Vassilis S. Kouikoglou

On the monotonicity of hierarchical sum--product fuzzy systems

Abstract Motivated by the authors’ previous work on the control of queueing systems, the assessment of sustainable development, and the measurement of material recyclability, this paper provides sufficient conditions on the parameters of hierarchical fuzzy systems under which the output of the system is monotonic with respect to its inputs. This property could be useful in designing multistage fuzzy inference systems and fuzzy controllers.

Trace bounds on the covariances of continuous-time systems with multiplicative noise

Matrix equations such as AP+PA/sup T/+FPF/sup T/+ Omega =0 and AQ+QA/sup T/+-QVQ+FPF/sup T/+ Omega =0, which arise in the estimation problem of systems with both additive and multiplicative noise, are treated. Trace bounds on the steady-state and error covariances P and Q are established, under complete and incomplete noise information. An example illustrates the usefulness of these bounds in determining the size of the estimation error. >

Sustainability Assessment of Nations and Related Decision Making Using Fuzzy Logic

This paper refines and extends in fundamental ways an existing model for the numerical assessment of sustainability called sustainability assessment by fuzzy evaluation (SAFE). SAFE, in its basic form, uses fuzzy logic to combine a large suite of basic indicators and then computes numerical values of sustainability for a number of composite indicators such as air, land, economy, health, etc. At a higher hierarchy it computes the sustainability of an ecological and a human component, and finally, it computes overall sustainability of a country or region. As state-of-the-art in fuzzy analysis has advanced, we are prompted to modify SAFE accordingly. The refined model uses the so-called Takagi-Sugeno-Kang inference scheme (TSK) which together with a few technical requirements guarantees monotonicity, i.e., an improvement of a basic indicator leads to an improvement of sustainability. Another refinement concerns the data inputs. To include the effects of past environmental pressures and development policies on the present state of sustainability, we use exponential smoothing to take account of the past with exponentially decaying weights. Finally, the model is now applied to all countries of the world for which data could be obtained and their corresponding sustainabilities are computed. Also, through sensitivity analysis, the most important indicators that affect sustainability are identified.

Discrete event modeling and optimization of unreliable production lines with random rates

We consider a serial production system with unreliable machines maintained by a limited number of repairmen, and finite storage between machines. Processing times may be random variables with exponential or gamma distributions, or deterministic. We develop a continuous-flow model for such a system utilizing simulation and analysis. Random processing times are approximated by sums of deterministic variables using a simple probabilistic technique. The model observes a limited number of events which are sufficient to determine system performance and mean buffer levels. By appropriately reducing the rates of starved and blocked machines and using analysis to compute the times of next event at each machine and buffer, discrete part computations are avoided. It is demonstrated that this approximate model is highly accurate and faster by a factor of 3 or more when compared to conventional simulators. The paper addresses also optimal repair allocation to maximize the expected throughput of the system. Two different approaches are proposed: perturbation analysis and experimental evaluation of various nonpreemptive rules for assigning a repairman to failed machines. >

A Review of Sustainability Assessment Models as System of Systems

Many people believe that our society is at the crossroads today because of societal and environmental problems of scales ranging from the local to the global. Such problems as global warming, species extinction, overpopulation, poverty, drought, to name but a few, raise questions about the degree of sustainability of our society. To answer sustainability questions, one has to know the meaning of the concept and possess mechanisms to measure it. In this paper, we examine a number of approaches in the literature that do just that. Our focus is on analytical quantitative approaches. Since no universally accepted definition and measuring techniques exist, different approaches lead to different assessments. Despite such shortcomings, rough ideas and estimates about the sustainability of countries or regions can be obtained. One common characteristic of the models herein is their hierarchical nature that provides sustainability assessments for countries in a holistic way. Such models fall in the category of system of systems. Some of these models can be used to assess corporate sustainability.

An exact discrete-event model and control policies for production lines with buffers

The authors present a hybrid simulation/analytic model for the analysis and design of unreliable production lines with buffers and discrete workparts. The model is exact and much faster than conventional piece-by-piece simulators. It can analyze, efficiently and accurately, lines of any size during either transient or steady-state periods by taking into account effectively all transients associated with the function of the line. It is demonstrated that the model is superior to both brute-force and event-driven models and is an efficient practical tool in the analysis and design of production lines. By incorporating the perturbation analysis technique into the proposed algorithm. the gradient estimation of the systems throughput can be performed during a single simulation run for various design parameters. A number of experimental results are reported for the repair allocation problem, and the optimality of various control policies is investigated. >

A continuous-flow model for production networks with finite buffers, unreliable machines, and multiple products

This paper presents a flow approximation of production networks with finite buffers and unreliable machines. Parts of various types compete for service before a machine, or they may be assembled before service to yield a composite part. Up times and down times of machines have arbitrary but known distributions and service times have gamma distributions, or may be constant quantities. Random service times are approximated by piece wise deterministic variables. Acyclic networks are considered first. The model is a combination of discrete-event simulation and analysis. The simulator keeps track of the buffer and machine states. Between two consecutive state transitions, flow rates remain constant and the model calculates the cumulative flow of each part type. Compared to a conventional simulator, the model is superior in speed and very accurate. An alternative model is developed for nonacyclic production networks where each machine provides service to different parts repetitively. The model is employed to si...

Analysis of Admission and Inventory Control Policies for Production Networks

Problems of inventory control and customer admission control are considered for a manufacturing system that produces one product to meet random demand. Four admission policies are investigated: lost sales, complete backordering, randomized admission, and partial backordering. These policies are combined with an integral inventory control policy, which releases raw items only when an incoming order is accepted and keeps the inventory position (total inventory minus outstanding orders) constant. The objective is to determine the inventory level and the maximum number of backorders, as well as the admission probability that maximize the mean profit rate of the system. The system is modeled as a closed queueing network and its performance is computed analytically. The optimal parameters for each policy are found using exhaustive search and convex analysis. Numerical results show that managing inventory levels and sales jointly through partial backordering achieves higher profit than other control policies.

An efficient discrete event model of assembly/disassembly production networks

This paper develops a discrete event simulation model of assembly/disassembly (AD) production networks with finite buffers and unreliable machines. The model is an extension of a previous continuous flow model, which simulates the system only when a machines production rate is altered. The events causing changes in the production rates are: a machine fails or is repaired and a buffer becomes full, empty, not full, or not empty. During operation between two events the system runs deterministically. Thus, given the state of the system (machine cumulative production, buffer levels and their statistics) at the time of occurrence of some event, the corresponding state variables upon the occurrence of the next event can be updated using analysis. The proposed model does not use repair, not-full, and not-empty events. This is achieved by considering the machine downtimes as transient times in which no parts are produced and by developing more complex state equations. Numerical results show that the model combines speed and accuracy.

Hybrid simulation models of production networks

1. Introduction.- 2. Fundamentals of Simulation Modeling.- 3. Two-Machine Systems.- 4. Production Lines.- 5. Production Networks.- 6. Optimization.- 7. Closure.- References.- Appendix A: Statistical Tables.