Interdependent Network Recovery Games

Recovery of interdependent infrastructure networks in the presence of catastrophic failure is crucial to the economy and welfare of society. Recently, centralized methods have been developed to address optimal resource allocation in postdisaster recovery scenarios of interdependent infrastructure systems that minimize total cost. In real-world systems, however, multiple independent, possibly noncooperative, utility network controllers are responsible for making recovery decisions, resulting in suboptimal decentralized processes. With the goal of minimizing recovery cost, a best-case decentralized model allows controllers to develop a full recovery plan and negotiate until all parties are satisfied (an equilibrium is reached). Such a model is computationally intensive for planning and negotiating, and time is a crucial resource in postdisaster recovery scenarios. Furthermore, in this work, we prove this best-case decentralized negotiation process could continue indefinitely under certain conditions. Accounting for network controllers' urgency in repairing their system, we propose an ad hoc sequential game-theoretic model of interdependent infrastructure network recovery represented as a discrete time noncooperative game between network controllers that is guaranteed to converge to an equilibrium. We further reduce the computation time needed to find a solution by applying a best-response heuristic and prove bounds on ε-Nash equilibrium, where ε depends on problem inputs. We compare best-case and ad hoc models on an empirical interdependent infrastructure network in the presence of simulated earthquakes to demonstrate the extent of the tradeoff between optimality and computational efficiency. Our method provides a foundation for modeling sociotechnical systems in a way that mirrors restoration processes in practice.     

Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.     

Retailer Transshipment versus Central Depot Allocation for Supply Network Design

We consider a supply chain structure with shipments from an external warehouse directly to retailers and compare two enhancement options: costly transshipment among retailers after demand has been realized vs. cost‐free allocation to the retailers from the development of a centralized depot. Stochastic programming models are developed for both the transshipment and allocation structures. We study the impact of cost parameters and demand coefficient of variation on both system structures. Our results show an increasing convex relationship between average costs and demand coefficient of variation, and furthermore that this increase is more pronounced for the allocation structure. We employ simulation and nonlinear search techniques to computationally compare the cost performance of allocation and transshipment structures under a wide range of system parameters such as demand uncertainty and correlation; lead times from the external warehouse to retailers, from warehouse to central depot, and from depot to retailers; and transshipment, holding, and penalty costs. The transshipment approach is found to outperform allocation for a broad range of parameter inputs including many situations for which transshipment is not an economically sound decision for a single period. The insights provided enable the manager to choose whether to invest in reducing lead times or demand uncertainty and assist in the selection of investments across identical and nonidentical retailers.     

Line Balancing in Parallel M/M/1 Lines and Loss Systems as Cooperative Games

We consider production and service systems that consist of parallel lines of two types: (i) M/M/1 lines and (ii) lines that have no buffers (loss systems). Each line is assumed to be controlled by a dedicated supervisor. The management measures the effectiveness of the supervisors by the long run expected cost of their line. Unbalanced lines cause congestion and bottlenecks, large variation in output, unnecessary wastes and, ultimately, high operating costs. Thus, the supervisors are expected to join forces and reduce the cost of the whole system by applying line‐balancing techniques, possibly combined with either strategic outsourcing or capacity reduction practices. By solving appropriate mathematical programming formulations, the policy that minimizes the long run expected cost of each of the parallel‐lines system, is identified. The next question to be asked is how to allocate the new total cost of each system among the lines' supervisors so that the cooperation's stability is preserved. For that sake, we associate a cooperative game to each system and we investigate its core. We show that the cooperative games are reducible to market games and therefore they are totally balanced, that is, their core and the core of their subgames are non‐empty. For each game a core cost allocation based on competitive equilibrium prices is identified.     

