalized tensor functions
Xia Li, Yong Wang and Zheng-Hai Huang
2021, 17(6): 3525-3550 doi: 10.3934/jimo.2020131 +[Abstract](934) +[HTML](454) +[PDF](405.9KB)
Abstract:

A large number of real-world problems can be transformed into mathematical problems by means of third-order real tensors. Recently, as an extension of the generalized matrix function, the generalized tensor function over the third-order real tensor space was introduced with the aid of a scalar function based on the T-product for third-order tensors and the tensor singular value decomposition; and some useful algebraic properties of the function were investigated. In this paper, we show that the generalized tensor function can inherit a lot of good properties from the associated scalar function, including continuity, directional differentiability, Fréchet differentiability, Lipschitz continuity and semismoothness. These properties provide an important theoretical basis for the studies of various mathematical problems with generalized tensor functions, and particularly, for the studies of tensor optimization problems with generalized tensor functions.

Research on the parallel–batch scheduling with linearly lookahead model
Chengwen Jiao and Qi Feng
2021, 17(6): 3551-3558 doi: 10.3934/jimo.2020132 +[Abstract](957) +[HTML](468) +[PDF](315.67KB)
Abstract:

In this paper, we consider the new online scheduling model with linear lookahead intervals, which has the character that at any time \begin{document}$ t $\end{document}, one can foresee the jobs that will coming in the time interval \begin{document}$ (t, \lambda t+\beta ] $\end{document} with \begin{document}$ \lambda\geq1, \beta\geq 0 $\end{document}. We consider online scheduling of unit length jobs on \begin{document}$ m $\end{document} identical parallel-batch machines under this new lookahead model to minimize the maximum flowtime and the makespan, respectively. We give some lower bounds for these problems with the batch capacity \begin{document}$ b = \infty $\end{document} and \begin{document}$ b<\infty $\end{document}, respectively. And for the bounded model to minimize makespan, we give an online algorithm with competitive ratio \begin{document}$ 1+\alpha $\end{document} for \begin{document}$ 1\leq \lambda <4/3, 0\leq \beta\leq \frac{4-3\lambda}{6} $\end{document} and \begin{document}$ \frac{3}{2} $\end{document} for \begin{document}$ \lambda\geq1, 0\leq\beta<1 $\end{document}, where \begin{document}$ \alpha $\end{document} is the positive root of \begin{document}$ \lambda\alpha^2+(\lambda+\beta)\alpha+\beta-1 = 0 $\end{document}. The online algorithm is best possible when \begin{document}$ 1\leq \lambda <4/3, 0\leq \beta\leq \frac{4-3\lambda}{6} $\end{document}.

Incentive contract design for supplier switching with considering learning effect
Qian Wei, Jianxiong Zhang and Xiaojie Sun
2021, 17(6): 3559-3580 doi: 10.3934/jimo.2020133 +[Abstract](932) +[HTML](445) +[PDF](464.19KB)
Abstract:

For minimizing purchase cost, a buying firm would switch to suppliers with providing more favorable prices. This paper investigates the optimal switching decision of a buyer that may switch to an entrant supplier with production learning ability (which is regarded as a private information) under a principal-agent framework. The results obtained show that the switching cost and the learning effect have significant impacts on the buyer's switching decision. Only when the fixed component of the switching cost is relatively low, the buyer can be better off from a partial switching strategy; otherwise, the buyer should take an all-or-nothing switching strategy or no switching strategy. As the learning ability of the entrant supplier increases, the buyer prefers to make more switching. Finally, a benefit-sharing contract is proposed to evaluate the performance of the principal-agent contract, and we demonstrate that the principal-agent contract almost completely dominates the benefit-sharing contract.

A multi-objective decision-making model for supplier selection considering transport discounts and supplier capacity constraints
Alireza Eydi and Rozhin Saedi
2021, 17(6): 3581-3602 doi: 10.3934/jimo.2020134 +[Abstract](1020) +[HTML](515) +[PDF](531.01KB)
Abstract:

The present study considers the transport discounts and capacity constraints for the suppliers and manufacturers simultaneously to provide a multi-objective decision-making model for supplier selection on a three-level supply chain. For this purpose, it begins with presenting a nonlinear mixed-integer model of the problem, where the objectives include the minimization of the logistics costs and lead time. Subsequently, the NSGA-Ⅱ algorithm is developed to solve the large-scale model of the problem and simultaneously optimize the two objectives to achieve Pareto-optimal solutions. To test the efficiency of the proposed algorithm, several synthetic examples of various sizes are then generated and solved. Finally, the paper compares the performance of the proposed metaheuristic algorithm with the augmented epsilon-constraint method. In summary, the findings of this study provided researchers and industries to easily access to a cohesive model of supplier selection considering transportation that are essential to the solution of many real-world challenging logistics issues.

