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IJE TRANSACTIONS C: Aspects Vol. 27, No. 6 (June 2014) 911-920

 A NODE-BASED MATHEMATICAL MODEL TOWARDS THE LOCATION ROUTING PROBLEM WITH INTERMEDIATE REPLENISHMENT FACILITIES UNDER CAPACITY CONSTRAINT M. Setak, S. Jalili Bolhassani and H. Karimi

( Received: June 23, 2013 – Accepted in Revised Form: November 07, 2013 )

 Abstract    In this paper, we study the location routing problem with replenishment facilities (LRPRF), an extension of the location routing problem (LRP) where the vehicles can replenish at some replenishment facilities. Vehicles leave the depot with load on-board, serve customers until out of load, and then either return to a replenishment facility to reload or return to the depot, completing their route. For this problem, we initiate a mathematical node-based mixed integer programming model. The objective of the problem is to find routes for vehicles to serve all the customers at a minimal cost in terms of number of routes (vehicles) and total travel cost, without violating the capacity constraint of the vehicles. The solution to the LRPRF is obtained through commercial software GAMS 23.5.1 and Genetic Algorithm (GA) in this paper. Computational results are obtained on a set of randomly generated instances and indicate the effectiveness of the proposed algorithm.

 Keywords    Location Routing Problem, Replenishment Facilities, Node-based, Mixed Integer Programming, Capacity Constraint, Genetic Algorithm

 چکیده    در این مقاله، مسئله مکان‌یابی- مسیریابی با تسهیلات بارگیری مجدد (LRPRF) را بررسی می‌کنیم که توسعه یافته مسئله مکان‌یابی- مسیریابی (LRP) است و در آن وسایل نقلیه می‌توانند در چند تسهیل، بارگیری مجدد انجام دهند. وسایل نقلیه با بار کامل از دپو شروع به حرکت می‌کنند، مشتریان را تا اتمام بار سرویس می‌دهند و سپس یا برای بارگیری مجدد به تسهیل بارگیری مجدد عزیمت می‌کنند یا جهت اتمام مسیرشان به دپو باز می‌گردند. برای این مسئله، یک مدل ریاضی برنامه ریزی عدد صحیح مختلط مبتنی بر گره معرفی می‌کنیم. هدف مسئله یافتن مسیر برای وسایل نقلیه جهت سرویس‌دهی به مشتریان به‌گونه‌ای است که بدون نقض کردن محدودیت ظرفیت وسایل نقلیه، تعداد مسیرها (وسایل نقلیه) و هزینه کل سفر کمینه شود. در این مقاله، مسئله LRPRF توسط نرم‌افزار GAMS 23.5.1 و الگوریتم ژنتیک حل می‌شود. نتایج محاسباتی از طریق چندین مسئله نمونه که به صورت تصادفی تولید می‌شوند بدست می‌آیند و کارائی الگوریتم پیشنهادشده را نشان می‌دهند.
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