نوع مقاله : مقاله پژوهشی - کاربردی

نویسندگان

گروه مهندسی صنایع، دانشکده مهندسی صنایع و سیستم‌ها، دانشگاه تربیت مدرس، تهران، ایران.

چکیده

هدف: مساله برداشت سفارش به‌عنوان یکی از فعالیت‌های لجستیکی انبار از اهمیت به­‌سزایی برخوردار است. این مساله، جمع‌­آوری سفارش‌ها از مکان­‌های مختلف انبار برای پاسخ به سفارش مشتریان در کمترین زمان ممکن تعریف شده است. هدف از این تحقیق، ارایه یک مدل برنامه‌ریزی ریاضی چندهدفه برای یکپارچه‌سازی تصمیمات دسته‌بندی، مسیریابی، زمان‌بندی برداشت‌کنندگان و ترکیب آن با مساله بسته‌بندی در محیط چندانباره است. تابع هدف مدل ریاضی پیشنهادی شامل کمینه‌سازی زمان تحویل دسته‌­ها و کمینه‌سازی مجموع هزینه‌های برداشت سفارش می­‌باشد.
روش‌شناسی پژوهش: در این پژوهش، ابتدا با مرور ادبیات در حوزه برداشت سفارش شکاف­‌های تحقیقاتی مساله شناسایی شده است. سپس، با در نظر گرفتن محدودیت­‌های اصلی مساله، یک مدل ریاضی چندهدفه برای مساله برداشت سفارش چندانباره فرموله شده است. برای حل مساله از الگوریتم بندرز کلاسیک و الگوریتم بندرز تسریع‌شده استفاده شده است. به جهت اعتبارسنجی و کاربردپذیری مدل پیشنهادی، از داده‌های مربوط به انبارهای یک شرکت تولیدکننده محصولات بهداشتی در ایران به‌عنوان مطالعه موردی استفاده شده و نتایج آن در مقاله گزارش شده است.
یافته‌ها: نتایج اجرای مدل پیشنهادی نشان داد که سیپلکس قادر است مساله برداشت سفارش ارایه شده را تا ابعادی کوچک در یک زمان قابل‌قبول حل کند. هم‌چنین، نتایج عددی نشان‌دهنده عملکرد الگوریتم تجزیه بندرز و الگوریتم بندرز تسریع شده به‌عنوان گزینه­‌هایی مناسب برای حل مدل در مسایل با ابعاد بزرگ است. نتایج محاسباتی حاصل از اجرای روش‌های حل برای مدل پیشنهادی نشان داد که از منظر تعداد تکرارها و زمان محاسباتی، الگوریتم بندرز تسریع‌شده نسبت به الگوریتم بندرز کلاسیک نتایج بهتری داشته است.
اصالت/ارزش‌افزوده علمی: در این تحقیق، برای نخستین بار مساله برداشت سفارش با ملاحظات یکپارچگی تصمیمات عملیاتی در قالب یک مدل ریاضی چندهدفه برای محیط چندانباره فرموله شده است. هم‌چنین در خصوص روش حل نیز، با در نظر گرفتن ساختار مساله، در این مقاله برای نخستین بار از رویکردهای حل دقیق استفاده شده است. نتایج مستخرج از محاسبات صورت­‌گرفته حاکی از آن است که الگوریتم‌­های مورداستفاده روشی کارا و مناسب برای حل مسایل بوده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A multi-objective mathematical model for the multi-warehouse order picking system using Benders decomposition algorithm

نویسندگان [English]

  • Fatemeh Nikkhoo
  • Ali Hosseinzadeh Kashan
  • Bakhtiar Ostadi
  • Ehsan Nikbakhsh

Department of Industrial Engineering, Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran.

چکیده [English]

Purpose: The order-picking problem is important as one of the warehouse's logistics activities. This problem is defined as collecting orders from different warehouse locations to respond to customers' orders quickly. This paper aims to provide a multi-objective mathematical programming model for integrating the decisions of batching, routing, and scheduling of selectors with the packaging problem in a multi-warehouse environment. The objective functions include depreciation of the delivery times and total order picking costs.
Methodology: In this research, first, by reviewing the literature in the field of order picking, the research gaps of the problem have been identified. Then, taking into account the main constraints of the problem, a multi-objective mathematical model has been formulated for the multi-warehouse order-picking problem. The classic Benders decomposition algorithm and the accelerated Benders decomposition algorithm have been used to solve the problem. The data related to the warehouses of a company producing sanitary products in Iran was used as a case study to validate the applicability of the proposed model, and its results were reported in the article.
Findings: The proposed model's results indicate that CPLEX can solve these problems up to small sizes in an acceptable time. Also, the numerical results show the performance of the Benders decomposition algorithm and the accelerated Benders algorithm as suitable alternatives for solving the model in large-sized problems. The calculation results obtained from the implementation of the solution methods for the proposed model showed that in terms of the number of iterations and the calculation time, the accelerated Benders algorithm had better results than the classic Benders algorithm.
Originality/Value: In this research, the order-picking problem with the integrity of operational decisions has been formulated as a multi-objective mathematical model for a multi-warehouse environment for the first time. Also, in this article regarding the solution method, exact solution approaches have been used for the first time considering the structure of the problem. The computation results show that the proposed algorithms are efficient and suitable methods for problem-solving.

