Abstract    Nowadays, a rapid growth in the rate of life expectancy can be seen especially in the developed countries. Accordingly, the population of elderlies has been increased. By another point of view, the number of hospitals, retirement homes along with medical staffs has not been grown with a same rate. Hence, Home Health Care (HHC) operations including a set of nurses and patients have been developed recently by both academia and health practitioners to consider elderlies’ preferences willing to receive their cares at their homes instead of hospitals or retirement homes. To alleviate the drawbacks of pervious works and make HHC more practical, this paper introduces not only a new mathematical formulation considering new suppositions in this research area but also a solution approach based on Lagrangian relaxation theory has been employed for the first time. The main strategy of used algorithm aims to fill the gap between the lower bound and upper bound of problem and finds a solution which has both optimality and feasibility properties. By generating a number of numerical examples, results show the performance of the proposed algorithm analyzed by different criteria as well as the efficiency of developed formulation through a set of sensitivity analyses

Keywords    home health care; vehicle routing problem; Lagrangian relaxation-based algorithm.

چکیده    امروزه، یک رشد سریعی در نرخ امید به زندگی در کشورهای توسعه یافته دیده می شد. با توجه به این موضوع جمعیت افراد کهنسال افزایش یافته است. از نگاهی دیگر، تعداد بیمارستان ها، خانه های سالمندان به همراه کمک های پزشکی در یک نرخ مشابه افزایش نیافته است. از این رو، عملیات مربوط به سلامت مراقبت خانگی شامل تعدادی پرستار و بیماران می شود که در سال های اخیر توسط مراکز دانشگاهی و مشارکان سلامت برای در نظر گرفتن تمایلات افراد مسن برای دریافت خدمات مراقبتی در خانه ی خود به جای بیمارستان یا خانه های سالمندان گسترش یافته است. برای کاهش کاستی های کارهای قبلی انجام شده و کاربردی کردن این مساله، این مقاله نه تنها یک مدل جدید را با فرضیات جدید در این حوزه معرفی میکند بلکه یک روش حل مبتنی بر الگوریتم آزاد سازی لاگرانژین برای اولین بار به کار گرفته شده است. ساختار اصلی الگوریتم استفاده شده برای پر کردن فاصله بین حد پایین و حد بالای مساله به منظور پیدا کردن یک جواب که مشخصه های شدنی بودن و بهینگی را داشته باشد. با تولید مجموعه ای از مثال های عددی، نتایج نشان از کارایی الگوریتم پیشنهادی که با معیار های مختلف مورد تحلیل قرار گرفته و هم چنین، اثر بخشی مدل توسعه یافته شده با تحلیل حساسیت های گوناگون را نشان می دهد.

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