Analysis of $ D $-$ BMAP/G/1 $ queueing system under $ N $-policy and its cost optimization
Rakesh Nandi, Sujit Kumar Samanta and Chesoong Kim
2021, 17(6): 3603-3631 doi: 10.3934/jimo.2020135 +[Abstract](965) +[HTML](508) +[PDF](679.47KB)
Abstract:

This article studies an infinite buffer single server queueing system under \begin{document}$ N $\end{document}-policy in which customers arrive according to a discrete-time batch Markovian arrival process. The service times of customers are independent and obey a common general discrete distribution. The idle server begins to serve the customers as soon as the queue size becomes at least \begin{document}$ N $\end{document} and serves the customers until the system becomes empty. We determine the queue length distribution at post-departure epoch with the help of roots of the associated characteristic equation of the vector probability generating function. Using the supplementary variable technique, we develop the system of vector difference equations to derive the queue length distribution at random epoch. An analytically simple and computationally efficient approach is also presented to compute the waiting time distribution in the queue of a randomly selected customer of an arrival batch. We also construct an expected linear cost function to determine the optimal value of \begin{document}$ N $\end{document} at minimum cost. Some numerical results are demonstrated for different service time distributions through the optimal control parameter to show the key performance measures.

A reformulation-linearization based algorithm for the smallest enclosing circle problem
Yi Jiang and Yuan Cai
2021, 17(6): 3633-3644 doi: 10.3934/jimo.2020136 +[Abstract](912) +[HTML](450) +[PDF](366.08KB)
Abstract:

In this paper, an effective algorithm based on the reformulation-linearization technique (RLT) is developed to solve the smallest enclosing circle problem. Extensive computational experiments demonstrate that the algorithm based on the RLT outperforms the existing algorithms in terms of the solution time and quality in average.

Maxillofacial surgical simulation system with haptic feedback
Jing Zhang, Jiahui Qian, Han Zhang, Ling He, Bin Li, Jing Qin, Hongning Dai, Wei Tang and Weidong Tian
2021, 17(6): 3645-3657 doi: 10.3934/jimo.2020137 +[Abstract](976) +[HTML](526) +[PDF](1186.36KB)
Abstract:

Due to the complexity of the maxillofacial surgery, the novice should be sufficiently trained before one is qualified to carry on the surgery. To reduce the training costs and improve the training efficiency, a virtual mandible surgical system with haptic feedback is proposed. This surgical simulation system offers users the haptic feedback while simulating maxillofacial surgery. An integrated model is introduced to optimize the system simulation process, which includes force output to a six-degree-of-freedom haptic device. Based on the anatomy structure of the bone tissue, a two-layer mechanism model is designed to balance the requirement of real-time response and the force feedback accuracy. Collision detection, force rendering, and grinding function are studied to simulate some essential operations: open reduction, osteotomy, and palate fixation. The proposed simulation platform can assist in the training and planning of these oral and maxillofacial surgeries. The fast response feature enables surgeons to design a patient-specific guide plate in real-time. Ten stomatology surgeons evaluated this surgical simulation system from the following four indexes: the level of immersion, user-friendliness, stability, and the effect of surgical training. The evaluation score is eight out of ten.

Two-echelon trade credit with default risk in an EOQ model for deteriorating items under dynamic demand
Puspita Mahata and Gour Chandra Mahata
2021, 17(6): 3659-3684 doi: 10.3934/jimo.2020138 +[Abstract](1144) +[HTML](409) +[PDF](659.96KB)
Abstract:

In today's competitive markets, offering delay payments has become a commonly adopted method. In this paper, we examine an optimal dynamic decision-making problem for a retailer selling a single deteriorating product, the demand rate of which varies simultaneously with on-hand inventory level and the length of credit period that is offered to the customers. In addition, the risk of default increases with the credit period length. In this study, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to his customer in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. A generalized model is presented to determine the optimal trade credit and replenishment strategies that maximize the retailer's total profit after the default risk occurs over a planning period. For the objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. Some properties of the optimal solutions are shown to find the optimal ordering policies of the considered problem. At the end of this paper, some numerical examples and the results of a sensitivity and elasticity analysis are used to illustrate the features of the proposed model; we then offer our concluding remarks.

New M-eigenvalue intervals and application to the strong ellipticity of fourth-order partially symmetric tensors
Haitao Che, Haibin Chen and Guanglu Zhou
2021, 17(6): 3685-3694 doi: 10.3934/jimo.2020139 +[Abstract](944) +[HTML](427) +[PDF](331.14KB)
Abstract:

M-eigenvalues of fourth-order partially symmetric tensors play an important role in nonlinear elasticity and materials. In this paper, we present some M-eigenvalue intervals to locate all M-eigenvalues of fourth-order partially symmetric tensors. It is proved that the new interval is tighter than the one proposed by He, Li and Wei [16]. Furthermore, we obtain some new checkable sufficient conditions for the strong ellipticity of fourth-order partially symmetric tensors. Three numerical examples arising from anisotropic materials are presented to verify the efficiency of the proposed results.

2020 Impact Factor: 1.801
5 Year Impact Factor: 1.688
2020 CiteScore: 1.8

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