Skip to main content
Log in

A review of multi-component maintenance models with economic dependence

  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

In this paper we review the literature on multi-component maintenance models with economic dependence. The emphasis is on papers that appeared after 1991, but there is an overlap with Section 2 of the most recent review paper by Cho and Parlar (1991). We distinguish between stationary models, where a long-term stable situation is assumed, and dynamic models, which can take information into account that becomes available only on the short term. Within the stationary models we choose a classification scheme that is primarily based on the various options of grouping maintenance activities: grouping either corrective or preventive maintenance, or combining preventive-maintenance actions with corrective actions. As such, this classification links up with the possibilities for grouped maintenance activities that exist in practice.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Archibald TW, Dekker R (1996) Modified block-replacement for multiple-component systems. IEEE Transactions on Reliability 45:75–83

    Google Scholar 

  • Assaf D, Shanthikumar JG (1987) Optimal group maintenance policies with continuous and periodic inspections. Management Science 33:1440–1452

    Google Scholar 

  • Aven T, Bergman B (1986) Optimal replacement times — a general set-up. Journal of Applied Probability 23:432–442

    Google Scholar 

  • Bäckert W, Rippin DWT (1985) The determination of maintenance strategies for plants subject to breakdown. Computers and Chemical Engineering 9:113–126

    Google Scholar 

  • Berg M (1976) Optimal replacement policies for two-unit machines with increasing running costs. Stochastic Processes and their Applications 4:89–106

    Google Scholar 

  • Berg M (1978) General trigger-off replacement procedures for two-unit systems. Naval Research Logistics Quarterly 25:15–29

    Google Scholar 

  • Berg M, Epstein B (1976) A modified block replacement policy. Naval Research Logistics Quarterly 23:15–24

    Google Scholar 

  • Cho DI, Parlar M (1991) A survey of maintenance models for multi-unit systems. European Journal of Operational Research 51:1–23

    Google Scholar 

  • Dagpunar JS (1982) Formulation of a multi item single supplier inventory problem. Journal of the Operational Research Society 33:285–286

    Google Scholar 

  • Dekker R, Dijkstra MC (1992) Opportunity-based age replacement: Exponentially distributed times between opportunities. Naval Research Logistics 39:175–190

    Google Scholar 

  • Dekker R, Frenk JBG, Wildeman RE (1996) How to determine maintenance frequencies for multicomponent systems? A general approach. In: Reliability and maintenance of complex systems, Springer-Verlag, Berlin, Proceedings of the NATO-ASI, Antalya, 1995, pp. 233–274

    Google Scholar 

  • Dekker R, Roelvink IFK (1995) Marginal cost criteria for preventive replacement of a group of components. European Journal of Operational Research 84:467–480

    Google Scholar 

  • Dekker R, Smeitink E (1991) Opportunity-based block replacement: The single component case. European Journal of Operational Research 53:46–63

    Google Scholar 

  • Dekker R, Smeitink E (1994) Preventive maintenance at opportunities of restricted duration. Naval Research Logistics 41:335–353

    Google Scholar 

  • Dekker R, Smit ACJM, Losekoot JA (1992) Combining maintenance activities in an operational planning phase: a set-partitioning approach. IMA Journal of Mathematics Applied in Business and Industry 3:315–331

    Google Scholar 

  • Dekker R, van Rijn C (1996) PROMPT, a decision support system for opportunity-based preventive maintenance. In: Reliability and maintenance of complex systems, Springer-Verlag, Proceedings of the NATO-ASI, Antalya, 1995, pp. 517–536

  • Dekker R, Wildeman RE, van Egmond R (1996) Joint replacement in an operational planning phase. European Journal of Operational Research 91:74–88

    Google Scholar 

  • Duffuaa SO, Ben-Daya M (1994) An extended model for the joint overhaul scheduling problem. International Journal of Operations & Production Management 14:37–43

    Google Scholar 

  • Epstein S, Wilamowsky Y (1985) Opportunistic replacement in a deterministic environment. Computers & Operations Research 12:311–322

    Google Scholar 

  • Fard N, Zheng X (1991) An approximate method for non-repairable systems based on opportunistic replacement policy. Reliability Engineering and System Safety 33:277–288

