Search results for: Integer programming
679 Dynamic Slope Scaling Procedure for Stochastic Integer Programming Problem
Authors: Takayuki Shiina
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Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic programming is a commonly used method for optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. In this study, we consider a stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure for solving this problem is developed by using a property of the expected recourse function. Numerical experiments demonstrate that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.Keywords: stochastic programming problem with recourse, simple integer recourse, dynamic slope scaling procedure
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1602678 Stochastic Programming Model for Power Generation
Authors: Takayuki Shiina
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We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1815677 Modern Method for Solving Pure Integer Programming Models
Authors: G. Shojatalab
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In this paper, all variables are supposed to be integer and positive. In this modern method, objective function is assumed to be maximized or minimized but constraints are always explained like less or equal to. In this method, choosing a dual combination of ideal nonequivalent and omitting one of variables. With continuing this act, finally, having one nonequivalent with (n-m+1) unknown quantities in which final nonequivalent, m is counter for constraints, n is counter for variables of decision.Keywords: Integer, Programming, Operation Research, Variables of decision.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1234676 Generic Model for Timetabling Problems by Integer Linear Programming Approach
Authors: N. A. H. Aizam, V. Uvaraja
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The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It is widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming models to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describes about creating a general model which solves different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.
Keywords: AIMMS mathematical software, integer linear programming, scheduling problems, timetabling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3019675 A New Integer Programming Formulation for the Chinese Postman Problem with Time Dependent Travel Times
Authors: Jinghao Sun, Guozhen Tan, Guangjian Hou
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The Chinese Postman Problem (CPP) is one of the classical problems in graph theory and is applicable in a wide range of fields. With the rapid development of hybrid systems and model based testing, Chinese Postman Problem with Time Dependent Travel Times (CPPTDT) becomes more realistic than the classical problems. In the literature, we have proposed the first integer programming formulation for the CPPTDT problem, namely, circuit formulation, based on which some polyhedral results are investigated and a cutting plane algorithm is also designed. However, there exists a main drawback: the circuit formulation is only available for solving the special instances with all circuits passing through the origin. Therefore, this paper proposes a new integer programming formulation for solving all the general instances of CPPTDT. Moreover, the size of the circuit formulation is too large, which is reduced dramatically here. Thus, it is possible to design more efficient algorithm for solving the CPPTDT in the future research.Keywords: Chinese Postman Problem, Time Dependent, Integer Programming, Upper Bound Analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2727674 Robot Path Planning in 3D Space Using Binary Integer Programming
Authors: Ellips Masehian, Golnaz Habibi
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This paper presents a novel algorithm for path planning of mobile robots in known 3D environments using Binary Integer Programming (BIP). In this approach the problem of path planning is formulated as a BIP with variables taken from 3D Delaunay Triangulation of the Free Configuration Space and solved to obtain an optimal channel made of connected tetrahedrons. The 3D channel is then partitioned into convex fragments which are used to build safe and short paths within from Start to Goal. The algorithm is simple, complete, does not suffer from local minima, and is applicable to different workspaces with convex and concave polyhedral obstacles. The noticeable feature of this algorithm is that it is simply extendable to n-D Configuration spaces.Keywords: 3D C-space, Binary Integer Programming (BIP), Delaunay Tessellation, Robot Motion Planning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2460673 Multi-Objective Optimization of Combined System Reliability and Redundancy Allocation Problem
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 654672 Airport Check-In Optimization by IP and Simulation in Combination
Authors: Ahmad Thanyan 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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2824671 Integer Programming Model for the Network Design Problem with Facility Dependent Shortest Path Routing
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1046670 A new Heuristic Algorithm for the Dynamic Facility Layout Problem with Budget Constraint
Authors: Parham Azimi, Hamid Reza Charmchi
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In this research, we have developed a new efficient heuristic algorithm for the dynamic facility layout problem with budget constraint (DFLPB). This heuristic algorithm combines two mathematical programming methods such as discrete event simulation and linear integer programming (IP) to obtain a near optimum solution. In the proposed algorithm, the non-linear model of the DFLP has been changed to a pure integer programming (PIP) model. Then, the optimal solution of the PIP model has been used in a simulation model that has been designed in a similar manner as the DFLP for determining the probability of assigning a facility to a location. After a sufficient number of runs, the simulation model obtains near optimum solutions. Finally, to verify the performance of the algorithm, several test problems have been solved. The results show that the proposed algorithm is more efficient in terms of speed and accuracy than other heuristic algorithms presented in previous works found in the literature.Keywords: Budget constraint, Dynamic facility layout problem, Integer programming, Simulation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1956669 A Mixed Integer Linear Programming Model for Flexible Job Shop Scheduling Problem
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1664668 Timetabling Communities’ Demands for an Effective Examination Timetabling Using Integer Linear Programming
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1991667 Minimizing Energy Consumption in Wireless Sensor Networks using Binary Integer Linear Programming
Authors: Chompunut Jantarasorn, Chutima Prommak
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The important issue considered in the widespread deployment of Wireless Sensor Networks (WSNs) is an efficiency of the energy consumption. In this paper, we present a study of the optimal relay station planning problems using Binary Integer Linear Programming (BILP) model to minimize the energy consumption in WSNs. Our key contribution is that the proposed model not only ensures the required network lifetime but also guarantees the radio connectivity at high level of communication quality. Specially, we take into account effects of noise, signal quality limitation and bit error rate characteristics. Numerical experiments were conducted in various network scenarios. We analyzed the effects of different sensor node densities and distribution on the energy consumption.
