Search results for: mathematical programming

Authors: Abolghasem Yousefi-Babadi, Ali Bozorgi-Amiri, Aida Kazempour, Reza Tavakkoli-Moghaddam, Maryam Irani

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All over the world, natural disasters (e.g., earthquakes, floods, volcanoes and hurricanes) causes a lot of deaths. Earthquakes are introduced as catastrophic events, which is accident by unusual phenomena leading to much loss around the world. Such could be replaced by disasters or any other synonyms strongly demand great long-term help and relief, which can be hard to be managed. Supplies and facilities are very important challenges after any earthquake which should be prepared for the disaster regions to satisfy the people's demands who are suffering from earthquake. This paper proposed disaster response facility allocation problem for disaster relief operations as a mathematical programming model. Not only damaged people in the earthquake victims, need the consumable commodities (e.g., food and water), but also they need non-consumable commodities (e.g., clothes) to protect themselves. Therefore, it is concluded that paying attention to disaster points and people's demands are very necessary. To deal with this objective, both commodities including consumable and need non-consumable commodities are considered in the presented model. This paper presented the multi-objective multi-period mathematical programming model regarding the minimizing the average of the weighted response times and minimizing the total operational cost and penalty costs of unmet demand and unused commodities simultaneously. Furthermore, a Chebycheff multi-objective solution procedure as a powerful solution algorithm is applied to solve the proposed model. Finally, to illustrate the model applicability, a case study of the Tehran earthquake is studied, also to show model validation a sensitivity analysis is carried out.

Keywords: facility location, multi-objective model, disaster response, commodity

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: all-or-none, computational modelling, mathematical model, transmembrane voltage, action potential

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Authors: Joelle Thng, Li Fang

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Objective: As programming becomes a highly valued and sought-after skill in the economy, many universities have started offering Python courses to help students keep up with the demands of employers. This study focuses on designing a university module that effectively educates undergraduate students on financial analysis using Python programming. Methodology: To better satisfy the specific demands for each sector, this study adopted a qualitative research modus operandi to craft a module that would complement students’ existing financial skills. The lessons were structured using research-backed educational learning tools, and important Python concepts were prudently screened before being included in the syllabus. The course contents were streamlined based on criteria such as ease of learning and versatility. In particular, the skills taught were modelled in a way to ensure they were beneficial for financial data processing and analysis. Results: Through this study, a 6-week course containing the chosen topics and programming applications was carefully constructed for finance students. Conclusion: The findings in this paper will provide valuable insights as to how teaching programming could be customised for students hailing from various academic backgrounds.

Keywords: curriculum development, designing effective instruction, higher education strategy, python for finance students

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Authors: George Nyori Makari

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Data on 92 industrial organizations point to the existence of relationships between advanced manufacturing technology (AMT) adoption and some aspects of organizational structure, including the number of specialized sub-units, the number of levels of authority, span of control, degree of role programming specification, degree of communication programming specification and the degree of output programming. Primary finding is that as the investments and integration of AMTs increases, the more likely the foregoing aspects of structure increase. The findings hold with size and a number of other organizational variables controlled. The results indicate that a company’s capacity to assimilate technology depends on its organizational capabilities. The study encapsulates the need for companies to increase their organizational capabilities during investment and integration of AMTs.

Keywords: advanced manufacturing technology, adoption, organizational structure, Kenya

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Authors: Francimar Alves, Marcos Castro, Marllus Lustosa

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In the context of the teaching of computer programming, the choice of tool to use is very important in the initiation and continuity of learning a programming language. The literature tools do not always provide usability and pedagogical dynamism clearly and accurately for effective learning. This hypothesis implies fall in productivity and difficulty of learning a particular programming language by students. The integrated development environments (IDEs) Dev-C ++ and Code :: Blocks are widely used in introductory courses for undergraduate courses in Computer Science for learning C and C ++ languages. However, after several years of discontinuity maintaining the source code of Dev-C ++ tool, the continued use of the same in the teaching and learning process of the students of these institutions has led to difficulties, mainly due to the lack of update by the official developers, which resulted in a sequence of problems in using it on educational settings. Much of the users, dissatisfied with the IDE Dev-C ++, migrated to Code :: Blocks platform targeting the more dynamic range in the learning process of the C and C ++ languages. Nevertheless, there is still the need to create a tool that can provide the resources of most IDE's software development literature, however, more interactive, simple, accurate and efficient. This motivation led to the creation of Falcon C ++ tool, IDE that brings with features that turn it into an educational platform, which focuses primarily on increasing student learning index in the early disciplines of programming and algorithms that use the languages ​​C and C ++ . As a working methodology, a field research to prove the truth of the proposed tool was used. The test results and interviews with entry-level students and intermediate in a postsecondary institution gave basis for the composition of this work, demonstrating a positive impact on the use of the tool in teaching programming, showing that the use of Falcon C ++ software is beneficial in the teaching process of the C and C ++ programming languages.

