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Journal of Industrial and Management Optimization

September 2022 , Volume 18 , Issue 5

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Stochastic comparisons of series-parallel and parallel-series systems with dependence between components and also of subsystems
Ghobad Barmalzan, Ali Akbar Hosseinzadeh and Narayanaswamy Balakrishnan
2022, 18(5): 3029-3053 doi: 10.3934/jimo.2021101 +[Abstract](1331) +[HTML](856) +[PDF](870.85KB)
Abstract:

In this paper, we consider series-parallel and parallel-series systems comprising dependent components that are drawn from a heterogeneous population consisting of \begin{document}$ m $\end{document} different subpopulations. The components within each subpopulation are assumed to be dependent, and the subsystems themselves are also dependent, with their joint distribution being modeled by an Archimedean copula. We consider a very general setting in which we assume that the subpopulations have different Archimedean copulas for their dependence. Under such a general setup, we discuss the usual stochastic, hazard rate and reversed hazard rate orders between these systems and present a number of numerical examples to illustrate all the results established here. Finally, some concluding remarks are made. The results established here extend the recent results of Fang et al. (2020) in which they have assumed all the subsystems to be independent.

Solving a constrained economic lot size problem by ranking efficient production policies
Antonio Sedeño-Noda and José M. Gutiérrez
2022, 18(5): 3055-3071 doi: 10.3934/jimo.2021102 +[Abstract](1103) +[HTML](464) +[PDF](3471.53KB)
Abstract:

We address the problem of finding the \begin{document}$ K $\end{document} best Zero-Inventory-Ordering (ZIO) policies of an Economic Lot-Sizing Problem (ELSP) with \begin{document}$ n $\end{document} time periods. To this end, we initially focus on devising an efficient algorithm to determine the Second Best ZIO policy. Based on both this latter algorithm and recent results from the state-of-the-art literature, we propose a solution method to compute the remaining \begin{document}$ K $\end{document} Best ZIO policies in \begin{document}$ O(n(K+n)) $\end{document} time and \begin{document}$ O(K+n^2 ) $\end{document} space. One claimed advantage of this approach is that it would efficiently solve a family of ELS problems, which includes a basic knapsack type constraint. A computational experiment is carried out to test the performance of the new algorithm \begin{document}$ K $\end{document}-ZIO and Constrained-ZIO for different values of \begin{document}$ K $\end{document} and \begin{document}$ n $\end{document}. For the particular case when the left-hand side coefficients in that constraint are equal, we provide an \begin{document}$ O(n^3 ) $\end{document} solution method.

A note on the paper "Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem"
Nazih Abderrazzak Gadhi
2022, 18(5): 3073-3081 doi: 10.3934/jimo.2021103 +[Abstract](1027) +[HTML](418) +[PDF](360.45KB)
Abstract:

In this work, some reasoning's mistakes in the paper by Kohli (doi:10.3934/jimo.2020114) are highlighted. Furthermore, we correct the flaws, propose a correct formulation of the main result (Theorem 5.1) and give alternative proofs.

Financing and ordering decisions in a capital-constrained and risk-averse supply chain for the monopolist and non-monopolist supplier
Zhiyuan Zhen, Honglin Yang and Wenyan Zhuo
2022, 18(5): 3083-3102 doi: 10.3934/jimo.2021104 +[Abstract](1183) +[HTML](541) +[PDF](655.14KB)
Abstract:

The paper focuses on a supply chain consisting of one supplier and one capital-constrained retailer. The retailer can solve the limited working capital problem through a bank, an investor, or its supplier. When facing business risks brought by uncertain demand, the retailer and the supplier are risk-averse behavior. To better explore the financing decision, we consider the supplier has two different cases: monopolist firm and non-monopolist firm. We first use the CVaR criterion to incorporate the members' risk-averse behavior into the objectives function. Then the equilibrium results of the supply chain are derived under three financing schemes, respectively. Our analysis finds when the supplier is a relatively low risk-averse monopolist firm, trade credit financing is the unique financing equilibrium. When the supplier is a relatively high risk-averse monopolist firm and non-monopolist firm, schemes, if the valuation level is relatively low, all members prefer bank credit financing. Otherwise, the members prefer equity financing. By tuning the valuation level, we obtain the conditions in which the supply chain realizes Pareto improvement relative to the other two financing schemes. Finally, we use numerical analysis to verify the above theoretical results.

Green cross-dock based supply chain network design under demand uncertainty using new metaheuristic algorithms
Arman Hamedirostami, Alireza Goli and Yousef Gholipour-Kanani
2022, 18(5): 3103-3131 doi: 10.3934/jimo.2021105 +[Abstract](1479) +[HTML](661) +[PDF](824.14KB)
Abstract:

This study concerns the optimization of green supply chain network design under demand uncertainty. The issue of demand uncertainty has been addressed using a scenario-based analysis approach. The main contribution of this research is to investigate the optimization of cross-dock based supply chain under uncertainty using scenario-based formulation and metaheuristic algorithms. The problem has been formulated as a two-objective mathematical model with the objectives of minimizing the costs and minimizing the environmental impact of the supply chain. Two metaheuristic algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective invasive weed optimization (MOIWO), have been developed to optimize this mathematical model. This paper focuses on the use of new metaheuristic algorithms such as MOIWO in green supply chain network design, which has received less attention in previous studies. The performance of the two solution methods has been evaluated in terms of three indices, which measure the quality, spacing, and diversification of solutions. Evaluations indicate that the developed MOIWO algorithm produces more Pareto solutions and solutions of higher quality than NSGA-II. A performance test carried out with 31 problem instances of different sizes shows that the two methods perform similarly in terms of the spread of solutions on the Pareto front, but MOIWO provides higher quality solutions than NSGA-II.

