Marlene Isabel Silva Marchena. Measuring and Implementing the Bullwhip Effect in Supply Chains. Tese de Doutorado

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1 Marlene Isabel Silva Marchena Measuring and Implementing the Bullwhip Effect in Supply Chains PUC-Rio - Certificação Digital Nº /CB Tese de Doutorado Thesis presented to the Postgraduate Program in Mathematics of the Departamento de Engenharia Elétrica, PUC-Rio as partial fulfillment of the requirements for the degree of Doutor em Engenharia Elétrica. Advisor: Prof. Álvaro de Lima Veiga Filho Rio de Janeiro December 2010

2 All rights reserved. Marlene Isabel Silva Marchena Marlene is a Master in Economics and Finance, graduated from the Federal University of Santa Catarina (Santa Catarina, Brazil). She spent one and a half year at the Centre for Innovation in Distributed Systems (CIDS) at Institute of Technology Tralee, Ireland, where she did research for his PhD thesis as a exchange student. Marchena, Marlene Isabel Silva Bibliographic data Measuring and implementing the bullwhip effect in supply chains / Marlene Isabel Silva Marchena ; advisor: Alvaro de Lima Veiga Filho; co advisor: Pat Doody f.:il.;30cm Tese (Doutorado em Métodos de Apoio a decisão)- Pontifícia Universidade Católica doriodejaneiro, Rio de Janeiro, Inclui bibliografia 1. Engenharia Elétrica Teses. 2. Efeito Chicote. 3. Cadeia de abastecimento. 4. Controle de estoque. 5. Previsão. 6. Estoque de segurança.7.modelos ARMA.I.Veiga,Alvaro de Lima. II. Doody, Pat. III. Pontifícia Universidade Católica do Rio de Janeiro. Departamento de Engenharia Elétrica. IV. Título. CDD: 510

3 Marlene Isabel Silva Marchena Measuring and Implementing the Bullwhip Effect in Supply Chains Thesis presented to the Postgraduate Program in Electrical Engineering of the Departamento de Engenharia Elétrica do Centro Técnico Científico da PUC-Rio, as partial fulfillment of the requirements for the degree of Doutor. PUC-Rio - Certificação Digital Nº /CB Prof. Alvaro de Lima Veiga Filho Advisor Departamento de Engenharia Elétrica PUC-Rio Prof. Cristiano Augusto Coelho Fernandes Departamento de Engenharia Elétrica PUC-Rio Prof. Alexandre Street de Aguiar Departamento de Engenharia Elétrica PUC-Rio Oscar Porto GAPSO Prof. Julio Michael Stern USP Prof. José Eugenio Leal Coordinator of the Centro Técnico Científico da PUC-Rio Rio de Janeiro, 06 de dezembro de 2010

4 Acknowledgments This Ph.D. has been supported by Brazilian state science foundation (CAPES), PUC Rio and partly by the Centre for Innovation in Distributed Systems (CIDS), Ireland. After the formal acknowledgements, I would like to thank all the people who contributed to my personal and professional development during my PhD. I will list people in chronological order not to forget anybody. I want to thank Caio Ibsen Rodrigues Almeida, who introduced me to Alvaro Veiga, my supervisor, five years ago and made me discover the Department of Electrical Engineering at PUC-Rio. I am very grateful to Alvaro who believed in me all the time and made the realization of this thesis possible. I want to thank professors at PUC, in particular Alvaro, Cristiano Fernandes,OscarPortoandMarleyVellascofortheiradviceduringmystudies. I would also like to thank my colleagues at PUC-Rio, in particular Márcio Candeias, Rodrigo Moreira Topin, Camila Epprecht, Mariana Paixão and Renato Alencar for making my time at PUC a memorable one. I am very grateful to the people at CIDS. Specially, I want to thank my co-supervisor Pat Doody who believed in me and let me stay for one year and half at CIDS, Andrew Shields for all the time he spent solving my computer problemsandbrigidcrowleyforhersupportandforallthegoodtimesthatwe spend together. I am truly grateful to have had the opportunity to learn and conduct research in the company of such talented, hard-working, and creative people. I could not have asked for a better group of people to work with. I will never forget our trip to the MIT. A special thank to Shoumen Datta. I will always remember our first meeting where he gave me my first logistics book. I want to thank the members of the R-help list and Mario Morales for thehelpwiththersoftware. I am grateful to my parents that did many sacrifices to let me get where I am now. Finally, I would like to thank my son Esteban for always brightening up my days and to my husband Henri, who has been by my side supporting me all the time, for his unconditional love and encouragement, and for sharing with me all the good and bad things of our life. This thesis is dedicated to Henri and Esteban.

5 Abstract Marchena, Marlene Isabel Silva; Veiga Filho, Álvaro de Lima (Advisor). Measuring and Implementing the Bullwhip Effect in Supply Chains. Rio de Janeiro, p. Tese de Doutorado Departamento de Engenharia Elétrica, Pontifícia Universidade Católica do Rio de Janeiro. PUC-Rio - Certificação Digital Nº /CB Keywords Bullwhip effect. Supply chain. Inventory control. Forecastinh. Safety stock. ARMA models.

6 Resumo Marchena, Marlene Isabel Silva; Veiga Filho, Álvaro de Lima (Orientador). Medindo e Implementando o Efeito Chicote em Cadeias de Oferta. Rio de Janeiro, p. Tese de Doutorado Departamento de Engenharia Elétrica, Pontifícia Universidade Católica do Rio de Janeiro. Palavras-chave Efeito Chicote. Cadeia de abastecimento. Controle de estoque. Previsão. Estoque de segurança. Modelo ARMA.

7 Contents 1 Introduction Thesis contributions 15 2 Formalbackground Time series and forecasting methods Inventory control theory 26 3 The Bullwhip Effect Consequences of the bullwhip effect Causes of the bullwhip effect Remedies for the bullwhip effect Methodologies to study the bullwhip effect Measurement of the Bullwhip Effect 57 4 Measuring the bullwhip effect under a generalized demand process Inventory model ARMA(p,q) case Economic implications of the use of time series analysis 74 5 Measuring the bullwhip effect with traditional forecasting methods Simple Moving Averages Exponential Smoothing Managerial implications 82 6 A Supply Chain Management package for R 85 7 Conclusions and future work 89 Bibliography 93 A Homogeneus linear difference equations 99 B The fundamental theorem of calculus 103 C Proofs Chapter D Proofs Chapter E Rcodes 113