Keywords: ide, education, learning, development, language

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Authors: Tai-Yue Wang, Yi-Ho Chen

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In this study, we investigate a two-echelon supply chain with two suppliers and three retailers among which one retailer dominates other retailers. A price competition demand function is used to model this dominant retailer, which is leading market. The promotion strategies and negotiation schemes are integrated to form decision-making models under different scenarios. These models are then formulated into different mathematical programming models. The decision variables such as promotional costs, retailer prices, wholesale price, and order quantity are included in these models. At last, the distributions of promotion costs under different cost allocation strategies are discussed. Finally, an empirical example used to validate our models. The results from this empirical example show that the profit model will create the largest profit for the supply chain but with different profit-sharing results. At the same time, the more risk a member can take, the more profits are distributed to that member in the utility model.

Keywords: supply chain, price promotion, mathematical models, dominant retailer

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Authors: Ahmed Tarek, Ahmed Alveed

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In the theory of computing, there are a wide variety of direct and indirect proof techniques. However, mathematical induction (MI) stands out to be one of the most powerful proof techniques for proving hypotheses, theorems, and new results. There are variations of mathematical induction-based proof techniques, which are broadly classified into three categories, such as structural induction (SI), weak induction (WI), and strong induction (SI). In this expository paper, several different variants of the mathematical induction techniques are explored, and the specific scenarios are discussed where a specific induction technique stands out to be more advantageous as compared to other induction strategies. Also, the essential difference among the variants of mathematical induction are explored. The points of separation among mathematical induction, recursion, and logical deduction are precisely analyzed, and the relationship among variations of recurrence relations, and mathematical induction are being explored. In this context, the application of recurrence relations, and mathematical inductions are considered together in a single framework for codewords over a given alphabet.

Keywords: alphabet, codeword, deduction, mathematical, induction, recurrence relation, strong induction, structural induction, weak induction

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Authors: Ahmed Al-Sultan

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The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: airport terminal, integer programming, scheduling, simulation

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Authors: Basil Manos, Parthena Chatzinikolaou, Fedra Kiomourtzi

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This paper presents a mathematical model for the sustainable management of agricultural resources in irrigated agriculture. This is a multicriteria mathematical programming model and used as a tool for the planning, analysis and simulation of farm plans in rural irrigated areas, as well as for the study of impacts of the various policies in irrigated agriculture. The model can achieve the optimum farm plan of an agricultural region taking in account different conflicting criteria as the maximization of gross margin and the minimization of fertilizers used, under a set of constraints for land, labor, available capital, common agricultural policy etc. The proposed model was applied to four prefectures in central Greece. The results show that in all prefectures, the optimum farm plans achieve greater income and less environmental impacts (less irrigated water use and less fertilizers use) than the existent plans.

Keywords: sustainable use of agricultural resources, irrigated agriculture, multicriteria analysis, optimum income

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Authors: Luis H. Gonzalez-Guerra, Armandina J. Leal-Flores

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Students attending classrooms nowadays are habituated to use digital devices all the time and for multiple things. They have been familiar with digital technology throughout their lives so they have developed skills that should be naturally adopted as part of their study strategies. New learning styles require taking in consideration the use of models that support and promote student motivation for learning and development of their creative thinking skills. To achieve student learning in programming courses, different strategies are used. One of them is a collaboration between students, which is a tool which faculty can take advantage of when teaching these kinds of courses. Moreover, cooperation is an essential skill that society should reinforce in order to promote a healthy social environment and cohabitation. Nevertheless, students will still require support and advice to get a complete and correct programming solution to successfully address and solve the problems given throughout the course. This paper present a model where collaboration between students is associated with an automatic tutoring platform providing an excellent approach for the individual learning in collaborative activities in programming courses, and also motivates students to increase their knowledge regarding the topics covered in the classroom.

Keywords: automatic tutoring, collaboration learning, creative thinking, motivation

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Authors: Hui-Chieh Li

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Circular economy promotes greater resource productivity and avoids pollution through greater recycling and re-use which bring benefits for both the environment and the economy. The concept is contrast to a linear economy which is ‘take, make, dispose’ model of production. A well-design reverse logistics service strategy could enhance the willingness of recycling of the users and reduce the related logistics cost as well as carbon emissions. Moreover, the recycle brings the manufacturers most advantages as it targets components for closed-loop reuse, essentially converting materials and components from worn-out product into inputs for new ones at right time and right place. This study considers demand-supply interaction, time-dependent recycle demand, time-dependent surplus value of recycled product and constructs models on recycle service strategy for the recyclable waste collector. A crucial factor in optimizing a recycle service strategy is consumer demand. The study considers the relationships between consumer demand towards recycle and product characteristics, surplus value and user behavior. The study proposes a recycle service strategy which differs significantly from the conventional and typical uniform service strategy. Periods with considerable demand and large surplus product value suggest frequent and short service cycle. The study explores how to determine a recycle service strategy for recyclable waste collector in terms of service cycle frequency and duration and vehicle type for all service cycles by considering surplus value of recycled product, time-dependent demand, transportation economies and demand-supply interaction. The recyclable waste collector is responsible for the collection of waste product for the manufacturer. The study also examines the impacts of utilization rate on the cost and profit in the context of different sizes of vehicles. The model applies mathematical programming methods and attempts to maximize the total profit of the distributor during the study period. This study applies the binary logit model, analytical model and mathematical programming methods to the problem. The model specifically explores how to determine a recycle service strategy for the recycler by considering product surplus value, time-dependent recycle demand, transportation economies and demand-supply interaction. The model applies mathematical programming methods and attempts to minimize the total logistics cost of the recycler and maximize the recycle benefits of the manufacturer during the study period. The study relaxes the constant demand assumption and examines how service strategy affects consumer demand towards waste recycling. Results of the study not only help understanding how the user demand for recycle service and product surplus value affects the logistics cost and manufacturer’s benefits, but also provide guidance such as award bonus and carbon emission regulations for the government.

Keywords: circular economy, consumer demand, product surplus value, recycle service strategy

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Authors: Tunjo Perič, Marin Fatović

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In this paper a new methodology for vendor selection and supply quotas determination (VSSQD) is proposed. The problem of VSSQD is solved by the model that combines revised weighting method for determining the objective function coefficients, and a multiple objective linear programming (MOLP) method based on the cooperative game theory for VSSQD. The criteria used for VSSQD are: (1) purchase costs and (2) product quality supplied by individual vendors. The proposed methodology is tested on the example of flour purchase for a bakery with two decision makers.

Keywords: cooperative game theory, multiple objective linear programming, revised weighting method, vendor selection

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Authors: T. T. Tham

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The aim of this study is to propose an integrated approach to determine the most suitable programs, based on Quality Function Deployment (QFD), Sensitivity Analysis (SA) and Multi-Objective Linear Programming model (MOLP). Firstly, QFD is used to determine business requirements and transform them into business and supply chain programs. From the QFD, technical scores of all programs are obtained. All programs are then evaluated through five criteria (productivity, quality, cost, technical score, and feasibility). Sets of weight of these criteria are built using Sensitivity Analysis. Multi-Objective Linear Programming model is applied to select suitable programs according to multiple conflicting objectives under a budget constraint. A case study from the Sai Gon-Mien Tay Beer Company is given to illustrate the proposed methodology. The outcome of the study provides a comprehensive picture for companies to select suitable programs to obtain the optimal solution according to their preference.

Keywords: business program, multi-objective linear programming model, quality function deployment, sensitivity analysis, supply chain management

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Authors: Rouhallah Bagheri, Morteza Mahmoudi, Hadi Moheb-Alizadeh

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In this paper, we develop a supplier selection and order allocation multi-objective model in stochastic environment in which purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability distribution. To do so, we use dependent chance programming (DCP) that maximizes probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. After transforming the above mentioned stochastic multi-objective programming problem into a stochastic single objective problem using minimum deviation method, we apply a genetic algorithm to get the later single objective problem solved. The employed genetic algorithm performs a simulation process in order to calculate the stochastic objective function as its fitness function. At the end, we explore the impact of stochastic parameters on the given solution via a sensitivity analysis exploiting coefficient of variation. The results show that as stochastic parameters have greater coefficients of variation, the value of objective function in the stochastic single objective programming problem is worsened.