Intra-Organizational and inter-organizational resource allocation in two-stage network systems

There are organizational systems, such as bank branches and two-stage supply chains, which are composed of multiple parallel two-stage structures. Resource allocation in these systems is to maximize the benefit of the overall organization from a global viewpoint. In this study, we consider two types of systems at an organizational level: a centralized organizational system treating the whole two-stage production process as a basic unit, and a decentralized organizational system including two sub-organizations (groups) treating one of the two-stage production processes as a basic unit. We propose intra-organizational and inter-organizational resource allocation plans for two different organizational systems, respectively. Specially, two modes of free intermediate resource allocation (Free IRA) and fixed intermediate resource allocation (Fixed IRA) are discussed for the decentralized organizational system. The proposed allocation plans are based on two-stage data envelopment analysis models with bi-level formulations, in which the upper-level model is to maximize the entire organizational effectiveness (total outputs minus total inputs) by determining the optimized input resources and output targets while the lower-level model is concerned with efficiency constraints of all decision-making units simultaneously. The developed methods are illustrated by an application to a real-world problem with 17 city bank branches.     

Goal partitioning in a hierarchical organization

A mathematical model of the resource allocation decision process in a two level decentralized organization is presented. The model and solution procedure are capable of representing a wide range of behavioral situations. Some important aspects of the model are: (1) It allows for informational autonomy at both levels of the organization. (2) The structure of the organization can affect the final decision. (3) The goal setting behavior of the superordinate and the subordinates explicitly accounts for the decision maker's “bounded rationality”. (4) The model explicitly allows for both the superordinate and the subordinates to have their own set of goals. (5) A final decision is reached through an iterative information exchange between the superordinate and the subordinates. (6) The solution procedure leads to a resource allocation plan which reflects both the superordinate's goals and the subordinates' goals.     

Robust Resource Allocation Decisions in Resource‐Constrained Projects*

The well‐known deterministic resource‐constrained project scheduling problem involves the determination of a predictive schedule (baseline schedule or pre‐schedule) of the project activities that satisfies the finish–start precedence relations and the renewable resource constraints under the objective of minimizing the project duration. This baseline schedule serves as a baseline for the execution of the project. During execution, however, the project can be subject to several types of disruptions that may disturb the baseline schedule. Management must then rely on a reactive scheduling procedure for revising or reoptimizing the baseline schedule. The objective of our research is to develop procedures for allocating resources to the activities of a given baseline schedule in order to maximize its stability in the presence of activity duration variability. We propose three integer programming–based heuristics and one constructive procedure for resource allocation. We derive lower bounds for schedule stability and report on computational results obtained on a set of benchmark problems.     

Just-in-time scheduling with controllable processing times on parallel machines

We study scheduling problems with controllable processing times on parallel machines. Our objectives are to maximize the weighted number of jobs that are completed exactly at their due date and to minimize the total resource allocation cost. We consider four different models for treating the two criteria. We prove that three of these problems are NP\mathcal{NP} -hard even on a single machine, but somewhat surprisingly, the problem of maximizing an integrated objective function can be solved in polynomial time even for the general case of a fixed number of unrelated parallel machines. For the three NP\mathcal{NP} -hard versions of the problem, with a fixed number of machines and a discrete resource type, we provide a pseudo-polynomial time optimization algorithm, which is converted to a fully polynomial time approximation scheme.     

关键基础设施及其安全管理

关键基础设施(CI)系统是复杂的、高度相互依存的、网络化的社会-技术系统,一旦系统被中断或者被破坏,将会对国民健康、国土安全、经济稳定以及政府的正常运转等产生重大的影响.主要研究关键基础设施及其安全管理过程中的若干问题,对CI的特点进行了分析和总结,建立了网络化CI系统的体系结构,并利用视图模型来描述系统,同时还给出了灾难处理的一般过程.最后,进一步探讨了如何使用系统工程的方法来分析和模拟网络化CI系统的运行方式、潜在的薄弱环节以及改进这些薄弱环节的实施方法.     

