AsiaPacific Journal of Operational Research
Journal Prestige (SJR): 0.477 Citation Impact (citeScore): 1 Number of Followers: 4 Hybrid journal (It can contain Open Access articles) ISSN (Print) 02175959  ISSN (Online) 17937019 Published by World Scientific [121 journals] 
 Online Portfolio Selection Strategy with Side Information Based on
Learning with Expert Advice
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Authors: Xingyu Yang, Xiaoteng Zheng, Lina Zheng
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Online portfolio selection is a decisionmaking problem of how to dynamically adjust asset positions based on historical price sequences. The existing works on online portfolio strategy are based on integrating static experts whose advice does not change with market states, which is inconsistent with the advice from dynamic experts in reality. In this paper, we propose a new online portfolio strategy by using side information states to characterize market states, getting advice from dynamic experts who dynamically adjust the strategy based on side information states and integrating their advice. To do so, we first regard all the state constant rebalanced portfolio strategies, which make portfolios dynamically according to side information states, as expert advice. Second, we apply the exponentially weighted average (EWA) algorithm to integrate the advice from the experts and propose a new strategy. Then, we prove that the strategy has the same asymptotic average logarithmic return rate as the best state constant rebalanced portfolio (BSCRP) strategy, i.e., it is universal. Finally, we conduct numerical experiments by using actual financial data from Chinese and American markets. The results indicate that our proposed strategy has good competitive performance.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20240205T08:00:00Z
DOI: 10.1142/S0217595923500410

 Research on Multiple Slack DueDate Assignments Scheduling with
PositionDependent Weights
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Authors: JiBo Wang, Han Bao, Congying Wan
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper considers a singlemachine scheduling problem where jobs have multiple slack duedate assignments, i.e., some jobs have a common flow allowance and all jobs have [math] ([math] is a given constant) common flow allowances. The objective is to determine the multiple common flow allowances and optimal job sequence that minimizes the weighted sum of earlinesstardiness penalty and slack duedate assignment cost, where the weights only depend on their positions in a sequence, i.e., the positiondependent weights. Optimal properties are given for this problem, and then the problem is shown to be polynomially solvable when the number of multiple slack duedate assignments is a given constant. The model with multiple slack duedate assignments can also be extended to position (time)dependent scheduling.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20240127T08:00:00Z
DOI: 10.1142/S0217595923500392

 Mathematical Models and Optimal Algorithms for Lot Scheduling Considering
Job Splitting and Due Dates in Green Logistics
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Authors: Ming Liu, Zhongzheng Liu, Feifeng Zheng, Chengbin Chu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Lot scheduling is a promising manufacturing mode in green logistics that can efficiently save energy and reduce production costs. It has been widely applied to integrate circuit tests in semiconductor factories, textile processing in garment workshops, etc. Each processing lot is of a fixed capacity and identical processing time, and completes more than one job simultaneously. Jobs with sizes and due dates are allowed to be arbitrarily split and processed in consecutive lots. They are delivered immediately upon completion. To the best of our knowledge, in the domain of lot scheduling, there exist no mathematical programming models that describe the above features simultaneously. In this work, we focus on the single machine environment and mainly consider two lot scheduling problems with the objectives of minimizing the maximum lateness and the total tardiness, respectively. For the problems, we first propose new mixed integer linear programming models (solved by commercial solvers), which enable a systematic understanding of the studied problems and serve as a mathematical programming basis for more complicated problems. We then prove that the Earliest DueDate (EDD) first rule and the Shortest Processing Time (SPT) first rule can optimally solve the two problems, respectively, provided that the due dates and job sizes are agreeable, i.e., a later due date indicates a larger size of job. Experimental results show the efficiency of our methods and managerial insights are drawn.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20240119T08:00:00Z
DOI: 10.1142/S0217595923500409

 Global Robust Newsvendor Operation Strategy for a TwoMarket Stochastic
Inventory System
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Authors: Xiaoli Yan, Hui Yu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Global markets increase sales and profitability opportunities for enterprises, but more environmental uncertainty poses new challenges for operational planning. This paper attempts to introduce the idea of distributionally robust optimization into the global operation problem of a twomarket stochastic inventory system, providing theoretical guidance and reference decisionmaking for enterprises to optimize and configure in a global market with nonoverlapping geographic locations and sales seasons. We find that the demand correlation and the lack of demand information will not substantially affect the operation strategy, and the enterprise’s industrial chain and supply chain remain stable. However, reducing intermarket tariffs or logistics costs will lead to a change in strategy, and the existence of the secondary market will lead to more capacity planning in the primary market. In addition, we find that enterprises’ transshipment strategies rely significantly on exchange rate volatility. Numerical experiments were conducted to demonstrate our theoretical results.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20240110T08:00:00Z
DOI: 10.1142/S0217595923500380

 Logistics Service Openness Strategy of Online Platforms with Vertical
Differentiation and Endogenous Service Level
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Authors: Yihong Hu, Yongrui Duan, Shengnan Qu, Jiazhen Huo
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper explores the strategic motivation for a platform to open its superior logistics service to a thirdparty seller with an endogenous service level. We consider a Stackelberg game between the platform and the seller who sells products to consumers who perceive the platform’s product as having a higher value than the seller’s product. We characterize the equilibrium results in two schemes regarding opening or not opening the service and present conditions for the platform to open the service and the seller to accept the service. In equilibrium, the platform’s logistics service remains at the same level before and after opening. Particularly, we demonstrate that the motivation for the platform to open the service is not simply collecting extra revenue from the service but can be understood from mitigating price competition and securing its demand and price. We find that the platform is always willing to open the logistics system because it provides the platform an additional tool to manipulate the seller’s pricing behavior and therefore improves its own profit. With a high commission rate, the platform is even willing to subsidize the seller for using the logistics service. A Pareto improvement can be realized for two firms when consumers are highly sensitive to the service level. Consumers are worse off after service opening in most cases. Our analysis offers insights into the incentives of one retailer providing highquality service for its rival when retailers differentiate in price and service.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20240103T08:00:00Z
DOI: 10.1142/S0217595923400225

