Markov models of occupational mobility: Theoretical development and empirical support. Part 1: Careers†

This paper, consisting of two parts, presents an analysis of the current state of Markov model , building for intragenerational occupational mobility. Part One examines theories of careers and Part Two theories of continuously operative job systems. Stress is given to the empirical support of the models and to the cumulative development of theory. Among the paper's findings are that several models proposed to span both occupational and geographical mobility have used only migration data; that analytic development is more cumulative for career models; and that there exists a basic divergence of findings from tests of models of careers and continuously operative job systems. In Part One we focus on individual behavior or subaggregates (cohorts).     

Vibrations of Elastic Strings: Mathematical Aspects, Part One

This paper is divided into two parts. Part One Chapter 1 contains the deduction of the model for vertical vibrations of elastic strings with moving ends and its relations to the models of d'Alembert and Kirchhoff-Carrier. Chapter 2 contains the results of investigations related to Kirchhoff-Carrier model during the last twenty years and an almost complete bibliography.Part Two Chapter 3 of the paper is dedicated to the model with moving ends. It contains new results obtained by the authors during the last five years.     

A bivariate duration model for job mobility of two-earner households

In recent years we have observed an increasing interest in the job mobility patterns of employed persons. A new issue in this context is the mutual dependence of job mobility choice of workers who belong to the same household. In the present paper, we focus on bivariate duration models of stock sampled data in which dependence is induced through mixing. We apply the estimation method on the basis of an empirical study on the mutual dependence of job mobility of workers belonging to a two-earner household in the Netherlands. An interesting empirical result is that the marginal willingness to pay for a reduction in commuting time in a two-wage earner household is higher than that usually found for single-earner workers.     

Processing-plus-wait due dates in single-machine scheduling

We study the problem of schedulingn jobs on a single machine. Each job is assigned a processing-plus-wait due date, which is an affine-linear function of its processing time. The objective is to minimize the symmetric earliness and tardiness costs. We analyze a combined decision model which includes computing both the optimal job sequence and optimal due date parameters. For the quadratic objective function, we propose a heuristic solution based on a bicriterion approach. Additionally, we provide computational results to compare this model with two simpler models. For the maximum objective function, we show that it is efficiently solved by the shortest processing time sequence.Part of this research was undertaken during a visit of the first author at the University of Manitobe, Canada in 1991. This visit was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant OPG0036424. The numerical results were obtained with the assistance of T. P. Lindenthal. The authors are thankful for his help.     

Comparing two queueing models for nonhomogeneous nonreliable terminal systems

This paper deals with two nonhomogeneous queueing models to describe the performance of finite, multiterminal systems subject to random breakdowns. The difference between the two models is relatively small, but we will see that the differences between some system performance characteristics are very large (100% or more). The other contribution of this paper is to introduce some new terminologies to queueing theory, which are necessary for the second model. All random variables involved here are independent and exponentially distributed. The models described here are generalizations of the homogeneous model treated earlier by different authors. At the end of this paper some numerical results illustrate the problem in question. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.     

Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations

This two-part paper deals with ??foundational?? issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.     

On the use of fuzzy inference techniques in assessment models: part II: industrial applications

In this paper, we study the applicability of the monotone output property and the output resolution property in fuzzy assessment models to two industrial Failure Mode and Effect Analysis (FMEA) problems. First, the effectiveness of the monotone output property in a single-input fuzzy assessment model is demonstrated with a proposed fuzzy occurrence model. Then, the usefulness of the two properties to a multi-input fuzzy assessment model, i.e., the Bowles fuzzy Risk Priority Number (RPN) model, is assessed. The experimental results indicate that both the fuzzy occurrence model and Bowles fuzzy RPN model are able to fulfill the monotone output property, with the derived conditions (in Part I) satisfied. In addition, the proposed rule refinement technique is able to improve the output resolution property of the Bowles fuzzy RPN model.     

Configurable node density generation with application to hotspot modelling

Mobility models are very relevant mainly when studying the performance of wireless systems by means of computer simulations. The main problem arises when deciding the best mobility model for a particular application. In some cases, it is very important to emulate hotspots or, in general, zones with different user (or node) densities. Current models do not allow complete control over hotspots, or in other words, they do not allow any general node density to be defined in the simulation area. Usually, when hotspots are modelled, closed zones are created with different numbers of users in each area, thus ensuring a fixed node density in each area. However, this approach results in an unfair comparison among users since they cannot move across zones.This paper proposes a new mechanism to solve these drawbacks. Using this mechanism, any general node density can be emulated allowing nodes to move around the entire simulation area. Any mobility model can be applied together with this density control mechanism, provided that the mobility model ensures a uniform node distribution.     