کلیدواژه‌ها [English]

  • Order batching
  • Picker routing
  • Multi-warehouse
  • Order picking
  • Benders decomposition
[1]     Tompkins, J. A., White, J. A., Bozer, Y. A., & Tanchoco, J. M. A. (2010). Facilities planning. John Wiley & Sons.
[2]     Wäscher, G. (2004). Order picking: a survey of planning problems and methods (pp. 323-347). Springer Berlin Heidelberg.
[3]     Lai, Y. J., Hwang, C. L., Lai, Y. J., & Hwang, C. L. (1994). Fuzzy multiple objective decision making. Springer.
[4]     Masae, M., Glock, C. H., & Grosse, E. H. (2020). Order picker routing in warehouses: A systematic literature review. International journal of production economics, 224, 107564. https://doi.org/10.1016/j.ijpe.2019.107564
[5]     Chan, F. T. S., & Chan, H. K. (2011). Improving the productivity of order picking of a manual-pick and multi-level rack distribution warehouse through the implementation of class-based storage. Expert systems with applications, 38(3), 2686–2700. DOI:10.1016/j.eswa.2010.08.058
[6]     Shqair, M., Altarazi, S., & Al-Shihabi, S. (2014). A statistical study employing agent-based modeling to estimate the effects of different warehouse parameters on the distance traveled in warehouses. Simulation modelling practice and theory, 49, 122–135. DOI:10.1016/j.simpat.2014.08.002
[7]     Dijkstra, A. S., & Roodbergen, K. J. (2017). Exact route-length formulas and a storage location assignment heuristic for picker-to-parts warehouses. Transportation research part E: logistics and transportation review, 102, 38–59. DOI:10.1016/j.tre.2017.04.003
[8]     Quader, S., & Castillo-Villar, K. K. (2018). Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics. Robotics and computer-integrated manufacturing, 50, 13–29. DOI:10.1016/j.rcim.2015.12.009
[9]     Zhang, R. Q., Wang, M., & Pan, X. (2019). New model of the storage location assignment problem considering demand correlation pattern. Computers and industrial engineering, 129, 210–219. DOI:10.1016/j.cie.2019.01.027
[10]   Matusiak, M., De Koster, R., Kroon, L., & Saarinen, J. (2014). A fast simulated annealing method for batching precedence-constrained customer orders in a warehouse. European journal of operational research, 236(3), 968–977. DOI:10.1016/j.ejor.2013.06.001
[11]   Cheng, C. Y., Chen, Y. Y., Chen, T. L., & Jung-Woon Yoo, J. (2015). Using a hybrid approach based on the particle swarm optimization and ant colony optimization to solve a joint order batching and picker routing problem. International journal of production economics, 170, 805–814. DOI:10.1016/j.ijpe.2015.03.021
[12]   Öncan, T. (2015). MILP formulations and an iterated local search algorithm with tabu thresholding for the order batching problem. European journal of operational research, 243(1), 142–155. DOI:10.1016/j.ejor.2014.11.025
[13]   Lin, C. C., Kang, J. R., Hou, C. C., & Cheng, C. Y. (2016). Joint order batching and picker Manhattan routing problem. Computers and industrial engineering, 95, 164–174. DOI:10.1016/j.cie.2016.03.009
[14]   Valle, C. A., Beasley, J. E., & da Cunha, A. S. (2017). Optimally solving the joint order batching and picker routing problem. European journal of operational research, 262(3), 817–834. DOI:10.1016/j.ejor.2017.03.069
[15]   Aerts, B., Cornelissens, T., & Sörensen, K. (2021). The joint order batching and picker routing problem: Modelled and solved as a clustered vehicle routing problem. Computers and operations research, 129, 105168. DOI:10.1016/j.cor.2020.105168
[16]   Kuhn, H., Schubert, D., & Holzapfel, A. (2021). Integrated order batching and vehicle routing operations in grocery retail – a general adaptive large neighborhood search algorithm. European journal of operational research, 294(3), 1003–1021. DOI:10.1016/j.ejor.2020.03.075
[17]   Wagner, S., & Mönch, L. (2023). A variable neighborhood search approach to solve the order batching problem with heterogeneous pick devices. European journal of operational research, 304(2), 461–475. DOI:10.1016/j.ejor.2022.03.056
[18]   Chen, C. M., Gong, Y., De Koster, R. B. M., & Van Nunen, J. A. E. E. (2010). A flexible evaluative framework for order picking systems. Production and operations management, 19(1), 70–82. DOI:10.1111/j.1937-5956.2009.01047.x