 Author Index Volume 40

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Abstract: AsiaPacific Journal of Operational Research, Volume 40, Issue 06, December 2023.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231202T08:00:00Z
DOI: 10.1142/S0217595923990014
Issue No: Vol. 40, No. 06 (2023)

 Optimality Conditions in Uncertain MultiObjective Optimization Problems
with a Variable Domination Structure
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Authors: Cong Fan, Qilin Wang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we first establish some new properties of a kind of nonlinear scalarization function. Second, based on set approaches, we introduce a class of new definitions of robustness for an uncertain multiobjective optimization problem with a variable domination structure. Finally, by applying the scalarization method, we obtain the necessary and sufficient optimality conditions of the robustness for the uncertain multiobjective optimization problem with a variable domination structure in a more general setting. Some of the obtained results extend and imply the corresponding ones in recent literature.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231209T08:00:00Z
DOI: 10.1142/S0217595923500318

 A Novel Affine RelaxationBased Algorithm for Minimax Affine Fractional
Program
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Authors: Hongwei Jiao, Binbin Li, Youlin Shang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper puts forward a novel affine relaxationbased algorithm for solving the minimax affine fractional program problem (MAFPP) over a polyhedron set. First of all, some new variables are introduced for deriving the equivalence problem (EP) of the MAFPP. Then, for the EP, the affine relaxation problem (ARP) is established by using the twostage affine relaxation method. The method provides a lower bound by solving the ARP in the branchandbound searching process. By subdividing the output space rectangle and solving a series of ARPs continuously, the feasible solution sequence generated by the algorithm converges to a global optimal solution of the initial problem. In addition, the algorithmic maximum iteration in the worst case is estimated by complexity analysis for the first time. Lastly, the practicability and effectiveness of the algorithm have been verified by numerical experimental results.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231128T08:00:00Z
DOI: 10.1142/S0217595923500367

 Nested Simulation for Conditional ValueatRisk with Discrete Losses

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Authors: Yu Ge, Guangwu Liu, Houcai Shen
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Nested simulation has been an active area of research in recent years, with an important application in portfolio risk measurement. While majority of the literature has been focusing on the continuous case where portfolio loss is assumed to follow a continuous distribution, monetary losses of a portfolio in practice are usually measured in discrete units, oftentimes due to the practical consideration of meaningful decimal places for a given level of precision in risk measurement. In this paper, we study a nested simulation procedure for estimating conditional ValueatRisk (CVaR), a popular risk measure, in the case where monetary losses of the portfolio take discrete values. Tailored to the discrete nature of portfolio losses, we propose a rounded estimator and show that when the portfolio loss follows a subGaussian distribution or has a sufficiently highorder moment, the mean squared error (MSE) of the resulting CVaR estimator decays to zero at a rate close to [math], much faster than the rate of the CVaR estimator in the continuous case which is [math], where [math] denotes the sampling budget required by the nested simulation procedure. Performance of the proposed estimator is demonstrated using numerical examples.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231128T08:00:00Z
DOI: 10.1142/S0217595923500379

 Implications of Refurbishing Authorization Strategy and Distribution
Channel Choice in a ClosedLoop Supply Chain
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Authors: Xujin Pu, Mingzhuo Dai, Wen Zhang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This study examines the optimal authorization strategy for an original equipment manufacturer (OEM), the optimal distribution channel choice for a platform, and their interactions. We developed four models based on the OEM’s two strategy choices — authorization and nonauthorization strategies, and the platform having two distribution channels for refurbished products: reselling and agency selling channels. Our results indicate that the authorization strategy is optimal for the OEM when consumer’s preference for refurbished products is not sufficiently high. Unlike conventional research, an increase in the production cost of a new product leads to different choices for the OEM. Specifically, the OEM prefers a nonauthorization strategy in the reselling channel and an authorization strategy in the agency selling channel. Moreover, under the OEM’s authorization strategy, the platform always adopts a reselling channel for refurbished products. However, under the OEM’s nonauthorization strategy, the platform’s choice is determined by the commission fee and the production cost of the new product.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231121T08:00:00Z
DOI: 10.1142/S0217595923500331

 Competitive Influence Maximization with Uncertain Competitor Sources and
the Bandwagon Effect in Social Networks
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Authors: Tao Sun, Suning Gong, GuoQiang Fan, Gongjie Xu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In today’s networked society, various sources of competitive information vie for attention and strive to enhance their social influence. Agents with valuable information aim to select a strategic set of influential individuals for information dissemination. This study delves into the Competitive Influence Maximization problem based on the independent cascade model, where an agent selects a seed set to maximize their social influence while contending with uncertain sources of competition. When adopting information, individuals exhibit a bandwagon effect. We begin by demonstrating that the objective function in our problem is neither supermodular nor submodular. Subsequently, we introduce upper and lower bound problems using the Sandwich approach, showcasing their objective functions as submodular and monotone nondecreasing. We propose a greedy algorithm to solve these bounds effectively. A theoretical analysis of the Sandwich approach’s performance is presented, followed by experimental evaluations to assess its effectiveness.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231118T08:00:00Z
DOI: 10.1142/S0217595923500343

 Optimality Conditions and Gradient Descent Newton Pursuit for 0/1Loss and
Sparsity Constrained Optimization
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Authors: Dongrui Wang, Hui Zhang, Penghe Zhang, Naihua Xiu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we consider the optimization problems with 0/1loss and sparsity constraints (0/1LSCO) that involve two blocks of variables. First, we define a [math]stationary point of 0/1LSCO, according to which we analyze the firstorder necessary and sufficient optimality conditions. Based on these results, we then develop a gradient descent Newton pursuit algorithm (GDNP), and analyze its global and locally quadratic convergence under standard assumptions. Finally, numerical experiments on 1bit compressed sensing demonstrate its superior performance in terms of a high degree of accuracy.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231118T08:00:00Z
DOI: 10.1142/S0217595923500355

