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.


1.     Andersson, H., Hoff, A., Christiansen, M., Hasle, G. and Løkketangen, A., "Industrial aspects and literature survey: Combined inventory management and routing", Computers & Operations Research,  Vol. 37, No. 9, (2010), 1515-1536.

2.     Kim, J.-U. and Kim, Y.-D., "A lagrangian relaxation approach to multi-period inventory/distribution planning", Journal of the Operational Research Society,  Vol. 51, No. 3, (2000), 364-370.

3.     Li, J., Chen, H. and Chu, F., "Performance evaluation of distribution strategies for the inventory routing problem", European Journal of Operational Research,  Vol. 202, No. 2, (2010), 412-419.

4.     Campbell, A.M. and Hardin, J.R., "Vehicle minimization for periodic deliveries", European Journal of Operational Research,  Vol. 165, No. 3, (2005), 668-684.

5.     Cheng, L. and Duran, M.A., "Logistics for world-wide crude oil transportation using discrete event simulation and optimal control", Computers & Chemical Engineering,  Vol. 28, No. 6-7, (2004), 897-911.

6.     Niakan, F. and Rahimi, M., "A multi-objective healthcare inventory routing problem; a fuzzy possibilistic approach", Transportation Research Part E: Logistics and Transportation Review,  Vol. 80, (2015), 74-94.

7.     Cheng, C., Qi, M., Wang, X. and Zhang, Y., "Multi-period inventory routing problem under carbon emission regulations", International Journal of Production Economics,  Vol. 182, (2016), 263-275.

8.     Cárdenas-Barrón, L.E., González-Velarde, J.L. and Treviño-Garza, G., "A new approach to solve the multi-product multi-period inventory lot sizing with supplier selection problem", Computers & Operations Research,  Vol. 64, (2015), 225-232.

9.     Moubed, M. and Mehrjerdi Zare, Y., "A hybrid dynamic programming for inventory routing problem in collaborative reverse supply chains", International Journal of Engineering, TRANSACTIONS A: Basics,  Vol. 29, No. 10, (2016), 1412-1420.

10.   Esmaili, M. and Sahraeian, R., "A new bi-objective model for a two-echelon capacitated vehicle routing problem for perishable products with the environmental factor", International Journal of Engineering-Transactions A: Basics,  Vol. 30, No. 4, (2017), 523-531.

11.   Fattahi, P., Tanhatalab, M. and Bashiri, M., "Bi-objectives approach for a multi-period two echelons perishable product inventory-routing problem with production and lateral transshipment", International Journal of Engineering-Transactions C: Aspects,  Vol. 30, No. 6, (2016), 876.

12.   Nolz, P.C., Absi, N. and Feillet, D., "A biobjective inventory routing problem for sustainable waste management under uncertainty", Journal of MultiCriteria Decision Analysis,  Vol. 21, No. 5-6, (2014), 299-314.

13.   Marhavilas, P.-K., Koulouriotis, D. and Gemeni, V., "Risk analysis and assessment methodologies in the work sites: On a review, classification and comparative study of the scientific literature of the period 2000–2009", Journal of Loss Prevention in the Process Industries,  Vol. 24, No. 5, (2011), 477-523.

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