Centralized resource allocation based on efficiency analysis for step-by-step improvement paths

The existing centralized resource allocation models often assume that all of the DMUs are efficient after resource allocation. For the DMU with a very low efficiency score, it means the dramatic reduction of the resources, which can cause the organizational resistance. In addition, in reality, it is particularly difficult for the DMUs to achieve their target efficiencies in a single step, especially when they are far from the efficient frontier. Thus, gradual progress towards benchmarking targets is gaining importance. In this paper, we present a new approach for resource allocation based on efficiency analysis under a centralized decision-making environment. Through our approach, the central decision-maker can obtain a sequence of intermediate benchmark targets based on efficiency analysis, which provide a level-wise improvement path to direct the DMUs to reach their ultimate targets on the efficient frontier in an implementable and realistic manner. Numerical examples are presented to illustrate the application procedure of the proposed approach.     

Centralized inventory in a farming community

A centralized inventory problem is a situation in which several agents face individual inventory problems and make an agreement to coordinate their orders with the objective of reducing costs. In this paper we identify a centralized inventory problem arising in a farming community in northwestern Spain, model the problem using two alternative approaches, find the optimal inventory policies for both models, and propose allocation rules for sharing the optimal costs in this context.     

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.     

DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches

This paper proposes new fixed cost allocation approaches for allocating a fixed cost among decision-making units (DMUs) with two-stage structures under the framework of data envelopment analysis (DEA). Firstly, we give the set of possible fixed cost allocations, prove that all DMUs can be overall efficient when evaluated by a common set of weights after fixed cost allocation. Secondly, from a centralized point of view, we consider the competition between the DMUs’ two stages in fixed cost allocation and regard these two kinds of stages as two unions. Then, we incorporate leader-follower models to propose a fixed cost allocation approach to handle the situation in which the two unions make decisions sequentially. Based on the result of these models, a concept of satisfaction degree of each union on a fixed cost allocation is presented. A satisfaction degree bargaining game model is then proposed to obtain a fixed cost allocation which is a bargaining equilibrium of the two unions. We show that the proposed approaches always obtain a fixed cost allocation that is proportionally invariant. Additionally, the satisfaction degree bargaining game approach automatically guarantees the uniqueness of the fixed cost allocation. These properties make the fixed cost allocation generated by our approaches more stable and more acceptable. Finally, a numerical example and an application of fixed cost allocation among bank branches are given to illustrate the proposed approach and to compare it with a benchmark approach among the current studies, respectively.     

A sustainable supply chain network considering lot sizing with quantity discounts under disruption risks: centralized and decentralized models

This study proposes a framework for the main parties of a sustainable supply chain network considering lot-sizing impact with quantity discounts under disruption risk among the first studies. The proposed problem differs from most studies considering supplier selection and order allocation in this area. First, regarding the concept of the triple bottom line, total cost, environmental emissions, and job opportunities are considered to cover the criteria of sustainability. Second, the application of this supply chain network is transformer production. Third, applying an economic order quantity model lets our model have a smart inventory plan to control the uncertainties. Most significantly, we present both centralized and decentralized optimization models to cope with the considered problem. The proposed centralized model focuses on pricing and inventory decisions of a supply chain network with a focus on supplier selection and order allocation parts. This model is formulated by a scenario-based stochastic mixed-integer non-linear programming approach. Our second model focuses on the competition of suppliers based on the price of products with regard to sustainability. In this regard, a Stackelberg game model is developed. Based on this comparison, we can see that the sum of the costs for both levels is lower than the cost without the bi-level approach. However, the computational time for the bi-level approach is more than for the centralized model. This means that the proposed optimization model can better solve our problem to achieve a better solution than the centralized optimization model. However, obtaining this better answer also requires more processing time. To address both optimization models, a hybrid bio-inspired metaheuristic as the hybrid of imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) is utilized. The proposed algorithm is compared with its individuals. All employed optimizers have been tuned by the Taguchi method and validated by an exact solver in small sizes. Numerical results show that striking similarities are observed between the results of the algorithms, but the standard deviations of PSO and ICA–PSO show better behavior. Furthermore, while PSO consumes less time among the metaheuristics, the proposed hybrid metaheuristic named ICA–PSO shows more time computations in all small instances. Finally, the provided results confirm the efficiency and the performance of the proposed framework and the proposed hybrid metaheuristic algorithm.

