IJE TRANSACTIONS C: Aspects Vol. 31, No. 6 (June 2018) 786-794   

downloaded Downloaded: 0   viewed Viewed: 214

M. Kabiri Naeini and Z. Elahi
( Received: August 14, 2017 – Accepted: February 04, 2018 )

Abstract    In this paper, a proposed three-level supply chain model that includes single supplier, several distribution centers and retailers are suites. For this purpose, the queuing approach at a mixed nonlinear integer programming model was formulated. Model with the objective of minimizing the total cost of the system to determine values as follows: 1) determine the number and location of candidated distribution centers should be opened; 2) examine the possibility of allocating each of the retailers to the distribution centers; 3) quantify the demand of retailers who responded; and 4) policy of distribution centers. In the proposed model, the cost of waiting in queue was also considered. It also took time to meet the demand both in advance and was considered possible which follow Exponential and Poisson distributions. Uncertainty for parameters based on continuous-time Markov process approach was introduced. The annual order quantity, the purchase, the lack of inventory is calculated using this approach. Finally, the proposed model was solved using GAMS software version 24.1.3.


Keywords    location- inventory problem, Queuing theory, Inventory control, Integrated supply chain


چکیده    در این مقاله، یک مدل زنجیره تأمین سه سطحی مطرح می­شود که شامل یک تأمین کننده، چندین مراکز توزیع و مجموعه­ای از خرده­فروشان می­باشد. به این منظور با اتخاذ رویکرد صف یک مدل عدد صحیح غیرخطی ترکیبی فرموله شد مدل با هدف کمینه کردن هزینه کل سیستم، به دنبال تعیین مقادیر ذیل می‌باشد: 1) تعیین تعداد و مکان مراکز پخشی که از بین مکان­های کاندید باید افتتاح شوند؛ 2) بررسی امکان تخصیص هر یک از خرده­فروشان به مراکز توزیع؛ 3) تعیین مقدار تقاضایی از خرده­فروش که پاسخ داده ­شود؛ و 4) تعیین سیاست موجودی مراکز توزیع. در مدل ارائه شده، هزینه انتظار در صف نیز در نظر گرفته شد. همچنین زمان پیشبرد و زمان برآوردن تقاضا هر دو به صورت احتمالی در نظر گرفته شد که به ترتیب از توزیع نمایی و پواسون پیروی می­کنند. عدم قطعیت به صورت پارامترهای تصادفی بر اساس رویکرد صف مارکوفی با زمان پیوسته مطرح شد مقدار سفارش سالیانه، میزان خرید، میزان کمبود و موجودی با استفاده از این رویکرد محاسبه گردید. در انتها مدل ارائه شده با استفاده از نرم افزار GAMS نسخه 24.1.3 حل گردید.

