Operations Research Perspectives最新文献_第4页

A hybrid optimization and data-driven approach to understand the role of the risk-aversion profile parameter in portfolio optimization problems with shorting constraints 一种混合优化和数据驱动的方法来理解风险规避剖面参数在有空头约束的投资组合优化问题中的作用

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-09-15 DOI: 10.1016/j.orp.2025.100353

Mariano Carbonero-Ruz , Francisco Fernández-Navarro , Antonio M. Durán-Rosal , Javier Pérez-Rodríguez

This study contributes to the optimization literature with an approach that would help investors understand how the risk-aversion profile hyperparameter affects excess returns, risk, and Sharpe ratio curves in portfolio optimization problems with short selling constraints. These curves were characterized by studying the original optimization problem and reducing it to a one-dimensional optimization problem. The problem variable was the excess return, and the minimum level of risk is expressed as a function of it. An approach to the functional form of the minimum risk level curve was also proposed, which allows us to determine an analytical expression for the aforementioned curves. The study provides significant results for the financial literature, such as (i) an upper and lower bound for the risk aversion profile hyperparameter; (ii) the optimal value for the risk aversion profile hyperparameter; (iii) a reduced version of the optimization problem that is easier to solve, and of course (iv) an analytical expression for the excess return, risk and Sharpe ratio curves as functions of the aforementioned hyperparameters. All of these results are reported using the Mean Squared Variance (MSV) portfolio optimization problem as the baseline model, representing the two objectives of the problem minimization function (excess return and risk) in the same unit.

本研究为优化文献提供了一种方法，帮助投资者理解在有卖空约束的投资组合优化问题中，风险规避剖面超参数如何影响超额收益、风险和夏普比率曲线。通过对原优化问题的研究，将其简化为一维优化问题，对这些曲线进行表征。问题变量是超额收益，最小风险水平表示为它的函数。提出了最小风险水平曲线的函数形式的一种方法，使我们能够确定上述曲线的解析表达式。该研究为金融文献提供了重要的结果，例如：(i)风险厌恶概况超参数的上下界；（ii）风险规避剖面超参数的最优值；（iii）更容易求解的简化版优化问题，当然（iv）作为上述超参数函数的超额收益、风险和夏普比率曲线的解析表达式。所有这些结果都是使用均方方差（MSV）投资组合优化问题作为基线模型报告的，代表了同一个单元中问题最小化函数的两个目标（超额收益和风险）。

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引用次数: 0

Recursive delivery multiple flying sidekicks traveling salesman problem: An enlightenment of the Covid-19 pandemic 递归配送多飞伴旅行商问题：新冠肺炎疫情的启示

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-10-16 DOI: 10.1016/j.orp.2025.100360

Fatemeh Jamshidian, Saeed Yaghoubi, Mohammad Sadeghi

The last-mile delivery of COVID-19 vaccines required a structured timeframe, particularly for double-dose vaccines, where follow-up deliveries had to occur after vaccine type-specific intervals. This recurring service pattern inspired the development of a novel recursive delivery concept—where services must be repeated based on prior deliveries and elapsed time. We define recursive delivery as a multi-period mechanism that dynamically establishes whether, when, and how each customer should be revisited, built upon both service history and time-based constraints. To capture such recursive service patterns, this paper introduces a coordinated truck-drone delivery system, where either vehicle may recursively revisit previously serviced locations depending on the type of service—single or recursive— provided in earlier periods. To formalize this concept, we present a new variant of the Traveling Salesman Problem, termed the Recursive delivery multiple Flying Sidekicks Traveling Salesman Problem

(R - m F S T S P)

. This model extends traditional

T S P

by incorporating dynamic, service-type-dependent revisit scheduling. The

R - m F S T S P

has wide applicability in various domains requiring structured, time-sensitive service repetition, such as maintenance, health services, and supply replenishment. We formulate the

R - m F S T S P

as a mixed-integer linear programming model aimed at minimizing total transportation costs. Given the computational limitations of exact solvers for large-scale instances, a tailored metaheuristic algorithm has been developed to address the structural characteristics of the proposed

R - m F S T S P

. Its performance has been benchmarked against results from a relevant study, demonstrating competitive outcomes. Furthermore, a lower bound is provided to evaluate the quality of the obtained solutions.

