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Multi-Item Two-Echelon Spare Parts Inventory Control Problem with Batch Ordering in the Central Warehouse

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Multi-Item Two-Echelon Spare Parts Inventory Control Problem with Batch Ordering in the Central Warehouse MULTI-ITEM TWO-ECHELON SPARE PARTS INVENTORY CONTROL PROBLEM WITH BATCH ORDERING IN THE CENTRAL WAREHOUSE A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY ENGIN˙ TOPAN IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN INDUSTRIAL ENGINEERING OCTOBER 2010 Approval of the thesis: MULTI-ITEM TWO-ECHELON SPARE PARTS INVENTORY CONTROL PROBLEM WITH BATCH ORDERING IN THE CENTRAL WAREHOUSE submitted by ENGIN˙ TOPAN in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Industrial Engineering Department, Middle East Tech- nical University by, Prof. Dr. Canan Ozgen¨ Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Sinan Kayalıgil Head of Department, Industrial Engineering Assist. Prof. Dr. Z. Pelin Bayındır Supervisor, Industrial Engineering Dept., METU Assist. Prof. Dr. Tarkan Tan Co-supervisor, School of Industrial Engineering, TU Eind- hoven Examining Committee Members: Prof. Dr. Omer¨ Kırca Industrial Engineering Dept., METU Assist. Prof. Dr. Z. Pelin Bayındır Industrial Engineering Dept., METU Prof. Dr. Nesim Erkip Industrial Engineering Dept., Bilkent University Prof. Dr. Geert-Jan Van Houtum School of Industrial Engineering, TU Eindhoven Assist. Prof. Dr. Ismail˙ Serdar Bakal Industrial Engineering Department, METU Date: I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last Name: ENGIN˙ TOPAN Signature : iii ABSTRACT MULTI-ITEM TWO-ECHELON SPARE PARTS INVENTORY CONTROL PROBLEM WITH BATCH ORDERING IN THE CENTRAL WAREHOUSE Topan, Engin Ph.D, Department of Industrial Engineering Supervisor : Assist. Prof. Dr. Z. Pelin Bayındır Co-Supervisor : Assist. Prof. Dr. Tarkan Tan October 2010, 187 pages In this dissertation, we consider a multi-item two-echelon inventory distribution sys- tem in which the central warehouse operates with (Q, R) policy, and each local ware- house implements base-stock policy. The objective is to find the policy parameters minimizing the relevant system-wide costs subject to an aggregate mean response time constraint at each facility. We first propose an exact solution procedure based on a branch-and-price algorithm to find the relevant policy parameters of the system considered. Then, we propose four alternative heuristics to find the optimal or near-optimal policy parameters of large practical-size systems. The first heuristic, which we call the Lagrangian heuris- tic, is based on the simultaneous approach and relies on the integration of a column generation method and a greedy algorithm. The other three heuristics are based on the sequential approach, in which first the order quantities are determined using a batch size heuristic, then the reorder levels at the central warehouse and the base- stock levels at the local warehouses are determined through the same method used iv for the Lagrangian heuristic. We also propose a lower bound for the system-wide cost. Later, we extend our study to compound Poisson demand. The performance of the Lagrangian heuristic is found to be extremely well and im- proves even further as the number of parts increases. Also the computational require- ment of the heuristic is quite tolerable. This makes the heuristic very promising for large practical industry-size problems. The performance of the sequential heuristics is also satisfactory, but not as much as the Lagrangian heuristic. Keywords: inventory, two-echelon, multi-item, batch ordering, spare parts v OZ¨ MERKEZI˙ DEPODA TOPLU SIPAR˙ IS¸˙ IN˙ OLDUGU˘ C¸OK UR¨ UNL¨ U¨ IK˙ I˙ SEVIYEL˙ I˙ YEDEK PARC¸A ENVANTER KONTROLU¨ Topan, Engin Doktora, Endustri¨ Muhendisli¨ gi˘ Bol¨ um¨ u¨ Tez Yoneticisi¨ : Yrd. Doc¸. Dr. Z. Pelin Bayındır Ortak Tez Yoneticisi¨ : Yrd. Doc¸. Dr. Tarkan Tan Ekim 2010, 187 sayfa Bu tezde, merkezi deponun (Q,R) politikası ile, ve yerel depoların ise seviye esaslı envanter sistemi ile c¸alıs¸tıgı˘ c¸ok ur¨ unl¨ u,¨ iki seviyeli yedek parc¸a envanter dagıtım˘ sis- temi incelenmis¸tir. Amac¸depolardaki ortalama toplas¸ık yanıt zamanı kısıtları altında sistemin but¨ un¨ une¨ ait maliyetleri enazlayan politika parametrelerinin bulunmasıdır. Uygun politika parametrelerini bulmak ic¸in ilk olarak kesin c¸oz¨ um¨ prosedur¨ u¨ olan dal-ve-fiyatlandırma algoritması tasarlanmıs¸tır. Daha sonra, buy¨ uk¨ olc¸ekli¨ gerc¸ek sistemlerin en iyi yada en iyiye yakın politika parametrelerini bulmak amacıyla dort¨ adet alternatif sezgisel metot gelis¸tirilmis¸tir. Lagranj sezgiseli adını verdigimiz˘ bir- inci sezgisel metot, es¸zamanlı yaklas¸ım baz alınarak sutun¨ turetimi¨ ve obur algo- ritma metotlarının birles¸imine dayanmaktadır. Diger˘ uc¸sezgisel¨ metot ise, ilk olarak siparis¸miktarının bol¨ ut¨ buy¨ ukl¨ u¨g˘u¨ sezgiseliyle, daha sonra merkezi deponun yeniden ısmarlama duzeyinin¨ ve yerel depoların seviye esaslı envanter duzeylerinin¨ Lagranj sezgiselinde kullanılan yontemlerin¨ kullanılmasıyla belirlendigi˘ ardıs¸ık yaklas¸ıma dayanmaktadır. Daha sonra, gelis¸tirdigimiz˘ yontemler¨ biles¸ik Poisson talep varsayımlı vi modeli kapsayacak s¸ekilde genis¸letilmis¸tir. Lagranj sezgiselinin performansı c¸ok iyi olup, parc¸a sayısı arttıkc¸a sezgiselin perfor- mansının daha da iyiles¸tigi˘ gor¨ ulm¨ us¸t¨ ur.