Efficient algorithms for shared backup allocation in networks with partial information

We study efficient algorithms for establishing reliable connections with bandwidth guarantees in communication networks. In the normal mode of operation, each connection uses a primary path to deliver packets from the source to the destination. To ensure continuous operation in the event of an edge failure, each connection uses a set of backup bridges, each bridge protecting a portion of the primary path. To meet the bandwidth requirement of the connection, a certain amount of bandwidth must be allocated the edges of the primary path, as well as on the backup edges. In this paper, we focus on minimizing the amount of required backup allocation by sharing backup bandwidth among different connections. We consider efficient sharing schemes that require only partial information about the current state of the network. Specifically, the only information available for each edge is the total amount of primary allocation and the cost of allocating backup bandwidth on this edge. We consider the problem of finding a minimum cost backup allocation together with a set of bridges for a given primary path. We prove that this problem is NP-hard and present an approximation algorithm whose performance is within of the optimum, where n is the number of edges in the primary path. We also consider the problem of finding both a primary path and backup allocation of minimal total cost. A preliminary version of this paper appears in the Proceedings of 13th Annual European Symposium on Algorithms - ESA 2005, Mallorca, Spain. J. (Seffi) Naor: This research is supported in part by a foundational and strategical research grant from the Israeli Ministry of Science, and by a US-Israel BSF Grant 2002276.     

考虑满意度的两阶段DEA固定成本分摊方法

考虑具有相同的投入和产出的两阶段决策单元的固定成本分摊问题。将待分摊的固定成本作为一种新的投入,建立两阶段加性DEA模型。首先证明了各决策单元从自身角度出发可以找到至少一种分摊方案,使其自身整体和阶段效率都达到Pareto有效。然后证明了在公共的权重下,至少存在一种分摊方案可以使得各决策单元整体和阶段效率都达到Pareto有效。并给出了这样的有效成本分摊方案集。为了得到公平的成本分摊方案,定义了各DMU各阶段对分摊方案的满意度,最大化最小的满意度,可以得到最终的成本分摊方案。将问题拓展到两阶段存在共享投入的生产系统中,这些性质定理同样成立。数值算例部分将本文与Yu等（2016）的研究结果进行了对比,验证了本文方法的有效性,指出了本文方法的优越性。本文的方法综合考虑了效率和公平,得到的固定成本分摊方案公平合理。     

OPTIMAL ALLOCATIONS OF JOINT (COMMON) COSTS: A PARAMETRIC PROGRAMMING APPROACH

A parametric programming model for allocating joint costs is described and illustrated. Given M mutually exclusive missions and P alternative systems for accomplishing such missions, the model first determines the optimal choice of systems for all missions simultaneously. It then allocates both joint and separable costs such that no mission receives a greater cost allocation than any other mission alternative that might be suboptimal for the mission but nonoptimal when all missions are simultaneously considered. Although the model initially assumes a mission priority ranking, this assumption is relaxed later on as alternative rankings are evaluated and cost allocation ranges under all priority rankings are evaluated.     

ALLOCATING AND SCHEDULING MOBILE DIAGNOSTIC IMAGING EQUIPMENT AMONG HOSPITALS

The allocation and weekly scheduling of mobile magnetic resonance imaging (MRI) units leased to a group of hospitals that share the equipment can be a complex problem. Similar problems occur in other domains where expensive equipment or facilities such as video conference facilities, aircraft, and supercomputers are leased. The crux of the problem was determining the number of days and which days of the week various types of equipment types should be leased to hospitals, so as to maximize the rental revenues and satisfy client preferences for days of the week and equipment types. We found rental revenues were a decreasing function of the number of days allocated to a hospital. We considered two sub-problems linked by a set of variables to model the problem. We show that one of these subproblems is a minimum cost network flow problem and the other is an integer multi-commodity transportation problem. We developed a procedure for solving the latter problem by exploiting earlier results for specialized networks. We conducted a computational study to evaluate the performance of this procedure and showed that it generally provides near-optimal integer solutions. We describe the development and implementation of a spreadsheet-based decision support system based on this model. This system was successfully implemented by a small firm with no expertise or prior experience using models.     

