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Journal of Industrial and Management Optimization

May 2022 , Volume 18 , Issue 3

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Semidefinite relaxation method for polynomial optimization with second-order cone complementarity constraints
Lin Zhu and Xinzhen Zhang
2022, 18(3): 1505-1517 doi: 10.3934/jimo.2021030 +[Abstract](1372) +[HTML](555) +[PDF](393.72KB)
Abstract:

Polynomial optimization problem with second-order cone complementarity constraints (SOCPOPCC) is a special case of mathematical program with second-order cone complementarity constraints (SOCMPCC). In this paper, we consider how to apply Lasserre's type of semidefinite relaxation method to solve SOCPOPCC. To this end, we first reformulate SOCPOPCC equivalently as a polynomial optimization and then solve the reformulated polynomial optimization with semidefinite relaxation method. For a special case of SOCPOPCC, we present another reformulation of polynomial optimization, which is of lower degree. SDP relaxation method is applied to solve the new polynomial optimization. Numerical examples are reported to show the efficiency of our proposed method.

Optimal health insurance with constraints under utility of health, wealth and income
Yan Zhang, Yonghong Wu and Haixiang Yao
2022, 18(3): 1519-1540 doi: 10.3934/jimo.2021031 +[Abstract](1296) +[HTML](564) +[PDF](621.24KB)
Abstract:

We consider an optimal health insurance design problem with constraints under utility of health, wealth and income. The preference framework we establish herein describes the trade-off among health, wealth and income explicitly, which is beneficial to distinguish health insurance design from other nonlife insurance designs. Moreover, the work takes into account the case that if the insured is severely or critically ill, the insured may not fully recover even after necessary medical treatment. By taking these special features into account, the health insurance design problem is formulated as a constrained optimization problem, and the optimal solutions are derived by using the Lagrange multiplier method and optimal control technique. Finally, two numerical examples are given to illustrate our results. Our research work gives new insights into health insurance design.

The finite-time ruin probability of a risk model with a general counting process and stochastic return
Baoyin Xun, Kam C. Yuen and Kaiyong Wang
2022, 18(3): 1541-1556 doi: 10.3934/jimo.2021032 +[Abstract](1084) +[HTML](502) +[PDF](403.09KB)
Abstract:

This paper considers a general risk model with stochastic return and a Brownian perturbation, where the claim arrival process is a general counting process and the price process of the investment portfolio is expressed as a geometric Lévy process. When the claim sizes are pairwise strong quasi-asymptotically independent random variables with heavy-tailed distributions, the asymptotics of the finite-time ruin probability of this risk model have been obtained.

Pricing and energy efficiency decisions by manufacturer under channel coordination
Shuhua Chang, Yameng Wang, Xinyu Wang and Kok Lay Teo
2022, 18(3): 1557-1582 doi: 10.3934/jimo.2021033 +[Abstract](1203) +[HTML](637) +[PDF](810.8KB)
Abstract:

The profit level of the green supply chain under two decision modes is explored in cooperative and non-cooperative games, where the variable decision timing in direct channel and retail channel within the manufacturer management is studied based on the theory of observable delay game. This paper discusses how the total profit of the green supply chain can realize the profit of the inferior copy of the superior under the two decision-making modes. In the existing literature, it is usually assumed that the pricing decisions of the manufacturers and retailers are made simultaneously. In this study, our model takes into account not only the decision on the pricing, but also on the product innovation. Decision makers can choose the levels of the decision variables as well as the decision times. The observable delay game theory is applied to the study of the decision-making of price levels and energy efficiency levels in multi-channel supply chains. Early pricing decisions can be extended to the study of the product development process. This is more in line with the development of the market in reality. The results of our model show that: (a) an increase of the product efficiency innovation by the manufacturers will lead to an increase in the demand at the retail channel; (b) the enhancement of consumers’ awareness of the environmental protection and the improvement of the price sensitivity of the double-channel crossing have positive effect on the profit level of the general channel; (c) the manufacturers are motivated to adopt a marketing strategy that masks disadvantages with advantages. After the manufacturer determines the energy efficiency level of the product, it is found that the direct channel to increase the pricing decision time and the creation of input from a high cost are more conducive to achieving higher revenue; (d) after comparing the total profits of the two decision models, the manufacturer can obtain all the surplus profit of the retailer by coordinating the fixed fee of the two-part tariff contract. At the same time, the perfect replication of decentralized decision-making and the total profit level of centralized decisionmaking are realized. Through the coordination of the choice of variable pricing time and tariff contract, not only the perfect Nash equilibrium of non cooperative game is formed, but also the optimal variable decision-making scheme of multi-channel green supply chain is provided for manufacturers to maximize their profits.

 

Addendum: “The National Natural Science Foundation of China (12101447)” is added so it reads “The first author is supported by the National Basic Research Program (2012CB955804), the Major Research Plan of the National Natural Science Foundation of China (91430108), the National Natural Science Foundation of China (11771322), and the Major Program of Tianjin University of Finance and Economics (ZD1302). The third author is supported by the National Natural Science Foundation of China (12101447), and the Humanities and Social Science Research Program of the Ministry of Education of China (19YJCZH174).”

