Search results for: Travelling Salesman Problem

Authors: Carol Okigbo

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Mathematical problem solving has long been accorded an important place in mathematics curricula at every education level in both advanced and emerging economies. Its classroom approaches have varied, such as teaching for problem-solving, teaching about problem-solving, and teaching mathematics through problem-solving. It requires engaging in tasks for which the solution methods are not eminent, making sense of problems and persevering in solving them by exhibiting processes, strategies, appropriate attitude, and adequate exposure. Teachers play important roles in helping students acquire competency in problem-solving; thus, they are expected to be good problem-solvers and have proper conceptions of problem-solving. Studies show that teachers’ conceptions influence their decisions about what to teach and how to teach. Therefore, how teachers view their roles in teaching problem-solving will depend on their pedagogical conceptions of problem-solving. If teaching problem-solving is a major component of secondary school mathematics instruction, as recommended by researchers and mathematics educators, then it is necessary to establish teachers’ conceptions, what they do, and how they approach problem-solving. This study is designed to determine secondary school teachers’ conceptions regarding mathematical problem solving, its current situation, how teachers’ conceptions relate to their demographics, as well as the interaction patterns in the mathematics classroom. There have been many studies of mathematics problem solving, some of which addressed teachers’ conceptions using single-method approaches, thereby presenting only limited views of this important phenomenon. To address the problem more holistically, this study adopted an integrated mixed methods approach which involved a quantitative survey, qualitative analysis of open-ended responses, and ethnographic observations of teachers in class. Data for the analysis came from a random sample of 327 secondary school mathematics teachers in two Nigerian states - Anambra State and Enugu State who completed a 45-item questionnaire. Ten of the items elicited demographic information, 11 items were open-ended questions, and 25 items were Likert-type questions. Of the 327 teachers who responded to the questionnaires, 37 were randomly selected and observed in their classes. Data analysis using ANOVA, t-tests, chi-square tests, and open coding showed that the teachers had different conceptions about problem-solving, which fall into three main themes: practice on exercises and word application problems, a process of solving mathematical problems, and a way of teaching mathematics. Teachers reported that no period is set aside for problem-solving; typically, teachers solve problems on the board, teach problem-solving strategies, and allow students time to struggle with problems on their own. The result shows a significant difference between male and female teachers’ conception of problems solving, a significant relationship among teachers’ conceptions and academic qualifications, and teachers who have spent ten years or more teaching mathematics were significantly different from the group with seven to nine years of experience in terms of their conceptions of problem-solving.

Keywords: conceptions, education, mathematics, problem solving, teacher

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Authors: Saad Al-Baddai, Karema Al-Subari, Elmar Lang, Bernd Ludwig

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Empirical mode decomposition (EMD), a new data-driven of time-series decomposition, has the advantage of supposing that a time series is non-linear or non-stationary, as is implicitly achieved in Fourier decomposition. However, the EMD suffers of mode mixing problem in some cases. The aim of this paper is to present a solution for a common type of signals causing of EMD mode mixing problem, in case a signal suffers of an intermittency. By an artificial example, the solution shows superior performance in terms of cope EMD mode mixing problem comparing with the conventional EMD and Ensemble Empirical Mode decomposition (EEMD). Furthermore, the over-sifting problem is also completely avoided; and computation load is reduced roughly six times compared with EEMD, an ensemble number of 50.

