2019 | 14 | 5-28
Article title

Spare Parts Quantity Problem Under Uncertainty – the Case of Entirely New Devices With Short Life Cycle

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The paper presents a new scenario-based decision rule for the spare parts quantity problem (SPQP) under uncertainty with unknown objective probabilities. The goal of SPQP is to ensure the right number of extra parts at the right place at the right time. In the literature, SPQP is usually regarded as a stochastic problem since the demand for extra parts is treated as a random variable with a known distribution. The optimal stock quantity minimizes the expected loss resulting from buying a given number of parts before potential failures. The novel approach is designed for the purchase of non-repairable spare parts for entirely new seasonal devices, where the estimation of frequencies is complicated because there are no historical data about previous failures. Additionally, the decision maker’s knowledge is limited due to the nature of the problem. The new procedure is a three-criteria method. It is based on the Hurwicz and Bayes decision rules and supported with a forecasting stage enabling one to set the scenario with the greatest subjective chance of occurrence. The method takes into account the decision maker’s attitude towards risk and the asymmetry of losses connected with particular stock quantities. We assume that the future unit purchase cost of a service part bought after the breakdown is also uncertain and given as an interval parameter. The approach is designed for short life cycle machines.
Physical description
  • Poznań University of Economics and Business. Department of Operations Research. Poznań, Poland
  • Aronis K.P., Magou I., Dekker R., Tagaras G. (2004), Inventory Control of Spare Parts Using a Bayesian Approach: A Case Study, European Journal of Operational Research, 154, 730-739.
  • Bartakke M.N. (1981), A Method of Spare Parts Inventory Planning, Omega, 9(1), 51-58.
  • Basili M., Chateauneuf A. (2011), Extreme Events and Entropy: A Multiple Quantile Utility Model, International Journal of Approximate Reasoning, 52, 1095-1102.
  • Bian J., Guo L., Yang Y., Wang N. (2013), Optimizing Spare Parts Inventory for Time-varying Task, Chemical Engineering Transactions, 33, 637-642.
  • Caplan B. (2001), Probability, Common Sense, and Realism: A Reply to Hulsmann and Block, The Quarterly Journal of Austrian Economics, 4(2), 69-86.
  • Carnap R. (1950), Logical Foundations of Probability, University of Chicago Press, Chicago.
  • Czerwinski Z. (1960), Enumerative Induction and the Theory of Games, Studia Logica, 10.
  • De Jonge B., Klingenberg W., Teunter R., Tinga T. (2015), Optimum Maintenance Strategy under Uncertainty in the Lifetime Distribution, Reliability Engineering and System Safety, 133, 59-67.
  • Ellsberg D. (2001), Risk. Ambiguity and Decision, Garland Publishing, New York.
  • Etner J., Jeleva M., Tallon J.-M. (2012), Decision Theory under Ambiguity, Journal of Economic Surveys, 26(2), 234-270.
  • Fera M., Lambiase A., Nenni M.E. (2010), A Proposal for Estimating the Order Level for Slow Moving Spare Parts Subject to Obsolescence, iBusiness, 2010, 2, 232-237.
  • de Finetti B. (1975), Theory of Probability. A Critical Introductory Treatment, Wiley & Sons, London.
  • Fortuin L. (1981), Reduction of the All-time Requirement for Spare Parts, International Journal of Operations and Production Management, 2, 29-37.
  • Fréchet M. (1938), The Diverse Definitions of Probability, Lecture read at the fourth International Congress for the Unity of Science, Erkenntnis.
  • García G.M.J., Hernández R.J.G., Hernández G.G.J. (2012), Making Decisions under Risk and Uncertainty of the Virtual Channel Manager of the Logistic Model Based on Positions, [in:] G. Dukic (ed.), Proceedings ICIL’2012, Croatia, University of Zagreb, 448-455.