    Google Scholar 

  • Federgruen A, Groenevelt H, Tijms HC (1984) Coordinated replenishments in a multi-item inventory system with compound poisson demands. Management Science 30:344–357

    Google Scholar 

  • Garey MR, Johnson DS (1979) Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Fransisco

    Google Scholar 

  • Gertsbakh IB (1977) Models of preventive maintenance. North-Holland, Amsterdam

    Google Scholar 

  • Gertsbakh IB (1984) Optimal group preventive maintenance of a system with observable state parameter. Advances in Applied Probability 16:923–925

    Google Scholar 

  • Goyal SK (1973) Determination of economic packaging frequency for items jointly replenished. Management Science 20:293–298

    Google Scholar 

  • Goyal SK, Gunasekaran A (1992) Determining economic maintenance frequency of a transport fleet. International Journal of Systems Science 4:655–659

    Google Scholar 

  • Goyal SK, Kusy MI (1985) Determining economic maintenance frequency for a family of machines. Journal of the Operational Research Society 36:1125–1128

    Google Scholar 

  • Goyal SK, Satir AT (1989) Joint replenishment inventory control: Deterministic and stochastic models. European Journal of Operational Research 38:2–13

    Google Scholar 

  • Hariga M (1994a) Coordinated overhaul scheduling of production units. Naval Research Logistics 41:565–577

    Google Scholar 

  • Hariga M (1994b) A deterministic maintenance-scheduling problem for a group of non-identical machines. International Journal of Operations & Production Management 14:27–36

    Google Scholar 

  • Hariga MA, Jackson PL (1990) The warehouse scheduling problem: Formulation and algorithm. Technical Report 932, School of OR & IE, Cornell University, Ithaca, NY

    Google Scholar 

  • Haurie A, L'Ecuyer P (1982) A stochastic control approach to group preventive replacement in a multicomponent system. IEEE Transactions on Automatic Control 27:387–393

    Google Scholar 

  • Jackson PL, Maxwell WL, Muckstadt JA (1985) The joint replenishment problem with a power-of-two restriction. HE Transactions 17:25–32

    Google Scholar 

  • Jansen J, van der Duyn Scheuten FA (1995) Maintenance optimization on parallel production units. IMA Journal of Mathematics Applied in Business & Industry 6:113–134

    Google Scholar 

  • Jorgenson DW, McCall JJ (1963) Optimal replacement policies for a ballistic missile. Management Science 9:358–379

    Google Scholar 

  • Kaspi M, Rosenblatt MJ (1991) On the economic ordering quantity for jointly replenished items. International Journal of Production Research 29:107–114

    Google Scholar 

  • Kralj BL, Petrovic R (1987) Optimal preventive maintenance scheduling of thermal generating units in power systems — a survey of problem formulations and solution methods. European Journal of Operational Research 35:1–15

    Google Scholar 

  • Liang TY (1985) Optimum piggyback preventive maintenance policies. IEEE Transactions on Reliability 34:529–538

    Google Scholar 

  • Maxwell WL, Muckstadt JA (1985) Establishing consistent and realistic reorder intervals in production-distribution systems. Operations Research 33:1316–1341

    Google Scholar 

  • McCall JJ (1963) Operating characteristics of opportunistic replacement and inspection policies. Management Science 10:85–97

    Google Scholar 

  • Ohashi M (1982) Group replacement policy for a maintained coherent system. Journal of the Operations Research Society of Japan 25:228–237

    Google Scholar 

  • Okumoto K, Elsayed EA (1983) An optimum group maintenance policy. Naval Research Logistics Quarterly 30:667–674

    Google Scholar 

  • Özekici S (1988) Optimal periodic replacement of multi-component reliability systems. Operations Research 36:542–552

    Google Scholar 

  • Radner R, Jorgenson DW (1963) Opportunistic replacement of a single part in the presence of several monitored parts. Management Science 10:70–84

    Google Scholar 

  • Ritchken P, Wilson JG (1990) (m, T) group maintenance policies. Management Science 36:632–639

    Google Scholar 

  • Sculli D, Wu SY (1981) Block replacement for units whose components have weibull life distributions. Computers and Operations Research 8:295–302

    Google Scholar 

  • Sheu SH (1991) A generalized block replacement policy with minimal repair and general random repair costs for a multi-unit system. Journal of the Operational Research Society 42:331–341