COVID-19疫苗的最后一英里交付需要一个结构化的时间框架，特别是对于双剂量疫苗，后续交付必须在疫苗特定类型间隔之后进行。这种循环服务模式激发了一种新的递归交付概念的开发，即必须根据先前的交付和经过的时间来重复服务。我们将递归交付定义为一种多周期机制，它基于服务历史和基于时间的约束，动态地确定是否、何时以及如何重新访问每个客户。为了捕获这种递归服务模式，本文引入了一种协调的卡车-无人机交付系统，其中任何一辆车都可以根据早期提供的服务类型递归地重新访问先前服务的位置——单次或递归。为了形式化这个概念，我们提出了旅行商问题的一个新变体，称为递归交付多飞伙伴旅行商问题（R - mFSTSP）。该模型通过合并动态的、依赖于服务类型的重访调度来扩展传统的TSP。R - mFSTSP广泛适用于各种需要结构化、时间敏感的服务重复的领域，如维护、卫生服务和补给。我们将R - mfstspa表述为一个混合整数线性规划模型，旨在使总运输成本最小化。考虑到大规模实例的精确解算器的计算限制，我们开发了一种定制的元启发式算法来解决所提出的R - mFSTSP的结构特征。它的表现以一项相关研究的结果为基准，展示了具有竞争力的结果。并给出了一个下界来评价所得到的解的质量。

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引用次数: 0

Scheduling with sequence-dependent setup times in short-term production planning: A main path analysis-based review 短期生产计划中与顺序相关的设置时间调度：基于主路径分析的评审

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2025-04-09 DOI: 10.1016/j.orp.2025.100340

Kuo-Ching Ying , Pourya Pourhejazy , Zhi-Rong Lin

The role of setup times in production planning and control was recognised in the late 1960s. Since then, a growing number of scheduling problems have accounted for sequence-dependent setup time variables. This study aims to provide a systematic review of setup times in the short-term production planning literature, using an objective, algorithm-based approach. The Main Path Analysis (MPA) and Cluster Analysis (CA) methods are employed to identify patterns of knowledge development and the most significant advancements in the field. Over 2100 articles published between 1986 and 2024 were considered in the review. The seminal articles contributing to the advances in setup times for production scheduling are reviewed. Meanwhile, the core optimisation technologies, model characteristics, and emerging issues at different stages of literature development are discussed. The key extensions of the main path are further explored to identify secondary research interests in the field. Twenty-two research themes were identified to provide an overall perspective and shed light on the technical features and challenges. Finally, future research directions are suggested based on the outcomes of this systematic review.

安装时间在生产计划和控制中的作用在20世纪60年代末得到了认可。从那时起，越来越多的调度问题都与序列相关的设置时间变量有关。本研究旨在使用客观的、基于算法的方法，对短期生产计划文献中的设置时间进行系统回顾。采用主路径分析（MPA）和聚类分析（CA）方法识别知识发展模式和该领域最显著的进展。在1986年至2024年间发表的2100多篇文章被纳入审查范围。对生产调度设置时间的进步作出贡献的开创性文章进行了回顾。同时，讨论了核心优化技术、模型特征以及文献发展不同阶段出现的问题。进一步探讨了主要路径的关键扩展，以确定该领域的次要研究兴趣。确定了22个研究主题，以提供总体观点，并阐明技术特点和挑战。最后，根据本系统综述的结果，提出了未来的研究方向。

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引用次数: 0

Cooperation and competition in an oligopolistic and mature industry: A case study on the cationic reagent industry based on an optimization model 寡头垄断成熟产业中的合作与竞争——基于优化模型的阳离子试剂产业案例研究

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2025-01-22 DOI: 10.1016/j.orp.2025.100325