 Improved Accelerated Gradient Algorithms with Line Search for Smooth
Convex Optimization Problems
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Authors: Ting Li, Yongzhong Song, Xingju Cai
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
For smooth convex optimization problems, the optimal convergence rate of firstorder algorithm is [math] in theory. This paper proposes three improved accelerated gradient algorithms with the gradient information at the latest point. For the step size, to avoid using the global Lipschitz constant and make the algorithm converge faster, new adaptive line search strategies are adopted. By constructing a descent Lyapunov function, we prove that the proposed algorithms can preserve the convergence rate of [math]. Numerical experiments demonstrate that our algorithms perform better than some existing algorithms which have optimal convergence rate.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231116T08:00:00Z
DOI: 10.1142/S0217595923500306

 On Proper Separation Theorems by Means of the QuasiRelative Interior with
Applications
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Authors: Tijani Amahroq, Hassan Khatite, Abdessamad Oussarhan
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we establish several proper separation theorems for an element and a convex set and for two convex sets in terms of their quasirelative interiors. Then, we prove that the separation theorem given by [Cammaroto, F and B Di Bella (2007). On a separation theorem involving the quasirelative. Proceedings of the Edinburgh Mathematical Society, 50(3), 605–610] in Theorem 2.5, is in fact a proper separation theorem for two convex sets in which the classical interior is replaced by the quasirelative interior. Besides, we extend some known results in the literature, such as [Adán, M and V Novo (2004). Proper efficiency in vector optimization on real linear spaces. Journal of Optimization Theory and Applications, 121, 515–540] in Theorem 2.1 and [Edwards, R (1965). Functional Analysis: Theory and Applications. New York: Reinhart and Winston] in Corollary 2.2.2, through the quasirelative interior and the quasiinterior, respectively. As an application, we provide Karush–Kuhn–Tucker multipliers for quasirelative solutions of vector optimization problems. Several examples are given to illustrate the obtained results.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231116T08:00:00Z
DOI: 10.1142/S021759592350032X

 Proximal Alternating Direction Method of Multipliers with Convex
Combination Proximal Centers
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Authors: Danqing Zhou, Haiwen Xu, Junfeng Yang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Proximal alternating direction method of multipliers (PADMM) is a classical primaldual splitting method for solving separable convex optimization problems with linear equality constraints, which have numerous applications in, e.g., signal and image processing, machine learning, and statistics. In this paper, we propose a new variant of PADMM, called PADMC, whose proximal centers are constructed by convex combinations of the iterates. PADMC is able to take advantage of problem structures and preserves the desirable properties of the classical PADMM. We establish iterate convergence as well as [math] ergodic and [math] nonergodic sublinear convergence rate results measured by function residual and feasibility violation, where [math] denotes the iteration number. Moreover, we propose two fast variants of PADMC, one achieves faster [math] ergodic convergence rate when one of the component functions is strongly convex, and the other ensures faster [math] nonergodic convergence rate measured by constraint violation. Finally, preliminary numerical results on the LASSO and the elasticnet regularization problems are presented to demonstrate the performance of the proposed methods.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231108T08:00:00Z
DOI: 10.1142/S021759592350029X

 An Accelerated DoubleProximal Gradient Algorithm for DC Programming

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Authors: Gaoxi Li, Ying Yi, Yingquan Huang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
The doubleproximal gradient algorithm (DPGA) is a new variant of the classical differenceofconvex algorithm (DCA) for solving differenceofconvex (DC) optimization problems. In this paper, we propose an accelerated version of the doubleproximal gradient algorithm for DC programming, in which the objective function consists of three convex modules (only one module is smooth). We establish convergence of the sequence generated by our algorithm if the objective function satisfies the Kurdyka–[math]ojasiewicz (K[math]) property and show that its convergence rate is not weaker than DPGA. Compared with DPGA, the numerical experiments on an image processing model show that the number of iterations of ADPGA is reduced by 43.57% and the running time is reduced by 43.47% on average.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231104T07:00:00Z
DOI: 10.1142/S0217595923500288

 An Inexact Semismooth NewtonBased Augmented Lagrangian Algorithm for
MultiTask Lasso Problems
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Authors: Lanyu Lin, YongJin Liu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper is concerned with the [math]norm ball constrained multitask learning problem, which has received extensive attention in many research areas such as machine learning, cognitive neuroscience, and signal processing. To address the challenges of solving largescale multitask Lasso problems, this paper develops an inexact semismooth Newtonbased augmented Lagrangian (Ssnal) algorithm. When solving the inner problems in the Ssnal algorithm, the semismooth Newton (Ssn) algorithm with superlinear or even quadratic convergence is applied. Theoretically, this paper presents the global and asymptotically superlinear local convergence of the Ssnal algorithm under standard conditions. Computationally, we derive an efficient procedure to construct the generalized Jacobian of the projector onto [math]norm ball, which is an important component of the Ssnal algorithm, making the computational cost in the Ssn algorithm very cheap. Comprehensive numerical experiments on the multitask Lasso problems demonstrate that the Ssnal algorithm is more efficient and robust than several existing stateoftheart firstorder algorithms.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20231007T07:00:00Z
DOI: 10.1142/S0217595923500276

 Controllable Processing Time Scheduling with Total Weighted Completion
Time Objective and Deteriorating Jobs
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Authors: JiBo Wang, YiChun Wang, Congying Wan, DanYang Lv, Lei Zhang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we consider two singlemachine scheduling problems with deteriorating jobs and controllable processing time. The job processing time is a function of its starting time and resource allocation. For the convex resource function, a bicriteria analysis is provided, where the first (respectively, second) criteria is to minimize total weighted completion time (respectively, total resource consumption cost). The first problem is to minimize the weighted sum of the total weighted completion time and the total resource consumption cost. The second problem is to minimize the total weighted completion time subject to the total resource consumption cost is bound. These both problems are NPhard, we propose some heuristic algorithms and a branchandbound algorithm to solve the problems.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230913T07:00:00Z
DOI: 10.1142/S0217595923500264

