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IJE TRANSACTIONS A: Basics Vol. 32, No. 1 (January 2019) 85-91

 A LAGRANGIAN DECOMPOSITION ALGORITHM FOR ROBUST GREEN TRANSPORTATION LOCATION PROBLEM A. Rouhani, M. Bashiri and R. Sahraeian

( Received: September 03, 2018 – Accepted in Revised Form: January 03, 2019 )

 Abstract    In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, caused consequently, increase the air pollution. In this paper, two green approaches are introduced which demand is the main uncertain parameter in both. These approaches are addressed to provide a trade-off between using available trucks and buying new hybrid trucks for evaluating total costs beside air pollution. Due to growing complexity, a Lagrangian decomposition algorithm is applied to find a tight lower bound for each approach. In this propounded algorithm, the main model is decomposed into master and subproblems to speed up convergence with a tight gap. Finally, the suggested algorithm is compared with commercial solver regarding total cost and computational time. Due to computational results for the proposed approach, the Lagrangian decomposition algorithm is provided a close lower bound in less time against commercial solver.

 Keywords    Lagrangean Decomposition, Robust Optimization, Chance Constraint, Green Transportation Location Problem, Mixed Integer Programming

 چکیده    در این مقاله یک مسئله حمل و نقل مکان‌یابی سبز با پارامتر تقاضای غیرقطعی در نظر گرفته شده است. افزایش استواری بر تعداد کامیون‌ها برای ارسال کالاها و محصولات تاثیر می‌گذارد و در نتیجه باعث افزایش آلودگی هوا می‌شود. در این مقاله، دو رویکرد سبز معرفی شده است که تقاضا پارامتر اصلی غیرقطعی در هر دو رویکرد می‌باشد. این رویکردها طراحی شده‌اند تا مقیاسی میان استفاده از وسایل نقلیه موجود و خرید وسایل نقلیه جدید برای ارزیابی هزینه‌های کل در کنار آلودگی هوا ایجاد شود. با توجه به افزایش پیچیدگی، یک الگوریتم تجزیه لاگرانژ برای پیدا کردن یک حد پایین مناسب برای هر رویکرد استفاده شده است. در الگوریتم پیشنهادی، مدل اصلی به یک مسئله اصلی محدود و دو زیر مسئله تجزیه می‌شود تا سرعت همگرایی الگوریتم برای رسیدن به یک گپ مناسب افزایش یابد. در نهایت، الگوریتم پیشنهاد شده با یک حل‌کننده تجاری با توجه هزینه کل و زمان محاسباتی مقایسه می‌شود. با توجه به نتایج محاسباتی برای رویکرد پیشنهادی، الگوریتم تجزیه لاگرانژ در زمان کمتری حد پایین مناسبی برای مسائل مورد بررسی پیدا می‌کند.
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