Approximation schemes for parallel machine scheduling with availability constraints

We investigate the problems of scheduling n weighted jobs to m parallel machines with availability constraints. We consider two different models of availability constraints: the preventive model, in which the unavailability is due to preventive machine maintenance, and the fixed job model, in which the unavailability is due to a priori assignment of some of the n jobs to certain machines at certain times. Both models have applications such as turnaround scheduling or overlay computing. In both models, the objective is to minimize the total weighted completion time. We assume that m is a constant, and that the jobs are non-resumable.For the preventive model, it has been shown that there is no approximation algorithm if all machines have unavailable intervals even if w_i=p_i for all jobs. In this paper, we assume that there is one machine that is permanently available and that the processing time of each job is equal to its weight for all jobs. We develop the first polynomial-time approximation scheme (PTAS) when there is a constant number of unavailable intervals. One main feature of our algorithm is that the classification of large and small jobs is with respect to each individual interval, and thus not fixed. This classification allows us (1) to enumerate the assignments of large jobs efficiently; and (2) to move small jobs around without increasing the objective value too much, and thus derive our PTAS. Next, we show that there is no fully polynomial-time approximation scheme (FPTAS) in this case unless P=NP.For the fixed job model, it has been shown that if job weights are arbitrary then there is no constant approximation for a single machine with 2 fixed jobs or for two machines with one fixed job on each machine, unless P=NP. In this paper, we assume that the weight of a job is the same as its processing time for all jobs. We show that the PTAS for the preventive model can be extended to solve this problem when the number of fixed jobs and the number of machines are both constants.     

Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ‘position-based learning’ in which the actual processing time of a job is a non-increasing function of its position to be processed. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases. Motivated by this observation, we propose two truncated learning models in single-machine scheduling problems and two-machine flowshop scheduling problems with ordered job processing times, respectively, where the actual processing time of a job is a function of its position and a control parameter. Under the proposed learning models, we show that some scheduling problems can be solved in polynomial time. In addition, we further analyse the worst-case error bounds for the problems to minimize the total weighted completion time, discounted total weighted completion time and maximum lateness.     

Structural properties of the optimal resource allocation policy for single-queue systems

This paper studies structural properties of the optimal resource allocation policy for single-queue systems. Jobs arrive at a service facility and are sent one by one to a pool of computing resources for parallel processing. The facility poses a constraint on the maximum expected sojourn time of a job. A central decision maker allocates the servers dynamically to the facility. We consider two models: a limited resource allocation model, where the allocation of resources can only be changed at the start of a new service, and a fully flexible allocation model, where the allocation of resources can also change during a service period. In these two models, the objective is to minimize the average utilization costs whilst satisfying the time constraint. To this end, we cast these optimization problems as Markov decision problems and derive structural properties of the relative value function. We show via dynamic programming that (1) the optimal allocation policy has a work-conservation property, and (2) the optimal number of servers follows a step function with as extreme policy the bang-bang control policy. Moreover, (3) we provide conditions under which the bang-bang control policy takes place. These properties give a full characterization of the optimal policy, which are illustrated by numerical experiments.     

Multicriteria order acceptance decision support in over-demanded job shops: A neural network approach

Order acceptance is an important issue in job shop production systems where demand exceeds capacity. In this paper, a neural network approach is developed for order acceptance decision support in job shops with machine and manpower capacity constraints. First, the order acceptance decision problem is formulated as a sequential multiple criteria decision problem. Then a neural network based preference model for order prioritization is described. The neural network based preference model is trained using preferential data derived from pairwise comparisons of a number of representative orders. An order acceptance decision rule based on the preference model is proposed. Finally, a numerical example is discussed to illustrate the use of the proposed neural network approach. The proposed neural network approach is shown to be a viable method for multicriteria order acceptance decision support in over-demanded job shops.     

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.     