Linear-quadratic optimal control for discrete-time stochastic descriptor systems
Yadong Shu and Bo Li
2022, 18(3): 1583-1602 doi: 10.3934/jimo.2021034 +[Abstract](1247) +[HTML](539) +[PDF](500.74KB)
Abstract:

In this paper, an optimal control model ruled by a class of linear discrete-time stochastic descriptor systems is considered under quadratic index performance. Employing dynamic programming method, a recurrence equation to simplify the optimal control problem is presented provided that the descriptor systems are both regular and impulse-free. When the objective function is quadratic, according to the recurrence equation, a discrete-time linear-quadratic optimal control problem is completely settled, that is, optimal controls and optimal values of the problem are both obtained through analytical expressions. At last, a numerical example about linear-quadratic optimal control for a discrete-time stochastic descriptor system is provided to illustrate the validness of the results derived.

Effects of take-back legislation on pricing and coordination in a closed-loop supply chain
Benrong Zheng and Xianpei Hong
2022, 18(3): 1603-1627 doi: 10.3934/jimo.2021035 +[Abstract](1243) +[HTML](690) +[PDF](586.03KB)
Abstract:

This study investigates the effects of take-back legislation and channel structures on pricing, collection, and coordination in a closed-loop supply chain (CLSC). By establishing the centralized, manufacturer-led, and retailer-led CLSC models, we analyze the equilibrium solutions of channel players and the government. We obtain the following results. (1) The manufacturer can accept a higher collection target and exit the market later in the centralized model than in decentralized decision-making models. Moreover, the manufacturer exists the market earlier in the retailer-led model with regulation compared with the manufacturer-led model. (2) The government's optimal collection target is the same under manufacturer-led and retailer-led models when the regulation comes into force. (3) Revenue-sharing and two-part tariff contracts can effectively coordinate manufacturer-led and retailer-led CLSCs under take-back legislation. Finally, we conduct several numerical examples and obtain relevant managerial insights. Our results indicate that the correlation between take-back legislation and channel structure has a significant impact on the pricing and coordination decisions of the CLSC; furthermore, the government should flexibly set the collection target when facing different supply chain and channel power structures in a CLSC.

Inventory replenishment policies for two successive generations price-sensitive technology products
Gaurav Nagpal, Udayan Chanda and Nitant Upasani
2022, 18(3): 1629-1650 doi: 10.3934/jimo.2021036 +[Abstract](1340) +[HTML](602) +[PDF](1813.09KB)
Abstract:

The high technology products come in generations, where the demand for newer technology generations is strongly influenced by the installed base of earlier generations (such as computers, cameras, notebooks, etc). However, the effect of technology substitution on inventory replenishment policies has received little attention in the supply chain literature. In the hi-technology market, consumers' purchasing capability, the utility of a product along with the entry of the advanced generation product influence the market expansion/contraction of the products. In this study, the impact of parallel diffusion of two successive generations' products on inventory policies of the monopolist has been analysed. The demand models have been characterised by considering the life-cycle dynamics for a P-type inventory system. The purpose of this paper is to develop a model for joint pricing and replenishment of technology generation products. The model has been solved by using a genetic algorithm technique. The impact of yearly price drop and the price sensitivity of demand on the profit margins vis-à-vis on replenishment policies has also been studied. The paper also brings forward the dynamics of the launch of newer generations and the pricing strategies on optimal inventory replenishment policies. Numerical illustrations have also been covered in the paper.

Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations
Namsu Ahn and Soochan Kim
2022, 18(3): 1651-1663 doi: 10.3934/jimo.2021037 +[Abstract](1388) +[HTML](903) +[PDF](596.97KB)
Abstract:

During military operations, obtaining information on remote battlefields is essential and recent advances in unmanned aerial vehicle technology have led to the use of drones to view battlefields. However, the use of drones in military operations introduces the new problem of determining travel routes for the drones. This type of problem is similar to the well-known classical vehicle routing problem, but the main difference is its objective function. For maintenance purposes, a minimized difference in travel distances is preferred. In addition, obtaining a shorter route in terms of travel distance is important. In this research, we propose a mathematical formulation and an optimal algorithm for the problem and suggest a simple heuristic to handle the large size instance of the problem. The computational results indicate that this algorithm can solve the real-scale instances of the problem, and the heuristic exhibits good performance even when the instance size of the problem is large.

Designing and analysis of a Wi-Fi data offloading strategy catering for the preference of mobile users
Xiaoyi Zhou, Tong Ye and Tony T. Lee
2022, 18(3): 1665-1688 doi: 10.3934/jimo.2021038 +[Abstract](967) +[HTML](468) +[PDF](1503.56KB)
Abstract:

In recent years, offloading mobile traffic through Wi-Fi has emerged as a potential solution to lower down the communication cost for mobile users. Users hope to reduce the cost while keeping the delay in an acceptable range through Wi-Fi offloading. Also, different users have different sensitivities to the cost and the delay performance. How to make a proper cost-delay tradeoff according to the user's preference is the key issue in the design of the offloading strategy. To address this issue, we propose a preference-oriented offloading strategy for current commercial terminals, which transmit traffic only via one channel simultaneously. We model the strategy as a three-state M/MMSP/1 queueing system, of which the service process is a Markov modulated service process (MMSP), and obtain the structured solutions by establishing a hybrid embedded Markov chain. Our analysis shows that, given the user's preference, there exists an optimal deadline to maximize the utility, which is defined as the linear combination of the cost and the delay. We also provide a method to select the optimal deadline. Our simulation demonstrates that this strategy with the optimal deadline can achieve a good performance.

First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits
Meiqiao Ai, Zhimin Zhang and Wenguang Yu
2022, 18(3): 1689-1707 doi: 10.3934/jimo.2021039 +[Abstract](1198) +[HTML](482) +[PDF](543.48KB)
Abstract:

This paper studies some first passage time problems in a refracted jump diffusion process with hyper-exponential jumps. Closed-form expressions for four functions associated with the first passage time are obtained by solving some ordinary integro-differential equations. In addition, the obtained results are used to value equity-linked death benefit products with state-dependent fees. Specifically, we obtain the closed-form Laplace transform of the fair value of barrier option, which is further recovered by the bilateral Abate-Whitt algorithm. Numerical results confirm that the proposed approach is efficient.

Multistage optimal control for microbial fed-batch fermentation process
Xiaohong Li, Mingxin Sun, Zhaohua Gong and Enmin Feng
2022, 18(3): 1709-1721 doi: 10.3934/jimo.2021040 +[Abstract](1289) +[HTML](551) +[PDF](361.16KB)
Abstract:

In this paper, we consider multistage optimal control of bioconversion glycerol to 1, 3-propanediol(1, 3-PD) in fed-batch fermentation process. To maximize the productivity of 1, 3-PD, the whole fermentation process is divided into three stages according to the characteristics of microbial growth. Stages 2 and 3 are discussed mainly. The main aim of stage 2 is to restrict accumulation of 3-hydroxypropionaldehyde and maximize the biomass in the shortest time, and the purpose of stage 3 is to get high productivity of 1, 3-PD. With these different objectives, multi-objective optimal control problems are proposed in stages 2 and 3. In order to solve the above optimal control problems, the multi-objective problems are transformed to the corresponding single-objective problems using the mass balance equation of biomass and normalization of the objective. Furthermore, the single-objective optimal control problems are transformed to two-level optimization problems by the control parametrization technique. Finally, numerical solution methods combined an improved Particle Swarm Optimization with penalty function method are developed to solve the resulting optimization problems. Numerical results show that the productivity of 1, 3-PD is higher than the reported results.

Solutions and characterizations under multicriteria management systems
Yu-Hsien Liao
2022, 18(3): 1723-1735 doi: 10.3934/jimo.2021041 +[Abstract](945) +[HTML](445) +[PDF](344.04KB)
Abstract:

In real situations, agents might take different activity levels to participate; agents might represent administrative areas of different scales. On the other hand, agents always face an increasing need to focus on multiple aims efficiently in their operational processes. Thus, we introduce two solutions to investigate distribution mechanism by applying the maximal level-marginal contributions among activity level (decision) vectors under multicriteria management systems. Based on a specific reduced game and some reasonable properties, we offer some characterizations to analyze the rationality for these two solutions. In order to desire that any utility could be distributed among the players and their activity levels in proportion to related differences, two weighted extensions are also proposed by means of different weight functions.

Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain
Kai Kang, Taotao Lu and Jing Zhang
2022, 18(3): 1737-1768 doi: 10.3934/jimo.2021042 +[Abstract](1225) +[HTML](479) +[PDF](583.63KB)
Abstract:

By applying Stackelberg game theory, this paper investigates the supply chain with a risk-neutral retailer and a risk-averse supplier, measuring risk-averse behavior by using conditional value-at-risk (CVaR). The equilibrium solutions of the supplier's wholesale price and the retailer's order quantity are obtained under two financing strategies: supplier financing (SF) and supplier investment (SI). It is found that the supplier's risk aversion is a crucial factor affecting both parties' financing decisions, and the supplier should offer different financing strategies to the retailer based on his risk attitude and the profit-sharing coefficient. However, the retailer prefers SF regardless of the supplier's risk aversion. Taking bank credit financing as a basic model, the advantages of SF and SI have been investigated. A Pareto improvement region for the two finance strategies has been identified and some suggestions are provided for the supplier's optimal utility. Then we extend to the situation that both parties are risk-averse and use the financing cost-sharing mechanism to achieve centralized decision-making.

Pricing new and remanufactured products based on customer purchasing behavior
Kai Li, Tao Zhou and Bohai Liu
2022, 18(3): 1769-1794 doi: 10.3934/jimo.2021043 +[Abstract](1320) +[HTML](550) +[PDF](570.59KB)
Abstract:

Firms' pricing strategies are largely influenced by customer purchasing behavior. By considering whether to invest in customer purchasing behavior analysis, firms can choose a discriminatory or a non-discriminatory pricing model. This paper presents a two-period duopoly that the original material supplier (OS) supplying new products faces a competition of an independent material supplier (IS) providing remanufactured products to analyze each party's competitive strategy under each pricing model. We also identify situations under which the firms would obtain more profits and cause less environmental impact under the model with price discrimination compared with the model without price discrimination. A numerical study is provided to illustrate the performance of the model. A sensitivity analysis with respect to primary parameters is used to assess the stability of the model. The proposed model could be applied in many industrial fields where the managers have the full awareness of extended producer responsibility, and they are willing to engage in the project related to remanufacturing.

Some scheduling problems with sum of logarithm processing times based learning effect and exponential past sequence dependent delivery times
Mehmet Duran Toksari, Emel Kizilkaya Aydogan, Berrin Atalay and Saziye Sari
2022, 18(3): 1795-1807 doi: 10.3934/jimo.2021044 +[Abstract](1082) +[HTML](473) +[PDF](416.13KB)
Abstract:

In recent years, significant on the past sequence dependent delivery times have been increasing for scheduling problems. An electronic component when waiting to process may be exposed to certain an electromagnetic field and is required to neutralize the effect of electromagnetism. In this case, it needs an extra time to eliminate adverse effect. In the scheduling literature, this extra time is called as past-sequence-dependent delivery times. In this paper we introduce single-machine scheduling problems with an exponential sum-of-actual-processing-time-based delivery times. By the exponential sum-of-actual-processing-time-based delivery times, we mean that the delivery times are defined by an exponential function of the sum of the actual processing times of the already processed jobs. On the other hand, the learning effect is reflected in decreasing processing times based on the job's position in schedule. In this paper, we also introduce both exponential past sequence dependent delivery times and learning effect where the job processing time is a function based on the sum of the logarithm of processing times of jobs already processed. We show that the single-machine scheduling problems to minimize makespan, total completion time, weighted total completion time and maximum tardiness with sum of logarithm processing times based learning effect and exponential past sequence dependent delivery times have polynomial time solutions.

Identifying and determining crowdsourcing service strategies: An empirical study on a crowdsourcing platform in China
Xu Zhang, Zhanglin Peng, Qiang Zhang, Xiaoan Tang and Panos M. Pardalos
2022, 18(3): 1809-1833 doi: 10.3934/jimo.2021045 +[Abstract](1332) +[HTML](526) +[PDF](560.47KB)
Abstract:

The crowdsourcing platforms, as mediators and service providers, play a critical role in crowdsourcing initiatives. The service quality of a platform has a direct impact on solver satisfaction, and ultimately affects the platform's continuous operation. Service quality can be measured by service quality attributes (SQAs). Thus, identifying and quantifying SQAs are crucial to enhance solver satisfaction. Besides, choosing pertinent strategies and determining priorities for the SQAs are another core issue. To address these issues, this study proposes a novel decision framework that combines the Fuzzy Analytical Kano (FAK) and the Importance-performance analysis (IPA) models. Firstly, 24 related SQAs are identified from five dimensions of service quality. Secondly, we quantify these SQAs into a polar form representation scheme in accordance with the FAK model. In addition, the pertinent service strategies and priorities of the SQAs are confirmed by using the IPA model and Kano categories. Finally, decision priority rules for corresponding strategies and priorities of SQAs are constructed. An empirical study is presented to demonstrate our proposed decision framework on ZBJ platform, which is one of the most widely used online crowdsourcing platform in China.

Quadratic surface support vector machine with L1 norm regularization
Ahmad Mousavi, Zheming Gao, Lanshan Han and Alvin Lim
2022, 18(3): 1835-1861 doi: 10.3934/jimo.2021046 +[Abstract](1408) +[HTML](476) +[PDF](902.12KB)
Abstract:

We propose \begin{document}$ \ell_1 $\end{document} norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish some desired theoretical properties, including the existence and uniqueness of the optimal solution, reduction to the standard SVMs over (almost) linearly separable data sets, and detection of true sparsity pattern over (almost) quadratically separable data sets if the penalty parameter on the \begin{document}$ \ell_1 $\end{document} norm is large enough. We also demonstrate their promising practical efficiency by conducting various numerical experiments on both synthetic and publicly available benchmark data sets.

Assembly system with omnichannel coordination
Zhisong Chen and Shong-Iee Ivan Su
2022, 18(3): 1863-1889 doi: 10.3934/jimo.2021047 +[Abstract](1449) +[HTML](561) +[PDF](668.92KB)
Abstract:

Assembly system with omnichannel is rarely studied in literature. This paper explores the equilibrium and coordination issues for an omnichannel assembly system. Four different game-theoretical model types applying four operational strategies - a total of sixteen analytical models - are developed and analyzed for both omnichannel and pure channel modes. The numerical analysis of an electronic product assembly system provides a clearer understanding of the solutions and their effects on the profits in the assembly system for different model types and operational strategies. A further sensitivity analysis with focus on an omnichannel with offline channel subsidy (OMS) creates better insights regarding how changes of key parameters affect the assembly system profits. It is found that the omnichannel mode with or without offline channel subsidy can deliver much better operational performance to the assembly system via mutual fusion effect than that of a pure online- or offline-channel mode. Furthermore, the offline channel subsidy can amplify to a very large extent the mutual fusion effect to increase the product demand dramatically and thus improving the operational performance of the assembly system in the omnichannel business scenario. The best operational strategy for the assembly system in the omnichannel business scenario is the coordination strategy with offline channel subsidy.

Optimal lot-sizing policy for a failure prone production system with investment in process quality improvement and lead time variance reduction
Sumon Sarkar and Bibhas C. Giri
2022, 18(3): 1891-1913 doi: 10.3934/jimo.2021048 +[Abstract](1086) +[HTML](431) +[PDF](465.67KB)
Abstract:

To survive in today's competitive market, it is not enough to produce low-cost products but also quality-related issues and lead time needs to be considered in the decision-making process. This paper extends the previous research by developing a stochastic economic manufacturing quantity (EMQ) model for a production system which is subject to process shifts from an in-control state to an out-of-control state at any random time. Moreover, we consider the option of investment to increase the process quality and decrease the lead-time variability. Closed-form solutions of the proposed models are obtained by applying the classical optimization technique. Some lemmas and theorems are developed to determine the optimal solution of the decision variables. Numerical results are obtained for each of these models and compared with those of the basic EMQ model without any investment. From the numerical analysis, it has been observed that our proposed model can significantly reduce the cost of the system compared to the basic model.

Free boundary problem for an optimal investment problem with a borrowing constraint
Chonghu Guan, Xun Li, Rui Zhou and Wenxin Zhou
2022, 18(3): 1915-1934 doi: 10.3934/jimo.2021049 +[Abstract](1236) +[HTML](425) +[PDF](442.24KB)
Abstract:

This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small.

Multi-aircraft cooperative path planning for maneuvering target detection
Yongkun Wang, Fengshou He and Xiaobo Deng
2022, 18(3): 1935-1948 doi: 10.3934/jimo.2021050 +[Abstract](959) +[HTML](467) +[PDF](1327.6KB)
Abstract:

Multi-aircraft cooperative path planning is a key problem in modern and future air combat scenario. In this paper, this problem is studied in aspect of airborne radar detection to maintain a continuous tracking of a manoeuvring air target. Firstly, the objective function is established in combination with multiple constraints considered, including Doppler blind zone constraint, radar viewing aspect constraint, baseline constraint, and so on. Then, the above optimal control problem is transformed into a nonlinear programming problem with a series of algebraic constraints by hp-adaptive Gauss pseudospectral method (HPAGPM). And it is solved by GPOPS software package based on MATLAB. Simulation results show that the optimized cooperative paths can be got to achieve continuous tracking of maneuvering air target by HPAGPM.

Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences
Shoufeng Ji, Jinhuan Tang, Minghe Sun and Rongjuan Luo
2022, 18(3): 1949-1977 doi: 10.3934/jimo.2021051 +[Abstract](1436) +[HTML](480) +[PDF](1053.45KB)
Abstract:

A combined location-routing-inventory system (CLRIS) in a three-echelon supply chain network is studied with environmental considerations. Specifically, a bi-objective mixed integer programming model is formulated for the CLRIS to deal with the trade-offs between the total cost and the carbon-capped difference (CCD). A multi-objective particle swarm optimization (MOPSO) heuristic solution procedure is developed and implemented to solve the bi-objective mixed integer programming problem. The bi-objective mixed integer programming model and the MOPSO heuristic procedure are applied to a real-life problem as an illustrative example. The approximate nondominated frontier formed by solutions not dominated by others can be used for the decision makers to make trade-offs between the total cost and the CCD. Sensitivity analyses are conducted, and the relationship among the carbon cap, CCD, the total cost and the carbon prices are examined, and relevant managerial insights are provided. Comparisons with other existing algorithms show that the MSPSO heuristic procedure has very good performance.

Fresh produce price-setting newsvendor with bidirectional option contracts
Chong Wang and Xu Chen
2022, 18(3): 1979-2000 doi: 10.3934/jimo.2021052 +[Abstract](943) +[HTML](544) +[PDF](800.71KB)
Abstract:

This paper examines a newsvendor problem for fresh produce with bidirectional option contracts, in which the stochastic demand is price-dependent. The bidirectional option, which may be exercised as either a call or put option, provides the newsvendor the flexibility to increase or decrease the initial order after real demand is realized, respectively. The condition of the fresh produce may deteriorate during circulation. The optimal order and pricing decisions for the newsvendor are analytically derived with the bidirectional option and circulation loss. Comparative statics analysis show that the optimal total order quantity and optimal retail price of the newsvendor decrease with the option price but increase with the exercise price. In addition, numerical examples show that the optimal total order quantity and optimal retail price of the newsvendor increase with the circulation loss. The optimal option order quantity first decreases then increases with the exercise price. The optimal firm order quantity first increases then decreases with the circulation loss. The maximum profit of the newsvendor decreases with the option price and circulation loss but increases with the exercise price. Furthermore, the values of bidirectional option contracts are more significant when the demand uncertainty and the circulation loss become more volatile.

Efficiency, RTS, and marginal returns from salary on the performance of the NBA players: A parallel DEA network with shared inputs
Saeed Assani, Muhammad Salman Mansoor, Faisal Asghar, Yongjun Li and Feng Yang
2022, 18(3): 2001-2016 doi: 10.3934/jimo.2021053 +[Abstract](1810) +[HTML](491) +[PDF](585.04KB)
Abstract:

National Basketball Association (NBA) is one of the popular sports leagues worldwide and is also a business source that generates enormous financial resources. Generally, the salary of sports players is associated with their performance in the field. However, the NBA players' performance in the game is related to specific technical features in the offensive and defensive activities. This paper aims to measure the impact of NBA players' salary on their efficiency levels using a big data set of eleven seasons (2604 players from 2005 to 2016) by considering the players' performance in offensive and defensive activities. First, we propose models to measure players' overall, offensive, and defensive efficiencies based on a non-homogeneous parallel data envelopment analysis (DEA) network. Then, we introduce input-output oriented network models to estimate the marginal returns from salary on the outcomes of both offensive and defensive activities. Results indicated that all players' average overall efficiency is low (63.5%), with 17 efficient players. The offensive efficiency is 12.8% higher than the defensive efficiency. When the impact of salary on offensive (defensive) activity is considered, about 73% (47%) of the players' observations indicate increasing marginal returns, respectively.

Nonlinear Grey Bernoulli model NGBM (1, 1)'s parameter optimisation method and model application
Maolin Cheng, Yun Liu, Jianuo Li and Bin Liu
2022, 18(3): 2017-2032 doi: 10.3934/jimo.2021054 +[Abstract](1184) +[HTML](450) +[PDF](418.45KB)
Abstract:

In the grey prediction, the nonlinear Grey Bernoulli model NGBM (1, 1) is an important type. The NGBM (1, 1) has good adaptability to data fitting and then small prediction errors, and thus has been applied widely. However, if we improve the modelling method, the prediction precision shall be improved to some extent. The important factors of prediction error are the approximation of background value and the approximation of power exponent. Therefore, the paper tries to combine the optimisation of background value with the optimisation of the power exponent of NGBM (1, 1) model and then improves the model from parameter estimation. The paper gives three methods for the following three cases respectively: the background value in the form of exponential curve, the background value in the form of the polynomial curve and the background value in the form of interpolation function, to combine background value optimisation with power exponent optimisation for parameter optimisation. The final section of the paper builds the NGBM (1, 1) models of China's GDP and energy consumption with three improvement methods. The simulation and prediction results show the three improvement methods all have high precision. The methods given offer good approaches for the in-depth study on nonlinear grey Bernoulli model, enrich the method system of grey modelling and can be applied to the studies on other grey models to promote the study and wide application of the grey model.

A partitioning column approach for solving LED sorter manipulator path planning problems
Sheng-I Chen and Yen-Che Tseng
2022, 18(3): 2033-2047 doi: 10.3934/jimo.2021055 +[Abstract](1090) +[HTML](536) +[PDF](439.48KB)
Abstract:

This study considers the path planning problem of picking light-emitting diodes on a silicon wafer. The objective is to find the shortest walk for the sorter manipulator covering all nodes in a fully connected graph. We propose a partitioning column approach to reduce the original graph's size, where adjacent nodes at the same column are seen as a required edge, and the connection of vertices at different required edges is viewed as a non-required edge. The path planning problem turns to find the shortest closed walk to traverse required edges and is modeled as a rural postman problem with a solvable problem size. We formulate a mixed-integer program to obtain the exact solution for the transformed graph. We compare the proposed method with a TSP solver, Concorde. The result shows that our approach significantly reduces the problem size and obtains a near-optimal solution. For large problem instances, the proposed method can obtain a feasible solution in time, but not for the benchmarking solver.

The optimal pricing and service strategies of a dual-channel retailer under free riding
Jinsen Guo, Yongwu Zhou and Baixun Li
2022, 18(3): 2049-2076 doi: 10.3934/jimo.2021056 +[Abstract](1322) +[HTML](480) +[PDF](575.35KB)
Abstract:

Free riding refers to that in a multi-channel market, consumers enjoy the presale service of a product at one channel but purchase the product at another channel. In this paper, we study the optimal pricing and service strategies for a dual-channel retailer, who sells a product through both a traditional retail channel and an online channel. We assume that the offline channel provides the presale service but the online channel does not. We investigate how the changes of the degree of free riding affect the pricing/service strategies and profits of the two channels under three different scenarios: Stackelberg competition, Bertrand competition and channel integration. Our analysis shows that when the dual-channel retailer operates the two channels separately, no matter under which competitive scenario, free riding has a negative effect on both channels. And it is much more beneficial for the dual-channel retailer to let one channel work as a leader and another channel as a follower than to let the two channels make their decision simultaneous. In contrast, when the dual-channel retailer runs the two channels jointly, i.e., employs the channel-integration scenario, free riding may be beneficial to the retailer. Finally, this paper proposes and analyzes a revenue-sharing contract to coordinate a decentralized dual-channel retailer to achieve beneficial outcomes for both channels.