 An ActiveSetBased Recursive Approach for Solving Convex Isotonic
Regression with Generalized Order Restrictions
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Authors: Xuyu Chen, Xudong Li, Yangfeng Su
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper studies the convex isotonic regression with generalized order restrictions induced by a directed tree. The proposed model covers various intriguing optimization problems with shape or order restrictions, including the generalized nearly isotonic optimization and the total variation on a tree. Inspired by the success of the pooladjacentviolator algorithm and its activeset interpretation, we propose an activesetbased recursive approach for solving the underlying model. Unlike the bruteforce approach that traverses an exponential number of possible activeset combinations, our algorithm has a polynomial time computational complexity under mild assumptions.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230801T07:00:00Z
DOI: 10.1142/S0217595923500252

 Comparison of Expected Distances in Traditional and NonTraditional
Layouts
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Authors: Mahmut Tutam, John A. White
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
The performance of a unitload warehouse depends on numerous parameters such as storage area, layout, aisle configuration, widthtodepth ratio, the number and locations of dock doors, storage policy, etc. These parameters typically relate to the layout configuration, which can be either traditional (rectangleshaped) or nontraditional (contourlineshaped). In this paper, we analyze the performance of rectangleshaped and contourlineshaped storage areas within a unitload warehouse having multiple dock doors. Expected distances traveled in rectangleshaped storage areas are compared with expected distances in their counterpart contourlinebased storage areas when an ABC classbased storage policy is used to assign unitloads. For a single product class, the expecteddistance for a rectangleshaped storage area is at most 6.07% greater than it is for the corresponding contourlineshaped storage area. Depending on the skewness of the ABC curve or storage areas for multiple classes, the expected distance for rectangleshaped storage areas can be no more than 0.59% greater than it is for the corresponding contourline shaped storage areas when multiple dock doors are distributed with a specified distance between them.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230727T07:00:00Z
DOI: 10.1142/S0217595923500240

 Minimizing Total Weighted Late Work in a Proportionate Flow Shop with
Job Rejection
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Authors: RenXia Chen, ShiSheng Li, Qi Feng
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we investigate a scheduling problem with optional job rejection in a proportionate flow shop setting, where the job processing times are machine independent. A solution to our problem is characterized by (i) partitioning the set of jobs into a set of accepted jobs and a set of rejected jobs, and (ii) scheduling the accepted jobs in a proportionate flow shop setting. The aim is to find a solution to minimize the sum of total weighted late work of the accepted jobs and total rejection cost of the rejected jobs. When all jobs share a common due date, we show that the singlemachine case is [math]hard by reduction from the Subset Sum problem. When the operations of all jobs have equal processing times, we solve the case in [math] time by reducing it into a linear assignment problem. For the general problem, we first provide a pseudopolynomialtime algorithm via the dynamic programming method, then we convert it into a fully polynomial time approximation scheme. As a byproduct, we also resolve an open question in the literature.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230710T07:00:00Z
DOI: 10.1142/S0217595923500239

 Correlated Queues with InterArrival Times Depending on Service Times

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Authors: Zhenzhen Jia, Weimin Dai, JianQiang Hu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
We consider a type of correlated queue in which the interarrival time between two consecutive customers linearly depends on the service time of the first customer. We first derive infinite systems of linear equations for the moments of the waiting time in two special cases, based on which we then develop several methods to calculate the moments of the waiting time by using MacLaurin series approximation, Padé approximation and truncation method. In addition, we show how the moments and covariances of the interdeparture times of the correlated queue can be calculated based on the moments of the waiting time. Finally, extensive numerical examples are provided to validate our methods.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230630T07:00:00Z
DOI: 10.1142/S0217595923500227

 SecondOrder Optimality Conditions and Duality for Multiobjective
SemiInfinite Programming Problems on Hadamard Manifolds
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Authors: Balendu Bhooshan Upadhyay, Arnav Ghosh, I. M. StancuMinasian
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper is devoted to the study of multiobjective semiinfinite programming problems on Hadamard manifolds. We consider a class of multiobjective semiinfinite programming problems (abbreviated as MSIP) on Hadamard manifolds. We use the concepts of secondorder Karush–Kuhn–Tucker stationary point and secondorder Karush–Kuhn–Tucker geodesic pseudoconvexity of the considered problem to derive necessary and sufficient secondorder conditions of efficiency, weak efficiency and proper efficiency for MSIP along with certain generalized geodesic convexity assumptions. Moreover, we formulate the secondorder Mond–Weirtype dual problem related to MSIP and deduce weak and strong duality theorems relating MSIP and the dual problem. The significance of our results is demonstrated with the help of nontrivial examples. To the best of our knowledge, this is the first time that secondorder optimality conditions for MSIP have been studied in Hadamard manifold setting.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230630T07:00:00Z
DOI: 10.1142/S0217595923500197

 An ADMM Approach of a Nonconvex and Nonsmooth Optimization Model for
LowLight or Inhomogeneous Image Segmentation
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Authors: Zheyuan Xing, Tingting Wu, Junhong Yue
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we propose a novel nonconvex and nonsmooth optimization model for lowlight or inhomogeneous image segmentation which is a hybrid of Mumford–Shah energy functional and Retinex theory. The given image is decomposed into the reflectance component and the illumination component by solving Retinexbased Mumford–Shah model with [math] regularizer. Indeed, the existence of the [math] regularizer means the nonsmooth term in the model is nonconvex. Thus, it is difficult to solve the proposed model directly. An alternating direction method of multipliers (ADMM) algorithm is developed to solve the proposed nonconvex and nonsmooth model. We apply a novel splitting technique in our algorithm to ensure that all subproblems admit closedform solutions. Theoretically, we prove that the sequence generated by our proposed algorithm converges to a stationary point under mild conditions. Next, once the reflectance is obtained, the [math]means clustering method is utilized to complete the segmentation. We compare the proposed Retinexbased method with other stateoftheart segmentation methods under special lighting conditions. Experimental results show that the proposed method has better performance for both grayscale images and color images efficiently in terms of the quantitative and qualitative results.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230630T07:00:00Z
DOI: 10.1142/S0217595923500215