     

Managing Retail Budget Allocation between Store Labor and Marketing Activities

The performance of a retail store depends on its ability to attract customer traffic, match labor with incoming traffic, and convert the incoming traffic into sales. Retailers make significant investments in marketing activities (such as advertising) to bring customers into their stores and in‐store labor to convert that traffic into sales. Thus, a common trade‐off that retail store managers face concerns the allocation of a store's limited budget between advertising and labor to enhance store‐level sales. To explore that trade‐off, we develop a centralized model to allocate limited store budget between store labor and advertising with the objective of maximizing store sales. We find that a store's inherent potential to drive traffic plays an important role, among other factors, in the relative allocation between advertising and store labor. We also find that as advertising instruments become more effective in bringing traffic to stores, managers should not always capitalize this effectiveness by increasing their existing allocations to advertising. In addition, we discuss a decentralized setting where budget allocation decisions cannot be enforced by a store manager and present a simple mechanism that can achieve the centralized solution. In an extension, we address the budget allocation problem in the presence of marketing efforts to shift store traffic from peak to off peak hours and show that our initial findings are robust. Further, we illustrate how the solution from the budget allocation model can be used to facilitate store level sales force planning/scheduling decisions. Based on the results of our model, we present several insights that can help managers in budget allocation and sales force planning.     

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.     

Centralized resource allocation BCC models

In two recent papers, Lozano and Villa [Centralized resource allocation using data envelopment analysis. Journal of Productivity Analysis 2004;22:143–61. [1]] and Lozano et al. [Centralized target setting for regional recycling operations using DEA. OMEGA 2004;32:101–10. [2]] introduce the concept of “centralized” data envelopment analysis (DEA) models, which aim at optimizing the combined resource consumption by all units in an organization rather than considering the consumption by each unit separately. This is particularly relevant for situations where some variables are controlled by a central authority (e.g. Head Office) rather than individual unit managers. In this paper we reconsider one of the centralized models proposed by the above-mentioned authors and suggest modifying it to only consider adjustments of previously inefficient units. We show how this new model formulation relate to a standard DEA model, namely as the analysis of the mean inefficient point. We also provide a procedure that can be used to generate alternative optimal solutions, enabling a decision maker to search through alternate solution possibilities in order to select the preferred one. We then extend the model to incorporate non-transferable as well as strictly non-discretionary variables and illustrate the models using an empirical example of a public service organization.     

需求不确定条件下的制造商订单分配模型

制造商的订单分配作为供应链模型微观层面的重要组成部分,对提升整个供应链效率有很大影响,但需求层面的不确定因素加大了订单分配的难度。以按比例分配为原则,讨论在需求不确定条件下完全信息与不完全信息两类多供应商-单制造商的订单分配模型。重点研究完全信息条件下各方的分散决策和集中决策,由于后者能避免各参与方对其他决策方的边际影响,所以能够实现供应链总利润的最大化;其次又将不完全信息引入模型,讨论制造商如何通过折算因子结合已有信息对供应商的私人信息进行估计,进而做出决策。最后以需求服从正态分布为例对两类模型进行验证。     

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.     

A Game Theory Approach for Assessment of Risk and Deployment of Police Patrols in Response to Criminal Activity in San Francisco

An efficient police patrol schedule must ensure the allocation of an appropriate number of officers sufficient to respond to the danger of criminal incidents, particularly in an urban environment, even when the available number of personnel is limited. This study proposes a framework that incorporates two game theory models designed for the allocation of police officers to patrol shifts. In the first step, the interactions of three factors between the criminal and the operation captain are modeled as a zero-sum, noncooperative game, after which a mixed strategy Nash equilibrium method is used to derive the risk value for each district to be patrolled. In the second step, the risk values are used to compute the Shapley value for all 10 districts, for three different threat levels. A fair allocation of police personnel based on the Shapley value is made with a minimum set of personnel deployment costs. The efficacy of the proposed method is verified using openly available data from the San Francisco City Police detailing incidents from the year 2016. The experimental results show that police planners can use this framework to quantitatively evaluate the criminal threat in each district when deciding upon the deployment of patrol officers for three shifts per day.     