  • Gaspars-Wieloch H. (2014a), Propozycja hybrydy reguł Hurwicza i Bayesa w podejmowaniu decyzji w warunkach niepewności [A Hybrid of the Hurwicz and Bayes Rules in Decision Making under Uncertainty], [in:] T. Trzaskalik (ed.), Modelowanie preferencji a ryzyko’14, Studia Ekonomiczne. Zeszyty Naukowe Uniwersytetu Ekonomicznego w Katowicach 178, 74-92 [in Polish].
  • Gaspars-Wieloch H. (2014b), Modifications of the Hurwicz’s Decision Rules, Central European Journal of Operations Research, 22(4), 779-794.
  • Gaspars-Wieloch H. (2014c), Modification of the Maximin Joy Criterion for Decision Making under Uncertainty, Quantitative Methods in Economics, 15(2), 84-93.
  • Gaspars-Wieloch H. (2015a), On a Decision Rule Supported by a Forecasting Stage Based on the Decision Maker’s Coefficient of Optimism, Central European Journal of Operations Research, 23(3), 579-594.
  • Gaspars-Wieloch H. (2015b), Innovative Products and Newsvendor Problem under Uncertainty without Probabilities, [in:] S.L. Zadnik, J. Zerovnik, M. Kljajic Borstnar, S. Drobne (eds.), Proceedings of the 13th International Symposium of Operational Research SOR’15. Slovenian Society INFORMATIKA (SDI). Section for Operational Research (SOR), 343-350.
  • Gaspars-Wieloch H. (2016a), Resource Allocation under Complete Uncertainty – Case of Asymmetric Payoffs, Organization and Management, 96, 247-258.
  • Gaspars-Wieloch H., Michalska E. (2016b), On Two Applications of the Omega Ratio: maxOmegamin and Omega(H+B), Research Papers of Wrocław University of Economics, 446, Metody i zastosowania badań operacyjnych, Wrocław, 21-36.
  • Gaspars-Wieloch H. (2017a), A Decision Rule Based on Goal Programming and One-stage Models for Uncertain Multi-criteria Mixed Decision Making and Games Against Nature, Croatian Operational Research Review, 8(1), 61-76.
  • Gaspars-Wieloch H. (2017b), Newsvendor Problem under Complete Uncertainty: A Case of Innovative Products, Central European Journal of Operations Research, 25(3), 561-585.
  • Gaspars-Wieloch H. (2018a), The Impact of the Structure of the Payoff Matrix on the Final Decision Made under Uncertainty, Asia-Pacific Journal of Operational Research, 35(1).
  • Gaspars-Wieloch H. (2018b), Podejmowanie decyzji w warunkach niepewności – planowanie scenariuszowe, reguły decyzyjne i wybrane zastosowania ekonomiczne [Decision Making under Uncertainty – Scenario Planning, Decision Rules and Selected Economic Applications], Wydawnictwo Uniwersytetu Ekonomicznego w Poznaniu, Poznań [in Polish].
  • Gaspars-Wieloch H. (2019a), Project Net Present Value Estimation under Uncertainty, Central European Journal of Operations Research, 27, 179-197.
  • Gaspars-Wieloch H. (2019b), Role of Scenario Planning and Probabilities in Economic Decisions Problems – Literature Review and New Conclusions, Contemporary Issues in Business, Management and Education – Conference Proceedings.
  • Gilboa I. (2009), Theory of Decision under Uncertainty, Cambridge University Press, Cambridge, New York.
  • Gilboa I., Schmeidler D. (1989), Maxmin Expected Utility with Non-unique Prior, Journal of Mathematical Economics, 18, 141-153.
  • Gu J., Li K. (2015), Efficient Aircraft Spare Parts Inventory Management under Demand Uncertainty, Journal of Air Transport Management, 42, 101-109.
  • Guide V.D.R., Srivastava R. (1997), Repairable Inventory Theory: Models and Applications, European Journal of Operational Research, 102, 1-20.