基于厂商理论的区域产业边界和最优要素配置结构

区域经济发展核心是产业结构优化升级和资源的优化配置。在全球经济结构亟待优化升级和要素资源呈现不同层次紧缺的大背景下,如何合理配置和引导区域资源配置,优化产业发展方向,确定包括新兴产业在内的产业发展战略,是每一个地区新形势下面临的重要问题。一方面,在经济全球化和零边际成本趋势驱动下,区域产业发展不再局限于区域内部资源禀赋,资源流动性加强,区域产业发展的选择更加广泛和灵活;另一方面,资源日益短缺和经济快速发展推动了劳动力成本和资本成本上升,产业的生产要素配置也随之变化。基于厂商理论,将区域作为市场经济中的生产主体,在考虑区域交易成本和生产要素成本的基础上,构建区域产业边界模型和产业的最佳要素配置结构模型,开创了资源和商品全球化趋势下的产业升级战略的研究范式,探索了成本约束下的产业生产要素优化配置模式,为经济新常态下的区域产业升级战略和资源配置研究提供理论指引,为区域制定个性化的产业发展战略提供实践依据,同时对零边际成本社会趋势下的产业格局进行了初步的探索。研究得出：产业边界能够在一定程度下反映区域产业长期演化趋势,在完全市场经济下产业边界是产业发展的最优规模;区域产业的要素配置格局取决于产业的资源占用和资源贡献情况,最优配置结构受各要素的相对贡献率和相对成本影响;产业边界与成本的关系取决于规模经济与否,在规模经济状态下与生产成本成正相关关系,与交易成本成负相关关系;大部分地区的农业有较大提升空间,最佳资源配置方案是加大机械动能投入。     

Integrating Operational and Organizational Aspects in Interdependent Infrastructure Network Recovery

Managing risk in infrastructure systems implies dealing with interdependent physical networks and their relationships with the natural and societal contexts. Computational tools are often used to support operational decisions aimed at improving resilience, whereas economics‐related tools tend to be used to address broader societal and policy issues in infrastructure management. We propose an optimization‐based framework for infrastructure resilience analysis that incorporates organizational and socioeconomic aspects into operational problems, allowing to understand relationships between decisions at the policy level (e.g., regulation) and the technical level (e.g., optimal infrastructure restoration). We focus on three issues that arise when integrating such levels. First, optimal restoration strategies driven by financial and operational factors evolve differently compared to those driven by socioeconomic and humanitarian factors. Second, regulatory aspects have a significant impact on recovery dynamics (e.g., effective recovery is most challenging in societies with weak institutions and regulation, where individual interests may compromise societal well‐being). And third, the decision space (i.e., available actions) in postdisaster phases is strongly determined by predisaster decisions (e.g., resource allocation). The proposed optimization framework addresses these issues by using: (1) parametric analyses to test the influence of operational and socioeconomic factors on optimization outcomes, (2) regulatory constraints to model and assess the cost and benefit (for a variety of actors) of enforcing specific policy‐related conditions for the recovery process, and (3) sensitivity analyses to capture the effect of predisaster decisions on recovery. We illustrate our methodology with an example regarding the recovery of interdependent water, power, and gas networks in Shelby County, TN (USA), with exposure to natural hazards.     