额外资源按需分配方法研究

文献Wei Quanling等^[1]的最后一段提出了这样一类额外资源分配问题：假设有一些额外的投入资源将要分配给全部或者部分决策单元,如果我们希望分配结果对于整个系统（该系统由全部决策单元组成）来说是最有益的,那么应当如何分配这些额外的投入资源?他们同时还指出系统中哪些决策单元能够获得额外的投入资源,这不仅取决于决策单元的效率,还需要考虑规模报酬。针对此类问题,本文提出一种额外资源按需分配方法：首先,综合决策单元的技术效率与其投影点的规模弹性构建发展曲线,并由决策单元的发展曲线获知其投入变动与产出变动的对应关系;然后,把额外资源分成若干等份,依次分配每一个等份的额外资源,每次分配使系统的总产出增加实现最大,直至分配完全部的额外资源,或者分配某一份额外资源不再带来任何的产出增加,分配就会停止;最后,把决策单元在每一次分配过程中获得的额外资源进行累加,得到这个决策单元最终的分配结果。全文的最后分别在"一个投入一个产出"和"两个投入一个产出"情况下给出两个具体的分配算例。分配结果表明,这种按需分配方法不会缩减任意一个决策单元当前占有的投入资源数量,并且还可以有效地在辨识出某种额外资源在规模上和结构上存在的冗余,从而有效地避免不必要的分配。     

Exploring the efficiency of Mexican universities: Integrating Data Envelopment Analysis and Multidimensional Scaling

National policy initiatives require the expenditure of large amounts of resources over several years. It is common for these initiatives to generate large amounts of data that are needed in order to assess their success. Educational policies are an obvious example. Here we concentrate on Mexico׳s “Educational Modernisation Programme” and try to see how this plan has affected efficiency in teaching and research at Mexico׳s universities. We use a combined approach that includes traditional ratios together with Data Envelopment Analysis models. This mixture allows us to assess changes in efficiency at each individual university and explore if these changes are related to teaching, to research, or to both. Using official statistics for 55 universities over a six year period (2007–2012), we have generated 12 ratios and estimated 21 DEA models under different definitions of efficiency. In order to make the results of the analysis accessible to the non-specialist we use models that visualise the main characteristics of the data, in particular scaling models of multivariate statistical analysis. Scaling models highlight the important aspects of the information contained in the data. Because the data is three-way (variables, universities, and years) we have chosen the Individual Differences Scaling model of Carroll and Chang. We complete the paper with a discussion of efficiency evolution in three universities.     

Toward an Application Guide for Safety Integrity Level Allocation in Railway Systems

The work in the article presents the development of an application guide based on feedback and comments stemming from various railway actors on their practices of SIL allocation to railway safety‐related functions. The initial generic methodology for SIL allocation has been updated to be applied to railway rolling stock safety‐related functions in order to solve the SIL concept application issues. Various actors dealing with railway SIL allocation problems are the intended target of the methodology; its principles will be summarized in this article with a focus on modifications and precisions made in order to establish a practical guide for railway safety authorities. The methodology is based on the flowchart formalism used in CSM (common safety method) European regulation. It starts with the use of quantitative safety requirements, particularly tolerable hazard rates (THR). THR apportioning rules are applied. On the one hand, the rules are related to classical logical combinations of safety‐related functions preventing hazard occurrence. On the other hand, to take into account technical conditions (last safety weak link, functional dependencies, technological complexity, etc.), specific rules implicitly used in existing practices are defined for readjusting some THR values. SIL allocation process based on apportioned and validated THR values is finally illustrated through the example of “emergency brake” subsystems. Some specific SIL allocation rules are also defined and illustrated.     

Elevator planning with stochastic multicriteria acceptability analysis

Modern elevator systems in high-rise buildings consist of groups of elevators with centralized control. The goal in elevator planning is to configure a suitable elevator group to be built. The elevator group must satisfy specific minimum requirements for a number of standard performance criteria. In addition, it is desirable to optimize the configuration in terms of other criteria related to the performance, economy and service level of the elevator group. Different stakeholders involved in the planning phase emphasize different criteria. Most of the criteria measurements are by nature uncertain. Some criteria can be estimated by using analytical models, while others, especially those related to the service level in different traffic patterns, require simulations.     