Performance analysis and system optimization of an energy-saving mechanism in cloud computing with correlated traffic
Xuena Yan, Shunfu Jin, Wuyi Yue and Yutaka Takahashi
2022, 18(5): 3133-3154 doi: 10.3934/jimo.2021106 +[Abstract](1264) +[HTML](641) +[PDF](460.61KB)
Abstract:

Energy consumption is becoming a significant part of overall operational cost in cloud data centers. For the purpose of satisfying the Service Level Agreement (SLA) of cloud users while enhancing the energy efficiency in cloud computing systems, in this paper we propose an energy-saving mechanism with a sleep mode. Taking into consideration the traffic's correlation and the stochastical behavior of data arrival requests in a random cloud environment with the proposed energy-saving mechanism, we model the system as a MAP/M/\begin{document}$ N $\end{document}/\begin{document}$ N $\end{document}+\begin{document}$ K $\end{document} queue with a synchronous multi-vacation. Then, we present a theoretical basis for analyzing and evaluating the system performance by taking a state transition rate matrix in the steady state. Next, we investigate the change trends for the energy saving rate of the system and the average latency of tasks by carrying out numerical experiments. Moreover, we give a

A robust multi-objective model for managing the distribution of perishable products within a green closed-loop supply chain
Maedeh Agahgolnezhad Gerdrodbari, Fatemeh Harsej, Mahboubeh Sadeghpour and Mohammad Molani Aghdam
2022, 18(5): 3155-3186 doi: 10.3934/jimo.2021107 +[Abstract](1763) +[HTML](749) +[PDF](670.96KB)
Abstract:

The required processes of supply chain management include optimal strategic, tactical, and operational decisions, all of which have important economic and environmental effects. In this regard, efficient supply chain planning for the production and distribution of perishable productsis of particular importance due to its leading role in the human food pyramid. One of the main challenges facing this chain is the time when products and goods are delivered to the customers and customer satisfaction will increase through this.In this research, a bi-objective mixed-integer linear programming (MILP)model is proposedto design a multi-level, multi-period, multi-product closed-loop supply chain (CLSC) for timely production and distribution of perishable products, taking into account the uncertainty of demand. To face the model uncertainty, the robust optimization (RO) method is utilized. Moreover, to solve and validate the bi-objective model in small-size problems, the \begin{document}$ \epsilon $\end{document}-constraint method (EC) is presented. On the other hand, a Non-dominated Sorting Genetic Algorithm (NSGA-II) is developed for solving large-size problems. First, the deterministic and robust models are compared by applying the suggested solutions methods in a small-size problem, and then, the proposed solution methods are compared in large-size problems in terms of different well-known metrics. According to the comparison, the proposed model has an acceptable performance in providing the optimal solutions and the proposed algorithm obtains efficient solutions.Finally, managerial insights are proposed using sensitivity analysis of important parameters of the problem.

Competitive strategies in the presence of consumers' expected service and product returns
Ting Zhang, Shuhua Chang, Yan Dong, Jingyi Yue and Kok Lay Teo
2022, 18(5): 3187-3214 doi: 10.3934/jimo.2021108 +[Abstract](1053) +[HTML](495) +[PDF](484.22KB)
Abstract:

This paper investigates the optimal strategies and profits of dual channel with product returns in the presence of customers' expected service. Customers' expected service is related to advertising effort and price. We build a two-stage decision making process to analyze the impact of expected services of customers. In addition, we analyze the parameter sensitivity and compare the competitive equilibrium strategies. The results show that the manufacturer will give a lower wholesale price to the retailer in some case. Furthermore, the dual-channel product returns will discourage advertising effort and the service level of the retailer, but it will enable the manufacturer to provide a higher service level. Thus, for managers, the survey of the expected service of customers is very important for the optimal strategies making, and it should not always blindly exploit the retailer's profit for the manufacturer. Finally, when the physical store allows unconditional return of goods, the service level of the online channel will be more considerate.

Generalized optimal liquidation problems across multiple trading venues
Qing-Qing Yang, Wai-Ki Ching, Jia-Wen Gu and Tak-Kuen Siu
2022, 18(5): 3215-3231 doi: 10.3934/jimo.2021109 +[Abstract](1103) +[HTML](378) +[PDF](784.77KB)
Abstract:

In this paper, we generalize the Almgren-Chriss's market impact model to a more realistic and flexible framework and employ it to derive and analyze some aspects of optimal liquidation problem in a security market. We illustrate how a trader's liquidation strategy alters when multiple venues and extra information are brought into the security market and detected by the trader. This study gives some new insights into the relationship between liquidation strategy and market liquidity, and provides a multi-scale approach to the optimal liquidation problem with randomly varying volatility.

