مساله ی مسیریابی روی کمان مبتنی بر همکاری با محدودیت زمان
محورهای موضوعی : تحقیق در عملیات
محمد صادق شیری
1
,
سید مصطفی خرمی زاده
2
1 - گروه ریاضی، دانشکده مهندسی و علوم پایه، واحد ارسنجان، دانشگاه آزاد اسلامی، ارسنجان، ایران
2 - گروه ریاضی، دانشکده ریاضی، دانشگاه صنعتی شیراز، شیراز، ایران
کلید واژه: Overtime, Profit, Arc routing problem, Collaboration,
چکیده مقاله :
در این مقاله مساله مسیریابی روی کمان مبتنی بر همکاری با پارامتر زمان مورد بررسی قرار گرفته که به صورت اضافه‌کاری برای حامل‌ها و خدمت‌دهی به مشتریان، با هدف بیشینه کردن سود ائتلاف مستقل از سود فردی هر حامل در نظر گرفته شده است. در مدل ارایه شده دو نوع مشتری به صورت ضروری و اشتراکی در نظر گرفته شده که خدمت‌دهی به هر دو سودآور است. خدمت‌دهی به مشتریان نوع اول الزامی و به مشتریان نوع دوم با توجه به میزان سود حاصله و محدودیت زمان صورت می‌گیرد. درکاربردهای واقعی، زمان ارایه فعالیت حامل‌ها محدود به زمان کاری مرسوم حامل‌ها و از پیش مشخص است که می‌توان به صورت قید سخت اعمال شود. در این مقاله، افزایش زمان فعالیت حامل‌ها در قالب اضافه‌کاری با در نظر گرفتن هزینه‌های مرتبط بررسی شده که منجر به افزایش تعداد مشتریان خدمت‌دهی شده و در نتیجه باعث سودآوری بیشتر حامل‌ها می‌شود. مساله به صورت یک مدل برنامه‌ریزی خطی صحیح فرمولبندی شده است و بر روی 118 نمونه از نمونه‌های مساله‌ی پستچی روستایی تست و نتایج آن گزارش شده است.
In this paper, the collaboration arc routing problem with the time parameter is investigated, which is considered as overtime for carriers and customer service, with the aim of maximizing coalition profits independent of the individual profits of each carrier. In the proposed model, two types of customers are considered as required and shared customers, and serving both is profitable. Service to the first type of customers is mandatory and to the second type of customers according to the amount of profit and time limit is optional. In actual applications, the activity time of the carriers is limited to the carriers' usual working time and can be strictly constrained. In this paper, increasing the activity time of carriers in the form of overtime is considered by considering the related costs, which leads to an increase in the number of customers served and thus makes carriers more profitable. The problem is formulated as an integer linear programming model and is tested on 118 instances of rural postman problem and its results are reported.
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