Joohang Kang, Byoungil Choi, Chaehong Lim, Joonyup Eun

A cationic reagent is an essential raw material in printing paper production. The market environment of the cationic reagent industry is influenced by the printing paper industry. Owing to the COVID-19 pandemic, the global expansion of remote work and home education has decreased the demand for printing papers. Consequently, competition among market players (i.e., suppliers and buyers) in the cationic reagent industry is intensifying. This study focuses on cooperation between market players in the cationic reagent industry, representing a typical oligopolistic and mature industry. It proposes a supply chain optimization model that minimizes the costs of the entire supply chain, incorporating buyers’ risk hedge tendency to address market uncertainty. The model is empirically tested using accessible and reliable data to assess its business applicability. Numerical experiments are conducted to explore scenarios that can occur in real market environment, such as levels of risk hedging, trade disputes, decreases in demand, and changes in production capacity. The experimental results provide managerial implications. As buyers maximize the degree to which they diversify their purchase quantities across multiple suppliers to reduce risks, differential costs of the entire supply chain increase by 19%, which are costs that cannot be reduced by suppliers’ capabilities and inevitably arise due to differences between suppliers (e.g., geography, politics, and government policies). However, in unfavorable market conditions, such as trade disputes and decreases in demand, less competitive suppliers can survive. This study shows that when market demand in the cationic reagent industry decreases, two suppliers may potentially experience operational outages. In reality, these two suppliers deteriorated under the challenging market conditions during the COVID-19 pandemic.

阳离子试剂是印刷纸生产中不可缺少的原料。阳离子试剂行业的市场环境受到印刷纸行业的影响。由于COVID-19大流行，远程工作和家庭教育在全球范围内的扩展减少了对印刷纸的需求。因此，市场参与者（即供应商和买家）在阳离子试剂行业之间的竞争正在加剧。本研究的重点是阳离子试剂行业的市场主体之间的合作，这是一个典型的寡头垄断和成熟的行业。提出了一种以整个供应链成本最小化为目标，结合买方风险对冲倾向来解决市场不确定性的供应链优化模型。使用可访问和可靠的数据对模型进行了实证测试，以评估其业务适用性。通过数值实验来探讨在真实市场环境中可能发生的情况，如风险对冲水平、贸易争端、需求减少和生产能力变化。实验结果提供了管理启示。当购买者最大限度地在多个供应商之间分散采购数量以降低风险时，整个供应链的差异成本增加了19%，这是供应商能力无法降低的成本，并且由于供应商之间的差异（例如地理，政治和政府政策）不可避免地产生的成本。然而，在不利的市场条件下，如贸易争端和需求减少，竞争力较弱的供应商可以生存。本研究表明，当阳离子试剂行业的市场需求下降时，两家供应商可能会经历运营中断。实际上，在2019冠状病毒病大流行期间，这两家供应商在充满挑战的市场条件下恶化了。

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引用次数: 0

The impact of information disclosure and smart technology integration on e-retailing performance: A production delivery policy framework 信息披露与智能技术集成对电子零售绩效的影响：一个产品交付政策框架

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2025-02-27 DOI: 10.1016/j.orp.2025.100328

Muhammad Tayyab , Hira Tahir , Muhammad Salman Habib

The electronic retailers face distinct challenges in information sharing compared to their purely offline counterparts, particularly in transparently communicating their environmental practices to increasingly eco-conscious consumers. This complexity increases in e-retailing due to the absence of direct interaction and makes it difficult for consumers to evaluate the sustainability efforts of retailing channel’s stakeholders. In response to it, manufacturers and e-retailers are leveraging social media and blockchain technology for personalized advertising to bridge this information transparency gap. This research presents a sustainable multi-item integrated model for manufacturer–retailer collaboration in e-retailing by incorporating multiple delivery policies and investments in technology aimed at information disclosure and environmental footprint reduction. The manufacturer adopts a smart production system and reuse returned goods in the manufacturing process while investing in Green Emissions Reduction Technology. Meanwhile, the e-retailer enhances product demand through Information Disclosure Technology on social media and blockchain by showcasing their environmental protection efforts. By employing a hybrid analytic-metaheuristic approach, we determine optimal production and delivery policies to improve green consumer service under varying budgetary and spatial constraints. The results demonstrate a 4.39% increase in online consumer demand through information sharing and a 3.86% improvement in profitability of the collaborative retailing system under single-setup multi-delivery policy that confirms robustness of the proposed model. Scenario analysis further provides decision-makers with actionable insights by showcasing 8.44% increment in the system profit by converting traditional production into smart production system. Moreover, the sensitivity of the proposed model to balancing the technology investments among emission control and information disclosure efforts suggests keeping track of the efficiency parameters of these investment options before making technology budget allocations.

与纯粹的线下零售商相比，电子零售商在信息共享方面面临着明显的挑战，特别是在向越来越有环保意识的消费者透明地传达他们的环保实践方面。由于缺乏直接的互动，这种复杂性在电子零售中增加了，这使得消费者很难评估零售渠道利益相关者的可持续性努力。为了应对这种情况，制造商和电子零售商正在利用社交媒体和区块链技术进行个性化广告，以弥合信息透明度的差距。本研究以资讯披露和环境足迹减少为目标，结合多种配送政策和技术投资，提出了电子零售中制造商-零售商合作的可持续多项目整合模型。制造商采用智能生产系统，在制造过程中重复使用退货，同时投资绿色减排技术。同时，电子零售商通过在社交媒体和区块链上的信息披露技术，展示他们的环保努力，提高产品需求。通过采用混合分析-元启发式方法，我们确定了在不同预算和空间约束下改善绿色消费者服务的最佳生产和交付政策。结果表明，通过信息共享，协同零售系统的在线消费者需求增加了4.39%，盈利能力提高了3.86%，验证了所提模型的稳健性。场景分析通过展示将传统生产转化为智能生产系统，系统利润增加8.44%，进一步为决策者提供可操作的见解。此外，该模型对平衡排放控制和信息披露努力之间的技术投资的敏感性建议在进行技术预算分配之前跟踪这些投资选项的效率参数。

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引用次数: 0

Decentralized message passing algorithm for heterogeneous multi-depot vehicle routing problems 异构多车场车辆路由问题的分散消息传递算法

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2025-04-28 DOI: 10.1016/j.orp.2025.100341

Byeong-Min Jeong , Dae-Sung Jang , Han-Lim Choi

In this paper, a novel message-passing algorithm, named AMP-R, based on belief propagation is proposed to solve the heterogeneous multi-depot vehicle routing problem (HMDVRP) in a distributed manner. Unlike traditional approaches, this is the first attempt to decentralize the solution process for the HMDVRP at the depot level, enabling each depot to independently compute and exchange messages to derive conflict-free solutions. The HMDVRP requires assigning customers to depots and determining routes that minimize total travel cost. By reformulating the problem as a maximum a posteriori estimation in a graphical model comprising depot and customer nodes, The proposed approach enables decentralized message calculation and exchange between depots, effectively addressing various types of the HMDVRP. In this process, it is derived that each message calculation can be reduced to a subset-visit traveling salesman problem or a capacitated vehicle routing problem, and approximation techniques are proposed to address these computational challenges. Furthermore, to ensure solution convergence and feasibility, message buffers and a refinement process are introduced. Extensive simulations demonstrate that the proposed AMP-R algorithm yields near-optimal solutions with computational efficiency, offering practical performance for complex large-scale instances where finding optimal solutions is challenging.

本文提出了一种基于信念传播的消息传递算法AMP-R，以分布式方式解决异构多车场车辆路由问题。与传统方法不同，这是第一次尝试在仓库级别分散HMDVRP的解决方案过程，使每个仓库能够独立计算和交换消息，以获得无冲突的解决方案。HMDVRP要求将客户分配到仓库，并确定使总旅行成本最小化的路线。通过将问题重新表述为包含仓库和客户节点的图形模型中的最大后验估计，所提出的方法实现了仓库之间的分散消息计算和交换，有效地解决了各种类型的HMDVRP。在此过程中，推导出每个消息计算可以简化为子集访问旅行商问题或有能力的车辆路由问题，并提出了近似技术来解决这些计算挑战。此外，为了保证解决方案的收敛性和可行性，还引入了消息缓冲区和改进过程。大量的仿真表明，所提出的AMP-R算法产生了具有计算效率的近最优解，为寻找最优解具有挑战性的复杂大规模实例提供了实用性能。

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引用次数: 0

Evaluating metaheuristic solution quality for a hierarchical vehicle routing problem by strong lower bounding 用强下边界评价分层车辆路径问题的元启发式解质量

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2025-03-15 DOI: 10.1016/j.orp.2025.100332

