Scatter search for trainees to software project requirements stable allocation

In this paper, we study a centralized, stable matching scheme, which allocates trainees to software project requirements, to minimize retraining and relocation costs when the preference lists of the project requirements may contain ties of arbitrary lengths. This particular trainees’ assignment problem is important because the allocation decisions not only influence the costs but also impact software project deliverables and intern attrition rates. It is also an NP-hard problem because of the inclusion of the ties, and the costs in the stable allocation model. We, therefore, have designed a GRASP-based scatter search method, to solve the large size instances of our assignment problem efficiently. The GRASP method uses randomized algorithms to generate initial trial solutions. A repair heuristic based on regret minimization idea is designed to convert an unstable solution to a stable solution during an improvement phase. Computational experiments suggest that the proposed algorithm significantly reduces run time compared to the CPLEX, and produces solutions that are at an average 4.5% away from the best CPLEX solutions for the large size problem instances. Moreover, our scatter search method consistently provides better quality solutions than the two state of the art methods from the prior literature.     

On the recoverable robust traveling salesman problem

We consider an uncertain traveling salesman problem, where distances between nodes are not known exactly, but may stem from an uncertainty set of possible scenarios. This uncertainty set is given as intervals with an additional bound on the number of distances that may deviate from their expected, nominal values. A recoverable robust model is proposed, that allows a tour to change a bounded number of edges once a scenario becomes known. As the model contains an exponential number of constraints and variables, an iterative algorithm is proposed, in which tours and scenarios are computed alternately. While this approach is able to find a provably optimal solution to the robust model, it also needs to solve increasingly complex subproblems. Therefore, we also consider heuristic solution procedures based on local search moves using a heuristic estimate of the actual objective function. In computational experiments, these approaches are compared.     

A robust algorithm for generalized geometric programming

Most existing methods of global optimization for generalized geometric programming (GGP) actually compute an approximate optimal solution of a linear or convex relaxation of the original problem. However, these approaches may sometimes provide an infeasible solution, or far from the true optimum. To overcome these limitations, a robust solution algorithm is proposed for global optimization of (GGP) problem. This algorithm guarantees adequately to obtain a robust optimal solution, which is feasible and close to the actual optimal solution, and is also stable under small perturbations of the constraints.     

The effects of splitting exponential stochastic Lanchester battles

The Exponential Stochastic Lanchester (ESL) model of attrition is well known and can be found in many combat models. This paper is concerned with exploring the effects of applying the ESL attrition model to battles which have been split into different arrangements of smaller engagements or fire fights. These fire fights were mainly resolved using a Markov chain formulation of the ESL model. Some interesting and non-intuitive trends were uncovered. It is shown that the ESL model predicts an increasing advantage for the defending side as a battle is split into a larger number of smaller parallel engagements.     

Designing a flexible approach for higher professional education by means of simulation modelling

Operational flexibility is a prerequisite for innovations in higher education. Educational programmes have an operational structure which restricts their flexibility. Design principles from the fields of operations management and instructional design were applied for the design of a flexible approach in educational programmes. In a case study, the curriculum and operational data from an institute for higher professional education in the Netherlands were used to develop a discrete-event simulation model, in order to demonstrate effects of operational changes on the flexibility of their educational programmes. Programme coordinators of the institute validated the model and considered it as a feasible solution for organizing their educational programmes, and as a contribution to educational innovation.     

A large deviation analysis of errors in measurement based admission control to buffered and bufferless resources

In measurement based admission control, measured traffic parameters are used to determine the maximum number of connections that can be admitted to a resource within a given quality constraint. The assumption that the measured parameters are the true ones can compromise admission control; measured parameters are random quantities, causing additional variability. This paper analyzes the impact of measurement error within the framework of Large Deviation theory. For a class of admission controls, large deviation principles are established for the number of admitted connections, and for the attained overflow rates. These are applied to admission to bufferless resources, and buffered resources in both the many sources and large buffer asymptotic. The sampling properties of effective bandwidths are presented, together with a discussion the impact of the temporal extent of individual samples on estimator variability. Sample correlations are shown to increase estimator variance; procedures to make admission control robust with respect to these are described.     

