IJE TRANSACTIONS C: Aspects Vol. 31, No. 6 (June 2018) 959-966   

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

Abstract    This paper presents a three-level supply chain model which includes single supplier, several distribution centers and sets of retailers. For this purpose, by adopting the queuing approach, a mixed nonlinear integer programming model is formulated. The proposed model follows minimizing the total cost of the system by determining: 1) the number and location of distribution centers between candidated ones; 2) the possibility of allocating each of the retailers to the distribution centers; 3) the amount of retailers demand; and 4) the policy of distribution centers. In the proposed model, the cost of waiting in queue is also considered. In order to make the problem more realistic, we consider uncertain demand and lead-time, which follow Poisson and Exponential distributions, respectively. Hence, we apply continuous-time Markov process approach to obtain the amount of annual ordering, purchase and inventory. Then, the results are used to formulate the location-inventory problem. Finally, the proposed model is 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 تأمین­کننده، چندین مراکز توزیع و مجموعه­ای از خرده­فروشان می­باشد. به این منظور با اتخاذ رویکرد صف یک مدل عدد صحیح غیرخطی ترکیبی فرموله می‌شود. 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 می‌شود. همچنین زمان پیشبرد و مقدار تقاضا هر دو به صورت احتمالی در نظر گرفته می‌شود 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 شده و مقدار سفارش سالیانه، میزان خرید، میزان کمبود و موجودی با استفاده از این رویکرد محاسبه می‌گردد. در انتها مدل ارائه شده با استفاده از نرم افزار GAMS نسخه 24.1.3 حل می‌شود.


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