Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 31, No. 5 (May 2018) 786-794    Article in Press

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  A QUEUING MODEL FOR STOCHASTIC LOCATION-INVENTORY PROBLEM WITH WAITING COST CONSIDERATIONS
 
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.

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