Keywords: empirical mode decomposition (EMD), mode mixing, sifting process, over-sifting

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Authors: Sabah Mohammed, Jinan Fiaidhi, Darien Sawyer

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Data integration of health through connected services can save lives in the event of a medical emergency or provide efficient and effective interventions for the benefit of the patients through the integration of bedside and bench side clinical research. Such integration will support all wind of change in healthcare by being predictive, pre-emptive, personalized, problem-oriented and participatory. Prototyping a healthcare system that enables data integration has been a big challenge for healthcare for a long time. However, an innovative solution started to emerge by focusing on problem lists where everything can connect the problem list forming a growing graph. This notion was introduced by Dr. Lawrence Weed in early 70’s, but the enabling technologies weren’t mature enough to provide a successful implementation prototype. In this article, we are describing our efforts in prototyping Dr. Lawrence Weed's problem-oriented medical record (POMR) and his patient case schema (SOAP) to shape a prototype for connected health. For this, we are using the TypeGraphQL API and our enterprise-based QL4POMR to describe a Web-Based gateway for healthcare services connectivity. Our prototype has reported success in connecting to the HL7 FHIR medical record and the OpenTarget biomedical repositories.

Keywords: connected health, problem-oriented healthcare record, SOAP, QL4POMR, typegraphQL

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Authors: Joselito Medina-Marin, Alexandr Karelin, Ana Tarasenko, Juan Carlos Seck-Tuoh-Mora, Norberto Hernandez-Romero, Eva Selene Hernandez-Gress

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A production line designer faces with several challenges in manufacturing system design. One of them is the assignment of buffer slots in between every machine of the production line in order to maximize the throughput of the whole line, which is known as the Buffer Allocation Problem (BAP). The BAP is a combinatorial problem that depends on the number of machines and the total number of slots to be distributed on the production line. In this paper, we are proposing a Petri Net (PN) Model to obtain the throughput in unreliable production lines, based on PN mathematical tools and the decomposition method. The results obtained by this methodology are similar to those presented in previous works, and the number of machines is not a hard restriction.

Keywords: buffer allocation problem, Petri Nets, throughput, production lines

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Authors: Elyas Shivanian

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In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the Cauchy problems of two-dimensional elliptic PDEs in doubly connected domains. It is obtained the unknown data on the inner boundary of the domain while overspecified boundary data are imposed on the outer boundary of the domain by using the SMRPI. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high order convergence rate. In this way, localization in SMRPI can reduce the ill-conditioning for Cauchy problem. Furthermore, we improve previous results and it is revealed the SMRPI is more accurate and stable by adding strong perturbations.

Keywords: cauchy problem, doubly connected domain, radial basis function, shape function

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Authors: Kanshio Richard Tyokyaa, Jagadish Singh

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In this paper, we examined the location and stability of Out-Of-Plane Equilibrium points in the elliptic restricted three-body problem of an infinitesimal body when both primaries are taken as oblate spheroids with oblateness up to zonal harmonic J₄. The positions of the Equilibrium points L₆,₇ and their stability depend on the oblateness of the primaries and the eccentricity of their orbits. We explored the problem numerically to show the effects of parameters involved in the position and stability of the Out-Of-Plane Equilibrium points for the systems: HD188753 and Gliese 667. It is found that their positions are affected by the oblateness of the primaries, eccentricity and the semi-major axis of the orbits, but its stability behavior remains unchanged and is unstable.

Keywords: out-of-plane, equilibrium points, stability, elliptic restricted three-body problem, oblateness, zonal harmonic

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Authors: Amine Ait-Ouahmed, Didier Josselin, Fen Zhou

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Free-Float car-sharing is an one-way car-sharing service where cars are available anytime and anywhere in the streets such that no dedicated stations are needed. This means that after driving a car you can park it anywhere. This car-sharing system creates an imbalance car distribution in the cites which can be regulated by staff agents through the redistribution of cars. In this paper, we aim to solve the car-reservation and agents traveling problem so that the number of successful cars’ reservations could be maximized. Beside, we also tend to minimize the distance traveled by agents for cars redistribution. To this end, we present a mixed integer linear programming formulation for the car-sharing problem.