¨ Ayrıca sezgiseli hesaplamak ic¸in gereken zaman kabul edilebilir olc¸¨ ulerdedir.¨ Bunlar, sezgisel metodun buy¨ uk¨ olc¸ekli¨ gerc¸ek endustriyel¨ sistemlerde kullanılabilmesi ic¸in umut verici oldugunu˘ gostermektedir.¨ Lagranj sezgiseli kadar olmasa da politika parametrelerinin ardıs¸ık belirlenmesini de tatmin edici sonuc¸lar vermis¸tir. Anahtar Kelimeler: envanter, iki seviyeli, c¸ok ur¨ unl¨ u,¨ toplu siparis¸, yedek parc¸a vii To my wife and my family, zzzz and zzzz in the memory of my grandfather Yusuf Engin viii ACKNOWLEDGMENTS I would like to thank my thesis supervisor Assist. Prof. Dr. Z. Pelin Bayındır and co- supervisor Assist. Prof. Dr. Tarkan Tan for their supervision, guidance and support throughout the dissertation. I heartily consider myself very lucky to have worked with them. I owe special thanks to the Thesis Monitoring Committee Members, Prof. Dr. Geert Jan Van Houtum, Assist. Prof. Dr. Sec¸il Savas¸aneril Tufekc¸i¨ and Assist. Prof. Dr. Ismail˙ Serdar Bakal for their monitoring and valuable contributions throughout my dissertation. I also thank to Prof. Dr Omer¨ Kırca, Prof. Dr. Nesim Erkip for serving as members of my thesis defense jury and for their valuable contributions and comments. I would like to express my sincere gratitude to my dean Prof. Dr. Levent Kandiller. His guidance makes it possible to take the correct steps before and during the disser- tation. I also thank everyone who directly or indirectly contributed to my study. Among those, I owe special thanks to my chairman Assist. Prof. Dr. Nureddin Kırkavak and Assist. Prof. Dr. Haluk Aygunes¸for¨ their understanding and support that I need especially towards the end of my dissertation. Special thanks go to my love, Ipek,˙ who has given me strength and morale that I need during the dissertation. She has provided me everything that one needs during a dissertation. I owe my deepest thanks to my parents, Gulsiye¨ and Huseyin¨ Topan for all the sacrifices they made. I also thank my brother Ersin Topan, and my parents-in- law Inci˙ and Oguz˘ Seyran for their support during my study. I would like to mention that my dissertation is funded by TUB¨ ITAK˙ BIDEB-2211.˙ Therefore, I would also like to thank to TUB¨ ITAK˙ for their financial support during the dissertation. ix TABLE OF CONTENTS ABSTRACT.................................... iv OZ.........................................¨ vi ACKNOWLEDGMENTS............................. ix TABLEOFCONTENTS ............................. x LISTOFTABLES ................................ xiii LISTOFFIGURES................................ xvi CHAPTERS 1 INTRODUCTION ........................... 1 2 LITERATUREREVIEW........................ 12 2.1 Multi-Echelon Inventory Distribution Systems . 12 2.1.1 Single-Item Systems . 18 2.1.2 Multi-Item Systems . 33 2.2 SequentialHeuristics . 39 3 ANEXACTSOLUTIONPROCEDURE. 42 3.1 Themodel ........................... 43 3.2 The branch-and-price algorithm . 49 3.2.1 Obtaining the Lagrangian dual bound for the prob- lem: Column Generation Method . 50 3.2.2 Solution Procedure for Subproblems: Single-item Two-echelon Batch Ordering Problem . 54 3.2.2.1 Finding Optimal Solution for Subprob- lems for Given Values of Reorder Level and Order Quantity . 59 3.2.3 Generating Upper Bounds: Greedy Algorithm . 61 x 3.3 Computational Results . 62 3.4 Conclusion........................... 62 4 HEURISTICPROCEDURES...................... 65 4.1 Lagrangian Heuristic . 66 4.2 SequentialHeuristics . 66 4.3 Asymptotic analysis of the Lagrangian dual bound . 70 4.4 Computational Study . 76 4.4.1 Experimental Design . 77 4.4.2 Performance of the Lagrangian Dual Bound . 80 4.4.3 Performance of the Lagrangian Heuristic . 81 4.4.4 Performance of the Sequential Heuristics . 90 4.4.5 Computational requirements of the solution proce- dures and experiments with Practical-Size Problems 94 4.5 Conclusion...........................100 5 EXTENSIONS TO COMPOUND POISSON DEMAND . 103 5.1 Themodel ...........................104 5.1.1 Obtaining the Lead Time Demand Distributions . 108 5.2 An Exact Evaluation Based on a Flow-Unit
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