Pricing vulnerable options under a jump-diffusion model with fast mean-reverting stochastic volatility
Wan-Hua He, Chufang Wu, Jia-Wen Gu, Wai-Ki Ching and Chi-Wing Wong
2022, 18(3): 2077-2094 doi: 10.3934/jimo.2021057 +[Abstract](1253) +[HTML](450) +[PDF](527.59KB)
Abstract:

In this paper, we propose a model to price vulnerable European options where the dynamics of the underlying asset value and the counter-party's asset value follow two jump-diffusion processes with fast mean-reverting stochastic volatility. First, we derive an equivalent risk-neutral measure and transfer the pricing problem into solving a partial differential equation (PDE) by the Feynman-Kac formula. We then approximate the solution of the PDE by pricing formulas with constant volatility via multi-scale asymptotic method. The pricing formula for vulnerable European options is obtained by applying a two-dimensional Laplace transform when the dynamics of the underlying asset value and the counter-party's asset value follow two correlated jump-diffusion processes with constant volatilities. Thus, an analytic approximation formula for the vulnerable European options is derived in our setting. Numerical experiments are given to demonstrate our method by using Laplace inversion.

New Z-eigenvalue localization sets for tensors with applications
Jun He, Guangjun Xu and Yanmin Liu
2022, 18(3): 2095-2108 doi: 10.3934/jimo.2021058 +[Abstract](939) +[HTML](437) +[PDF](431.82KB)
Abstract:

In this paper, let \begin{document}$ \mathcal{A} = (a_{i_1 i_2 \cdots i_m } )\in{\mathbb{R}}^{[m, n]} $\end{document}, when \begin{document}$ m\geq 4 $\end{document}, based on the condition \begin{document}$ ||x||_2 = 1 $\end{document}, a new \begin{document}$ Z $\end{document}-eigenvalue localization set for tensors is given. And we extend the Geršhgorin-type localization set for Z-eigenvalues of fourth order tensors to higher order tensors. As an application, a sharper upper bound for the Z-spectral radius of nonnegative tensors is obtained. Let \begin{document}$ \mathcal{H} $\end{document} be a \begin{document}$ k $\end{document}-uniform hypergraph with \begin{document}$ k\geq 4 $\end{document} and \begin{document}$ \mathcal{A}(\mathcal{H}) $\end{document} be the adjacency tensor of \begin{document}$ \mathcal{H} $\end{document}, a new upper bound for the Z-spectral radius \begin{document}$ \rho (\mathcal{H}) $\end{document} is also presented. Finally, a checkable sufficient condition for the positive definiteness of even-order tensors and asymptotically stability of time-invariant polynomial systems is also given.

Stereo visual odometry based on dynamic and static features division
Hui Xu, Guangbin Cai, Xiaogang Yang, Erliang Yao and Xiaofeng Li
2022, 18(3): 2109-2128 doi: 10.3934/jimo.2021059 +[Abstract](1206) +[HTML](533) +[PDF](7240.84KB)
Abstract:

Accurate camera pose estimation in dynamic scenes is an important challenge for visual simultaneous localization and mapping, and it is critical to reduce the effects of moving objects on pose estimation. To tackle this problem, a robust visual odometry approach in dynamic scenes is proposed, which can precisely distinguish between dynamic and static features. The key to the proposed method is combining the scene flow and the static features relative spatial distance invariance principle. Moreover, a new threshold is proposed to distinguish dynamic features.Then the dynamic features are eliminated after matching with the virtual map points. In addition, a new similarity calculation function is proposed to improve the performance of loop-closure detection. Finally, the camera pose is optimized after obtaining a closed loop. Experiments have been conducted on TUM datasets and actual scenes, which shows that the proposed method reduces tracking errors significantly and estimates the camera pose precisely in dynamic scenes.

Optimal pricing and ordering policy for defective items under temporary price reduction with inspection errors and price sensitive demand
Guiyang Zhu
2022, 18(3): 2129-2161 doi: 10.3934/jimo.2021060 +[Abstract](1115) +[HTML](619) +[PDF](1029.99KB)
Abstract:

This paper studies the retailer's optimal promotional pricing, special order quantity and screening rate for defective items when a temporary price reduction (i.e., TPR) is offered. Although previous studies have examined the similar issue, they assume a constant demand and an error-free screening process. A subversion of these two assumptions differentiates our paper. First, using a price-sensitive demand, we analyze that the original screening rate may be insufficient, and propose the CPD (i.e., control the promotional demand) and the ISR (i.e., increase the screening rate through investment) strategy to handle it. Second, we incorporate both Type I and Type II inspection errors into our model. Then we establish an inventory model aiming to maximize the retailer's profit under CPD and ISR, respectively. Finally, numerical examples are conducted and several results are obtained: (1) a higher portion of defects makes ISR more profitable; (2) both a higher probability of a Type I error and a Type II error decrease the profit under CPD and ISR, but a Type I error has a more pronounced negative impact; and (3) comparing with the existing studies with a constant demand, our model generates a higher profit especially in markets with a higher price sensitivity.