Keywords: one-way car-sharing, vehicle redistribution, car reservation, linear programming

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Authors: Abdullah Ali H. Ahmadini, Firoz Ahmad, Intekhab Alam

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Geometric programming problem (GPP) is a well-known non-linear optimization problem having a wide range of applications in many engineering problems. The structure of GPP is quite dynamic and easily fit to the various decision-making processes. The aim of this paper is to highlight the bounded solution method for GPP with special reference to variation among right-hand side parameters. Thus this paper is taken the advantage of two-level mathematical programming problems and determines the solution of the objective function in a specified interval called lower and upper bounds. The beauty of the proposed bounded solution method is that it does not require sensitivity analyses of the obtained optimal solution. The value of the objective function is directly calculated under varying parameters. To show the validity and applicability of the proposed method, a numerical example is presented. The system reliability optimization problem is also illustrated and found that the value of the objective function lies between the range of lower and upper bounds, respectively. At last, conclusions and future research are depicted based on the discussed work.

Keywords: varying parameters, geometric programming problem, bounded solution method, system reliability optimization

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Authors: Gizem Akcan, Erdinc Ozturk

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When it is examined as historically, it has caught attention that homosexual people try to behave as heterosexual or come out to have a place in community. Homosexual people have identity confusion during identity development, they have high levels of need for absolute truth and their psychological well being is affected negatively because of high levels of need for absolute truth and they have problems about self concept clarity. People who have problems about self concept clarity have problems on problem solving and show lots of symptoms of stress. People who have clear self concept use healthier coping strategies to solve problems. The purpose of this study is to show whether need for absolute truth predicts problem solving and symptoms of stress via mediator effect of self concept clarity or not on homosexual men. The participants of this study were 200 homosexual men. The ages of participants were 20-50. In addition, Demographic Information Form, Self Concept Clarity Scale, Need for Absolute Truth Scale, Stres Self-Assessment Checklist and Problem Solving Inventory were applied to the participants. The assessment of the data was made with confirmatory factor analysis and structural equation modeling analysis. According to the results of this study, need for absolute truth predicts problem solving and symptoms of stress via mediator effect of self concept clarity on homosexual men.

Keywords: need for absolute truth, self concept clarity, symptoms of stress, problem solving

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Authors: M. H. Hussain, I. Musirin, A. F. Abidin, S. R. A. Rahim

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This paper presents the implementation of Artificial Bees Colony (ABC) algorithm in solving Directional OverCurrent Relays (DOCRs) coordination problem for near-end faults occurring in fixed network topology. The coordination optimization of DOCRs is formulated as linear programming (LP) problem. The objective function is introduced to minimize the operating time of the associated relay which depends on the time multiplier setting. The proposed technique is to taken as a technique for comparison purpose in order to highlight its superiority. The proposed algorithms have been tested successfully on 8 bus test system. The simulation results demonstrated that the ABC algorithm which has been proved to have good search ability is capable in dealing with constraint optimization problems.

Keywords: artificial bees colony, directional overcurrent relay coordination problem, relay settings, time multiplier setting

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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Authors: K. A. Razhiyah

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Disruptive behavior is a problem that is usually associated with those with autism. There is a need to overcome this behavioral problem because the negative impact of this problem does not only effect the social relation of the students but also can cause uneasiness to those around them. This condition will be worse if the techniques used failed to motivate students to change the behaviour. The purpose of this study was to determine the effect of the circus games technique on the disruptive behavior amongst students with autism. The positive results of the intervention that was carried out for three months show the reduction in disruptive behaviour, and also improvement in the turn-taking and focusing ability aspect. Positive changes shown by the students had an encouraging effect and in a way are helping them in the teaching and learning process.

Keywords: autism, desruptive behaviour, circus, effect

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Authors: Badr M. Alshammari, T. Guesmi

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This study presents a modified version of the artificial bee colony (ABC) algorithm by including a local search technique for solving the non-convex economic power dispatch problem. The local search step is incorporated at the end of each iteration. Total system losses, valve-point loading effects and prohibited operating zones have been incorporated in the problem formulation. Thus, the problem becomes highly nonlinear and with discontinuous objective function. The proposed technique is validated using an IEEE benchmark system with ten thermal units. Simulation results demonstrate that the proposed optimization algorithm has better convergence characteristics in comparison with the original ABC algorithm.