Marduch Tadaros , Athanasios Migdalas , Nils-Hassan Quttineh , Torbjörn Larsson

We study a vehicle routing problem that originates from a Nordic distribution company and includes the essential decision-making components of the company’s logistics operations. The problem considers customer deliveries from a depot using heavy depot vehicles, swap bodies, optional switch points, and lighter local vehicles; a feature is that deliveries are made by both depot and local vehicles. The problem has earlier been solved by a fast metaheuristic, which does however not give any quality guarantee. To assess the solution quality, two strong formulations of the problem based on the column generation approach are developed. In both of these the computational complexity is mitigated through an enumeration of the switch point options. The formulations are evaluated with respect to the quality of the linear programming lower bounds in relation to the bounds obtained from a compact formulation. The strong lower bounding quality enables a significant reduction of the optimality gap compared to the compact formulation. Further, the bounds verify the high quality of the metaheuristic solutions, and for several problem instances the optimality gap is even closed.

我们研究了一个来自北欧分销公司的车辆路线问题，包括该公司物流业务的基本决策组成部分。该问题考虑客户使用重型仓库车辆、交换体、可选开关点和较轻的本地车辆从仓库交付；它的一个特点是由仓库车辆和当地车辆共同配送。之前已经有一种快速的元启发式方法解决了这个问题，但是这种方法不能保证质量。为了评估解决方案的质量，基于柱生成方法的问题的两个强公式被开发。在这两种方法中，通过枚举切换点选项来减轻计算复杂性。根据线性规划下界相对于由紧化公式得到的下界的质量，对这些公式进行了评价。与紧凑的公式相比，强大的下限质量可以显著减少最优性差距。此外，边界验证了元启发式解的高质量，并且对于一些问题实例的最优性差距甚至是封闭的。

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引用次数: 0

Facility location based on Adjusted Present Value 基于调整后现值的设施位置

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2024-12-20 DOI: 10.1016/j.orp.2024.100319

Hamidreza Rezaei , Nathalie Bostel , Vincent Hovelaque , Olivier Péton , Jean-Laurent Viviani

Supply chain network design aims to optimize strategic decisions such as facility location decisions.

These decisions have a major impact on the supply chain, but also on the financial value of the company. However, financial considerations are often omitted from facility location mathematical models.

This paper addresses the challenge of identifying a relevant financial indicator that can be practically implemented in facility location models across different industries.

This paper makes several contributions: the Adjusted Present Value (APV) is identified as such a financial indicator; we propose a mathematical formulation that embeds the APV in a facility location model maximizing firm value; computational experiments demonstrate the tractability of the model. Finally, we compare the mathematical model with a sequential approach that first optimizes logistical decisions and then financial decisions. The proposed model improves the sequential approach up to 5.5%, increases the market coverage and anticipates facility location decisions.

供应链网络设计的目的是优化战略决策，如设施选址决策。这些决策不仅对供应链有重大影响，而且对公司的财务价值也有重大影响。然而，在设施选址数学模型中往往忽略了财务方面的考虑。本文解决了确定相关财务指标的挑战，该指标可以在不同行业的设施选址模型中实际实施。本文做出了以下贡献：将调整后的现值（APV）确定为这样一个财务指标；我们提出了一个数学公式，将APV嵌入到企业价值最大化的设施选址模型中；计算实验证明了该模型的可跟踪性。最后，我们将数学模型与顺序方法进行比较，顺序方法首先优化物流决策，然后优化财务决策。所提出的模型将顺序方法提高了5.5%，增加了市场覆盖率，并预测了设施选址决策。

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引用次数: 0

Enhancing industrial maintenance planning: Optimization of human error reduction and spare parts management 加强工业维护规划：优化减少人为错误和备件管理

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2025-04-01 DOI: 10.1016/j.orp.2025.100336