Decision framework for location and selection of container multimodal hubs: A case in china under the belt and road initiative
Xinfang Zhang, Jing Lu and Yan Peng
2022, 18(3): 2163-2190 doi: 10.3934/jimo.2021061 +[Abstract](1027) +[HTML](585) +[PDF](18029.32KB)
Abstract:

The location and selection of logistics nodes that facilitate the China Railway Express and rail-sea intermodal transportation has received increasing attention in China under the Belt and Road Initiative. The objective is to solve problems caused by the increasing number of origin cities opening international trains, such as disorderly competition, insufficient cargoes and low overall coordination. This study screens 22 cities as candidate Chinese international container multimodal hubs (CICMHs) in consideration of the actual situation of China's trade transportation. Thirteen indicators are screened using the information contribution rate-information substitutability method. Then, a comprehensive evaluation model is proposed to evaluate the candidate CICMHs and rank them. The model is based on the extended grey relational analysis-technique for order preference similar to ideal solution in combination with prospect theory. Chongqing, Guangzhou, Shanghai, Wuhan, Chengdu, Xi'an, Nanjing, Tianjin, Zhengzhou and Dalian are selected as the CICMHs. Moreover, a sensitivity analysis of the index weight fluctuations and decision-makers' preference and a comparative analysis of different decision-making methods are performed. The robustness and stability of the proposed model are demonstrated. This study can support the location and selection of CICMHs and expand the methods and applications in the decision-making field.

Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort
Jun Tu, Zijiao Sun and Min Huang
2022, 18(3): 2191-2220 doi: 10.3934/jimo.2021062 +[Abstract](1423) +[HTML](494) +[PDF](647.0KB)
Abstract:

Promoting the sale of green agriculture products through online platforms has become the main focus of agricultural industries. In a supply chain consisting of an e-tailer and third-party logistics (TPL), both the promotion effort of the e-tailer and the logistics service effort of TPL can affect the demand. Considering that logistics service contracts may be provided by the e-tailer or TPL, this study defines two different timing sequences. Three types of contracts, i.e., fixed-price, revenue-sharing, and cost-sharing contracts, are used to coordinate the supply chain. The game models under different timing sequences and different contract scenarios are established and solved. The promotion effort and logistics service effort under different scenarios are compared theoretically and numerically. The results indicate that both the promotion effort and logistics service effort change with timing sequences and contract types. The timing sequences depending on the contract provider significantly affect the performance of the supply chain. The cost-sharing contract provided by the TPL can motivate the e-tailer to apply the largest effort, and vice versa. The cost-sharing contract provided by the e-tailer can achieve the largest demand that is optimal for both the e-tailer and supply chain. However, the optimal contract for the TPL is conditional.

Design of path planning and tracking control of quadrotor
Yi Gao, Rui Li, Yingjing Shi and Li Xiao
2022, 18(3): 2221-2235 doi: 10.3934/jimo.2021063 +[Abstract](1028) +[HTML](530) +[PDF](847.95KB)
Abstract:

In this paper, we first design a motion planning system based on the Batch Informed Trees (BIT*) algorithm for quadrotor and a linear model predictive control (LMPC) is applied to solve the path tracking problem for a quadrotor. BIT* algorithm is used to plan a barrier-free trajectory quickly in an obstructed environment. Then we apply linear model predictive control for the full state quadrotor system model to track the generated trajectory. Finally, the BIT* algorithm simulation case is presented using RVIZ visual interface and some simulation cases are presented using MATLAB / Simulink. The results demonstrate the capability and the effectiveness of the control strategy in fast path tracking and the quadrotor stability, while the desired performance is achieved.

A novel risk ranking method based on the single valued neutrosophic set
Kuei-Hu Chang
2022, 18(3): 2237-2253 doi: 10.3934/jimo.2021065 +[Abstract](1295) +[HTML](629) +[PDF](395.28KB)
Abstract:

Risk assessment is a key issue in the process of product design and manufacturing. Traditionally risk assessment uses the risk priority number (RPN) method to rank the extent of a threat. However, this simultaneously includes quantitative and qualitative evaluation factors in the process of risk assessment. Moreover, the information provided by different experts for evaluation factors contain ambiguous, incomplete and inconsistent information. These problems lead to more difficulty for risk assessment, and cannot be effectively solved by the traditional RPN method. To solve some limits of the traditional risk analysis method, this paper integrates the single valued neutrosophic set and subsethood measure method to rank the extent of the threat. For missing or incomplete information in the information aggregation process, the minimum, averaging and maximum operators are used to perform data imputation to avoid the distortion of decision results. Finally, a numerical example of high-dose-rate (HDR) brachytherapy treatments is provided to demonstrate the effectiveness and feasibility of the proposed method, and a comparative analysis with some other existing methods is given.

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

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