Regression Estimation in Simulation

In simulation an input variable like interarrival time is sampled, and hence its average deviates from its known expectation. This information can be used to improve the estimated simulation response: regression sampling or control variate technique. The usual crude estimator is shown to be biased. If local linearity holds, then the regression estimator becomes unbiased. Moreover its variance becomes smaller under mild conditions. The assumption of local linearity is an alternative to the normality assumption of other authors. This paper further emphasizes the difference between results ex ante (unconditional) and ex post (given the experimental input values). A telephone-exchange simulation provides a case study.     

A method for analysing operational complexity in supply chains

This paper proposes a method for analysing the operational complexity in supply chains by using an entropic measure based on information theory. The proposed approach estimates the operational complexity at each stage of the supply chain and analyses the changes between stages. In this paper a stage is identified by the exchange of data and/or material. Through analysis the method identifies the stages where the operational complexity is both generated and propagated (exported, imported, generated or absorbed). Central to the method is the identification of a reference point within the supply chain. This is where the operational complexity is at a local minimum along the data transfer stages. Such a point can be thought of as a ‘sink’ for turbulence generated in the supply chain. Where it exists, it has the merit of stabilising the supply chain by attenuating uncertainty. However, the location of the reference point is also a matter of choice. If the preferred location is other than the current one, this is a trigger for management action. The analysis can help decide appropriate remedial action. More generally, the approach can assist logistics management by highlighting problem areas. An industrial application is presented to demonstrate the applicability of the method.     

Centralized resource allocation DEA models based on revenue efficiency under limited information

In this paper, we extend the centralized DEA models by Lozano et al (2011) to allocate resources based on revenue efficiency across a set of DMUs under a centralized decision-making environment. The aim is to allocate resources so as to maximize the total output revenue produced by all the DMUs under limited information. To uncover the sources of total revenue increase from the centralized resource allocation model, we further decompose the aggregate revenue efficiency into three components: the aggregate output-oriented technical efficiency, the aggregate output allocative efficiency and the aggregate revenue re-allocative efficiency. Finally, two empirical data sets are presented to show that our proposed approach is not only an efficient tool to allocate the resources among the DMUs based on the revenue efficiency but additionally provides the central DM with guidance on how to identify the weak areas where more effort should be devoted to improve the total outputs.     

Stability and the immediate acceptance rule when school priorities are weak

In a model of school choice, we allow school priorities to be weak and study the preference revelation game induced by the immediate acceptance (IA) rule (also known as the Boston rule), or the IA game. When school priorities can be weak and matches probabilistic, three stability notions—ex post stability, ex ante stability, and strong ex ante stability—and two ordinal equilibrium notions—sd equilibrium and strong sd equilibrium—become available (“sd” stands for stochastic dominance). We show that for no combination of stability and equilibrium notions does the set of stable matches coincide with the set of equilibrium matches of the IA game. This stands in contrast with the existing result that the two sets are equal when priorities are strict. We also show that in the presence of weak priorities, the transition from the IA rule to the deferred acceptance rule may, in fact, harm some students.     

供应链企业社会责任治理决策研究——基于SD-演化博弈分析法

采用演化博弈模型和系统动力学相结合的方法探讨不同治理措施情景下的供应链企业社会责任决策问题,并进行了仿真分析。结果表明,供应链各环节企业决策之间存在着相互影响作用;当制造商和零售商有一方具有较高的履行企业社会责任意识,另一方具有较低的履行意识时,具有较高意识的一方无论有无激励措施,最终都会趋于履行企业社会责任,而较低一方选择不履行决策,除非有力度较大的激励措施出现;当二者以中性态度对企业社会责任的履行进行决策时,激励措施的实施对制造商更有效;制造商相对于零售商履行企业社会责任,对消费者偏好所带来的市场效应更加依赖;政府补贴在短期内是较为有效的激励方式;惩罚力度越强,激励作用越好,持续时间越久;若两种激励措施搭配使用,可以更好地发挥激励作用。     

An incentive charging scheme for video-on-demand

Video-on-demand (VOD) systems can provide either an individual service or batch service. For individual service, a user can receive video immediately after making a request and he/she can perform interactive operations (such as pause, jump, fast forward and rewind), and the system uses one video stream to serve one user. For batch service, a user has to wait after making a request and cannot perform interactive operations, but the system can use one video stream to serve a batch of users. Therefore, individual service has a better quality while batch service requires less resources to serve each user. In this paper, we consider a VOD system providing both services and propose an incentive charging scheme to optimize the coexistence of both services. This scheme imposes a lower service charge on batch service in order to attract users to choose this service. Consequently, the service provider can get more revenue by serving more concurrent users via batch service and users can choose their preferred services. We analyze the incentive charging scheme and maximize the mean revenue subject to a given availability specification. The numerical results show that the incentive charging scheme is particularly effective in peak hours when the demand for the VOD service is large.     