Using optimal control to optimize the extraction rate of a durable non-renewable resource with a monopolistic primary supplier
Enric Fossas and Albert Corominas
2022, 18(5): 3233-3246 doi: 10.3934/jimo.2021110 +[Abstract](961) +[HTML](368) +[PDF](421.32KB)
Abstract:

The problem dealt with in this paper is that of optimizing the path of the extraction rate (and, consequently, the price) for the monopolistic owner of the primary sources of a totally or partially durable non-renewable resource (such as precious metals or gemstones) in a continuous-time frame, assuming that there is an upper bound on the extraction rate and with an interest rate equal to zero. The durability of the resource implies that, unlike the case of non-durable resources, at any time there is a stock of already-used amounts of the resource that are still potentially reusable, in addition to the resource available in the ground for extraction. The problem is addressed using the Maximum Principle of Pontryagin in the framework of optimal control theory, which allows identifying the patterns that the optimal policies can adopt. In this framework, the Hamiltonian is linear in the control input, which implies a bang-bang control policy governed by a switching surface. There is an underlying geometry to the problem that determines the solutions. It is characterized by the switching surface, its time derivative, the intersection point (if any) and the bang-bang trajectories through this point.

Sparse minimax portfolio and Sharpe ratio models
Chenchen Zu, Xiaoqi Yang and Carisa Kwok Wai Yu
2022, 18(5): 3247-3262 doi: 10.3934/jimo.2021111 +[Abstract](1252) +[HTML](489) +[PDF](1777.67KB)
Abstract:

In this paper, we investigate sparse portfolio selection models with a regularized \begin{document}$ l_p $\end{document}-norm term \begin{document}$ (0<p\leq 1) $\end{document} and negatively bounded shorting constraints. We obtain some basic properties of several linear \begin{document}$ l_p $\end{document}-sparse minimax portfolio models in terms of the regularization parameter. In particular, we introduce an \begin{document}$ l_1 $\end{document}-sparse minimax Sharpe ratio model by guaranteeing a positive denominator with a pre-selected parameter and design a parametric algorithm for finding its global solution. We carry out numerical experiments of linear \begin{document}$ l_p $\end{document}-sparse minimax portfolio models with 1200 stocks from Hang Seng Index, Shanghai Securities Composite Index, and NASDAQ Index and compare their performance with \begin{document}$ l_p $\end{document}-sparse mean-variance models. We test the effect of the regularization parameter and the negatively bounded shorting parameter on the level of sparsity, risk, and rate of return respectively and find that portfolios including fewer stocks of the linear \begin{document}$ l_p $\end{document}-sparse minimax models tend to have lower risks and lower rates of return. However, for the \begin{document}$ l_p $\end{document}-sparse mean-variance models, the corresponding changes are not so significant.

Determining optimal marketing and pricing policies by considering customer lifetime network value in oligopoly markets
Sahar Vatankhah and Reza Samizadeh
2022, 18(5): 3263-3282 doi: 10.3934/jimo.2021112 +[Abstract](1214) +[HTML](656) +[PDF](503.52KB)
Abstract:

Nowadays, the customer network effects are becoming a central issue for the companies, while the previous studies have been only limited to customer lifetime value and its related models. Therefore, this paper aims to presents a model for calculating customer lifetime value, and simultaneously the network effects are considered. For this purpose, an oligopoly market is considered in which companies compete with each other. The companies individually have a number of buyers and sellers. Interestingly, their policy is based on offering services to their buyers free, and receiving the membership fees from the sellers instead. Customers influence each other, and their word-of-mouth marketing leads to a change in the number of companies' customers. This interaction is also observed among the sellers. In the absence of buyers, the presence of sellers is meaningless. In other words, there is a remarkable proportion between the number of buyers and sellers, which directly affects the companies' profitability. Each company seeks to determine the optimal marketing and pricing policies, considering the effects of the network. By applying differential game theory, the companies are able to receive the market share, advertising, and pricing strategy. The Genetic Algorithm is employed to solve the model. Finally, a numerical example and model validation are provided to demonstrate the proposed model capabilities.

Capital asset pricing model under distribution uncertainty
Yu Chen, Zixian Cui, Shihan Di and Peibiao Zhao
2022, 18(5): 3283-3313 doi: 10.3934/jimo.2021113 +[Abstract](2343) +[HTML](934) +[PDF](2519.92KB)
Abstract:

In this paper, we investigate and demonstrate the capital asset pricing model (CAPM) based on distribution uncertainty (or ambiguity, defined as uncertainty about unknown probability).

We first achieve directly capital asset pricing model based on spectral risk measures (abbreviated as SCAPM) in the case of normal distributions; Then we can characterize SCAPM under the condition of uncertain distributions of returns by solving a robust optimal portfolio model based on spectral measures. Specifically, we do it in the following two folds: 1) Completing first the corresponding effective frontier fitting; 2) Getting the valuation of the market portfolio return \begin{document}$ r_m $\end{document} and the risk parameters of \begin{document}$ \beta_\phi $\end{document} in use of the kernel density estimation under the distribution uncertainty of returns.