Regularized robust optimization: the optimal portfolio execution case

An uncertainty set is a crucial component in robust optimization. Unfortunately, it is often unclear how to specify it precisely. Thus it is important to study sensitivity of the robust solution to variations in the uncertainty set, and to develop a method which improves stability of the robust solution. In this paper, to address these issues, we focus on uncertainty in the price impact parameters in an optimal portfolio execution problem. We first illustrate that a small variation in the uncertainty set may result in a large change in the robust solution. We then propose a regularized robust optimization formulation which yields a solution with a better stability property than the classical robust solution. In this approach, the uncertainty set is regularized through a regularization constraint, defined by a linear matrix inequality using the Hessian of the objective function and a regularization parameter. The regularized robust solution is then more stable with respect to variation in the uncertainty set specification, in addition to being more robust to estimation errors in the price impact parameters. The regularized robust optimal execution strategy can be computed by an efficient method based on convex optimization. Improvement in the stability of the robust solution is analyzed. We also study implications of the regularization on the optimal execution strategy and its corresponding execution cost. Through the regularization parameter, one can adjust the level of conservatism of the robust solution.     

Solving network manpower problems with side constraints

A number of authors have used goal-programming to solve manpower problems. Some of these authors have also formulated goal-programming manpower models in a network so as to take advantage of the rapid codes now available for the solution of capacitated transportation problems. In this paper, a number of methods of dealing with side constraints (those not included in the network formulation) are explored. Of particular interest are constraints for dealing with attrition and for expressing budgetary restrictions.     

Retrial queue with discipline of adaptive permanent pooling

A novel customer service discipline for a single-server retrial queue is proposed and analysed. Arriving customers are accumulated in a pool of finite capacity. Customers arriving when the pool is full go into orbit and attempt to access the service later. It is assumed that customers access the service as a group. The size of the group is defined by the number of customers in the pool at the instant the service commences. All customers within a group finish receiving the service simultaneously. If the pool is full at the point the service finishes, a new service begins immediately and all customers from the pool begin to be served. Otherwise, the customer admission period starts. The duration of this period is random and depends on the number of customers in the pool when the admission period begins. However, if the pool becomes full before the admission period expires, this period is terminated and a new service begins. The system behaviour is described by a multi-dimensional Markov chain. The generator and the condition of ergodicity of this Markov chain are derived, and an algorithm for computing the stationary probability distribution of the states of the Markov chain is given. Formulas for computing various performance measures of the system are presented, and the results of numerical experiments show that these measures essentially depend on the capacity of the pool and the distribution of the duration of the admission period. The advantages of the proposed customer service discipline over the classical discipline and the discipline in which customers cannot enter the pool during the service period are illustrated numerically.     

Robust location of new housing developments using a choice model

We consider the issue of choosing a subset of locations to construct new housing developments maximizing the satisfaction of potential buyers, which has not been previously studied in the literature. The allocation of demands to the selected locations is modeled by a choice model, based on the distance to the location, real-estate prices and incomes. We study two robust counterparts of the optimal location problem, where uncertainty lies on demand volumes for the first one, and on customer preferences for the second one. In both cases, the parameters subject to uncertainty appear both in the objective function and constraints. The second robust model combines a scenario-based approach with nominal, price-centric and distance-centric scenarios on customers preferences, and an uncertainty budget approach that limits the number of customers that can deviate from the nominal scenario. We show that the subproblem of finding the worst-case deviation of parameters subject to uncertainty is tractable and leads to linear formulations of the robust problem. Computational experiments conducted on instances of the Paris region show that the average loss of value of the robust solution is reasonably low when compared to the optimal solution of deviated instances. We also derive insights for the new housing development issue.     

FCCU transition-probability model

The adequacy of the use of transition-probability matrices for modelling fluidised catalyst cracker unit emissions was investigated. A number of different-sized matrices that modelled the processes of attrition and agglomeration were used, and it was found that an 8×8 sized matrix provided the best results. The processes of attrition within the matrix were studied, indicating an oscillatory attrition curve, and may suggest a preferred attrition size range. Studies on the effects that the agglomeration parameters had on the model indicated that, as time and the size of the matrix increased, agglomeration became more important. The results of the modelling were compared with laboratory experiments, and indicated very good agreement between the model outputs and the observed emissions.     

Robust scheduling of parallel machines with sequence-dependent set-up costs

In this paper we propose a robust approach for solving the scheduling problem of parallel machines with sequence-dependent set-up costs. In the literature, several mathematical models and solution methods have been proposed to solve such scheduling problems, but most of which are based on the strong assumption that input data are known in a deterministic way. In this paper, a fuzzy mathematical programming model is formulated by taking into account the uncertainty in processing times to provide the optimal solution as a trade-off between total set-up cost and robustness in demand satisfaction. The proposed approach requires the solution of a non-linear mixed integer programming (NLMIP), that can be formulated as an equivalent mixed integer linear programming (MILP) model. The resulting MILP model in real applications could be intractable due to its NP-hardness. Therefore, we propose a solution method technique, based on the solution of an approximated model, whose dimension is remarkably reduced with respect to the original counterpart. Numerical experiments conducted on the basis of data taken from a real application show that the average deviation of the reduced model solution over the optimum is less than 1.5%.     