A Minimum-Cost Analysts Assignment Model for Asset Evaluation of Insolvent Saving and Loan Institutions

Audit staff planning has been a challenging problem for accounting, auditing and real estate firms. This paper presents a mathematical model and a solution methodology for determining the minimum-cost analysts assignment, when analysts should travel from geographically dispersed locations to evaluate assets of an insolvent Saving and Loan institution. Computational experiments with the solution algorithm on 27 randomly generated projects show (a) that the solution methodology efficiently generates an optimal solution, and (b) provides the decision maker with alternative next best plans through ex post sensitivity analysis. Although specific, variations of the model and algorithm presented here can be applied to a variety of audit staff assignment problems in accounting and real estate firms.     

Division algebras of prime degree with infinite genus

The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D′] ∈ Br(F), where D′ is a central division F-algebra having the same maximal subfields as D. For any prime p, we construct a division algebra of degree p with infinite genus. Moreover, we show that there exists a field K such that there are infinitely many nonisomorphic central division K-algebras of degree p and any two such algebras have the same genus.     

Operational complexity and supplier–customer integration: case study insights and complexity rebound

The main contribution of this paper is the demonstration that, contrary to conventional thinking, a measurable increase in the operational complexity of the production scheduling function between two companies can occur following closer supply chain integration. The paper presents the practical application of previous work carried out and validated by the authors in terms of (a) methodology for measuring operational complexity, (b) predicted implications of Supplier–Customer integration and (c) derivation of an operational complexity measure applied to before and after Supplier–Customer integration. This application is illustrated via a longitudinal case study. The analysis is based on information theory, whereby operational complexity of a Supplier–Customer system is defined as the amount of information required to describe the state of this system. The results show that operational complexity can increase when companies decide to integrate more closely, which is a fact likely to be overlooked when making decisions to pursue closer Supply-Chain integration. In this study, operational complexity increases due to reduced buffering arising from reduction in the Supplier's inventory capacity. The Customer did not change their operational practices to improve their schedule adherence post-integration, and, consequently, suffered an increase in complexity due to complexity rebound. Both the Supplier's and Customer's decision-making processes after the case study reported in this paper were enhanced by being able to quantify the complex areas to prioritise and direct managerial efforts towards them, through the use of the operational complexity measure. Future work could extend this study (in the ‘low product customisation’ and ‘low product value impact’ quadrant) to investigate Supplier–Customer integration in other quadrants resulting from further combinations between ‘product customisation’ and ‘product value impact’ levels.     

Operational Research for Strategic Decision-Making: The Role of World-View

Standard Operational Research analysis of the problem is of limited value to those making complex strategic decisions for which adequate modelling is rarely possible. It may be more helpful to provide models which make explicit the decision-making process. These could enable the decision-maker to be more aware of possible dangers leading to less preferred outcomes. As a demonstration, a dynamic systems model is developed and used to investigate the decision-making of the Kennedy Administration during the Cuban Missile Crisis. Conclusions from this, and several case studies by other authors, emphasize the great importance of the world-view of the decision-making group in determining their actions.     

Measuring consensus in decision making: an application to maritime command and control

An important component of maritime command and control is the information that has value to Royal Navy commanders in making campaign decisions. Studies aimed at identifying information requirements generally do so in a wargame context with several test subjects assuming command roles. An important adjunct to this work then is the assessment of how closely the subjects agree that the proposed information set is indeed valuable. In this paper, we focus on assessing the degree to which the test subjects participating in a MoD sponsored maritime command and control study agreed to a proposed set of information elements deemed valuable to taking combat decisions. The methodology involves the simulation of naval combat. The participants (former Royal Navy Captains and Admirals) are asked to choose a course of action that best accomplishes a stated mission. Information is provided on request. Each pair of participants is characterized by its set of information requirements. The objectives are (1) to define an overall information set that minimizes disagreement among the participants in some way; and (2) to develop a metric that assesses the amount of disagreement among the participants. Two metrics are presented: a mean consensus and a median consensus.     

Properly discontinuous group actions on affine homogeneous spaces

Let G be a real algebraic group, H ≤ G an algebraic subgroup containing a maximal reductive subgroup of G, and Γ a subgroup of G acting on G/H by left translations. We conjecture that Γ is virtually solvable provided its action on G/H is properly discontinuous and ΓG/H is compact, and we confirm this conjecture when G does not contain simple algebraic subgroups of rank ≥2. If the action of Γ on G/H (which is isomorphic to an affine linear space Aⁿ) is linear, our conjecture coincides with the Auslander conjecture. We prove the Auslander conjecture for n ≤ 5.     