Keywords: Binary Integer Linear Programming, BILP, Energy consumption, Optimal node placement and Wireless sensor networks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2190666 Development of a Comprehensive Electricity Generation Simulation Model Using a Mixed Integer Programming Approach
Authors: Erik Delarue, David Bekaert, Ronnie Belmans, William D'haeseleer
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This paper presents the development of an electricity simulation model taking into account electrical network constraints, applied on the Belgian power system. The base of the model is optimizing an extensive Unit Commitment (UC) problem through the use of Mixed Integer Linear Programming (MILP). Electrical constraints are incorporated through the implementation of a DC load flow. The model encloses the Belgian power system in a 220 – 380 kV high voltage network (i.e., 93 power plants and 106 nodes). The model features the use of pumping storage facilities as well as the inclusion of spinning reserves in a single optimization process. Solution times of the model stay below reasonable values.
Keywords: Electricity generation modeling, Unit Commitment(UC), Mixed Integer Linear Programming (MILP), DC load flow.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2029665 Optimal Production Planning in Aromatic Coconuts Supply Chain Based On Mixed-Integer Linear Programming
Authors: Chaimongkol Limpianchob
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This work addresses the problem of production planning that arises in the production of aromatic coconuts from Samudsakhorn province in Thailand. The planning involves the forwarding of aromatic coconuts from the harvest areas to the factory, which is classified into two groups; self-owned areas and contracted areas, the decisions of aromatic coconuts flow in the plant, and addressing a question of which warehouse will be in use. The problem is formulated as a mixed-integer linear programming model within supply chain management framework. The objective function seeks to minimize the total cost including the harvesting, labor and inventory costs. Constraints on the system include the production activities in the company and demand requirements. Numerical results are presented to demonstrate the feasibility of coconuts supply chain model compared with base case.
Keywords: Aromatic coconut, supply chain management, production planning, mixed-integer linear programming.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2743664 Mathematical Rescheduling Models for Railway Services
Authors: Zuraida Alwadood, Adibah Shuib, Norlida Abd Hamid
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This paper presents the review of past studies concerning mathematical models for rescheduling passenger railway services, as part of delay management in the occurrence of railway disruption. Many past mathematical models highlighted were aimed at minimizing the service delays experienced by passengers during service disruptions. Integer programming (IP) and mixed-integer programming (MIP) models are critically discussed, focusing on the model approach, decision variables, sets and parameters. Some of them have been tested on real-life data of railway companies worldwide, while a few have been validated on fictive data. Based on selected literatures on train rescheduling, this paper is able to assist researchers in the model formulation by providing comprehensive analyses towards the model building. These analyses would be able to help in the development of new approaches in rescheduling strategies or perhaps to enhance the existing rescheduling models and make them more powerful or more applicable with shorter computing time.
Keywords: Mathematical modelling, Mixed-integer programming, Railway rescheduling, Service delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3236663 A Multi-Objective Model for Supply Chain Network Design under Stochastic Demand
Authors: F. Alborzi, H. Vafaei, M.H. Gholami, M.M. S. Esfahani
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In this article, the design of a Supply Chain Network (SCN) consisting of several suppliers, production plants, distribution centers and retailers, is considered. Demands of retailers are considered stochastic parameters, so we generate amounts of data via simulation to extract a few demand scenarios. Then a mixed integer two-stage programming model is developed to optimize simultaneously two objectives: (1) minimization the fixed and variable cost, (2) maximization the service level. A weighting method is utilized to solve this two objective problem and a numerical example is made to show the performance of the model.Keywords: Mixed Integer Programming, Multi-objective Optimization, Stochastic Demand, Supply Chain Design, Two Stage Programming
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2315662 Solving the Teacher Assignment-Course Scheduling Problem by a Hybrid Algorithm
Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh
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This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.
Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4562661 Optimal Planning of Waste-to-Energy through Mixed Integer Linear Programming
Authors: S. T. Tan, H. Hashim, W. S. Ho, C. T. Lee
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Rapid economic development and population growth in Malaysia had accelerated the generation of solid waste. This issue gives pressure for effective management of municipal solid waste (MSW) to take place in Malaysia due to the increased cost of landfill. This paper discusses optimal planning of waste-to-energy (WTE) using a combinatorial simulation and optimization model through mixed integer linear programming (MILP) approach. The proposed multi-period model is tested in Iskandar Malaysia (IM) as case study for a period of 12 years (2011 -2025) to illustrate the economic potential and tradeoffs involved in this study. In this paper, 3 scenarios have been used to demonstrate the applicability of the model: (1) Incineration scenario (2) Landfill scenario (3) Optimal scenario. The model revealed that the minimum cost of electricity generation from 9,995,855 tonnes of MSW is estimated as USD 387million with a total electricity generation of 50MW /yr in the optimal scenario.Keywords: Mixed Integer Linear Programming (MILP), optimization, solid waste management (SWM), Waste-to-energy (WTE).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2974660 Determining Optimum Time Multiplier Setting of Overcurrent Relays Using Mixed Integer Linear Programming
Authors: P. N. Korde, P. P. Bedekar
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The time coordination of overcurrent relays (OCR) in a power distribution network is of great importance, as it reduces the power outages by avoiding the mal-operation of the backup relays. For this, the optimum value of the time multiplier setting (TMS) of OCRs should be chosen. The problem of determining the optimum value of TMS of OCRs in power distribution networks is formulated as a constrained optimization problem. The objective is to find the optimum value of TMS of OCRs to minimize the time of operation of relays under the constraint of maintaining the coordination of relays. A power distribution network can have a combination of numerical and electromechanical relays. The TMS of numerical relays can be set to any real value (which satisfies the constraints of the problem), whereas the TMS of electromechanical relays can be set in fixed step (0 to 1 in steps of 0.05). The main contribution of this paper is a formulation of the problem as a mixed-integer linear programming (MILP) problem and application of Gomory's cutting plane method to find the optimum value of TMS of OCRs. The TMS of electromechanical relays are taken as integers in the range 1 to 20 in the step of 1, and these values are mapped to 0.05 to 1 in the step of 0.05. The results obtained are compared with those obtained using a simplex method and its variants. It has been shown that the mixed-integer linear programming method outperforms the simplex method (and its variants) in the case of a system having a combination of numerical and electromechanical relays.
Keywords: Backup protection, constrained optimization, Gomory's cutting plane method, mixed-integer linear programming, overcurrent relay coordination, simplex method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 410659 Supplier Selection by Considering Cost and Reliability
Authors: K. -H. Yang
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Supplier selection problem is one of the important issues of supply chain problems. Two categories of methodologies include qualitative and quantitative approaches which can be applied to supplier selection problems. However, due to the complexities of the problem and lacking of reliable and quantitative data, qualitative approaches are more than quantitative approaches. This study considers operational cost and supplier’s reliability factor and solves the problem by using a quantitative approach. A mixed integer programming model is the primary analytic tool. Analyses of different scenarios with variable cost and reliability structures show that the effectiveness of this approach to the supplier selection problem.Keywords: Mixed integer programming, quantitative approach, supplier’s reliability, supplier selection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2546658 Use of Linear Programming for Optimal Production in a Production Line in Saudi Food Co.
Authors: Qasim M. Kriri
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Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.
Keywords: Parameter linear programming, objective function, sensitivity analysis, optimize profit.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2890657 Optimization of Petroleum Refinery Configuration Design with Logic Propositions
Authors: Cheng Seong Khor, Xiao Qi Yeoh
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This work concerns the topological optimization problem for determining the optimal petroleum refinery configuration. We are interested in further investigating and hopefully advancing the existing optimization approaches and strategies employing logic propositions to conceptual process synthesis problems. In particular, we seek to contribute to this increasingly exciting area of chemical process modeling by addressing the following potentially important issues: (a) how the formulation of design specifications in a mixed-logical-and-integer optimization model can be employed in a synthesis problem to enrich the problem representation by incorporating past design experience, engineering knowledge, and heuristics; and (b) how structural specifications on the interconnectivity relationships by space (states) and by function (tasks) in a superstructure should be properly formulated within a mixed-integer linear programming (MILP) model. The proposed modeling technique is illustrated on a case study involving the alternative processing routes of naphtha, in which significant improvement in the solution quality is obtained.Keywords: Mixed-integer linear programming (MILP), petroleum refinery, process synthesis, superstructure.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1715656 Discrete Time Optimal Solution for the Connection Admission Control Problem
Authors: C. Bruni, F. Delli Priscoli, G. Koch, I. Marchetti
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The Connection Admission Control (CAC) problem is formulated in this paper as a discrete time optimal control problem. The control variables account for the acceptance/ rejection of new connections and forced dropping of in-progress connections. These variables are constrained to meet suitable conditions which account for the QoS requirements (Link Availability, Blocking Probability, Dropping Probability). The performance index evaluates the total throughput. At each discrete time, the problem is solved as an integer-valued linear programming one. The proposed procedure was successfully tested against suitably simulated data.