A discussion on the conservatism of robust linear optimization problems

In 2004, Bertsimas and Sim proposed a robust approach that can control the degree of conservatism by applying a limitation Γ to the maximum number of parameters that are allowed to change. However, the robust approach can become extremely conservative even when Γ is relatively small. In this paper, we provide a theoretical analysis to explain why this extreme conservatism occurs. We further point out that the robust approach does not reach an extremely conservative state when Γ is less than k, where k is the number of nonzero components of the optimal solution of the extremely conservative robust approach. This research also shows that care must be taken when adjusting the value of Γ to control the degree of conservatism because the approach may result in greater conservatism than was intended. We subsequently apply our analysis to additive combinatorial optimization problems. Finally, we illustrate our results on numerical simulations.     

On the weighting of the mean-absolute-deviation cost minimization model

The mean-absolute-deviation cost minimization model, which aims to minimize sum of the mean value and the absolute deviation (AD) of the total cost multiplied by a given non-negative weighting, is one of a number of typical robust optimization models. This paper first uses a straightforward example to show that the solution obtained by this model with some weightings is not actually an optimal decision. This example also illustrates that the mean-absolute-deviation cost minimization model cannot be regarded as the conventional weighted transformation of the relevant multiobjective minimization model aiming to simultaneously minimize the mean value and AD. This paper further proves that the optimal solution obtained by the mean-absolute-deviation cost minimization model with the weighting not exceeding 0.5 will not be absolutely dominated by any other solution. This tight upper bound provides a useful guideline for practical applications.     

The Lanchester square-law model extended to a (2,2) conflict

A natural extension of the Lanchester (1,1) square-law modelis the (M,N) linear model in which M forces oppose N forceswith constant attrition rates. The (2,2) model is treated fromboth direct and inverse viewpoints. The inverse problem meansthat the model is to be fitted to a minimum number of observedforce levels, i.e. the attrition rates are to be found fromthe initial force levels together with the levels observed attwo subsequent times. An approach based on Hamiltonian dynamicshas enabled the authors to derive a procedure for solving theinverse problem, which is readily computerized. Conflicts inwhich participants unexpectedly rally or weaken must be excluded.     

Robust analysis on promotion duration for two competitive brands

There are few studies that provide a useful tool or model to determine the promotion duration during the transition state of customers' switching between different brands. This implies that marketing managers usually decide the promotion duration based on their past experiences. The study integrates the Markov chain, entropy, and diffusion theory to model the problem and find a solution. Furthermore, the Taguchi method is also used to capture the uncertain parameters of the model to solve the problem. A numerical example is used to illustrate how the model determines optimal promotion duration.     

On flipping first-semester calculus: a case study

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are ‘flipping’ (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.     

Stable recovery of signals from frame coefficients with erasures at unknown locations

In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.     

Valuation of employee stock options using the exercise multiple approach and life tables

Employee stock options (ESOs) are common in performance-based employee remuneration. Financial reporting standards such as IFRS2 and AASB2 require public corporations to report on the cost of providing ESOs, and mandate the incorporation of voluntary and involuntary early exercise. In this paper we extend the exercise multiple approach of Hull and White (2004) and decompose the attrition unadjusted voluntary exercise ESO into a gap call option and two partial-time barrier options. We use exit probabilities obtained from empirically determined multiple decrement or life tables to model involuntary early exercise or forfeiture. We provide a new analytic valuation formula which expresses the ESO value in terms of a portfolio of exotic European bivariate power options and which correctly accounts for both voluntary exercise and employee attrition. Recent approaches seek to model employee attrition using a constant hazard rate. Our approach uses an empirically driven actuarial method for incorporating employee attrition in the valuation.     

Pareto optimality and robustness in bi-blending problems

The mixture design problem for two products concerns finding simultaneously two recipes of a blending problem with linear, quadratic and semi-continuity constraints. A solution of the blending problem minimizes a linear cost objective and an integer valued objective that keeps track of the number of raw materials that are used by the two recipes, i.e. this is a bi-objective problem. Additionally, the solution must be robust. We focus on possible solution approaches that provide a guarantee to solve bi-blending problems with a certain accuracy, where two products are using (partly) the same scarce raw materials. The bi-blending problem is described, and a search strategy based on Branch-and-Bound is analysed. Specific tests are developed for the bi-blending aspect of the problem. The whole is illustrated numerically.