  • Guo P. (2011), One-shot Decision Theory, IEEE Transactions on Systems, Man and Cybernetics, Part A, 41(5), 917-926.
  • Hau R., Pleskac T.J., Hertwig R. (2009), Decisions from Experience and Statistical Probabilities: Why They Trigger Different Choices than a Priori Probabilities? Journal of Behavioral Decision Making, 23(1), 48-68.
  • Hayashi T. (2008), Regret Aversion and Opportunity Dependence, Journal of Economic Theory, 139(1), 242-268.
  • Hildebrandt P., Knoke T. (2011), Investment Decisions under Uncertainty A Methodological Review on Forest Science Studies, Forest Policy and Economics, 13, 1-15.
  • Hurwicz L. (1952), A Criterion for Decision Making under Uncertainty, Technical Report 355, Cowles Commission.
  • Inderfurth K., Mukherjee K. (2008), Decision Support for Spare Parts Acquisition in Post Product Life Cycle, Central European Journal of Operations Research, 16(1), 17-42.
  • Ioan C., Ioan G. (2011), A Method of Choice of the Best Alternative in the Multiple Solutions Case in the Games Theory, Journal of Accounting and Management, 1(1), 5-8.
  • Kennedy W.J., Patterson J.W., Fredendall L.D. (2002), An Overview of Recent Literature on Spare Parts Inventories, International Journal of Production Economics, 76, 201-215.
  • Knight F.H. (1921), Risk. Uncertainty. Profit, Hart. Boston MA, Schaffner & Marx, Houghton Mifflin Co.
  • Kolmogorov A.N. (1933), Grundbegriffe der Wahrscheinlichkeitsrechnung, Julius Springer Verlag, Berlin.
  • Louit D., Banjevic D., Jardine A.K.S. (2005), Optimization of Spare Parts Inventories Composed of Non-repairable or Repairable Parts, Proceedings of the International Conference of Maintenance Societies, ICOMS, paper 23, Hobart, Australia.
  • Marinacci M. (2002), Probabilistic Sophistication and Multiple Priors, Econometrica, 70, 755-764.
  • Milnor J. (1954), Games Against Nature, [in:] R.M. Thrall, C.H. Coombs, R.L. Davis (eds.), Decision Processes, Wiley, New York, 49-60.
  • von Mises L. (1949), Human Action. A Treatise on Economics, The Ludwig von Mises Institute, Auburn, Alabama.
  • von Mises R. (1957), Probability, Statistics and Truth, The Macmillan Company, New York.
  • Papathanassiu B., Tsouros C. (1986), Determining the Optimal Place and Capacity of Spare Parts Warehouses in the Construction Industry, European Journal of Operational Research, 27(1), 91-94.
  • Pastore E., Alferi A., Zotteri G. (2015), Managing Different Demand Classes in a Spare Parts Inventory: A Practical Dynamic Allocation Strategy, Proceedings of the 13th International Symposium on Operational Research, SOR’15, 79-84.
  • Pereira Jr J.G., Ekel P. Ya, Palhares R.M., Parreiras R.O. (2015), On Multicriteria Decision Making under Conditions of Uncertainty, Information Sciences, 324, 44-59.
  • Perez D.E., Hernandez J.G., Garcia M.J., Hernandez G.J. (2015), Hurwicz Method Modified and the Amplitude Model (TAM), [in:] N. Delener et al. (ed.), GBATA2015 Reading book, USA : GBATA, 559-566.
  • Petrovic R., Senborn A., Vujosevic M. (1986), Hierarchical Spare Parts Inventory Systems, Studies in Production and Engineering Economics 5, Elsevier, Amsterdam.
  • Petrovic R., Senborn A., Vujosevic M. (1989), A New Adaptive Algorithm for Determination of Stocks in Spare Parts Inventory Systems, Engineering Costs and Production Economics, 15(1), 405-410.
  • Piegat A. (2010), Uncertainty of Probability, Workshop on Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Warsaw, Poland.
