IJE TRANSACTIONS A: Basics Vol. 31, No. 4 (April 2018) 292-299    Article in Press

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R. Arab, S.F. Ghaderi and R. Tavakkoli-Moghaddam
( Received: July 02, 2017 – Accepted: January 04, 2018 )

Abstract    This paper considers a multi-period, multi-product inventory-routing problem in a two-level supply chain consisting of a distributor and a set of customers. This problem is modeled with the aim of minimizing bi-objectives, namely the total system cost (including startup, distribution and maintenance costs) and risk-based transportation. Products are delivered to customers by some heterogeneous vehicles with specific capacities through a direct delivery strategy. Additionally, storage capacities are considered limited and the shortage is assumed to be impermissible. To validate this new bi-objective model, the ε-constraint method is used for solving small-sized problems. Since problems without distribution planning are very complex to solve optimally, the problem considered in this paper also belongs to a class of NP-hard ones. Therefore, a non-dominated sorting genetic algorithm (NSGA-II) as a well-known multi-objective evolutionary algorithm is used and developed to solve a number of test problems. Furthermore, the computational results are compared to show the performance of the NSGA-II


Keywords    Inventory-Routing problem, Multi-objective optimization, ε-constraint method, NSGA-II.


چکیده    اين مقاله به بررسي مسأله مسيريابي-موجودي چند محصولي چند دوره­ اي در يك زنجيره تأمین دو سطحي شامل يك توزیع­ کننده و مجموعه­ اي از خرده­ فروشان اختصاص دارد. مسأله دو هدفه، با اهداف کمينه­ سازي مجموع هزينه­ هاي سيستم (شامل هزينه ­هاي راه ­اندازي، توزيع و نگهداری موجودی) و حداقل سازی ریسک حمل و نقل مدلسازي شده است. محصولات توسط ناوگاني از وسایل حمل ناهمسان با ظرفيت محدود تحت استرات‍ژي ارسال مستقیم به خرده ­فروشان (مشتریان) تحويل داده مي­شوند. همچنين، ظرفيت نگهداري محدود و كمبود غيرمجاز فرض شده است. نشان داده شده است كه مسایل مشابه بدون در نظر داشتن برنامه ريزي توزيع در زمره مسایل با پيچيدگي سخت قرار دارند، بنابراين مسأله فوق نيز، مسأله­ اي با پيچيدگي سخت است. از اين رو، در اين مقاله الگوريتم بهينه­ سازي ژنتیک با مرتب سازی نامغلوب جديدي براي حل آن توسعه داده شده است و مسائل نمونه مختلفی به کمک آن حل شده است. مقایسه نتايج محاسباتي بيانگر عملکرد مناسب الگوريتم پيشنهادي است.

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