Keywords: dependent chance programming, genetic algorithm, minimum deviation method, order allocation, supplier selection

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Authors: Manwendra Kumar Tripathi, Subhas Ganguly

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A few glass forming ability expressions in terms of characteristic temperatures have been proposed in the literature. Attempts have been made to correlate the expression with the critical diameter of the bulk metallic glass composition. However, with the advent of new alloys, many exceptions have been noted and reported. In the present approach, a genetic programming based code which generates an expression in terms of input variables, i.e., three characteristic temperatures viz. glass transition temperature (Tg), onset crystallization temperature (Tx) and offset temperature of melting (Tl) with maximum correlation with a critical diameter (Dmax). The expression evolved shows improved correlation with the critical diameter. In addition, the expression can be explained on the basis of time-temperature transformation curve.

Keywords: glass forming ability, genetic programming, bulk metallic glass, critical diameter

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Authors: N. Gharbi

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Constraint Satisfaction problems are mathematical problems that are often used to model many real-world problems for which we look if there exists a solution satisfying all its constraints. Table constraints are important for modeling parts of many problems since they list all combinations of allowed or forbidden values. However, they admit practical limitations because they are sometimes too large to be represented in a direct way. In this paper, we present a survey of the different categories of the proposed approaches to compress table constraints in order to reduce both space and time complexities.

Keywords: constraint programming, compression, data mining, table constraints

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Authors: Taehan Lee

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We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: integer programming, multicommodity network design, routing, shortest path

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Authors: Dao Phuong Nam, Do Trong Tan, Pham Tam Thanh, Le Duy Tung, Tran Hoang Anh

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This paper considers the problem of cascade control system for unmanned aerial vehicles (UAVs). Due to the complicated modelling technique of UAV, it is necessary to separate them into two subsystems. The proposed cascade control structure is a hierarchical scheme including a robust control for inner subsystem based on H infinity theory and trajectory generator using genetic algorithm (GA), outer loop control law based on multi-parametric programming (MPP) technique to overcome the disadvantage of a big amount of calculations. Simulation results are presented to show that the equivalent path has been found and obtained by proposed cascade control scheme.

Keywords: genetic algorithm, GA, H infinity, multi-parametric programming, MPP, unmanned aerial vehicles, UAVs

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Authors: Hitesh Tahbildar

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The cost of test data generation for a program is computationally very high. In general case, no algorithm to generate test data for all types of algorithms has been found. The cost of generating test data for different types of algorithm is different. Till date, people are emphasizing the need to generate test data for different types of programming constructs rather than different types of algorithms. The test data generation methods have been implemented to find heuristics for different types of algorithms. Some algorithms that includes divide and conquer, backtracking, greedy approach, dynamic programming to find the minimum cost of test data generation have been tested. Our experimental results say that some of these types of algorithm can be used as a necessary condition for selecting heuristics and programming constructs are sufficient condition for selecting our heuristics. Finally we recommend the different heuristics for test data generation to be selected for different types of algorithms.

Keywords: ongest path, saturation point, lmax, kL, kS

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Authors: Philippe Larvet

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This paper presents the concept of an object-based programming language where tests (if... then... else) and control structures (while, repeat, for...) disappear and are replaced by conditions on data. According to the object paradigm, by using this concept, data are still embedded inside objects, as variable-value couples, but object methods are expressed into the form of logical propositions (‘conditions on data’ or COD).For instance : variable1 = value1 AND variable2 > value2 => variable3 = value3. Implementing this approach, a central inference engine turns and examines objects one after another, collecting all CODs of each object. CODs are considered as rules in a rule-based system: the left part of each proposition (left side of the ‘=>‘ sign) is the premise and the right part is the conclusion. So, premises are evaluated and conclusions are fired. Conclusions modify the variable-value couples of the object and the engine goes to examine the next object. The paper develops the principles of writing CODs instead of complex algorithms. Through samples, the paper also presents several hints for implementing a simple mechanism able to process this ‘COD language’. The proposed approach can be used within the context of simulation, process control, industrial systems validation, etc. By writing simple and rigorous conditions on data, instead of using classical and long-to-learn languages, engineers and specialists can easily simulate and validate the functioning of complex systems.