Scheduling controllable processing time jobs in a deteriorating environment

In many real-life applications, job processing times are a function of the waiting time prior to their execution. In the most general setting, each job comprises of a basic processing time, which is independent of its start time, and a start time-dependent deterioration function. Some common examples of deteriorating systems include fire fighting, pollution containment, and medical treatments. To date, research has focused on scheduling models where the basic processing time of jobs is constant. However, job processing times are often controllable through the allocation of a limited non-renewable resource. We study a single-machine setting that combines these two models under the assumptions of general linear deterioration and convex resource functions. We develop a polynomial time solution for minimizing the makespan. For the total flowtime criterion, we compute the optimal resource allocation policy for a given job instance and show that the sequencing problem is at least as hard as the case with non-controllable jobs. We follow by discussing the properties of several special cases.     

Scheduling job families on non-identical parallel machines with time constraints

This paper studies the scheduling of lots (jobs) of different product types (job family) on parallel machines, where not all machines are able to process all job families (non-identical machines). A special time constraint, associated to each job family, should be satisfied for a machine to remain qualified for processing a job family. This constraint imposes that the time between the executions of two consecutive jobs of the same family on a qualified machine must not exceed the time threshold of the family. Otherwise, the machine becomes disqualified. This problem comes from semiconductor manufacturing, when Advanced Process Control constraints are considered in scheduling problems. To solve this problem, two Mixed Integer Linear Programming models are proposed that use different types of variables. Numerical experiments show that the second model is much more effective, and that there is a trade-off between optimizing the scheduling objective and maximizing the number of machines that remain qualified for the job families. Two heuristics are also presented and studied in the numerical experiments.     

Operational research and critical systems thinking—an integrated perspective

On the basis of a review of the role of systems thinking in the history of OR, Part 1 of this essay proposed a systematic understanding of OR as applied systems thinking. Further, it identified the contribution of ‘critical’ systems thinking (CST) in a combined ability of its two strands, critical systems heuristics (CSH) and total systems intervention (TSI), to enhance the conceptual sophistication of OR. Part 2 aims to translate this understanding into a framework for good professional practice. How exactly can CST strengthen the competence profile of OR professionals? Drawing on three experience-based archetypes of professional service and some basic argumentation-theoretical considerations, a new understanding of OR and applied systems thinking as argumentative practice emerges. In this new understanding CST finds a systematic place and some exemplary uses of CSH and TSI can be located—an integrated perspective.     

New approaches to due date assignment in job shops

In this study, two new approaches for due date assignment in job shops are evaluated. Proposed approaches use statistical prediction techniques for dynamic prediction of job flowtimes in a job shop environment as the job arrives to the shop floor. Primary objective of this research is to compare the performance of the proposed due date assignment model (PDDAM) with several conventional due date assignment models (CDDAM). For this purpose, simulation models are developed and comparisons of the PDDAM and CDDAM are made in terms of the mean absolute percent error (MAPE), mean percent error (MPE) and mean tardiness (MT). Simulation experiments showed that for many test conditions, PDDAM dominates CDDAM. Therefore, case by case findings are summarized in the paper.     

Operational Decisions in AGV-Served Flowshop Loops: Scheduling

This paper considers operational issues that arise in repetitive manufacturing systems served by automated guided vehicles (AGVs) in loops with unidirectional material flow. The objective considered is the minimization of the steady state cycle time required to produce a minimal job set (or equivalently, throughput rate maximization). Our models allow for delays caused by AGV conflicts. We define and analyze three nondominated and widely used AGV dispatching policies. For each policy, we describe algorithms and intractability results for combined job scheduling and material handling problems. We describe a genetic algorithm that estimates the cycle time within 5% on average for instances with up to 10 machines and four AGVs. Some related fleet sizing and loop decomposition issues are discussed in the companion paper [19].     

FLOODING ON THE EEL RIVER: SYSTEM THEORETIC TIME SERIES,TRANSFER FUNCTION TIME SERIES,AND STRUCTURAL MODEL FORECASTS

Three models are developed to forecast precipitation, stream flow, and suspended sediment load for the Middle Fork Eel River basin near Dos Rios, California. The models are a structural model, a transfer function time series model, and a multivariate time series model based on the ideas of linear systems theory. Monthly observations from 1961 through 1970 were used to specify and estimate the models, and their performance was evaluated using 36 observations from 1971 through 1973. The comparisons show that all of the models are able to simulate the general trend of the data fairly well but that the two time series models capture the detail better. The system theoretic time series model fares the best, providing consistently better forecasts of all three series. We conclude that this model would be valuable for use in planning water supply systems in the Eel River basin.