Finally, by selecting 10 stocks from the constituent stocks of the HS300 Index, and comparing the valuation results from the SCAPM formula with the actual yield in the market, we verify the model proposed in the present paper is reasonable and effective.

Performance evaluation of the Chinese high-tech industry: A two-stage DEA approach with feedback and shared resource
Dawei Wang, Linlin Zhao, Feng Yang and Kehong Chen
2022, 18(5): 3315-3338 doi: 10.3934/jimo.2021114 +[Abstract](1275) +[HTML](929) +[PDF](775.02KB)
Abstract:

The operational process of high-tech industry can be separated into a research and development stage (RDS) and a commercialization stage (CS). Within this, the research employees are shared by both stages, and part of the economic output of the CS becomes a feedback factor and continuously flows back to the RDS. Using this framework, this study establishes cooperative and non-cooperative two-stage data envelopment analysis (DEA) models to explore the efficiencies of regional high-tech industries in China. The proposed approach can calculate the overall efficiency and stage efficiencies simultaneously. Based on empirical data of high-tech industries in 29 regions of China from 2012 to 2016, it is concluded that (1) a harmony exists between the RDS and the CS in the cooperative case, while a disharmony happens between the RDS and CS in the non-cooperative case; (2) there exist distinct geographic characteristics regarding the stage inefficiencies of these regional high-tech industries.

Filled function method to optimize supply chain transportation costs
Deqiang Qu, Youlin Shang, Dan Wu and Guanglei Sun
2022, 18(5): 3339-3349 doi: 10.3934/jimo.2021115 +[Abstract](1365) +[HTML](415) +[PDF](386.23KB)
Abstract:

The transportation-based supply chain model can be formulated as the constrained nonlinear programming problems. When solving such problems, the classic optimization algorithms are often limited to local minimums, causing the difficulty to find the global optimal solution. Aiming at this problem, a filled function method with a single parameter is given to cross the local minimum. Based on the characteristics of the filled function, a new filled function algorithm that can obtain the global optimal solution is designed. Numerical experiments verify the feasibility and effectiveness of the algorithm. Finally, the filled function algorithm is applied to the solution of supply chain problems, and the numerical results show that the algorithm can also address decision-making problems of supply chain transportation effectively.

Approximation algorithm with constant ratio for stochastic prize-collecting Steiner tree problem
Jian Sun, Haiyun Sheng, Yuefang Sun, Donglei Du and Xiaoyan Zhang
2022, 18(5): 3351-3363 doi: 10.3934/jimo.2021116 +[Abstract](1150) +[HTML](414) +[PDF](426.82KB)
Abstract:

Steiner tree problem is a typical NP-hard problem, which has vast application background and has been an active research topic in recent years. Stochastic optimization problem is an important branch in the field of optimization. Compared with deterministic optimization problem, it is an optimization problem with random factors, and requires the use of tools such as probability and statistics, stochastic process and stochastic analysis. In this paper, we study a two-stage finite-scenario stochastic prize-collecting Steiner tree problem, where the goal is to minimize the sum of the first stage cost, the expected second stage cost and the expected penalty cost. Our main contribution is to present a primal-dual 3-approximation algorithm for this problem.

Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition
Dingzhong Feng, Xiaofeng Zhang and Ye Zhang
2022, 18(5): 3365-3392 doi: 10.3934/jimo.2021117 +[Abstract](1220) +[HTML](499) +[PDF](1672.34KB)
Abstract:

With the increasing growth of consumers' request for recovery channels, in addition to collecting price, the collecting service has gradually become a competitive point for collectors to collect used products. Focusing on a closed-loop supply chain (CLSC) with recovery competition (on collecting price and collecting service) and distinguishing collecting quality, we propose two models (decentralized and centralized models) to study the collection strategies and profits of the CLSC. Moreover, we analyze the impact of the collecting competition and quality on the CLSC. Finally, a revenue-cost sharing contract (RCSC) is introduced to coordinate the supply chain. And a numerical example is illustrated to verify the contract's efficiency. It is found that the collected quantities and profits of the CLSC members are positively correlated with the remanufacturable ratio. The collecting competition dampens consumers' enthusiasm for recycling, which is not conducive to collectors to carry out collecting activity, resulting in the reduction of the CLSC's profit. The collectors appropriately improving collecting prices and service levels can increase the collected quantities, but to cope with the increasing competition, increasing collecting price is the main means for collectors to attract consumers to recycle. In addition, the designed RCSC can effectively improve the CLSC's efficiency and increase the profits of each party.

