IJE TRANSACTIONS A: Basics Vol. 31, No. 4 (April 2018) 588-596    Article in Press

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R. Arab, S.F. Ghaderi and R. Tavakkoli-Moghaddam
( Received: July 02, 2017 – Accepted in Revised Form: 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 problems. The ε-constraint method is an exact method for solving multi-objective problems, which offers Pareto's solutions, such as meta-heuristic algorithms. 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. In this paper, 20 sample problems with the e-constraint method and NSGA-II are solved and compared in different dimensions based on Pareto's solutions and the time of resolution. Furthermore, the computational results showed the better performance of the NSGA-II.


Keywords    Inventory-Routing Problem; Multi-objective Optimization; ε-constraint Method; Non-dominated Sorting Genetic Algorithm


چکیده    در این مقاله، یک مسئله مسیریابی- موجودی چند هدفه، چند محصولی و چند دوره­ای در یک زنجیره تامین دو سطحی شامل یک توزیع کننده و جندین مشتری ارائه می­شود. مسئله با هدف حداقل سازی کل هزینه­های سیستم (شامل هزینه راه­اندازی، توزیع و نگهداری) و حداقل کردن ریسک حمل و نقل، مدل می­باشد. محصولات توسط یک ناوگان حمل ناهمگن با ظرفیت حمل مشخص توسط استراتژی حمل مستقیم توزیع می­شوند. ضمنا ظرفیت حمل نیز معین و محدود است و کمبود موجودی نیز غیر مجاز فرض می­شود. برای اعتبارسنجی مدل دو هدفه جدید ارائه شده، از روش محدودیت اپسیلون که روشی دقیق در حل مسائل چندهدفه به شمار می­آید، استفاده می­شود. همچنین به دلیل سخت بودن مسئله، از الگوریتم ژنتیک چندهدفه مبتنی بر مرتب­سازی نامغلوب (NSGA-II) که مانند روش اپسیلون بر مبنای جبهه­های پارتو عمل می­کند، استفاده می­شود. در این مساله، تعداد 20 نمونه تولید شده و سپس با روش­های مذکور حل و مورد تجزیه و تحلیل قرار می­گیرد. در نهایت، نتایج محاسباتی نشان می­دهد که عملکرد NSGA-II در حل مسئله مورد نظر، کارایی بالایی دارد.


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