[19]   Hsieh, L. F., & Huang, Y. C. (2011). New batch construction heuristics to optimise the performance of order picking systems. International journal of production economics, 131(2), 618–630. DOI:10.1016/j.ijpe.2011.02.006
[20]   Ene, S., & Öztürk, N. (2012). Storage location assignment and order picking optimization in the automotive industry. International journal of advanced manufacturing technology, 60(5–8), 787–797. DOI:10.1007/s00170-011-3593-y
[21]   Henn, S., & Wäscher, G. (2012). Tabu search heuristics for the order batching problem in manual order picking systems. European journal of operational research, 222(3), 484–494. DOI:10.1016/j.ejor.2012.05.049
[22]   Chackelson, C., Errasti, A., Ciprés, D., & Lahoz, F. (2013). Evaluating order picking performance trade-offs by configuring main operating strategies in a retail distributor: a design of experiments approach. International journal of production research, 51(20), 6097–6109.
[23]   Scholz, A., & Wäscher, G. (2017). Order batching and picker routing in manual order picking systems: the benefits of integrated routing. Central european journal of operations research, 25(2), 491–520. DOI:10.1007/s10100-017-0467-x
[24]   van Gils, T., Caris, A., Ramaekers, K., & Braekers, K. (2019). Formulating and solving the integrated batching, routing, and picker scheduling problem in a real-life spare parts warehouse. European journal of operational research, 277(3), 814–830. DOI:10.1016/j.ejor.2019.03.012
[25]   Kübler, P., Glock, C. H., & Bauernhansl, T. (2020). A new iterative method for solving the joint dynamic storage location assignment, order batching and picker routing problem in manual picker-to-parts warehouses. Computers and industrial engineering, 147, 106645. DOI:10.1016/j.cie.2020.106645
[26]   Rasmi, S. A. B., Wang, Y., & Charkhgard, H. (2022). Wave order picking under the mixed-shelves storage strategy: A solution method and advantages. Computers and operations research, 137, 105556. DOI:10.1016/j.cor.2021.105556
[27]   Vanheusden, S., van Gils, T., Braekers, K., Ramaekers, K., & Caris, A. (2022). Analysing the effectiveness of workload balancing measures in order picking operations. International journal of production research, 60(7), 2126–2150. DOI:10.1080/00207543.2021.1884307
[28]   Farhadi Sartangi, M., Kashan, A., Haleh, H., & Kazemi, A. (2022). Optimization of a multi-period order picking and multi-trip order-picker routing to minimize total tardiness. Journal of decisions and operations research, 7(1), 91-110. (In Persian). https://www.journal-dmor.ir/article_138384_en.html
[29]   D’Haen, R., Braekers, K., & Ramaekers, K. (2023). Integrated scheduling of order picking operations under dynamic order arrivals. International journal of production research, 61(10), 3205–3226. DOI:10.1080/00207543.2022.2078747
[30]   Saylam, S., Çelik, M., & Süral, H. (2023). The min–max order picking problem in synchronised dynamic zone-picking systems. International journal of production research, 61(7), 2086–2104. DOI:10.1080/00207543.2022.2058433
[31]   Nikkhoo, F., Kashan, A. H., Ostadi, B., & Nikbakhsh, E. (2023). An integrated approach based on madm and modm for order picking system considering human factors. International journal of information technology and decision making, 1–48. DOI:10.1142/S0219622023500657
[32]   Chen, T. L., Cheng, C. Y., Chen, Y. Y., & Chan, L. K. (2015). An efficient hybrid algorithm for integrated order batching, sequencing and routing problem. International journal of production economics, 159, 158–167. DOI:10.1016/j.ijpe.2014.09.029
[33]   Benders, J. F. (2005). Partitioning procedures for solving mixed-variables programming problems. Computational management science, 2(1), 3–19.
[34]   Pishvaee, M. S., Razmi, J., & Torabi, S. A. (2014). An accelerated Benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain. Transportation research part E: logistics and transportation review, 67, 14–38.
[35]   Magnanti, T. L., & Wong, R. T. (1981). Accelerating benders decomposition: algorithmic enhancement and model selection criteria. Operations research, 29(3), 464–484. DOI:10.1287/opre.29.3.464