IJE TRANSACTIONS B: Applications Vol. 31, No. 5 (May 2018) 626-635    Article in Press

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M. Forghani, M. A. Vahdat Zad and A. Sadegheih
( Received: July 30, 2017 – Accepted: February 15, 2018 )

Abstract    One of the most important points in a supply chain is customer-driven modeling, which reduces the bullwhip effect in the supply Chain, as well as the costs of investment on the inventory and efficient transshipment of the products. The homogeneity of them is reflected in the Inventory Routing Problem, which is a combination of distribution and inventory management. In this paper, with regard to the literature, the classical Inventory Routing Problem has been expanded based on the Multiple Delivery Strategy along with one of the functionalities of routing problem, namely, "backhauls", with a priority consideration for linehaul customers. Then it has been modeled in the form of a problem with Multi-period, multi-product, and multi- vehicle planning horizons that stock out is not allowed. Moreover, for an optimal use of the vehicle capacity to serve the linehaul and backhaul customers, the problem of “split service” has been added to the model, which also increases the complexity of the problem. First, considering the above-mentioned assumptions, a new mathematical model is proposed in the form of mixed integer programming for the problem defined in this paper. Then, since the stated problem can be considered among the non-deterministic polynomial-time hard, an efficient meta-heuristic genetic algorithm is provided for solving it. At the end, the numerical results obtained by this algorithm are analyzed using the randomized testing problems.


Keywords    Inventory-routing, backhauls, Logistics, heterogeneous fleet, split delivery, Genetic algorithm, multi product.


چکیده    یکی از نکات بسیار مهم در یک زنجیره تأمین، مدلسازي بر مبناي میزان مصرف مشتریان که منجر به کاهش اثر شلاقی زنجیره و نیز هزینه­ هاي حاصل از سرمایه­ گذاري بر موجودي و حمل ونقل کارآمد محصولات می­ شود، است. بطوریکه یکپارچگی آن­ها در مسأله مسیریابی-موجودی که ترکیبی از مدیریت توزیع و موجودی می­ باشد، نمود پیدا می­ کند. در این مقاله با توجه به ادبیات موضوع مسأله کلاسیک مسیریابی- موجودی را تحت استراتژی توزیع ارسال در طی مسیر به همراه یکی از ویژگی­های کاربردی مسایل مسیریابی یعنی «حمل در بازگشت» با اولویت مشتریان خط رفت، بسط داده و در قالب یک مسأله با افق برنامه ­ریزی چنددوره­ ای، چند محصولی و چندوسیله­ ای که کمبود مجاز نمی ­باشد، مدلسازی شده است. همچنین برای استفاده بهینه از ظرفیت وسایل نقلیه جهت خدمت ­رسانی به مشتریان خط رفت و برگشت موضوع «تقسیم تقاضا» به مدل اضافه شده که این موضوع پیچیدگی مسأله را نیز افزایش می­ دهد. با توجه به مفروضات فوق، ابتدا یک مدل ریاضی جدید در قالب برنامه ­ریزی عددصحیح مختلط برای مسأله تعریف شده در این مقاله ارایه شده و به دلیل اینکه مسأله مذکور در زمره مسایل چند جمله ­اي نامعین سخت قرار دارد، در ادامه یک الگوریتم متاهیوریستیک «ژنتیک کارا» برای حل آن تشریح و در پایان به تحلیل نتایج عددي حاصل از این الگوریتم با استفاده از مسایل نمونه تصادفی طراحی شده، پرداخته می­ شود.

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