Keywords: conditions on data, logical proposition, programming without code, object-oriented programming, system simulation, system validation

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Authors: Yin-Yann Chen, Jia-Ying Li

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Assembly line balancing problems can be categorized into one-sided, two-sided, and multi-manned ones by using the number of operators deployed at workstations. This study explores the balancing problem of a resource-constrained assembly line with multi-manned workstations. Resources include machines or tools in assembly lines such as jigs, fixtures, and hand tools. A mathematical programming model was developed to carry out decision-making and planning in order to minimize the numbers of workstations, resources, and operators for achieving optimal production efficiency. To improve the solution-finding efficiency, a genetic algorithm (GA) and a simulated annealing algorithm (SA) were designed and developed in this study to be combined with a practical case in car making. Results of the GA/SA and mathematics programming were compared to verify their validity. Finally, analysis and comparison were conducted in terms of the target values, production efficiency, and deployment combinations provided by the algorithms in order for the results of this study to provide references for decision-making on production deployment.

Keywords: heuristic algorithms, line balancing, multi-manned workstation, resource-constrained

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Authors: Zahra Khalid, Gul Muhammad Khan, Arbab Masood Ahmad

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Cartesian Genetic Programming (CGP) is explored to design an optimal circuit capable of early stage breast cancer detection. CGP is used to evolve simple multiplexer circuits for detection of malignancy in the Fine Needle Aspiration (FNA) samples of breast. The data set used is extracted from Wisconsins Breast Cancer Database (WBCD). A range of experiments were performed, each with different set of network parameters. The best evolved network detected malignancy with an accuracy of 99.14%, which is higher than that produced with most of the contemporary non-linear techniques that are computational expensive than the proposed system. The evolved network comprises of simple multiplexers and can be implemented easily in hardware without any further complications or inaccuracy, being the digital circuit.

Keywords: breast cancer detection, cartesian genetic programming, evolvable hardware, fine needle aspiration

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Authors: Shyam Sajan, Kamal Bijlani

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The widespread effects of digital media help people to explore the world more and get entertained with no effort. People became fond of these kind of sedentary life style. The increase in sedentary time and a decrease in physical activities has negative impacts on human health. Even though the addiction to video games has been exploited in exergames, to make people exercise and enjoy game challenges, the contribution is restricted only to physical wellness. This paper proposes creation and implementation of a game with the help of digital media in a virtual environment. The game is designed by collaborating ideas from neural linguistic programming and Stroop effect that can also be used to identify a person’s mental state, to improve concentration and to eliminate various phobias. The multiplayer game is played in a virtual environment created with Kinect sensor, to make the game more motivating and interactive.

Keywords: exergaming, Kinect Sensor, Neural Linguistic Programming, Stroop Effect

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Authors: N. F. Jamaluddin, N. A. H. Aizam

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This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

Keywords: demands, educational timetabling, integer linear programming, scheduling, university examination timetabling problem (UETP)

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Authors: V. Pourmostaghimi, M. Zadshakoyan

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Efficiency and productivity of the finish hard turning can be enhanced impressively by utilizing accurate predictive models for cutting tool wear. However, the ability of genetic programming in presenting an accurate analytical model is a notable characteristic which makes it more applicable than other predictive modeling methods. In this paper, the genetic equation for modeling of tool flank wear is developed with the use of the experimentally measured flank wear values and genetic programming during finish turning of hardened AISI D2. Series of tests were conducted over a range of cutting parameters and the values of tool flank wear were measured. On the basis of obtained results, genetic model presenting connection between cutting parameters and tool flank wear were extracted. The accuracy of the genetically obtained model was assessed by using two statistical measures, which were root mean square error (RMSE) and coefficient of determination (R²). Evaluation results revealed that presented genetic model predicted flank wear over the study area accurately (R² = 0.9902 and RMSE = 0.0102). These results allow concluding that the proposed genetic equation corresponds well with experimental data and can be implemented in real industrial applications.

Keywords: cutting parameters, flank wear, genetic programming, hard turning

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Authors: Darsh N. Patel, Eric Olson

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Fractals can be found everywhere, whether it be the shape of a leaf or a system of blood vessels. Fractals are used to help study and understand different physical and mathematical processes; however, their artistic nature is also beautiful to simply explore. This project explores fractals generated by a cubically convergent extension to Newton's method. With this iteration as a starting point, a complex plane spanning from -2 to 2 is created with a color wheel mapped onto it. Next, the polynomial whose roots the fractal will generate from is established. From the Fundamental Theorem of Algebra, it is known that any polynomial has as many roots (counted by multiplicity) as its degree. When generating the fractals, each root will receive its own color. The complex plane can then be colored to indicate the basins of attraction that converge to each root. From a computational point of view, this project’s code identifies which points converge to which roots and then obtains fractal images. A zoom path into the fractal was implemented to easily visualize the self-similar structure. This path was obtained by selecting keyframes at different magnifications through which a path is then interpolated. Using parallel processing, many images were generated and condensed into a video. This project illustrates how practical techniques used for scientific visualization can also have an artistic side.