  • Pomerol J.C. (2001), Scenario Development and Practical Decision Making under Uncertainty, Decision Support Systems, 31(2), 197-204.
  • Popper K. (1959), The Propensity Interpretation of Probability, The British Journal of the Philosophy of Science, 10(37), 25-42.
  • Qu L., Zhang Q. (2006), An Overview of Inventory Management for Spare Parts, Research and Exploration in Laboratory, 7, 004.
  • Ramsey F. (1931), Truth and Probability, [in:] F. Ramsey, The Foundations of Mathematics and Other Logical Essays, Kegan Paul, London: Routledge, 156-198.
  • Ravindran A.R. (2007), Operations Research and Management Science Handbook, CRC Press, Boca Raton, London, New York.
  • Rego J.R., Mesquita M.A. (2011), Spare Parts Inventory Control: A Literature Review, Producao, 21(4), 656-666.
  • Rodriguez M.A., Vecchietti A., Harjunkoski I., Grossmann I.E. (2013), Optimal Supply Chain Design and Management over a Multi-period Horizon under Demand Uncertainty, Part I: MINLP and MILP models, Computers and Chemical Engineering, 62, 194-210.
  • Romeijnders W., Teunter R., van Jaarsveld W. (2012), A Two-step Method for Forecasting Spare Parts Demand Using Information on Component Repairs, European Journal of Operational Research, 220(2), 386-393.
  • Rustenburg W.D., van Houtum G.J., Zijm W.H.M. (2000), Spare Parts Management for Technical Systems: Resupply of Spare Parts under Limited Budgets, IIE Transactions, 32, 1013-1026.
  • Savage L. (1961), The Foundations of Statistics Reconsidered, Studies in Subjective Probability, Wiley, New York, 173-188.
  • Schuh P., Schneider D., Funke L., Tracht K. (2015), Cost-optimal Spare Parts Inventory Planning for Wind Energy Systems, Logistics Research, 8, 4.
  • Sheikh A.K., Younas M., Raouf A. (2000), Reliability Based Spare Parts Forecasting and Procurement Strategies, [in:] M. Ben-Daya, S.O. Duffuaa, A. Raouf (eds.), Maintenance, Modeling and Optimization, Kluwer Academic Publishers, Boston.
  • Sikora W. (ed.) (2008), Badania Operacyjne [Operations research], Polskie Wydawnictwo Ekonomiczne, Warszawa [in Polish].
  • Stirling W.C. (2003), Satisficing Games and Decision Making. With Applications to Engineering and Computer Science, Cambridge University Press, New York.
  • Tversky A., Kahneman D. (1992), Advances in Prospect Theory: Cumulative Representation of Uncertainty, Journal of Risk and Uncertainty, 5, 297-323.
  • Van Lambalgen M. (1996), Randomness and Foundations of Probability: von Mises' Axiomatization of Random Sequences, Statistics, Probability and Game Theory: Papers in Honor of David Blackwell, Institute of Mathematical Statistics, University of Amsterdam.
  • Verrijdt J., Adan I., Dekok T. (1998), A Trade off Between Emergency Repair and Inventory Investment, IIE Transactions, 30, 119-132.
  • Wald A. (1950), Statistical Decision Functions, Wiley, New York.
  • Wong J.Y.F., Chung D.W.C., Ngai B.M.Y., Banjevic D., Jardine A.K.S. (1997), Evaluation of Spares Requirements Using Statistical and Probability Analysis Techniques, Transactions of Mechanical Engineering, I.E.Aust., 22, 77-84.
  • Zhu X., Guo P. (2016), The One-shot Decision Theory Based Production Planning Models, IEEE International Conference on Industrial Engineering and Engineering Management (IEEM).
  • Zio E., Pedroni N. (2013), Methods for Representing Uncertainty, A Literature Review, Apports de la recherche, 2013-3: Risk Analysis, Les Cahiers de la Sécurité Industrielle, FONCSI.
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