Vahideh Bafandegan Emroozi , Mostafa Kazemi , Mahdi Doostparast

Maintenance is pivotal in the industrial sector, influencing efficiency, reliability, safety, and profitability. An organized spare parts inventory supports maintenance efforts by minimizing downtime, ensuring safety, and optimizing maintenance budgets. Effective spare parts management enhances maintenance operations and improves cash flow. Conversely, human error can greatly diminish the effectiveness of maintenance efforts. This paper presents a mathematical model aimed at minimizing costs through optimized preventive maintenance (PM) planning, effective spare parts inventory control, and reduction of human error. The study provides decision-makers with crucial insights for strategically managing maintenance procedures while accounting for the effect of human error. The model is validated in real-world scenarios through sensitivity analysis, focusing on the shape parameter of the Weibull distribution, and the equipment's effective rate. Findings reveal that as the number of periods increases, maintenance operations follow a specific, predictable cycle. Moreover, the optimal human error probability (HEP) for cost minimization is identified as 0.02. These insights guide decision-makers in recognizing factors influencing human error and implementing proactive strategies to enhance maintenance performance.

维护在工业领域至关重要，影响着效率、可靠性、安全性和盈利能力。有组织的备件库存通过减少停机时间、确保安全性和优化维护预算来支持维护工作。有效的备件管理提高了维护操作，改善了现金流。相反，人为错误会大大降低维护工作的有效性。本文提出了一个数学模型，旨在通过优化预防性维护（PM）计划、有效的备件库存控制和减少人为错误来最小化成本。该研究为决策者提供了战略性管理维护程序的关键见解，同时考虑了人为错误的影响。通过灵敏度分析，重点关注威布尔分布的形状参数和设备的效率，在实际场景中对模型进行了验证。研究结果表明，随着周期的增加，维护操作遵循一个特定的、可预测的周期。此外，成本最小化的最优人为错误概率（HEP）被确定为0.02。这些见解指导决策者识别影响人为错误的因素，并实施主动策略以提高维护性能。

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引用次数: 0

Smart allocation of a developer's spending on product quality and non-salary employee benefits in a supply chain of apps 在应用程序供应链中，明智地分配开发者在产品质量和非工资员工福利上的支出

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-06-01 Epub Date: 2024-12-05 DOI: 10.1016/j.orp.2024.100320

Leonard Omer Maly, Tal Avinadav

Qualified and capable employees are crucial for the success of high-tech companies. With an ever-shrinking pool of talent, employers are forced to devise creative recruitment and retention methods, which increasingly take the form of heavy spending on non-salary benefits. The present study contributes to the existing supply-chain literature through examining the role played by such benefits in a two-agent system consisting of a platform and an app developer. In particular, we examine the effect of non-salary benefits on the outgoing quality created by the employees of the app developer. The parties follow a Stackelberg sequential game led by the platform to accurately reflect the interaction in the market, allowing us to reach equilibrium using backward induction. Our results indicate that when app developers are more risk averse or face greater uncertainty, they spend a greater amount on non-salary benefits and comparatively less on app quality. This finding highlights the importance of investing in workers, particularly in uncertain times. We further extend the applicability and robustness of our findings by introducing multiple developers to our two-agent system. The extension proves that the platform charges a universal commission rate, irrespective of the number of developers – a finding that is consistent with current practice. Given the non-linear effect of key model parameters on the profits of the supply-chain members in both the single and the multiple-developer setups, we also utilize numerical analyses and arrive at telling managerial implications for all parties.

合格和有能力的员工对高科技公司的成功至关重要。随着人才库的不断萎缩，雇主们被迫设计出创造性的招聘和留住方法，这些方法越来越多地以在非工资福利上的巨额支出为形式。本研究通过考察这些利益在由平台和应用程序开发商组成的双代理系统中所起的作用，为现有的供应链文献做出了贡献。特别是，我们研究了非工资福利对应用程序开发人员的员工创造的离职质量的影响。各方遵循由平台主导的Stackelberg序贯博弈，准确反映市场中的相互作用，使我们能够利用逆向归纳达到均衡。我们的研究结果表明，当应用开发者更厌恶风险或面临更大的不确定性时，他们会在非工资福利上投入更多，而在应用质量上投入较少。这一发现凸显了投资于员工的重要性，尤其是在不确定时期。通过将多个开发人员引入我们的双代理系统，我们进一步扩展了我们发现的适用性和健壮性。扩展证明，该平台收取普遍的佣金率，无论开发人员的数量-这一发现与目前的做法是一致的。考虑到关键模型参数在单一和多个开发商设置下对供应链成员利润的非线性影响，我们还利用数值分析并得出对各方的管理影响。

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