The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy
Fatemeh Kangi, Seyed Hamid Reza Pasandideh, Esmaeil Mehdizadeh and Hamed Soleimani
2022, 18(5): 3393-3431 doi: 10.3934/jimo.2021118 +[Abstract](1713) +[HTML](694) +[PDF](810.68KB)
Abstract:

The main reason for the development of this research refers to the increased attention of businesses to the CLSC concept due to the social responsibilities, strict international legislations and economic motives. Hence, this study investigates the issue of optimizing a CLSC problem involving multiple manufacturers, a hybrid cross-dock/collection center, multiple retailers and a disposal center in deterministic, multi-product and multi-period contexts. The bi-objective MILP model developed here is to simultaneously minimize total costs and total processing time of CLSC. Both strategic and tactical decisions are considered in the model where retailer demands and capacity constraints are satisfied. Since the presented model is NP-hard, NSGAII and MOPSO are hired to find near-to-optimal results for practical problem sizes in polynomial time.Then, to increase the accuracy of solutions by tuning the algorithms' parameters, the Taguchi method is applied. The practicality of the developed

The application of model predictive control on stock portfolio optimization with prediction based on Geometric Brownian Motion-Kalman Filter
Wawan Hafid Syaifudin and Endah R. M. Putri
2022, 18(5): 3433-3443 doi: 10.3934/jimo.2021119 +[Abstract](1300) +[HTML](655) +[PDF](927.92KB)
Abstract:

A stock portfolio is a collection of assets owned by investors, such as companies or individuals. The determination of the optimal stock portfolio is an important issue for the investors. Management of investors' capital in a portfolio can be regarded as a dynamic optimal control problem. At the same time, the investors should also consider about the prediction of stock prices in the future time. Therefore, in this research, we propose Geometric Brownian Motion-Kalman Filter (GBM-KF) method to predict the future stock prices. Subsequently, the stock returns will be calculated based on the forecasting results of stock prices. Furthermore, Model Predictive Control (MPC) will be used to solve the portfolio optimization problem. It is noticeable that the management strategy of stock portfolio in this research considers the constraints on assets in the portfolio and the cost of transactions. Finally, a practical application of the solution is implemented on 3 company's stocks. The simulation results show that the performance of the proposed controller satisfies the state's and the control's constraints. In addition, the amount of capital owned by the investor as the output of system shows a significant increase.

Optimal investment-reinsurance strategy in the correlated insurance and financial markets
Xiaoyu Xing and Caixia Geng
2022, 18(5): 3445-3459 doi: 10.3934/jimo.2021120 +[Abstract](1889) +[HTML](465) +[PDF](395.44KB)
Abstract:

Within the correlated insurance and financial markets, we consider the optimal reinsurance and asset allocation strategies. In this paper, the risk asset is assumed to follow a general continuous diffusion process driven by a Brownian motion, which correlates to the insurer's surplus process. We propose a novel approach to derive the optimal investment-reinsurance strategy and value function for an exponential utility function. To illustrate this, we show how to derive the explicit closed strategies and value functions when the risk asset is the CEV model, 3/2 model and Merton's IR model respectively.

Robust optimal asset-liability management with penalization on ambiguity
Yu Yuan and Hui Mi
2022, 18(5): 3461-3485 doi: 10.3934/jimo.2021121 +[Abstract](1078) +[HTML](551) +[PDF](531.82KB)
Abstract:

In this paper, we study the robust optimal asset- problems for an ambiguity-averse investor, who does not have perfect information in the drift terms of the risky asset and liability processes. Two different kinds of objectives are considered: \begin{document}$ (i) $\end{document} Maximizing the minimal expected utility of the terminal wealth; \begin{document}$ (ii) $\end{document} Minimizing the maximal cumulative deviation. The ambiguity in both problems is described by a set of equivalent measures to the reference model. By the stochastic dynamic programming approach and Hamilton-Jacobi-Bellman (HJB) equation, we derive closed-form expressions for the value function and corresponding robust optimal investment strategy in each problem. Furthermore, some special cases are provided to investigate the effect of model uncertainty on the optimal investment strategy. Finally, the economic implication and parameter sensitivity are analyzed by some numerical examples. We also compare the robust optimal investment strategies in two different problems.

An exact algorithm for stable instances of the $ k $-means problem with penalties in fixed-dimensional Euclidean space
Fan Yuan, Dachuan Xu, Donglei Du and Min Li
2022, 18(5): 3487-3498 doi: 10.3934/jimo.2021122 +[Abstract](930) +[HTML](446) +[PDF](415.2KB)
Abstract:

We study stable instances of the \begin{document}$ k $\end{document}-means problem with penalties in fixed-dimensional Euclidean space. An instance of the problem is called \begin{document}$ \alpha $\end{document}-stable if this instance exists a sole optimal solution and the solution keeps unchanged when distances and penalty costs are scaled by a factor of no more than \begin{document}$ \alpha $\end{document}. Stable instances of clustering problem have been used to explain why certain heuristic algorithms with poor theoretical guarantees perform quite well in practical. For any fixed \begin{document}$ \epsilon > 0 $\end{document}, we show that when using a common multi-swap local-search algorithm, a \begin{document}$ (1+\epsilon) $\end{document}-stable instance of the \begin{document}$ k $\end{document}-means problem with penalties in fixed-dimensional Euclidean space can be solved accurately in polynomial time.