Keywords: fractals, cubic method, Julia programming language, basin of attraction

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Authors: Walid Moudani

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The Crew Reserve Assignment Problem (CRAP) considers the assignment of the crew members to a set of reserve activities covering all the scheduled flights in order to ensure a continuous plan so that operations costs are minimized while its solution must meet hard constraints resulting from the safety regulations of Civil Aviation as well as from the airlines internal agreements. The problem considered in this study is of highest interest for airlines and may have important consequences on the service quality and on the economic return of the operations. In this communication, a new mathematical formulation for the CRAP is proposed which takes into account the regulations and the internal agreements. While current solutions make use of Artificial Intelligence techniques run on main frame computers, a low cost approach is proposed to provide on-line efficient solutions to face perturbed operating conditions. The proposed solution method uses a dynamic programming approach for the duties scheduling problem and when applied to the case of a medium airline while providing efficient solutions, shows good potential acceptability by the operations staff. This optimization scheme can then be considered as the core of an on-line Decision Support System for crew reserve assignment operations management.

Keywords: airlines operations management, combinatorial optimization, dynamic programming, crew scheduling

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Authors: Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis

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The vehicle routing problem (VRP) is a well-known problem in Operations Research and has been widely studied during the last fifty-five years. The context of the VRP is that of delivering or collecting products to or from customers who are scattered in a geographical area and have placed orders for these products. A vehicle or a fleet of vehicles start their routes from a depot and visit the customers in order to satisfy their demands. Special attention has been given to the capacitated VRP in which the vehicles have limited carrying capacity for the goods that are delivered or collected. In the present work, we present a specific capacitated stochastic vehicle routing problem which has many realistic applications. We develop and analyze a mathematical model for a specific vehicle routing problem in which a vehicle starts its route from a depot and visits N customers according to a particular sequence in order to collect from them two similar but not identical products. We name these products, product 1 and product 2. Each customer possesses items either of product 1 or product 2 with known probabilities. The number of the items of product 1 or product 2 that each customer possesses is a discrete random variable with known distribution. The actual quantity and the actual type of product that each customer possesses are revealed only when the vehicle arrives at the customer’s site. It is assumed that the vehicle has two compartments. We name these compartments, compartment 1 and compartment 2. It is assumed that compartment 1 is suitable for loading product 1 and compartment 2 is suitable for loading product 2. However, it is permitted to load items of product 1 into compartment 2 and items of product 2 into compartment 1. These actions cause costs that are due to extra labor. The vehicle is allowed during its route to return to the depot to unload the items of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. The objective is to find the optimal routing strategy, i.e. the routing strategy that minimizes the total expected cost among all possible strategies for servicing all customers. It is possible to develop a suitable dynamic programming algorithm for the determination of the optimal routing strategy. It is also possible to prove that the optimal routing strategy has a specific threshold-type strategy. Specifically, it is shown that for each customer the optimal actions are characterized by some critical integers. This structural result enables us to design a special-purpose dynamic programming algorithm that operates only over these strategies having this structural property. Extensive numerical results provide strong evidence that the special-purpose dynamic programming algorithm is considerably more efficient than the initial dynamic programming algorithm. Furthermore, if we consider the same problem without the assumption that the customers are ordered, numerical experiments indicate that the optimal routing strategy can be computed if N is smaller or equal to eight.

Keywords: dynamic programming, similar products, stochastic demands, stochastic preferences, vehicle routing problem

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Ivan Stanev, Maria Koleva

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Described are challenges to the Bulgarian e-Customs (BeC) related to low level of interoperability and standardization, inefficient use of available infrastructure, lack of centralized identification and authorization, extremely low level of software process automation, and insufficient quality of data stored in official registers. The technical requirements for BeC are prepared with a focus on domain independent common platform, specialized customs and excise components, high scalability, flexibility, and reusability. The Knowledge Based Automated Software Engineering (KBASE) Common Platform for Automated Programming (CPAP) is selected as an instrument covering BeC requirements for standardization, programming automation, knowledge interpretation and cloud computing. BeC stage 3 results are presented and analyzed. BeC.S3 development trends are identified.

Keywords: service oriented architecture, cloud computing, knowledge based automated software engineering, common platform for automated programming, e-customs

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