مساله مکان‌یابی-تخصیص در مسیریابی احتمالی برای برنامه ریزی بهینه مدارس و سیستم حمل ونقل شهری

نوع مقاله : علمی - پژوهشی

نویسنده

استادیار، گروه مهندسی صنایع، دانشکده فنی و مهندسی، دانشگاه گرمسار، گرمسار، ایران

چکیده

در هر سیستم آموزشی، انتخاب مکان­های مناسب برای احداث مدارس در سطح شهر و تخصیص دانش­آموزان هر منطقه به این مدارس جزء تصمیمات اساسی و تاثیرگذار هستند. همچنین، یافتن مسیر بهینه برای حمل­ونقل دانش­آموزان در کمترین زمان ممکن نیز بسیار ضروری است. به منظور حضور روزانه دانش­آموزان در مدارس، تردد جمعیت در خیابان­ها به­طور فزاینده­ای افزایش می­یابد. بنابراین، زمان لازم برای پیمودن یک خیابان افزایش خواهد یافت. علاوه بر این، عوامل تصادفی همچون تصادفات و ترافیک می­توانند روی زمان سفر بین دو منطقه موثر باشند. واضح است که با افزایش تردد در هر خیابان احتمال وقوع این حوادث نیز افزایش می­یابد. در مدل ارائه شده، بر خلاف مدل­های موجود در این زمینه، تاثیر تردد جمعیت و عوامل تصادفی روی مکان­یابی مدارس، تخصیص دانش­آموزان به مدارس و مسیریابی سرویس مدرسه، بصورت همزمان در نظر گرفته شده است. به­طور کلی، هدف انتخاب مکان یا مکان­های بهینه برای احداث مدرسه، تخصیص بهینه دانش­آموزان یا سرویس­های مدرسه موجود در هر منطقه به این مدارس و تعیین مسیر بهینه حمل و نقل دانش­آموزان یا سرویس­های مدرسه برای رسیدن به مدرسه مربوطه با در نظر گرفتن تاثیر مستقیم عوامل تصادفی و تردد جمعیت روی زمان­های سفر احتمالی هر خیابان است به­طوری­که زمان انتظاری کل کمینه شود. در اینجا، ظرفیت­ خیابان­ها و مدارس برای پذیرش دانش­اموزان محدود فرض شده است. ابتدا یک تابع برای محاسبه زمان سفر وابسته به جمعیت معرفی می­شود و با در نظر گرفتن عوامل تصادفی، یک مدل برنامه­ریزی غیرخطی صحیح-مختلط ارایه می­گردد. برای حل مسایل بزرگ، یک الگوریتم ترکیبی با تعامل الگوریتم ژنتیک و الگوریتم شبیه سازی تبرید معرفی شده است.همچنین برای بررسی کارآیی الگوریتم پیشنهادی، مسایل نمونه متعددی حل می­شود و نتایج بدست آمده مورد تحلیل قرار می­گیرد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Probabilistic Location- Allocation-Routing Problem for Optimal Planning of Schools and Urban Transportation System

نویسنده [English]

  • Saber Shiripour
Assistant Professor, Faculty of Engineering, University of Garmsar, Garmsar, Iran
چکیده [English]

In all educational systems, selection of appropriate locations for schools in the city and allocation of students to these schools are part of the basic decisions. Also, finding the optimal route for the transportation of students is very necessary. In order to daily presence of students in schools, the traveling population in streets increases significantly. Thus, the required time for travelling a street increases. Also, stochastic events such as accidents and traffics can affect the travel time between two regions. It is obvious that with increase in the population flow in the street, probabilities of occurrence of these events increase. In the provided model, contrary to existing models in this field, the impact of population travelling and stochastic events on the location of schools, the allocation of students to the schools and routing are considered simultaneously. Generally, the aim is to determine appropriate locations as schools locations, allocate the existing students in each region to schools and find the movement path of each student to reach its corresponding school by considering direct impact of the stochastic factors and the population flow on the probabilistic travel times so that the total expected transportation time is minimized. Here, it is assumed that schools and streets have limited capacities for accepting the population. First, a function to compute the population-dependent travel times is defined and then, considering stochastic factors, a mixed-intiger nonlinear programming model is provided. To solve large problems, a hybrid algorithm incorporating genetic algorithm and simulated annealing algorithm is introduced. To validate the proposed model, a sample problem is considered and analyzed. Comparative numerical results demonstrate the potential effectiveness of the presented algorithms.

کلیدواژه‌ها [English]

  • Urban transportation network
  • location-allocation-routing problem
  • population-dependent probabilistic travel times
  • stochastic factors
  • hybrid algorithm
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