Weakly mixing property and chaos

In this paper, we define and study strong Kato chaos for a group action on a compact metric space. Let X be a compact metric space without isolated points, and let G be a topologically commutative group on X. If the dynamical system (X, G) is weakly mixing, then it is chaotic in the strong sense of Kato.     

Controlled Envelopment by Face Extension in DEA

Data Envelopment Analysis (DEA) is an approach to assess the relative efficiency of organizations using multiple inputs to produce multiple outputs. This assessment is made from the standpoint most favourable to each organization. If an organization is not well enveloped, in the sense that it is not comparable to a sufficient number of other organizations (called referents), DEA may understate inefficiency. A lower bound on the efficiency measure may be obtained by requiring that the organization being evaluated be compared with at least k non-redundant referents. For any feasible choice of k, the procedure proposed here selects the most favourable set of referents, and guarantees a greatest lower bound on the efficiency measure, thus usefully complementing the information provided by conventional DEA.     

Polycyclic groups admitting a regular automorphism of order four

Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g~φ= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C_G(α~2) and G/[G, α~2] are both abelian-by-finite.     

On Analyses of the Solution to a Linear Programming Problem

Many complex problem situations in various contexts have been represented in recent years by the linear programming model. The simplex method can then be used to give the optimal values of the variables corresponding to a given set of values of the parameters. However, in many situations it is useful to have the solution to many other related problems which differ from the original problem only in the values of some of the parameters. This paper presents procedures by which the solutions to the changed problems can be derived from the simplex solution tableau corresponding to the original problem. The method will be illustrated by means of an example problem, and it will be shown how quantitative information obtained from such analyses can aid management in decision making.     

<Emphasis Type="Italic">IFPBM</Emphasis>s and their application to multiple attribute group decision making

The Bonferroni mean (BM) had been generalized for its capacity to capture the interrelationship between input arguments. In order to obtain much more information in the process of group decision making, especially in the cases that the relationships between the fused data are considered, this paper combines the power average operator with the intuitionistic fuzzy Bonferroni mean (IFBM) and develops the intuitionistic fuzzy power Bonferroni mean (IFPBM) and the weighted intuitionistic fuzzy power Bonferroni mean (WIFPBM). We investigate the desirable properties of these new extensions of BM and discuss their special cases. We give a comparison of the new extensions of BM with the corresponding existing IFBMs. Furthermore, the detailed steps of multiple attribute group decision making with the presented IFPBM or WIFPBM are given and numerical examples are illustrated to show the validity and feasibility of the new approaches.     

On some generalizations of theorems by Landau and Pólya

If F(s), the Mellin transform ?(x) (real valued), satisfies certain regularity conditions and if its behaviour on the abscissa of convergence is known, then theorems of Landau and Pólya give information concerning sign changes of ?(x). In the present paper, corresponding conclusions are obtained when F(s) does not satisfy the regularity conditions of the theorems of Landau Pólya.     

Division closed partially ordered rings

Fuchs called a partially-ordered integral domain, say D, division closed if it has the property that whenever a > 0 and ab > 0, then b > 0. He showed that if D is a lattice-ordered division closed field, then D is totally ordered. In fact, it is known that for a lattice-ordered division ring, the following three conditions are equivalent: a) squares are positive, b) the order is total, and c) the ring is division closed. In the present article, our aim is to study \({\ell}\)-rings that possibly possess zerodivisors and focus on a natural generalization of the property of being division closed, what we call regular division closed. Our investigations lead us to the concept of a positive separating element in an \({\ell}\)-ring, which is related to the well-known concept of a positive d-element.     

Effects of Centralization on Expected Costs in a Multi-location Newsboy Problem

This is a single-period, single-product inventory model with several individual sources of demand. It is a multi-location problem with an opportunity for centralization. The holding and penalty cost functions at each location are assumed to be identical. Two types of inventory system are considered in this paper: the decentralized system and the centralized system. The decentralized system is a system in which a separate inventory is kept to satisfy the demand at each source of demand. The centralized system is a system in which all demands are satisfied from one central warehouse. This paper demonstrates that, for any probability distribution of a location's demands, the following properties are always true: given that the holding and penalty cost functions are identical at all locations, (1) if the holding and penalty cost functions are concave functions, then the expected holding and penalty costs in a decentralized system exceed those in a centralized system, except that (2) if the holding and penalty cost functions are linear functions, and for any i≠j, P_ij, the coefficient of correlation between the ith location's demand and the jth location's demand is equal to 1, then the expected holding and penalty costs in a decentralized system are equal to those in a centralized system.