Keywords: economic power dispatch, artificial bee colony, valve-point loading effects, prohibited operating zones

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Authors: Zahra Ranjbar

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Interpretive structural modeling (ISM) is a well-established methodology for identifying relationships among specific variables, which define a problem or an issue. In this study most important variables that have critical role in children obesity problem were introduce by ISM questionnaire technique and their relationships were determine. Our findings suggested that sedentary activities are top level variables and school teachers and administrators, public education and scientific collaborations are bottom level variables in children obesity problem. Control of dietary, Physical education program, parents, government and motivation strategies variables are depend to other variables. They are very sensitive to external variables. Also, physical education program, parents, government, motivation, school teachers and administrators, public education and collaboration variables have strong driving power. They are linkage factors; it means that they can be effective on children obesity problem directly.

Keywords: ISM, variable, obesity, physical education, children

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Authors: Mohsen Ziaee

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In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: scheduling, flexible job shop, makespan, mixed integer linear programming

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Authors: Vijaya K. Srivastava, Davide Spinello

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This paper presents established 3ⁿ enumeration procedure for mixed integer optimization problems for solving multi-objective reliability and redundancy allocation problem subject to design constraints. The formulated problem is to find the optimum level of unit reliability and the number of units for each subsystem. A number of illustrative examples are provided and compared to indicate the application of the superiority of the proposed method.

Keywords: integer programming, mixed integer programming, multi-objective optimization, Reliability Redundancy Allocation

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Authors: Bezhan Ghvaberidze

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A multiple criteria optimization approach for the solution of the Fuzzy Vehicle Routing Problem (FVRP) is proposed. For the possibility environment the levels of movements between customers are calculated by the constructed simulation interactive algorithm. The first criterion of the bi-criteria optimization problem - minimization of the expectation of total fuzzy travel time on closed routes is constructed for the FVRP. A new, second criterion – maximization of feasibility of movement on the closed routes is constructed by the Choquet finite averaging operator. The FVRP is reduced to the bi-criteria partitioning problem for the so called “promising” routes which were selected from the all admissible closed routes. The convenient selection of the “promising” routes allows us to solve the reduced problem in the real-time computing. For the numerical solution of the bi-criteria partitioning problem the -constraint approach is used. An exact algorithm is implemented based on D. Knuth’s Dancing Links technique and the algorithm DLX. The Main objective was to present the new approach for FVRP, when there are some difficulties while moving on the roads. This approach is called FVRP for extreme conditions (FVRP-EC) on the roads. Also, the aim of this paper was to construct the solving model of the constructed FVRP. Results are illustrated on the numerical example where all Pareto-optimal solutions are found. Also, an approach for more complex model FVRP with time windows was developed. A numerical example is presented in which optimal routes are constructed for extreme conditions on the roads.

Keywords: combinatorial optimization, Fuzzy Vehicle routing problem, multiple objective programming, possibility theory

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Authors: Muhammad Rezal Kamel Ariffin, Muhammad Asyraf Asbullah

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The square root modulo problem is a known primitive in designing an asymmetric cryptosystem. It was first attempted by Rabin. Decryption failure of the Rabin cryptosystem caused by the 4-to-1 decryption output is overcome efficiently in this work. The proposed scheme to overcome the decryption failure issue (known as the AAβ-cryptosystem) is constructed using a simple mathematical structure, it has low computational requirements and would enable communication devices with low computing power to deploy secure communication procedures efficiently.

Keywords: Rabin cryptosystem, 4-to-1 decryption failure, square root modulo problem, integer factorization problem

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Authors: Khaled Al-Mansour, Nawaf Esmael, Abdulaziz Al-Zaid, Mohammed Al Ateeqi, Ali Al-Yousfi, Sayed Al-Zalzalah

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In this project we will create the new schedule of nurse according to the preference of them. We did our project in Mubarak Al Kabeer Hospital (in Kuwait). The project aims to optimize the schedule of nurses in Mubarak Al Kabeer Hospital. The schedule of the nurses was studied and understood well to do any modification for their schedule to make the nurses feel as much comfort as they are. First constraints were found to know what things we can change and what things we can’t, the hard constraints are the hospital and ministry policies where we can’t change anything about, and the soft constraints are things that make nurses more comfortable. Data were collected and nurses were interviewed to know what is more better for them. All these constraints and date have been formulated to mathematical equations. This report will first contain an introduction to the topic which includes details of the problem definition. It will also contain information regarding the optimization of a nurse schedule and its contents and importance; furthermore, the report will contain information about the data needed to solve the problem and how it was collected. The problem requires formulation and that is also to be shown. The methodology will be explained which will state what has already been done. We used the lingo software to find the best schedule for the nurse. The schedule has been made according to what the nurses prefer, and also took consideration of the hospital policy when we make the schedule.

Keywords: nurse schedule problem, Kuwait, hospital policy, optimization of schedules

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Authors: Yang Zhou, Kangfeng Zheng, Wei Ni, Ren Ping Liu

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Software-defined networking (SDN) provides a solution for scalable network framework with decoupled control and data plane. However, this architecture also induces a particular distributed denial-of-service (DDoS) attack that can affect or even overwhelm the SDN network. DDoS attack detection problem has to date been mostly researched as entropy comparison problem. However, this problem lacks the utilization of SDN, and the results are not accurate. In this paper, we propose a DDoS attack detection method, which interprets DDoS detection as a signature matching problem and is formulated as Earth Mover’s Distance (EMD) model. Considering the feasibility and accuracy, we further propose to define the cost function of EMD to be a generalized Kullback-Leibler divergence. Simulation results show that our proposed method can detect DDoS attacks by comparing EMD values with the ones computed in the case without attacks. Moreover, our method can significantly increase the true positive rate of detection.

Keywords: DDoS detection, EMD, relative entropy, SDN

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Authors: Saghar Heidari

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In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

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Authors: Balgaisha Mukanova, Natalya Glazyrina, Sergey Glazyrin

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The formulated problem of optimization of the technological process of water treatment for thermal power plants is considered in this article. The problem is of multiparametric nature. To optimize the process, namely, reduce the amount of waste water, a new technology was developed to reuse such water. A mathematical model of the technology of wastewater reuse was developed. Optimization parameters were determined. The model consists of a material balance equation, an equation describing the kinetics of ion exchange for the non-equilibrium case and an equation for the ion exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion exchange. A direct problem of calculating the impurity concentration at the outlet of the water treatment plant was numerically solved. The direct problem was approximated by an implicit point-to-point computation difference scheme. The inverse problem was formulated as relates to determination of the parameters of the mathematical model of the water treatment plant operating in non-equilibrium conditions. The formulated inverse problem was solved. Following the results of calculation the time of start of the filter regeneration process was determined, as well as the period of regeneration process and the amount of regeneration and wash water. Multi-parameter optimization of water treatment process for thermal power plants allowed decreasing the amount of wastewater by 15%.

Keywords: direct problem, multiparametric optimization, optimization parameters, water treatment

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Authors: Nileshkumar Vaishnav, Aditya Tatu

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An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing

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Authors: Christian Meinecke, Bernd Scholz-Reiter

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The integrated problem of production and distribution scheduling is relevant in many industrial applications. Thus, many heuristics to solve this integrated problem have been developed in the last decade. Most of these heuristics use a sequential working principal or a single decomposition and integration approach to separate and solve sub-problems. A heuristic using a multi-step decomposition and integration approach is presented in this paper and evaluated in a case study. The result show significant improved results compared with sequential scheduling heuristics.

