mathematical programming
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Scientia Iranica, Volume:30 Issue: 4, Jul-Aug 2023, PP 1423 -1434This paper discusses a special situation in project management in which an analyst wants to prioritize several independent activities to handle all them one after another, in such a way that there are no precedence relationships over the activities. As a novel idea, in this research, the notion is that the structure of prioritized activities is a linear arrangement, and therefore it could be taken into account as a combinatorial optimization problem. The paper formulates a mathematical model, develops a row-generation solving procedure, and reports the computational results for the problem instances of size up to 300 activities. The results demonstrate the applicability and efficiency of the proposed methodology.Keywords: Activity Prioritizing Problem (APP), Mathematical Programming, Branch-and-Cut, Row generation, Combinatorial optimization
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استفاده از ادوات FACTS به دلیل بهبود ظرفیت انتقال خطوط و کاهش تلفات و هزینه های مربوط به سیستم قدرت در حال افزایش می باشد و به همین دلیل ادوات جدیدی مورد استفاده قرار می گیرد. یکی از این ادوات، کنترل کننده پخش توان بین خطوط (IPFC) می باشد که وظیفه اصلی آن، کنترل توان بین خطوطی سیستم انتقال است و یکی از جدیدترین ادوات FACTS می باشد. در این مقاله به جایابی و تنظیم پارامترهای قابل کنترل IPFC به صورت بهینه پرداخته شده است. هدف اصلی این جایابی بهینه IPFC به صورت چند هدفه در شبکه قدرت به منظور کاهش همزمان تلفات سیستم، هزینه و همچنین بهبود بارپذیری سیستم با در نظر گرفتن قیود مربوطه می باشد. به منظور انجام مطالعات جایابی از الگوریتم انتخاب مبتنی بر شکل دهی پرتو یا PESA_II، استفاده شده است و روند جایابی بر روی شبکه 30 باسه IEEE صورت گرفته است. نتایج نشان می دهد که کلیه شاخص ها بهبود یافته است به نحوی که نسبت به حالتی که IPFC در شبکه حضور ندارد، تلفات توان اکتیو (%) 43/59 کاهش، بارپذیری (%) 08/32 افزایش، تلفات توان راکتیو (%) 63/26 کاهش و هزینه سوخت نیروگاه ها (%) 01/59 کاهش داشته است.
کلید واژگان: الگوریتم بهینه سازی، برنامه ریزی ریاضی، جایابی بهینه IPFC، کاهش تلفات و هزینهJournal of Applied Research in Electrical, Computer and Energy Systems, Volume:1 Issue: 1, 2023, PP 41 -54The use of FACTS devices is increasing due to the improvement of the transmission capacity of lines and the reduction of losses and costs related to the power system, and for this reason, new devices are used. One of these tools is the of interline power flow controller (IPFC), whose main task is to control the inter-line power of the transmission system, and it is one of the newest FACTS tools. In this article, the placement and regulation of the controllable parameters of IPFC has been discussed in an optimal way. The main goal of this optimal placement of IPFC in a multi-objective manner in the power network is to simultaneously reduce system losses, cost, and also improve system load taking into account the relevant constraints. In order to carry out placement studies, the selection algorithm based on beam forming or PESA_II has been used, and the placement process has been carried out on the IEEE 30-bus network. The results show that all indicators have improved so that compared to the case where IPFC is not present in the network, active power loss (%) is reduced by 59.43, load capacity (%) is increased by 32.08, reactive power loss ( 26.63% reduction and power plant fuel cost has decreased 59.01%.document.
Keywords: Optimization algorithm, mathematical programming, optimal placement of IPFC, reduction of losses, cost -
In this research the master surgical scheduling (MSS) problem at the tactical level of hospital planning and scheduling is studied. Before constructing the MSS, a strategic level problem, i.e. case mix planning problem (CMPP), shall be solved to allocate the capacity of operating room (OR) to each surgical specialty. In order to make an effective coordination between CMPP and MSS, the results obtained from solving the CMPP is used as an input for the respective MSS. In the MSS, frequently performed elective surgeries are planned in a cyclic manner for a pre-defined planning period. As a part of the planning process, it is required to level downstream limited resources such as intensive care unit (ICU) and ward beds with patient flow. In this study, a mathematical model is developed to construct an MSS. The proposed model is based on a lexicographic goal programming approach which is aimed at minimizing the OR spare time while considering the results of the CMPP. In this paper, data required to solve MSS, is collected from a medium-sized Iranian hospital. Hence, a robust estimation method is applied to reduce the effect of outliers in the decision making process. The results testify the performance of the proposed method against the solution put in practice in the hospital.Keywords: Master Surgical Scheduling, Mathematical Programming, Goal Programming, Robust Estimation
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Scientia Iranica, Volume:24 Issue: 6, Nove-Dec 2017, PP 3324 -3344Train scheduling is one of the significant issues in the railway industry in recent years since it has an important role in efficacy of railway infrastructure. In this paper, the timetabling problem of a multiple tracked railway network is discussed. More specifically, a general model is presented here in which a set of operational and safety requirements is considered. The model handles the trains overtaking in stations and considers the stations capacity. The objective function is to minimize the total travel time. Unfortunately, the problem is NP-hard and real size problems cannot be solved in an acceptable amount of time. In order to reduce the processing time, we presented some heuristic rules, which reduce the number of binary variables. These rules are based on problem's parameters such as travel time, dwell time and safety time of stations and try to remove the impracticable areas of the solution space. Furthermore, a Lagrangian Relaxation algorithm model is presented in order to find a lower-bound. Finally, comprehensive numerical experiments on the Tehran Metro case are reported. Results show the efficiency of the heuristic rules and also the Lagrangian Relaxation method in a way that for all analyzed problems the optimum value are obtained.Keywords: Transportation, Train timetabling, Mathematical programming, Heuristic, Lagrangian relaxation
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Scientia Iranica, Volume:24 Issue: 6, Nove-Dec 2017, PP 3287 -3296The rectangular two-dimensional Single Knapsack Problem (SKP) consists of packing a fixed rectangular space (so-called pallet) with a subset of smaller rectangular shapes (so-called pieces) of different dimensions, and without rotation. Pieces have different values. The objective is to maximize the sum of the values of the pieces packed. This paper proposes a new method for solving rectangular two-dimensional SKP based on the column generation approach. Mathematical formulation of the proposed model is simplest than the present mathematical formulations in the state-of-the art. The computational performance indicates that it is an effective method in the view of quality of solution.Keywords: Cutting, Packing, Two-dimensional knapsack problem, Mathematical programming, Column generation approach
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