基于患者两阶段医疗服务过程的病床资源优化

随着医疗需求的日益增长，供需不平衡的矛盾日益显著，病床资源短缺已经成为制约医疗服务发展的重要因素之一。针对病床资源供需失衡的问题，本文构建患者两阶段医疗服务过程的病床资源优化模型。考虑患者的医疗服务是一个两阶段串联排队过程，第一阶段是强制治疗阶段，第二阶段是康复阶段。在患者排队系统中，服务台总数固定的前提下，本文利用增补变量方法给出了该排队系统的概率等式，通过求解偏微分方程得出系统的状态概率，并推导出医院拒绝患者的概率、平均康复时间等相关指标。考虑部分患者因病床资源不足而无法入院和康复阶段患者提前出院两种风险因素，本文基于排队指标构建多病种间的病床分配模型，再利用动态规划的求解思路得到病床分配的最优解。最后，本文采用2017年卫生统计数据和模拟数据相结合进行数值分析。研究结果表明与传统单阶段模型相比，两阶段模型对不同病种间病床数差别影响显著，并且患者入院率对病床分配影响较大。进一步，基于数值结果给出了医疗管理建议和研究展望。     

RESOURCE ALLOCATION TO IMPROVE SERVICE QUALITY PERCEPTIONS IN MULTISTAGE SERVICE SYSTEMS

Service quality improvement has become an imperative in today's service firms. In this paper, we present a modeling framework that combines marketing and operations viewpoints for resource allocation. The framework can be used to allocate resources to the different stages of a multistage service system, where the manager's goal is to improve customers' perceptions of service quality, given some budget. Optimal allocation guidelines are provided, and the interplay of three factors on the resulting allocation scheme is captured. These factors are the current level of customers' perceptions of service quality at each stage, the cost of implementing a service quality improvement at each stage, and the importance placed by customers at each stage. Sensitivity analysis to provide additional managerial insights is also performed. We demonstrate the applicability of the modeling framework, using data from a real life health care environment. Model limitations and future research are also discussed.     

A coordination mechanism with fair cost allocation for divergent multi-echelon inventory systems

In this paper we study the coordination of inventory control in divergent multi-echelon inventory systems under periodic review and decentralized control. Under decentralized control the installations decide upon replenishment policies that minimize their individual inventory costs. In general these policies do not coincide with the optimal policies of the system under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. We present a simple coordination mechanism that removes this cost inefficiency. The upstream installations increases its base stock level while the downstream installations compensate their supplier for increased costs and provide it with additional side payments. We show that this mechanism coordinates the system; the global optimal policy of the system is the unique Nash equilibrium of the corresponding strategic game. Furthermore, the mechanism results in a fair allocation of the costs; all installations enjoy cost savings.     

Social Optimal Location of Facilities with Fixed Servers,Stochastic Demand,and Congestion

We consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand, and congestion. Motivating applications include virtual call centers, consisting of geographically dispersed centers, walk‐in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems. The choice of locations for such facilities influences both the travel cost and waiting times of users. In contrast to most previous research, we explicitly embed both customer travel/connection and delay costs in the objective function and solve the location–allocation problem and choose facility capacities simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (Scenario 1) or choosing the number of servers (Scenario 2). We express the optimal service rate in closed form in Scenario 1 and the (asymptotically) optimal number of servers in closed form in Scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed‐integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure.     

Do the contingencies of external monitoring, ownership incentives, or free cash flow explain opposing firm performance expectations?

Neoclassical and strategy frameworks stipulate that managers promote corporate performance and shareholder interests in their resource allocation decisions. Agency related works anticipate that executives seek their own personal interests at a cost to performance and shareholder wealth in their resource allocation choices. In this study, an attempt is made to resolve these conflicting anticipations. We propose that changes in levels of resource allocations (advertising expenditure, R&D spending, capital intensity) may be more positively associated with changes in levels of subsequent corporate performance for firms with greater external monitoring or with higher CEO ownership incentives. We also propose that changes in levels of resource allocations may directly (inversely) affect changes in levels of subsequent performance of the actively (passively) monitored enterprises, lacking (possessing) free cash flow. Additionally, we propose that changes in levels of resource allocations may directly (inversely) affect changes in levels of subsequent performance of firms with high (low) CEO ownership incentives in the absence (presence) of free cash flow. Regression models are utilized to test our proposals on a longitudinal sample obtained from the Compustat database. The empirical findings are generally supportive of our proposals.