Keywords: production and outbound distribution, integrated planning, heuristic, decomposition, integration

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Authors: Hichem Kmimech, Achref Jabeur Telmoudi, Lotfi Nabli

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The estimation of the initial marking minimum (MIM) is a crucial problem in labeled Petri nets. In the case of multiple choices, the search for the initial marking leads to a problem of optimization of the minimum allocation of resources with two constraints. The first concerns the firing sequence that could be legal on the initial marking with respect to the firing vector. The second deals with the total number of tokens that can be minimal. In this article, the MIM problem is solved by the meta-heuristic particle swarm optimization (PSO). The proposed approach presents the advantages of PSO to satisfy the two previous constraints and find all possible combinations of minimum initial marking with the best computing time. This method, more efficient than conventional ones, has an excellent impact on the resolution of the MIM problem. We prove through a set of definitions, lemmas, and examples, the effectiveness of our approach.

Keywords: marking, production system, labeled Petri nets, particle swarm optimization

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Elijah Cavan

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In Major League Sports (MLB, NBA, NHL, NFL), it is the Front Office Staff (FOS) who make decisions about who plays for their respective team. The FOS bear the brunt of the responsibility for acquiring players through drafting, trading and signing players in free agency while typically contesting with maximum roster salary constraints. The players themselves are volatile assets of these teams- their value fluctuates with age and performance. A simple comparison can be made when viewing players as assets. The problem here is similar to that of optimizing your investment portfolio. The The goal is ultimately to maximize your periodic returns while tolerating a fixed risk (degree of uncertainty/ potential loss). Each franchise may value assets differently, and some may only tolerate lower risk levels- these are examples of factors that introduce additional constraints into the model. In this talk, we will detail the mathematical formulation of this problem as a constrained optimization problem- which can be solved with classical machine learning methods but is also well posed as a problem to be solved on quantum computers

Keywords: optimization, financial mathematics, sports analytics, simulated annealing

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Authors: Francys Souza, Alberto Ohashi, Dorival Leao

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We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.

Keywords: dynamic programming equation, optimal control, stochastic control, stochastic differential equation

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Authors: Dorra Kallel, Ines Kanoun, Diala Dhouib

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This paper elaborates a Systematic Literature Review SLR) to select the most outstanding studies that address the Menu Planning Problem (MPP) and to classify them according to the to the three following criteria: the used methods, types of patients and the required constraints. At first, a set of 4165 studies was selected. After applying the SLR’s guidelines, this collection was filtered to 13 studies using specific inclusion and exclusion criteria as well as an accurate analysis of each study. Second, the selected papers were invested to answer the proposed research questions. Finally, data synthesis and new perspectives for future works are incorporated in the closing section.

Keywords: Menu Planning Problem (MPP), Systematic Literature Review (SLR), classification, exact and approaches methods

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Authors: J. Andrade-Garda, A. Anguera, J. Ares-Casal, M. Hidalgo-Lorenzo, J.-A. Lara, D. Lizcano, S. Suárez-Garaboa

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In the current constantly changing economic context, collaborative networks allow partners to undertake projects that would not be possible if attempted by them individually. These projects usually involve the performance of a group of tasks (named roles) that have to be distributed among the partners. Thus, an allocation/matching problem arises that will be referred to as Role-Partner Allocation problem. In real life this situation is addressed by negotiation between partners in order to reach ad hoc agreements. Besides taking a long time and being hard work, both historical evidence and economic analysis show that such approach is not recommended. Instead, the allocation process should be automated by means of a centralized matching scheme. However, as a preliminary step to start the search for such a matching mechanism (or even the development of a new one), the problem and its core components must be specified. To this end, this paper establishes (i) the definition of the problem and its constraints, (ii) the key features of the involved elements (i.e., roles and partners); and (iii) how to create preference lists both for roles and partners. Only this way it will be possible to conduct subsequent methodological research on the solution method.     

Keywords: collaborative network, matching, partner, preference list, role

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