 Some New Descent Nonlinear Conjugate Gradient Methods for Unconstrained
Optimization Problems with Global Convergence
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Authors: Min Li
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we develop some three term nonlinear conjugate gradient methods based on the Hestenes–Stiefel (HS), the Polak–Ribière–Polyak (PRP) and the Liu–Storey (LS) methods. The proposed algorithms always generate sufficient descent directions which satisfy [math]. When the Wolfe or the Armijo line search is used, we establish the global convergence of the proposed methods in a concise way. Moreover, the linear convergence rate of the methods is discussed as well. The extensive numerical results show the efficiency of the proposed methods.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230612T07:00:00Z
DOI: 10.1142/S0217595923500203

 A Resource Allocation Problem with Convex ResourceDependent Processing
Times Under A TwoMachine Flow Shop Environment
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Authors: ByungCheon Choi, JunHo Lee
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
We consider the resource allocation problem under a twomachine flow shop environment where the job sequence has been determined in advance. The resource is used to reduce the processing time that is inversely proportional to the resource consumption amount. Furthermore, there exist the lower and upper bounds on the amount of the resources consumed by each job. The objective is to minimize the makespan plus the total resource consumption cost. We show that the problem can be solved in strongly polynomial time.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230605T07:00:00Z
DOI: 10.1142/S0217595923500185

 A NonParameter Filled Function Method for Unconstrained Global
Optimization Problems
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Authors: Yingchun Liu, Yuelin Gao, Suxia Ma, Eryang Guo
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In the paper, we give a new nonparameter filled function method for finding global minimizer of global optimization programming problems, the filled function consists of a inverse cosine function and a logarithm function, and without parameter. Its theoretical residences are proved. A new filled function algorithm is given based on the proposed new parameterless filled function, The results of numerical with ten experiments verify the efficient and reliability for the algorithm.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230531T07:00:00Z
DOI: 10.1142/S0217595923500136

 Minimizing the Expected Renewable Resource Costs in a Project with
Stochastic Resource Availability
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Authors: Hossein Moghaddaszadeh, Mohammad Ranjbar, Negin Jamili
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we study the wellknown resource availability cost problem with stochastic resource availability. The objective is to determine the initial levels of all renewable resources and establish a schedule corresponding to each scenario such that the expected resource availability cost is minimized. We assume that resource shortfalls can be compensated externally but at a noticeable higher cost. We formulate the problem as a twostage stochastic programming model (TSSPM). We also develop an exact decompositionbased algorithm (DBA) for the particular case of the problem with at most two resources, which also functions as a heuristic for the original problem. Since the number of scenarios influences the performance of the developed solution approaches, we utilize a fast scenario reduction method to reduce the number of scenarios. Computational results indicate that the DBA outperforms the TSSPM formulation in solution quality and CPU runtime.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230527T07:00:00Z
DOI: 10.1142/S0217595923500082

 A Weighted Inverse Minimum [math] Cut Problem with Value Constraint Under
the BottleneckType Hamming Distance
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Authors: Elham Ramzani Ghalebala, Massoud Aman, Nasim Nasrabadi
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Given a network [math] and an [math] cut [math] with the capacity [math] and the constant value [math], an inverse minimum [math] cut problem with value constraint is to modify the vector capacity [math] as little as possible to make the [math] cut [math] become a minimum [math] cut with the capacity [math]. The distinctive feature of this problem with the inverse minimum cut problems is the addition of a constraint in which the capacity of the given cut has to equal to the preassumed value [math]. In this paper, we investigate the inverse minimum [math] cut problem with value constraint under the bottleneck weighted Hamming distance. We propose two strongly polynomial time algorithms based on a binary search to solve the problem. At each iteration of the first one, we solve a feasible flow problem. The second algorithm considers the problem in two cases [math] and [math]. In this algorithm, we first modify the capacity vector such that the given cut becomes a minimum [math] cut in the network and then, by preserving optimality this [math] cut, adjust it to satisfy value constraint.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230527T07:00:00Z
DOI: 10.1142/S0217595923500094

 Nonmonotone Alternative Direction Method Based on Simple Conic Model for
Unconstrained Optimization
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Authors: Lijuan Zhao
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we propose a nonmonotone Alternative Direction Method (ADM) based on simple conic model for unconstrained optimization. Unlike traditional trust region method, the subproblem in our method is a simple conic model, where the Hessian of the objective function is replaced by a scalar approximation, the trust region subproblem is solved by ADM which was first proposed by Zhu and Ni. When the trial point isn’t accepted by trust region, line search technique is used to find an acceptable point instead of resolving the trust region subproblem. The new method needs less memory capacitance and computational complexity. The global convergence of the algorithm is established under some mild conditions. Numerical results on a series of standard test problems are reported to show the new method is effective and robust.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230527T07:00:00Z
DOI: 10.1142/S0217595923500112

 Theoretically Scrutinizing Kinks on Efficient Frontiers and
Computationally Reporting Nonexistence of the Tangent Portfolio for the
Capital Asset Pricing Model by ParametricQuadratic Programming
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Authors: Yue Qi, Yu Zhang, Su Zhang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Researchers traditionally compute isolated points for an efficient frontier and assume a line which passes through a riskfree asset [math] and is tangent to the frontier. The tangency plays pivotal roles for the capital asset pricing model (CAPM). However, the assumption may not hold in the presence of kinks (as nondifferentiable points) on efficient frontiers. Kinks are detected by parametricquadratic programming only and not by ordinary portfolio optimization. Up until now, there has been no research to theoretically scrutinize kink properties (especially implications to CAPM) and systematically quantify the nonexistence of the tangency. In such an area, this paper contributes to the literature. In theorems and corollaries, we prove the nonexistence of the tangency and substantiate that expectedreturn axis is composed of piecewisely connected intervals for which the tangency does not exist and intervals for which the tangency exists. Computationally, we reveal universal existence of kinks (e.g., 0.2 to 8.0 kinks for 5stock to 1800stock portfolio selections) and the tangencynonexistence ratios as about 0.066.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230527T07:00:00Z
DOI: 10.1142/S0217595923500124