Optimal replenishment, pricing and preservation technology investment policies for non-instantaneous deteriorating items under two-level trade credit policy
Chandan Mahato and Gour Chandra Mahata
2022, 18(5): 3499-3537 doi: 10.3934/jimo.2021123 +[Abstract](1205) +[HTML](653) +[PDF](978.69KB)
Abstract:

In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. In this paper, we consider an inventory model for non-instantaneous deteriorating items with price sensitive demand, time varying deterioration rate under two-level trade credit policy. Besides, to reduce deterioration rate, retailers invest some cost to prevent product degradation/decay, known as preservation technology, is also inserted. Consumption of such items within shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In the sequel, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to the customers 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. The main objective is to determine the optimal replenishment, pricing and preservation technology investment strategies including whether or not invest in preservation technology and how much to invest in order to maximize the average profit of the system. It is proved that the optimal replenishment policy not only exists but is unique for any given selling price and preservation technology cost. An algorithm is presented to derive the optimal solutions of the model. Numerous theorems and lemmas have been inserted to obtain the optimal solution. Finally, numerical examples and managerial implications are incorporated to validate the proposed model.

A unified derivative-free projection method model for large-scale nonlinear equations with convex constraints
Yigui Ou and Wenjie Xu
2022, 18(5): 3539-3560 doi: 10.3934/jimo.2021125 +[Abstract](998) +[HTML](416) +[PDF](477.63KB)
Abstract:

Motivated by recent derivative-free projection methods proposed in the literature for solving nonlinear constrained equations, in this paper we propose a unified derivative-free projection method model for large-scale nonlinear equations with convex constraints. Under mild conditions, the global convergence and convergence rate of the proposed method are established. In order to verify the feasibility and effectiveness of the model, a practical algorithm is devised and the corresponding numerical experiments are reported, which show that the proposed practical method is efficient and can be applied to solve large-scale nonsmooth equations. Moreover, the proposed practical algorithm is also extended to solve the obstacle problem.

Inter-organizational contract control of advertising strategies in the supply chain
Yafei Zu
2022, 18(5): 3561-3585 doi: 10.3934/jimo.2021126 +[Abstract](1040) +[HTML](513) +[PDF](550.44KB)
Abstract:

Advertising has a crucial impact on a product's goodwill. To further improve a product's goodwill and make more profit, member firms in the supply chain use various contracts to coordinate the channel. Considering the dynamic effect of advertising, this paper studies a two-level supply chain consisting of one manufacturer and one retailer. The two members focus on maximizing their profits through advertising and pricing strategies under two types of contracts: the wholesale price contract and the consignment contract. The Stackelberg differential game is introduced, and the optimal advertising effort, wholesale and retail pricing strategies in the two situations are studied. Numerical examples and sensitivity analyses are conducted to explore the models further. The results show that the retailer's revenue proportion and the product's goodwill according to consumers significantly affect the strategies and the contract choice of the partner firms in the supply chain. A proportion of too high or too low revenue may lead to a contract selection conflict between the two partner firms. However, when consumers care more about the product's goodwill, this contract selection conflict can be weakened.

The impacts of digital content piracy and copyright protection policies when consumers are loss averse
Yan-Xin Chai, Steven Ji-Fan Ren and Jian-Qiang Zhang
2022, 18(5): 3587-3612 doi: 10.3934/jimo.2021127 +[Abstract](1025) +[HTML](647) +[PDF](584.46KB)
Abstract:

Recent technological advances in digitization and online communications have enabled unauthorized reproduction and illegal file-sharing. However, controversies still exist over the impacts of digital content piracy and copyright protection policies. Using a game-theoretic framework, we examine the impacts of digital content piracy and copyright protection policies on product quality, firm profitability, consumer surplus, and social welfare when consumers exhibit loss aversion in the quality dimension. Specifically, consumers are initially uncertain about the product quality and will form an expectation, but once they buy the licensed product or use piracy, they know the actual product quality and compare it with their expectation. When consumers are loss averse, consumer propensity to an option is more negatively affected by product quality above the expectation than positively affected by product quality below the expectation. Our analysis shows that although piracy exerts a negative cannibalization effect in the absence of loss aversion, it can exert an additional positive information effect when the degree of loss aversion on the licensed product is higher than the degree of loss aversion on piracy. We find that when the information effect dominates the cannibalization effect, piracy can lead to a win-win situation for firm profitability and consumer surplus. Moreover, under certain circumstances, anti-protection policies can simultaneously raise product quality, firm profitability and consumer surplus. The rationale behind the positive impacts of piracy and anti-protection policies is rooted in the influences of loss aversion behavior on consumer purchase decisions. The results show that it is essential to quantify the degree of consumer loss aversion for firms in formulating pricing and quality strategies and for policymakers to develop copyright protection policies.

