A heuristic procedure for solving the dynamic probabilistic project expediting problem

Because of activity duration uncertainties, large-scale projects can often be modeled most realistically as probabilistic activity networks. The complex interactions among activities with uncertain durations virtually assures a low probability that these projects will be completed before predetermined due dates. As a result, it is often necessary to expedite individual activities in these projects to improve due date performance. This research introduces a dynamically applied matrix simulation approach for selecting expediting options in order to control the probability of successful project completion before predefined due dates. Experiments are conducted to demonstrate the ability of this new approach to generate quality alternatives and efficiently evaluate large-scale projects.     

A case for a research based methodology in OR problem solving

Many Operational Research techniques assume the existence of sound data, whilst projects are often carried out using, perforce, limited or unreliable data. It is contended that even in such adverse circumstances good, stable solutions can often be found by researching the structure of the problem to be solved, using such data as are available. The contention is illustrated by examples drawn from the authors' experience.     

A discrete bilevel brain storm algorithm for solving a sales territory design problem: a case study

A sales territory design problem faced by a manufacturing company that supplies products to a group of customers located in a service region is addressed in this paper. The planning process of designing the territories has the objective to minimizing the total dispersion of the customers without exceeding a limited budget assigned to each territory. Once territories have been determined, a salesperson has to define the day-by-day routes to satisfy the demand of customers. Currently, the company has established a service level policy that aims to minimize total waiting times during the distribution process. Also, each territory is served by a single salesperson. A novel discrete bilevel optimization model for the sales territory design problem is proposed. This problem can be seen as a bilevel problem with a single leader and multiple independent followers, in which the leader’s problem corresponds to the design of territories (manager of the company), and the routing decision for each territory corresponds to each follower. The hierarchical nature of the current company’s decision-making process triggers some particular characteristics of the bilevel model. A brain storm algorithm that exploits these characteristics is proposed to solve the discrete bilevel problem. The main features of the proposed algorithm are that the workload is used to verify the feasibility and to cluster the leader’s solutions. In addition, four discrete mechanisms are used to generate new solutions, and an elite set of solutions is considered to reduce computational cost. This algorithm is used to solve a real case study, and the results are compared against the current solution given by the company. Results show a reduction of more than 20% in the current costs with the solution obtained by the proposed algorithm. Furthermore, a sensitivity analysis is performed, providing interesting managerial insights to improve the current operations of the company.     

A study of ACO capabilities for solving the maximum clique problem

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses “pheromone trails” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph. We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.     

A dynamic recruitment problem

We introduce a sequential recruitment problem in which the employepool needs continual replenishment due to random depletionsof personnel. We determine an optimal selection policy and discussits monotonicity and asymptotic properties.     

Operating room planning and scheduling: solving a surgical case sequencing problem

This text summarizes the PhD dissertation that was defended by the author in January 2009 under the supervision of Erik Demeulemeester at the Katholieke Universiteit Leuven (Belgium). The text is written in English and is available from the author upon request. The PhD dissertation is situated within the health care services domain and studies the impact of planning and scheduling procedures in the operating room. It incorporates an extensive review of both scientific contributions and the current operating room planning and scheduling practices of hospitals in Flanders (Belgium). The emphasis of the research, though, is directed towards the development, the testing and the application of surgery sequencing algorithms in a day-care environment.     

Numerical methods of singular integral equation for solving some problem in fluid dynamic

Consider a contact problem of two different layers under certain conditions. The aim of this work is obtaining the stress potential function between the two layers and obtaining the solution numerically using two different method Toeplitz matrix method and Product Nystrom method Numerical results are considered and the error, in each case, is computed.     

A method of solving dynamic problems of viscoelasticity

The "direct" numerical method is extended to the calculation of wave processes and dynamic stresses in bodies composed of viscoelastic material.Baranov Central Institute of Aviation Engine Building, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 727–729, July–August, 1971.     

Singaporean students' mathematical thinking in problem solving and problem posing: an exploratory study

This study explored Singaporean fourth, fifth, and sixth grade students' mathematical thinking in problem solving and problem posing. The results of this study showed that the majority of Singaporean fourth, fifth, and sixth graders are able to select appropriate solution strategies to solve these problems, and choose appropriate solution representations to clearly communicate their solution processes. Most Singaporean students are able to pose problems beyond the initial figures in the pattern. The results of this study also showed that across the four tasks, as the grade level advances, a higher percentage of students in that grade level show evidence of having correct answers. Surprisingly, the overall statistically significant differences across the three grade levels are mainly due to statistically significant differences between fourth and fifth grade students. Between fifth and sixth grade students, there are no statistically significant differences in most of the analyses. Compared to the findings concerning US and Chinese students' mathematical thinking, Singaporean students seem to be much more similar to Chinese students than to US students.     