 Procurement Contract Design Under Asymmetric Information of Random Yield

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Authors: Qingkai Ji, Feng Liu, Jun Zhuang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Unreliable suppliers may pose a substantial threat to supply chains, especially when they hold private information of their reliability. We consider a dyadic supply chain where the information of supplier reliability (in the form of random production yield) is asymmetric. We propose a new mechanismdesign model and derive the buyer’s optimal procurement contract menu offered to suppliers with private information. We prove that the contract menu is as simple as offering two different inflated order amounts and setting the procuring price sufficiently low to let the suppliers earn zero reservation profits. These results are derived analytically under uniform distribution. We test them numerically under beta distribution and find them hold as well. However, the informational rent will become positive when the supplier’s reservation profit is positive. Positive informational rent is also found when we consider another structure of the supplier’s production cost. This paper provides some new insights into supply chain management under asymmetric information of uncertain supply.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230527T07:00:00Z
DOI: 10.1142/S0217595923500161

 A Study of CongestionBased Information Guidance Policy for Hierarchical
Healthcare Systems
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Authors: Miao Yu, Jie Xu, Xiangling Li, Dandan Yu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper develops a queueing system model to analyze the operations of a hierarchical healthcare system consisting of general hospitals (GHs) and community healthcare centers (CHCs). GHs typically provide a higher level of health care service than CHCs, and thus are preferred choices for many patients’ healthcare service needs. Consequently, GHs are often heavily congested and patients often incur excessive waiting time. In contrast, CHCs are often idle and resources are underutilized. To help balance the utilization of resources in GHs and CHCs, a congestionbased information guidance policy is proposed in this paper to inform patients in the GH service queue about the anticipated delay. Upon being informed the delay for GH service, patients may balk, remain in queue for GH service, or switch to receive service at CHCs. This policy is thus expected to relieve the congestion at GHs and promote CHC usage. To study the effects of the proposed policy, a hierarchical healthcare system is modeled as a queueing system with strategic patients. Stationary performance measures of the system are analytically characterized using a Markov chain model. Stochastic and numerical analyses provide insights on how to design information guidance policy that would help improve overall health care service quality under different scenarios.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230527T07:00:00Z
DOI: 10.1142/S0217595923500173

 Research on Delivery Times Scheduling With Sum of Logarithm Processing
TimesBased Learning Effect
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Authors: Weidong Lei, Linhui Sun, Na Ren, Xue Jia, JiBo Wang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we address singlemachine scheduling with sum of logarithm processing timesbased learning effect. Under exponential pastsequencedependent delivery times, we proved that the makespan and total completion time minimizations can be solved by the smallest processing time (SPT) first rule. Under the agreeable weight condition and agreeable due date condition, we show that the total weighted completion time minimization and maximum tardiness minimization can be solved in polynomial time, respectively.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230526T07:00:00Z
DOI: 10.1142/S0217595923500148

 Service Time and Pricing Decisions in Online Retailing with DropShipping
and Guaranteed Service Framework
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Authors: Linjing Zhang, Yi Ding, Yaxin Shi
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Many online retailers have adopted dropshipping as their main order fulfillment strategy. Against this backdrop, this paper studies the service time and pricing decisions in an online retailing system in which the single retailer is served by either monopolistic or duopolistic suppliers. The suppliers are dominant in the Stackelberg game. We employ the guaranteed service framework to model the intricate relationship between service time and inventory. The model stipulates that the delivery of online orders must be completed within guaranteed service time. The equilibrium service times and prices are derived for both cases of monopolistic and duopolistic suppliers. In addition, we systematically analyze the impact of operational and market factors on service time, respectively, and rich insights have been obtained. Interestingly, we find that the presence of competition does not necessarily lead to more rapid delivery service. Suppliers in the duopoly market tend to adopt a pricebased competitive strategy, i.e., they are better off by lowering price at the expense of longer service time, especially for the new entrant. However, as competition intensifies to some extent, suppliers are recommended to leverage on more responsive service to maintain or expand the customer base.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230526T07:00:00Z
DOI: 10.1142/S021759592350015X

 Embedding BestWorst Method into Data Envelopment Analysis

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Authors: Yu Yu, Dariush Khezrimotlag
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In reallife applications, there generally exist Decision Makers (DMs) who have preferences over outputs and inputs. Choosing appropriate weights for different criteria by DMs often arises as a problem. The BestWorst Method (BWM) in Multiple Criteria DecisionMaking (MCDM) depends on very few pairwise comparisons and just needs DMs to identify the most desirable and the least desirable criteria. Unlike MCDM, Data Envelopment Analysis (DEA) does not generally assume a priority for an output (an input) over any other outputs (inputs). The link between DEA and MCDM can be introduced by considering DecisionMaking Units (DMUs) as alternatives, outputs as criteria to be maximized, and inputs as criteria to be minimized. In this study, we propose a linear programming model to embed DEA and BWM appropriately. We first propose a modified BWM linear programming model to satisfy all conditions that DMs can assume. We then illustrate how a conventional DEA model can be developed to include the BWM conditions. From our approach, the MCDM problem to obtain the optimal weights of different criteria are measured. At the same time, the relative efficiency scores of DMUs corresponding to the MCDM criteria are also calculated. We provide the foundation of measuring the efficiency scores when most desirable and the least desirable inputs and outputs are known. To show the process of the proposed approach, a numerical example (including 17 DMUs with seven inputs and outputs) is also discussed.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230522T07:00:00Z
DOI: 10.1142/S0217595923500100

 An Efficient Splitting Algorithm for Solving the CDT Subproblem

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Authors: Jinyu Dai
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
The CDT subproblem, which minimizes a quadratic function over the intersection of two ellipsoids, is a classical quadratic programming problem. In this paper, we study a method of solving CDT with a positive Lagrangian duality gap. An efficient splitting algorithm is proposed for finding the global optimal solutions. A cutting plane is firstly added to divide the feasible set of CDT into two subsets, and then two new quadratic programming problems with ellipsoidal and linear constraints are generated accordingly. Using the newly developed technique — secondorder cone constraints to enhance the efficiencies of the SDP relaxationbased algorithms on the two subproblems, an optimal solution of CDT can be acquired by comparing the objective values of the two subproblems. Numerical experiments show that the new algorithm outperforms the two recent SDP relaxationbased algorithms, the twoparameter eigenvaluebased algorithm and the solver Gurobi 9.5 for certain types of CDT.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230512T07:00:00Z
DOI: 10.1142/S0217595923500070

 The [math]Sombor Index of Trees

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Authors: Fangxia Wang, Baoyindureng Wu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
For a positive real number [math], the [math]Sombor index of a graph [math], introduced by Réti et al, is defined as SOk(G) =∑uv∈E(G)d(u)k + d(v)kk, where [math] denotes the degree of the vertex [math] in [math]. By the definition, [math] is exactly the Sombor index of [math], while [math] is the first Zagreb index of [math]. In this paper, for [math] we present the extremal values of the [math]Sombor index of trees with some given parameters, such as matching number, the number of pendant vertices, diameter. This generalizes the relevant results on Sombor index due to Chen, Li and Wang ((2002). Extremal values on the Sombor index of trees, MATCH Communications in Mathematical and in Computer Chemistry, 87, 23–49). Handling [math] appears to be different for [math] in contrast to the case when [math]. To demonstrate this, we also characterize the extremal trees with respect to the [math] with matching number, the number of pendant vertices and diameter. In addition, three relevant conjectures are proposed.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230421T07:00:00Z
DOI: 10.1142/S0217595923500021

 Retailer Information Sharing Strategy with Counterfeiter Encroachment

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Authors: Mingzhu Yu, Qi Gao, Zelong Yi
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we examine the retailer’s information sharing decision in an authentic supply chain with a single supplier and a single retailer under different counterfeiter encroachment situations. We propose a Stackelberg game model to analyze the optimal wholesale price of the supplier, the optimal order quantity of the retailer and the optimal production quantity of the counterfeiter. We obtain the information sharing strategies of the retailer and analyze the impact of the counterfeiter on the authentic supply chain. It is revealed that: (1) under certain conditions, the retailer will voluntarily share information with the upstream supplier and (2) the existence of the counterfeiter may increase the profit of the authentic supply chain.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230417T07:00:00Z
DOI: 10.1142/S021759592350001X

 SemiOnline Scheduling on Two Identical Parallel Machines with
InitialLookahead Information
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Authors: Feifeng Zheng, Yuhong Chen, Ming Liu, Yinfeng Xu
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This work investigates a new semionline scheduling problem with lookahead. We focus on job scheduling on two identical parallel machines, where deterministic online algorithms only know the information of [math] initial jobs (i.e., the initiallookahead information), while the following jobs still arrive onebyone in an overlist fashion. We consider makespan minimization as the objective. The study aims at revealing the value of knowing [math] initial jobs, which are used to improve the competitive performance of those online algorithms without such initiallookahead information. We provide the following findings: (1) For the scenario where the [math] initial jobs are all the largest jobs with length [math], we prove that the classical LIST algorithm is optimal with competitive ratio [math]; (2) For the scenario where the total length of these [math] jobs is at least [math], we show that any online algorithm has a competitive ratio at least 3/2, implying that the initiallookahead knowledge is powerless since there exists a 3/2competitive online algorithm without such information; (3) For the scenario where the total length of these [math] jobs is at least [math] ([math]), we propose an online algorithm, named as LPTLIST, with competitive ratio of [math], implying that the initiallookahead information indeed helps to improve the competitiveness of those online algorithms lacking such information.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230331T07:00:00Z
DOI: 10.1142/S0217595923500033

 A Newsvendor Problem Considering Decision Biases of Strategic Customers
with Private Product Value Information
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Authors: Yanan Song, Zexin Yue, Junlin Chen, Xiaobo Zhao
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we consider a newsvendor system with strategic customers, who are boundedly rational and risk averse in terms of buying during the selling season or waiting for a clearance sale with price discounts. The newsvendor’s decision is to determine the optimal stock quantity. An optimization problem is formulated with the incorporation of competition among strategic customers with private product value information. We embed risk aversion within the quantal response equilibrium to characterize the strategic customer behavior. The influences of the decision biases of strategic customers on the newsvendor’s decision and profit are discussed. We find that the risk aversion considered alone always benefits the newsvendor. However, the bounded rationality considered alone benefits the newsvendor conditionally. Combining the two behavioral factor influences, the decision biases cause the newsvendor to order more and be better off when the critical fractile is high but to order less and be worse off when the critical fractile is low.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230331T07:00:00Z
DOI: 10.1142/S0217595923500045

 Systematic Review of the Latest Scientific Publications on the Vehicle
Routing Problem
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Authors: Kellen D. Endler, Cassius T. Scarpin, Maria T. A. Steiner, Alexandre C. Choueiri
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
The vehicle routing problem (VRP) and its variants are a class of network problems that have attracted the attention of many researchers in recent years, owing to their pragmatic approach to solving issues in logistics management. Most surveys/reviews of the extant literature often focus on specific variants or aspects of the VRP. However, a few reviews of the overall VRP literature are available. The focus of these papers is to identify which VRP literature characteristics are the most popular in recent studies. To this end, we analyze 229 articles published between 2015 and 2017. We provide a systematic literature review evaluating the Scenario Characteristics and Problem Physical Characteristics that are most frequently addressed by VRP researchers, the Type of Study and Data Characteristics that they address, the most cited works that constitute the theoretical pillars of the field, and details of three specific problem variants that have been studied extensively in recent years and their opportunities for future research.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230325T07:00:00Z
DOI: 10.1142/S0217595922500464

 Study on DueDate Assignment Scheduling with Setup Times and General
Truncated Learning Effects
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Authors: Yifu Feng, Zonghai Hu, Rui Si, JiBo Wang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
This paper concentrates on the singlemachine scheduling problem with pastsequencedependent setup times and general truncated learning effects, where the job processing times are nonincreasing function of their positions in a sequence. Under common, slack and different (unrestricted) duedate assignments, our goal is to minimize the weighted sum of number of early/tardy jobs and duedate assignment cost, where the weight is not related to the job but to a position, i.e., the positiondependent weight. Under the three duedate assignments, some optimal properties and three optimal solution algorithms are proposed to solve these problems, respectively.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230321T07:00:00Z
DOI: 10.1142/S0217595923500069

 Online SingleProcessor Scheduling with an Unexpected Breakdown

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Authors: Sainan Guo, Yannan Chen, Yaping Mao, Xiaoyan Zhang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we consider two singleprocessor online scheduling problems with an unexpected breakdown. Speaking specifically, there is a group of nonresumable jobs being processed on the single processor. Note that the breakdown will emerge on the processor suddenly, which signifies that its beginning time and its length are unknown in advance. In this study, we are interested in scheduling the jobs so as to minimize the maximum weighted completion time. Most noticeably, when all jobs respect an agreeable condition, i.e., for each two jobs [math] and [math], [math] means that [math], we design an optimal online algorithm. In addition, for the general version, we propose an online algorithm with a competitive ratio of at most 2.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230311T08:00:00Z
DOI: 10.1142/S0217595923500057

 An Improved TOPSIS Within the DEA Framework

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Authors: JinCheng Lu, MeiJuan Li
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Decisionmaker (DM) can assign the weights of the distance measures in the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS) for achieving his/her desirable ranking of alternatives. This phenomenon is called strategically setting distance measure weights in this study, which may affect the fairness of the results. In order to prevent this phenomenon, the idea of data envelopment analysis (DEA) is introduced to determine the objective weights of distance measures, and an improved TOPSIS is proposed in this study. The proposed method not only determines weights of the distance measures from an objective perspective and achieves the fully ranking of alternatives, but also provides the directions for improvement. Moreover, in comparison with the other methods, the advantages of the proposed method are analyzed, and the meanings and properties of the new relative closeness are discussed and proved. Finally, an example of evaluating the innovation development of hightech industries in central and western regions of China is investigated to illustrate the effectiveness and the usefulness of the proposed method.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230309T08:00:00Z
DOI: 10.1142/S0217595922500348

 WolfeType Duality for Mathematical Programs with Switching Constraints

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Authors: Gaoxi Li, Liping Tang, Liying Liu, Zhongping Wan
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
The mathematical program with switching constraints (MPSC), which has been introduced recently, is a difficult class of optimization problems. The reason for the difficulty is that the existence of the switching constraint makes the standard constraint qualifications invalid at local minimizers. This paper proposes the Wolfetype dual (WD) model of this problem without switching constraints. Under the assumptions of convexity and strict convexity, we derive the weak, strong, converse, restricted converse, and strict converse duality results between MPSC and WD.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230309T08:00:00Z
DOI: 10.1142/S0217595922500439

 The Augmented Lagrangian Method for Mathematical Programs with Vertical
Complementarity Constraints Based on Inexact Scholtes Regularization
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Authors: Na Xu, FanYun Meng, LiPing Pang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
Mathematical program with vertical complementarity constraints (MPVCC) plays an important role in economics and engineering. Due to the vertical complementarity structure, most of the standard constraint qualifications fail to hold at a feasible point. Without constraint qualifications, the Karush–Kuhn–Tucker (KKT) conditions are not necessary optimality conditions. The classical methods for solving constrained optimization problems applied to MPVCC are likely to fail. It is necessary to establish efficient algorithms for solving MPVCC from both theoretical and numerical points of view. We present an algorithm to obtain stationarity of MPVCC by solving a sequence of Scholtes regularized problems. We consider the Scholtes regularization method with the sequence of approximate KKT points only. We prove that, under strictly weaker constraint qualifications, the accumulation point of the approximate KKT points is Clarke (C) stationary point. In particular, we can get Mordukhovich (M) or strongly (S) stationary point under additional assumptions. From these results, we apply an augmented Lagrangian method to obtain a solution of MPVCC and give the convergence analysis. In particular, the accumulation point of the generated iterates is an Sstationary point if some boundedness conditions hold. The numerical results show that it is an effective way to solve MPVCC.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230208T08:00:00Z
DOI: 10.1142/S0217595922500427

 On SecondOrder SemiDifferentiability of Index [math] of Perturbation
Maps in Parametric Vector Optimization Problems
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Authors: ThanhHung Pham
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
In this paper, we prove that the Henig global proper efficient solution map and the Henig global proper efficient perturbation map of a parametric vector optimization problem are secondorder semidifferentiable with index [math] under some suitable qualification conditions. Several examples are given to illustrate the obtained results.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230125T08:00:00Z
DOI: 10.1142/S0217595922500415

 A Unified Approach to SingleMachine Scheduling with PositionBased
Processing Times, Machine Availability, and Job Rejection
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Authors: Min Ji, Kaili Qi, T. C. E. Cheng, Yiwei Jiang
Abstract: AsiaPacific Journal of Operational Research, Ahead of Print.
We present a unified approach to singlemachine scheduling with positionbased processing times, an availability constraint, and job rejection. The approach uses two general positionbased processing time functions to model both the learning and aging effects in scheduling. In addition, taking machine availability and job rejection into consideration, the models are more realistic, which seek to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. We present fully polynomialtime approximation schemes to address the two NPhard problems.
Citation: AsiaPacific Journal of Operational Research
PubDate: 20230105T08:00:00Z
DOI: 10.1142/S0217595922500403