Median location problem with two probabilistic line barriers: Extending the Hook and Jeeves algorithm
Saber Shiripour and Nezam Mahdavi-Amiri
2022, 18(5): 3613-3639 doi: 10.3934/jimo.2021128 +[Abstract](912) +[HTML](321) +[PDF](6167.07KB)
Abstract:

We consider a median location problem in the presence of two probabilistic line barriers on the plane under rectilinear distance. It is assumed that the two line barriers move on their corresponding horizontal routes uniformly. We first investigate different scenarios for the position of the line barriers on the plane and their corresponding routes, and then define the visibility and invisibility conditions along with their corresponding expected barrier distance functions. The proposed problem is formulated as a mixed-integer nonlinear programming model. Our aim is to locate a new facility on the plane so that the total weighted expected rectilinear barrier distance is minimized. We present efficient lower and upper bounds using the forbidden location problem for the proposed problem. To solve the proposed model, the Hooke and Jeeves algorithm (HJA) is extended. We investigate various sample problems to test the performance of the proposed algorithm and appropriateness of the bounds. Also, an empirical study in Kingston-upon-Thames, England, is conducted to illustrate the behavior and applicability of the proposed model.

Investigating a green supply chain with product recycling under retailer's fairness behavior
Chirantan Mondal and Bibhas C. Giri
2022, 18(5): 3641-3677 doi: 10.3934/jimo.2021129 +[Abstract](1275) +[HTML](564) +[PDF](843.15KB)
Abstract:

Due to the rapid increment of environmental pollution and advancement of society, recently many manufacturing firms have started greening their products and focusing on product remanufacturing. The retailing firms are also taking several efforts for marketing those products and thinking more about the fairness of the business. Keeping this in mind, this study investigates the effect of recycling activity and the retailer's fairness behavior on pricing, green improvement, and marketing effort in a closed-loop green supply chain. In the forward channel, the manufacturer sells the green product through the retailer while in the reverse channel, either the manufacturer or the retailer or an independent third-party collects used products. The centralized model and six decentralized models are developed depending on the retailer's fairness behavior and/or product recycling. The optimal results are derived and compared analytically. The analytical results are verified by exemplifying a numerical example. A restitution-based wholesale price contract is developed to resolve the channel conflicts and coordinate the supply chain. Our results reveal that (ⅰ) the manufacturer never selects the third-party as a collector of used products under fair-neutral retailer, (ⅱ) the fairness behavior of the retailer improves her profitability but it diminishes the manufacturer's profit, and (ⅲ) if the manufacturer does not pay much transfer price, then the collection through the third-party is preferable to the fair-minded retailer.

Optimization of the product service supply chain under the influence of presale services
Xiaohui Ren, Daofang Chang and Jin Shen
2022, 18(5): 3679-3699 doi: 10.3934/jimo.2021130 +[Abstract](1253) +[HTML](731) +[PDF](1061.34KB)
Abstract:

For some high-value and technology-intensive products, customers first ask service integrators to provide presales consulting services for products with potential demand. Improving the service level of presales service will increase service costs and reduce profits, but it can also increase the demand for products. The change in market demand under the influence of services will result in a series of chain reactions, such as changes in supply chain inventory costs and distribution costs. Thus, this paper considers the changes in the product service supply chain (PSSC) network caused by changes in presale service levels and service prices from the overall perspective of the supply chain and chooses a reasonable service level and price so that service integrators and product suppliers in PSSCs can achieve a win-win situation while meeting customer needs. First, a PSSC network optimization model is established considering the presale service level and price. Then, a double-layer nested genetic algorithm with constraint reasoning is proposed to solve this problem. Finally, by calculating the PSSC case of a building material company that produces a water mist spray system for ships, the feasibility and practicability of the algorithm was verified.

Two-level optimization approach with accelerated proximal gradient for objective measures in sparse speech reconstruction
Hai Huyen Dam, Siow Yong Low and Sven Nordholm
2022, 18(5): 3701-3717 doi: 10.3934/jimo.2021131 +[Abstract](910) +[HTML](420) +[PDF](403.65KB)
Abstract:

Compressive speech enhancement makes use of the sparseness of speech and the non-sparseness of noise in time-frequency representation to perform speech enhancement. However, reconstructing the sparsest output may not necessarily translate to a good enhanced speech signal as speech distortion may be at risk. This paper proposes a two level optimization approach to incorporate objective quality measures in compressive speech enhancement. The proposed method combines the accelerated proximal gradient approach and a global one dimensional optimization method to solve the sparse reconstruction. By incorporating objective quality measures in the optimization process, the reconstructed output is not only sparse but also maintains the highest objective quality score possible. In other words, the sparse speech reconstruction process is now quality sparse speech reconstruction. Experimental results in a compressive speech enhancement consistently show score improvement in objectives measures in different noisy environments compared to the non-optimized method. Additionally, the proposed optimization yields a higher convergence rate with a lower computational complexity compared to the existing methods.

Relaxation schemes for the joint linear chance constraint based on probability inequalities
Yanjun Wang and Shisen Liu
2022, 18(5): 3719-3733 doi: 10.3934/jimo.2021132 +[Abstract](919) +[HTML](396) +[PDF](483.95KB)
Abstract:

This paper is concerned with the joint chance constraint for a system of linear inequalities. We discuss computationally tractble relaxations of this constraint based on various probability inequalities, including Chebyshev inequality, Petrov exponential inequalities, and others. Under the linear decision rule and additional assumptions about first and second order moments of the random vector, we establish several upper bounds for a single chance constraint. This approach is then extended to handle the joint linear constraint. It is shown that the relaxed constraints are second-order cone representable. Numerical test results are presented and the problem of how to choose proper probability inequalities is discussed.