Keywords: Connection Admission Control, Optimal Control, Integer valued Linear Programming, Quality of Service Requirements, Robust Control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1252655 Mathematical Model and Solution Algorithm for Containership Operation/Maintenance Scheduling
Authors: Hun Go, Ji-Su Kim, Dong-Ho Lee
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This study considers the problem of determining operation and maintenance schedules for a containership equipped with components during its sailing according to a pre-determined navigation schedule. The operation schedule, which specifies work time of each component, determines the due-date of each maintenance activity, and the maintenance schedule specifies the actual start time of each maintenance activity. The main constraints are component requirements, workforce availability, working time limitation, and inter-maintenance time. To represent the problem mathematically, a mixed integer programming model is developed. Then, due to the problem complexity, we suggest a heuristic for the objective of minimizing the sum of earliness and tardiness between the due-date and the starting time of each maintenance activity. Computational experiments were done on various test instances and the results are reported.Keywords: Containerships, operation and preventive maintenance schedules, integer programming, heuristic
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1601654 A Mixed Integer Programming for Port Anzali Development Plan
Authors: Mahdieh Allahviranloo
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This paper introduces a mixed integer programming model to find the optimum development plan for port Anzali. The model minimizes total system costs taking into account both port infrastructure costs and shipping costs. Due to the multipurpose function of the port, the model consists of 1020 decision variables and 2490 constraints. Results of the model determine the optimum number of berths that should be constructed in each period and for each type of cargo. In addition to, the results of sensitivity analysis on port operation quantity provide useful information for managers to choose the best scenario for port planning with the lowest investment risks. Despite all limitations-due to data availability-the model offers a straightforward decision tools to port planners aspiring to achieve optimum port planning steps.
Keywords: MILP, Multipurpose Terminal, Port Operation Optimization, Port Anzali.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1640653 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t
Authors: Ahmet Tekcan, Betül Gezer, Osman Bizim
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Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.
Keywords: Pell equation, Diophantine equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2368652 The Pell Equation x2 − Py2 = Q
Authors: Ahmet Tekcan, Arzu Özkoç, Canan Kocapınar, Hatice Alkan
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Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it.Keywords: Pell equation, solutions of Pell equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2093651 Low-Level Modeling for Optimal Train Routing and Scheduling in Busy Railway Stations
Authors: Quoc Khanh Dang, Thomas Bourdeaud’huy, Khaled Mesghouni, Armand Toguy´eni
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This paper studies a train routing and scheduling problem for busy railway stations. Our objective is to allow trains to be routed in dense areas that are reaching saturation. Unlike traditional methods that allocate all resources to setup a route for a train and until the route is freed, our work focuses on the use of resources as trains progress through the railway node. This technique allows a larger number of trains to be routed simultaneously in a railway node and thus reduces their current saturation. To deal with this problem, this study proposes an abstract model and a mixed-integer linear programming formulation to solve it. The applicability of our method is illustrated on a didactic example.Keywords: Busy railway stations, mixed-integer linear programming, offline railway station management, train platforming, train routing, train scheduling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 721650 Accelerating Integer Neural Networks On Low Cost DSPs
Authors: Thomas Behan, Zaiyi Liao, Lian Zhao, Chunting Yang
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In this paper, low end Digital Signal Processors (DSPs) are applied to accelerate integer neural networks. The use of DSPs to accelerate neural networks has been a topic of study for some time, and has demonstrated significant performance improvements. Recently, work has been done on integer only neural networks, which greatly reduces hardware requirements, and thus allows for cheaper hardware implementation. DSPs with Arithmetic Logic Units (ALUs) that support floating or fixed point arithmetic are generally more expensive than their integer only counterparts due to increased circuit complexity. However if the need for floating or fixed point math operation can be removed, then simpler, lower cost DSPs can be used. To achieve this, an integer only neural network is created in this paper, which is then accelerated by using DSP instructions to improve performance.Keywords: Digital Signal Processor (DSP), Integer Neural Network(INN), Low Cost Neural Network, Integer Neural Network DSPImplementation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1782