    Google Scholar 

  • Silver EA (1976) A simple method of determining order quantities in joint replenishments under deterministic demand. Management Science 22:1351–1361

    Google Scholar 

  • Sivazlian BD, Mahoney JF (1978) Group replacement of a multicomponent system which is subject to deterioration only. Advances in Applied Probability 10:867–885

    Google Scholar 

  • Stinson JP, Khumawala BM (1987) The replacement of machines in a serially dependent multimachine production system. International Journal of Production Research 25:677–688

    Google Scholar 

  • Suie DR, Harmon B (1979) Determination of coordinated maintenance scheduling frequencies for a group of machines. AIIE Transactions 11:48–53

    Google Scholar 

  • Tatsuno K, Ohi F, Nishida T (1983) Opportunistic maintenance policy with minimal repair. Mathematica Japonica 28:327–335

    Google Scholar 

  • Thomas LC (1986) A survey of maintenance and replacement models for maintainability and reliability of multi-item systems. Reliability Engineering 16:297–309

    Google Scholar 

  • Van der Duyn Schouten FA, Vanneste SG (1990) Analysis and computation of (n, N)-strategies for maintenance of a two-component system. European Journal of Operational Research 48:260–274

    Google Scholar 

  • Van der Duyn Schouten FA, Vanneste SG (1993) Two simple control policies for a multicomponent maintenance systems. Operations Research 41:1125–1136

    Google Scholar 

  • Van Dijkhuizen G, van Harten A (1996) Optimal clustering of repetitive frequency-constrained maintenance jobs with shared setups. Technical report, University of Twente, The Netherlands, to appear in the European Journal of Operational Research

    Google Scholar 

  • Van Eijs MJG (1994) On the determination of the control parameters of the optimal can-order strategy. Zeitschrift für Operations Research 39:289–304

    Google Scholar 

  • Van Eijs MJG, Heuts RMJ, Kleijnen JPC (1992) Analysis and comparison of two strategies for multi-item inventory systems with joint replenishment costs. European Journal of Operational Research 59:405–412

    Google Scholar 

  • Vanneste SG (1992) A generalized age-replacement model. Probability in the Engineering and Informational Sciences 6:525–541

    Google Scholar 

  • Vergin RC, Scriabin M (1977) Maintenance scheduling for multicomponent equipment. AIIE Transactions 9:297–305

    Google Scholar 

  • Vos de Wael S (1995) A decision support system for LampRemplace (in Dutch: Strategieën voor LampRemplace). Master's thesis, Tilburg University, The Netherlands

    Google Scholar 

  • Wijnmalen DJD, Hontelez JAM (1996) Coordinated condition-based repair strategies for components of a multi-component maintenance system with discounts. To appear in the European Journal of Operational Research

  • Wildeman RE, Dekker R (1996) Dynamic influences in multi-component maintenance. Technical Report 9630/A, Econometric Institute, Erasmus University Rotterdam, submitted for publication; report available on internet http://www.eur.nl/few/ei/papers/# Reports

  • Wildeman RE, Dekker R, Smit ACJM (1996) A dynamic policy for grouping maintenance activities. Technical Report 9537/A, Econometric Institute, Erasmus University Rotterdam, to appear in the European Journal of Operational Research; report available on internet http://www.eur.nl/few/ei/papers/ # Reports

  • Wildeman RE, Frenk JBG, Dekker R (1996) An efficient optimal solution method for the joint replenishment problem. Technical Report 9542/A, Econometric Institute, Erasmus University Rotterdam, to appear in the European Journal of Operational Research; report available on internet http://www.eur.nl/few/ei/papers/# Reports

  • Wildeman RE, Frenk JBG, Dekker R, van Egmond R (1995) A general approach for the coordination of maintenance frequencies. Technical Report 9539/A, Econometric Institute, Erasmus University Rotterdam, submitted for publication; report available on internet http://www.eur.nl/few/ei/papers/# Reports

  • Worm JM, van Harten A (1996) Model based decision support for planning of road maintenance. Reliability Engineering & System Safety 51:305–316

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dekker, R., Wildeman, R.E. & van der Duyn Schouten, F.A. A review of multi-component maintenance models with economic dependence. Mathematical Methods of Operations Research 45, 411–435 (1997). https://doi.org/10.1007/BF01194788

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01194788

Key words

Navigation