Curriculum developers and problem solving: the case of Israeli elementary school projects

Problem solving has been a main focus in mathematics education for several decades, yet it seems that its definition and classroom implementation are far from being consensual. We explore the views and approaches of a small community: the project leaders of five elementary mathematics curriculum development projects in Israel, working within a centralized system, which dictates the syllabus. We describe and analyze their views along six categories: What are problems? What are not problems? Classification of problems, problem solving and individual differences, the ratio of problem solving tasks to other tasks in the project, and the role of heuristics and metacognition in teaching problem solving. We describe, exemplify, interpret and discuss the (few) points of convergence and the many different approaches. Finally, we reflect on the possible role of research in settling those differences. We speculate that our analysis and results go beyond the local and the idiosyncratic.     

Spatial visualization and measurement of area: A case study in spatialized mathematics instruction

The purpose of this study was to explore the influence of spatial visualization skills when students solve area tasks. Spatial visualization is closely related to mathematics achievement, but little is known about how these skills link to task success. We examined middle school students’ representations and solutions to area problems (both non-metric and metric) through qualitative and quantitative task analysis. Task solutions were analyzed as a function of spatial visualization skills and links were made between student solutions on tasks with different goals (i.e., non-metric and metric). Findings suggest that strong spatial visualizers solved the tasks with relative ease, with evidence for conceptual and procedural understanding. By contrast, Low and Average Spatial students more frequently produced errors due to failure to correctly determine linear measurements or apply appropriate formula, despite adequate procedural knowledge. A novel finding was the facilitating role of spatial skills in the link between metric task representation and success in determining a solution. From a teaching and learning perspective, these results highlight the need to connect emergent spatial skills with mathematical content and support students to develop conceptual understanding in parallel with procedural competence.     

A model of knowledge activation and insight in problem solving

This article presents a model of insight that offers predictions on how and when insights are likely to occur as an individual solves problems. This model is based on a fundamental trade‐off between the conscious cognition that underlies how people decide among alternatives and the unconscious cognition that underlies insight. I argue that the attention controls how much thought (i.e., knowledge activation) goes to conscious cognition, and whatever activation is left over will go to finding an insight. I validate this model by replicating the common pattern of insight in problem solving (preparation—impasse—incubation—verification). The model implies that 1) one should be able to increase the frequency of insight by lessening the demand for conscious cognition, 2) impasse is not necessary for insight, and 3) incubation time increases if a person engages in any activity with a high demand on attention. Understanding how insight occurs during problem solving provides practical suggestions to make people and groups more creative and innovative; it also provides avenues for future research on the cognitive dynamics of insight. © 2004 Wiley Periodicals, Inc. Complexity 9: 17–24, 2004     

A multimethod technique for solving optimal control problem

A multimethod algorithm for solving optimal control problems is implemented in the form of parallel iteration processes of optimization with the choice of the best approximation. The multimethod algorithm is based on a sequence of different methods to provide fast convergence to an optimal solution. Such a technology allows one to take into account some particularities of the problem at all stages of its solution process and improve the efficiency of optimal control search.     

A method for solving an inverse biharmonic problem

This paper deals with the problem of determining of an unknown coefficient in an inverse boundary value problem. Using a nonconstant overspecified data, it has been shown that the solution to this inverse problem exists and is unique.     

A multi-heuristic approach for solving the pre-marshalling problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the pre-marshalling problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method. The improvement is twofold, both in the quality of found solutions, and in the computational effort.     

A cooperative strategy for solving dynamic optimization problems

Optimization in dynamic environments is a very active and important area which tackles problems that change with time (as most real-world problems do). In this paper we present a new centralized cooperative strategy based on trajectory methods (tabu search) for solving Dynamic Optimization Problems (DOPs). Two additional methods are included for comparison purposes. The first method is a Particle Swarm Optimization variant with multiple swarms and different types of particles where there exists an implicit cooperation within each swarm and competition among different swarms. The second method is an explicit decentralized cooperation scheme where multiple agents cooperate to improve a grid of solutions. The main goals are: firstly, to assess the possibilities of trajectory methods in the context of DOPs, where populational methods have traditionally been the recommended option; and secondly, to draw attention on explicitly including cooperation schemes in methods for DOPs. The results show how the proposed strategy can consistently outperform the results of the two other methods.     

A hybrid algorithm for solving the economic lot and delivery scheduling problem in the common cycle case

The ELDSP problem is a combined lot sizing and sequencing problem. A supplier produces and delivers components of different types to a consumer in batches. The task is to determine the cycle time, i.e., the time between deliveries, which minimizes the total cost per time unit. This includes the determination of the production sequence of the component types within each cycle.We investigate the computational behavior of two published algorithms, a heuristic and an optimal algorithm. With large number of component types, the optimal algorithm has long running times. We devise a hybrid algorithm, which is both optimal and efficient.     

A new approach for solving the Stokes problem

In this paper, a new approach for finding the approximate solution of the Stokes problem is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used to approximate the velocity functions by piecewise linear functions. Then, the approximate values of pressure are obtained by a finite difference scheme.     

Lp-based combinatorial problem solving

A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given. Design aspects of a combinatorial problem solver are discussed in general terms. Three computational studies in combinatorial problem solving using the polyhedral theory developed in the past fifteen years are surveyed: one addresses the symmetric traveling salesman problem, another the optimal triangulation of input/output matrices, and the third the optimization of large-scale zero-one linear programming problems.