References    [1]. Modares yazdi,m, first published, Tehran,nashr danesh gahi, page 260, ,1370. [2]. Melo.M.T ., Nickel . S ., Saldanha-da-Gama F. ," Facility location and supply chain management – A review" , European Journal of Operational Research, Volume 196,(2010) ,issue 2 , pp 401-412.                                                                        [3]. Wang . K, Lin . Y.S, Jonas C.P. Yu ,''Optimizing inventory products with time sensitive deteriorating rates in a multi-echelon supplychain",International Journal of Production Economics, Volume 130, (2011)و Issue 1, pp 66-76.                                                                             [4]. Tung Chen, Ch., and Fen Hung, S., ''Order fulfillment ability analysis in the supply chain system with Fuzzy operation times''. International Journal of production Economis ,101, (2006)..185– 193.                                                                       [5]. Atul Pandeya, Michael Masinb, ''Vittal Prabhua. Adaptive logistic controller for integrated design of distributed supply chains'' .Journal of Manufacturing Systems 26(2007) ,108–115.   [6]. Drezner, Z, Hamacher, H.W.,"Facility Location: Applications and Theory", Springer- Verlag Berlin and Heidelberg GmbH & Co. K., (2004).  [7]. Pishvaee.M S., Rabbani .M., Torabi.S.A.,"A robust optimization approach to closed-loop supply chain network design under uncertainly",Applied Mathematical Modelling, (2011).,pp 637-649.  [8]. Krishnamoorthy. A., Nair S.S., Narayanan V.C., ''An inventory model with serverinterruptions, '': Proceedings of the Fifth International Conferenceon Queueing Theory and Network Applications, ACM, , (2010). pp. 132–139.  [9]. Gabor.A.F.,.W.van Ommeren J.C., ''An approximation algorithm for a facility location problem with stochastic demands and inventories'',Oper. Res. Lett 34, (2006). [10]. Sigman, K.  D. Simchi-Levi, ''Light traffic heuristic for an M/G/1 queue with limited inventory'', Ann. Oper. Res. 40, (1992) ,371–380. [11]. Ahmadi Javid, A., Azad, N. “Incorporating location, routing and inventory decisions in supply chain network design” Transportation Research Part E 46: (2010). 582-597.  [12]. Kaya O, Urek B.'' A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain''. Computers & Operations Research65, (2016)93–103.  [13]. Azaron, A., Brown, K. N., Tarim, S. A., Modarres, M.. ''A multi-objective stochastic programming approach for supply chain design considering  risk''. International  Journal of  Production Economics. 116(1): (2008). 129-138. [14]. Krishnamoorthy A.,. Lakshmy B, Manikandan R., ''A survey on inventory models with positive service time'', Op search48, (2011). ,153–169. [15]. Diabat A, Theodorou E. ''A location-inventory supply chain problem: reformulation and piecewise linearization''. Comput Ind Eng (2015);90:381–9.  [16]. Max Shen, Z.-J.  L. Qi, ''Incorporating inventory and routing costs in strategic location models'', Eur. J. Oper. Res.179, (2007). , 372–389. [17]. Snyder, L.V M.S. Daskin,C.-P. Teo,The stochastic location model with risk pooling, Eur. J. Oper. Res. 179, (2007). ,1221–1238. [18]. Diabat A, Battaia O, Nazzal D. ''An improved lagrangian relaxation-based heuristic for a joint location-inventory problem''. Comput Oper Res (2015);61:170–8. [19]. Alhaj MA, Svetinovic D, Diabat A. ''A carbon-sensitive two-echelon-inventory supply chain model with stochastic demand, Resources''. Conserv Recycl (2016);108:82–7. [20]. Saffari. M, Haji R, Queueing system with ''inventory for two-echelon supply chain, in'': International Conference on Computers & Industrial Engineering, 2009. CIE 2009, IEEE, (2009), pp. 835–838. [21]. Saffari,  M. . Asmussen S, Haji R, ''The M/M/1 queue with inventory, lost sale, and general lead times'', Queueing Syst. 75 (2013) 65–77. [22]. Chen Q, Li X., Ouyang Y., ''Joint inventory-location problem under the risk of probabilistic facility disruptions'', Transp. Res. Part B: Methodol. 45 (2011) 991–1003. [23]. Tancrez J.-S, J.-C. Lange, P. Semal, ''A location-inventory model for large three-level supply chains'', Transp. Res. Part E: Logist. Transp. Rev. 48 (2012) 485–502. [24]. Tsao, Y.-C. Mangotra, D J.-C. Lu, M. Dong, ''A continuous approximation approach for the integrated facility-inventory allocation problem'', Eur. J. Oper. Res. 222 (2012) 216–228. [25]. Berman O, . Krass,  DM.M. Tajbakhsh, ''A coordinated location-inventory model'', Eur. J. Oper. Res. 217 (2012) 500–508. [26]. Diabat A., Abdallah ,T, Henschel A., ''A closed-loop location-inventory problem with spare parts consideration'', Comput. Oper. Res. (2013). [27]. Ozsen, L Coullard, C.R. . Daskin M.S, ''Capacitated warehouse location model with risk pooling'', Naval Res. Logist. 55 (2008) 295–312.  [28]. Miranda,P.A., Garrido, R.A. ''Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity'', Transp. Res. Part E: Logist. Transp. Rev. 44 (2008) 47–65. [29]. Chang,  K.-H. Lu Y.-S., ''Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system'', Appl. Math. Model. 34 (2010)978–991. [30]. Otten S, Krenzler R, Daduna H. ''Models for integrated production-inventory systems: steady state and cost analysis''. Int J Prod Res (2016) ;54:6174–91. [31]. Srivathsan, S., Viswanathan, S.,''A queueing-based optimization model for planning inventory of repaired components in a service center''Computers & Industrial Engineering., (2017), S0360-8352(17)30039-6. [32]. Van Jaarsveld, W., Dollevoet, T. & Dekker, R. ''Improving spare parts inventory control at a repair shop''. Omega, (2015).  57, 217-229. 

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir