Abstract
The paper concerns with analysis of operational complexity of company supplier–customer relations. Well-known approach for measuring of operational complexity is based upon entropy. However, there are several approaches thereon. In the first part, we discuss various general measures of uncertainty of states, the power entropies in particular. In the second part, we use Shannon entropy as a base framework for our two case studies—the first, a supplier–customer system which implements managerial thresholds for processing product delivery term deviations, the second, a supplier system of the most important commodity in brewery industry, the malted barley. In both cases, we assume an existence of problem-oriented databases, which contain detailed records of all product orders, deliveries and forecasts in quantity and time having been scheduled and realized. Our general procedure elaborated consists of three basic steps—pre-processing of data with consistency checks in Java, calculation of histograms and empirical distribution functions, and finally, evaluation of conditional entropy. The last two steps are realized by Mathematica modules. Illustrative results of operational complexity measurement using entropy are provided for both case studies.
Similar content being viewed by others
References
Axsaeter S (2006) Inventory control. Springer, New York
Baranger M (2002) Chaos, complexity and entropy: a physics talk for non-physicists. http://www.necsi.edu/Projects/baranger/cce.pdf. Accessed 20 March 2014
Chryssolouris G, Efthymiou K, Papakostas D, Mourtzis G (2013) Flexibility and complexity: Is it a trade off? Int J Prod Res 51(23/24):6788–6802
Efthymiou K, Pagoropoulos A, Papakostas D, Mourtzis G, Chryssolouris G (2012) Manufacturing systems complexity review: challenges and outlook. Procedia CIRP 3:644–649
ElMaraghy W, ElMaraghy H, Tomiyama T, Monostori L (2012) Complexity in engineering design and manufacturing chains. CIRP Annals Manuf Technol 61:793–814
Feder M, Merhav N (1994) Relations between entropy and error probability. IEEE Trans Inform Theory 40:259–266
Filiz I (2010) An entropy-based approach for measuring complexity in supply chains. Int J Prod Res 48(12):3681–3696
Fugate BS, Autry ChW, Davis-Sramek B, Germain RN (2012) Does knowledge management facilitate logistics-based differentiation? The effect of global manufacturing reach. Int J Prod Econ 139: 496–509
Gao J, Liu F, Zhang J, Hu J, Cao Y (2013) Information entropy as a basic building block of complexity theory. Entropy 15:3396–3418
Hofman J, Lukáš L (2012) Quantitative measuring of operational complexity of supplier-customer system with control thresholds. Proceedings of the Mathematical Methods in Economics, pp 302–308
Hofman J, Lukáš L (2013) Measurement of operational complexity of supplier-customer system using entropy. Proceedings of the Mathematical Methods in Economics, pp 267–272
Hu SJ, Zhu X, Wang H, Koren Y (2008) Product variety and manufacturing complexity in assembly systems and supply chains. CIRP Annals Manuf Technol 57:45–48
Ivanov D, Sokolov B (2013) Control and system-theoretic identification of the supply chain dynamics domain for planning, analysis and adaptation of performance under uncertainty. Eur J Oper Res 224:313–323
Jacobs MA (2013) Complexity: toward an empirical measure. Technovation 33(4–5):111–118
Jain S, Srinivasa Raghavan NR (2009) A queuing approach for inventory planning with batch ordering in multi-echelon supply chains. Cent Eur J Oper Res 17(1):95–110
Jha PK, Jha R, Datt R, Guha SK (2011) Entropy in good manufacturing system: tool for duality assurance. Eur J Oper Res 211:658–665
Kaynak H, Hartley JL (2008) A replication and extension of quality management into the supply chain. J Oper Manag 26(4):468–489
Liberopoulos G, Papadopoulos CT, Tan B, MacGregor Smith J, Gershwin SB (2006) Stochastic modeling of manufacturing systems: advances in design, performance evaluation, and control issues. Springer, Berlin
Lukáš L (2012) Probabilistic models in management: Inventory theory and statistical description of demand (in Czech). Academia, Prague
Mala A (2013) Measuring of supplier–customer relations complexity using quantitative measures in specific company (Bachelor thesis, in Czech). University of West Bohemia, Plzeň
Martinez-Olvera C (2008) Entropy as an assessment tool of supply chain information sharing. Eur J Oper Res 185:405–417
Modrak V, Marton D (2012) Modelling and complexity assessment of assembly supply chain systems. Procedia Eng 48:428–435
Morales D, Vajda I (2012) Generalized information criteria for Bayes decisions. Kybernetika 48:714–749
Panda S, Saha S, Basu M (2009) An EOQ model for perishable products with discounted selling price and stock dependent demand. Cent Eur J Oper Res 17(1):31–53
Prajoto D, Olhager J (2012) Supply chain integration and performance: the effects of long-term relationships, information technology and sharing, and logistics integration. Int J Prod Econ 135:514–522
Prochorov JB, Rozanov JA (1967) Teorija verojatnostej (Theory of probability, in Russian). Nauka, Moscow
Schwarz M (2004) Stochastic models in inventory theory. Shaker Verlag GmbH, Aachen
Serdasaran S (2013) A review of supply chain complexity drivers. Comput Ind Eng 66(3):533–540
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(379–423):623–656
Sivadasan S, Efstathiou J, Frizelle G, Shirazi R, Calinescu A (2002) An information-theoretic methodology for measuring the operational complexity of supplier-customer systems. Int J Prod Manag 22(1):80–102
Sivadasan S, Efstathiou J, Calinescu A, Huaccho Huatuco L (2006) Advances on measuring the operational complexity of supplier-customer systems. Eur J Oper Res 171:208–226
Soldanova K (2012) Measuring of supplier-customer relations complexity using quantitative measures in Lubricant, Ltd. (Bachelor thesis, in Czech). University of West Bohemia, Plzeň, p 64
Takaoka T, Nakagawa Y (2010) Entropy as computational complexity. J Inf Proces 18:227–241
Vereshchagin NK, Muchnik AA (2011) On joint conditional complexity (entropy). Proc Steklov Inst Math 274(1):90–104. doi:10.1134/S008154381106006X
Wu X (2012) Calculation of the minimum computational complexity based on information entropy. Int J Comput Sci Appl 2(1):73–82
Wu Y, Frizelle G, Efstathiou J (2007) A study on the cost of operational complexity in customer–supplier systems. Int J Prod Econ 106:217–229
Wu YR, Huatuco LH, Frizelle G, Smart J (2013) A Method for analysing operational complexity in supply chains. J Oper Res Soc 64:654–667
Zhang Z (2011) Modeling complexity of cellular manufacturing systems. Appl Mathe Model 35(9):4189–4195
Acknowledgments
The research project was supported partially by the Grant SGS2014-047 Quantitative modelling and experiments for general and business economics of University of West Bohemia in Pilsen, Czech Republic, and partially by the Grant P403-15-20405S of the Grant Agency, Prague, Czech Republic.
The authors thank two anonymous referees for their helpful comments and insightful suggestions which improved the paper in numerous ways.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lukáš, L., Plevný, M. Using entropy for quantitative measurement of operational complexity of supplier–customer system: case studies. Cent Eur J Oper Res 24, 371–387 (2016). https://doi.org/10.1007/s10100-015-0386-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10100-015-0386-7