Steepest-descent block-iterative methods for a finite family of quasi-nonexpansive mappings
Nguyen Buong
2022, 18(5): 3735-3748 doi: 10.3934/jimo.2021133 +[Abstract](932) +[HTML](372) +[PDF](444.41KB)
Abstract:

In this paper, for solving the variational inequality problem over the set of common fixed points of a finite family of demiclosed quasi-nonexpansive mappings in Hilbert spaces, we propose two new strongly convergent methods, constructed by specific combinations between the steepest-descent method and the block-iterative ones. The strong convergence is proved without the boundedly regular assumptions on the family of fixed point sets as well as the approximately shrinking property for each mapping of the family, that are usually assumed in recent literature for similar problems. Applications to the multiple-operator split common fixed point problem (MOSCFPP) and the problem of common minimum points of a finite family of lower semi-continuous convex functions with numerical experiments are given.

On the linear convergence of the general first order primal-dual algorithm
Kai Wang and Deren Han
2022, 18(5): 3749-3770 doi: 10.3934/jimo.2021134 +[Abstract](961) +[HTML](460) +[PDF](1029.0KB)
Abstract:

In this paper, we consider the general first order primal-dual algorithm, which covers several recent popular algorithms such as the one proposed in [Chambolle, A. and Pock T., A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis., 40 (2011) 120-145] as a special case. Under suitable conditions, we prove its global convergence and analyze its linear rate of convergence. As compared to the results in the literature, we derive the corresponding results for the general case and under weaker conditions. Furthermore, the global linear rate of the linearized primal-dual algorithm is established in the same analytical framework.

Direct optimal control for time-delay systems via a lifted multiple shooting algorithm
Canghua Jiang, Cheng Jin, Ming Yu and Zongqi Xu
2022, 18(5): 3771-3786 doi: 10.3934/jimo.2021135 +[Abstract](975) +[HTML](306) +[PDF](1480.07KB)
Abstract:

Aiming at efficient solution of optimal control problems for continuous nonlinear time-delay systems, a multiple shooting algorithm with a lifted continuous Runge-Kutta integrator is proposed. This integrator is in implicit form to remove the restriction of smaller integration step sizes compared with delays. A tangential predictor is applied in the integrator such that Newton iterations required can be reduced considerably. If one Newton iteration is applied, the algorithm has the same structure as direct collocation algorithms whereas derives a condensed nonlinear programming problem. Then, the solution of variational sensitivity equation is decoupled from forward simulation by utilizing the implicit function theorem. Under certain conditions, this function evaluation and derivative computation procedure is proved to be convergent with a global order. Complexity analysis shows that the computational cost can be largely reduced by this lifted multiple shooting algorithm. Then, parallelizable optimal control solver can be constructed by embedding this algorithm in a general-purpose nonlinear programming solver. Simulations on a numerical example demonstrate that the computational speed of multi-threading implementation of this algorithm is increased by \begin{document}$ 36\% $\end{document} compared with non-lifted one, and increased by a factor of \begin{document}$ 6.64 $\end{document} compared with traditional sequential algorithm; meanwhile, the accuracy loss is negligible.

Effects of channel encroachment on the software and service decisions in it supply chains
Tinghai Ren, Nengmin Zeng, Dafei Wang and Shuwei Cheng
2022, 18(5): 3787-3806 doi: 10.3934/jimo.2021136 +[Abstract](1205) +[HTML](493) +[PDF](1063.04KB)
Abstract:

Currently, many upstream software developers not only sell software through downstream service providers, but also directly sell it to clients. However, in the field of IT service supply chain management, there is a lack of research on the channel encroachment of software developers. In this study, we consider an IT service supply chain with a software developer, a service provider and client enterprises. Clients can either purchase the software (developed by the software developer) from the provider with a high price and additional pre-sale services, or directly purchase it from the developer with a low price but without pre-sale service. After purchasing the software, the clients can also purchase the extended warranty service from the developer. The study shows that the market size occupied by the developer and the intensity of competition between the two parties will neither affect the developer's product and service pricing decisions, nor influence the total demand for software products and extended warranty services, and thus will not impact his own profit. However, these factors will impact the provider's decisions for pre-sale service quality and software sales price, thereby affecting the provider's software demand and profit, and thus impact the performance of the supply chain. In addition, as the intensity of competition between both parties increases, the provider will simultaneously choose to reduce the pre-sales service quality and the software sales price to compete with the developer. Different from conclusions of the existing research on competition, we surprisingly observe that as the sensitivity of client enterprises to the extended warranty services price increases, both parties will increase the software price to compete. The encroachment of the developer will reduce the provider's software demand and profit, and thus lead to a decline in the performance of the supply chain. Therefore, the encroachment of the developer is an act of squeezing out partners by decreasing the profit of the provider, but without affecting his own profit.

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

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