Pricing,Allocation, and Overbooking in Dynamic Service Network Competition When Demand Is Uncertain

We study the problem of combined pricing, resource allocation, and overbooking by service providers involved in dynamic noncooperative oligopolistic competition on a network that represents the relationships of the providers to one another and to their customers when service demand is uncertain. We propose, analyze, and compute solutions for a model that is more general than other models reported in the revenue management literature to date. In particular, previous models typically consider only three or four of five key revenue management features that we have purposely built into our model: (1) pricing, (2) resource allocation, (3) dynamic competition, (4) an explicit network, and (5) uncertain demand. Illustrative realizations of the abstract problem we study are those of airline revenue management and service provision by companies facing resource constraints. Under fairly general regularity conditions, we prove existence and uniqueness of a pure strategy Nash equilibrium for dynamic oligopolistic service network competition described by our model. We also show, for an appropriate notion of regularity, that competition leads to the underpricing of network services, a finding numerically illustrated by an example of intermediate size. Our proposed algorithm can be implemented using well‐known off‐the‐shelf commercial software.     

Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution

We consider cooperatives games (TU-games) enriched by a system of a priori unions and a communication forest graph which are independent from each other. These two structures reflect the limitations of cooperation possibilities. In this framework, we introduce four Owen-type allocation rules, which are defined by a two-step application of an allocation rule à la Owen (in: Henn R, Moeschlin O (eds) Essays in mathematical economics and game theory, Springer, Berlin, 1977) to TU-games with a priori unions where the TU-game is replaced by Myerson’s (Math Oper Res 2:225–229, 1977) graph-restricted TU-game. The four possibilities arise by applying, at each step, either the Myerson value (Myerson 1977) or the average tree solution (Herings et al. in Games Econ Behav 62:77–92, 2008). Our main result offers comparable axiomatizations of these four allocation rules.

     

Stage efficiency evaluation in a two-stage network data envelopment analysis model with weight priority

Conventional DEA models treat the entire production system as a black box and ignore its internal structures. To address this issue, many studies have examined the DEA efficiencies of two-stage systems in which all outputs of the first stage are the only inputs to the second stage. Based on game theory, the non-cooperative model and centralized model were developed for such a two-stage network structure. However, for the centralized model with multiple optimal solutions and the non-cooperative model, an assumption is required as to whether the first or second stage should be assigned the absolute priority for optimization. In many cases, certain circumstances might exist in which one stage does not completely dominate the other stage. In this paper, we develop a methodology for assessing the overall and stage efficiencies by considering the different and DMU-specific degree of priority given to the stages. Particularly, the non-cooperative model and the centralized model can be deemed as special cases. Moreover, we compare the proposed approaches with the existing approaches, which indicates that our approaches can greatly reduce the computational burden. Two empirical examples are used to demonstrate the proposed approach.     

基于突变的项目组合共享资源竞争拥挤研究

对于以项目方式进行管理或生产的企业来说,共享资源在多项目、特别是项目组合(project portfolio,PP)中的合理配置是企业运营所需要解决的重要问题,对企业实现可持续发展起着关键的支撑作用。本文将突变理论引入项目组合管理问题中,在类比交通系统中车辆对交通资源竞争的基础上,提出了项目组合系统共享资源竞争拥挤概念,并对其基础变量进行了详细分析;其次,本文分析了项目组合共享资源竞争拥挤势函数和竞争稳定性,构建了以系统效率最大化为决策目标的项目组合共享资源竞争拥挤模型;最后,通过HD集团的案例分析对项目组合共享资源竞争拥挤模型的可实践性进行了验证,并以此为基础,针对项目组合管理提出了共享资源的改进管理方案。     

不同货架空间分配顺序下农产品供应链优化问题研究

货架是超市和生鲜便利店的重要资源，不仅具有储存和展示农产品的功能，同时货架空间大小对农产品的销量具有重要影响。针对产品需求受货架空间与零售价格共同影响的两级农产品供应链，在考虑供应商主导和零售商主导的情况下，分别对零售商在销售季节来临前和来临后分配货架空间四种分散式农产品供应链的最优决策与利润进行了分析，并与一体化供应链的最优决策进行了比较。研究发现，不论是在供应商主导还是在零售商主导的农产品供应链中，零售商在销售季节来临前分配货架空间，相比在销售季节来临后分配货架空间，农产品的批发价格与零售价格更高，分配的货架空间更小，供应商和零售商均获得更少的利润，相应的农产品供应链整体利润更少。因此，零售商在销售季节来临后分配货架空间对农产品供应链更有利。相比一体化供应链，分散式供应链的零售价格更高，分配的货架空间更小，供应链整体利润小于一体化供应链的最优利润，本文给出了基于利润共享与成本共担的合同对分散式供应链进行协调。最后，通过数值算例研究了参数变化对最优决策和供应链利润的影响。