Skip to main content
Springer Nature Link
Log in

A theoretical validation of the DDMRP reorder policy

  • Original Paper
  • Published:
Computational Management Science Aims and scope Submit manuscript

Abstract

A recent heuristic called Demand Driven MRP, widely implemented using modern ERP systems, proposes reorder policy based on buffers. Buffers are amounts of inventory positioned and set to control the net flow position, responding to stochastic demand and lead time. Our primary goal is to propose a theoretical foundation for such a heuristic approach. To this aim, we develop an optimization model inspired by the main principles behind the heuristic algorithm. Specifically, optimal policies are of the type (s(t), S(t)) with time-varying thresholds that react to short-run real orders. We introduce constraints related to the service levels, that are written as tail risk measures to ensure fulfillment of realized demand with a predetermined probability. Interestingly, it turns out that such constraints allow to analytically justify an empirical rule that the DDMRP employs to set the risk parameters used in the heuristic. Finally, we use our model as a benchmark to theoretically validate and contextualize the aforementioned heuristic.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. An explicit formulation for \({\tilde{d}}_s\) will be provided when running simulations in Sect. 4.

  2. According to the DDMRP methodology, the green zone can also take into account the presence of minimum order quantities or order cycles. For more details on these aspects, see Slack et al. (2010) or Jacobs et al. (2011).

  3. Time-varying standard deviations could also be considered, but this would make notations and derivations more cumbersome.

  4. Formally, it is defined a filtered probability space \((\Omega , \mathcal F, (\mathcal F_t)_{0\le t\le T} \mathbb P)\) such that \(L,\,D,\,\Xi \) are \(\mathcal F\)-measurable. \(h_t\) and \(ADU_t\) are, instead, \(\mathcal F_t\) measurable; in this respect, they are “known”at time t.

  5. Concerning constraints (15)–(16), \(\ell \) fictitious values of \(u_s\), \(s=-\ell +1, \dots , 0\) are set to zero.

  6. \(VaR_{\varepsilon }\) is defined as the (smallest) quantity \(x\in \mathbb R\) such that \(\mathbb P(D\ge x)\le \varepsilon \). The parameter \(\varepsilon \) can be fixed considering the decision-maker’s risk aversion; for example, if \(\varepsilon =0.1\), then \(\Phi ^{-1}(1-\varepsilon )\approx 1.28\); if \(\varepsilon =0.3\), \(\Phi ^{-1}(1-\varepsilon )\approx 0.52\) (McNeil et al. 2015). \(\varepsilon = 0.1\) means that an out-of-stock event occurs with probability 10%.

  7. In detail, \(\sqrt{1+z^2}\approx 1+\frac{1}{2} z^2\) and \(e^z=1+z+\frac{1}{2}z^2\), if z is small.

  8. Concerning constraints (23)–(24), \(\ell \) fictitious values of \(u_s\), \(s=-\ell +1, \dots , 0\) are set to zero.

  9. Having set \(q_2=0\), the computation of the peak involves only one period into the future (see Equation (21)).

  10. The seed in the numerical simulation is fixed to ensure the comparability of all instances of the different experiments.

  11. Depending on the lead time, each simulation is run over a time period defined as \(T+\ell \). Ex post, we neglect the first \(\ell \) periods to reach a stationary behavior of inventory, ensuring the comparability of the three experiments. Concerning the computation time, the more demanding case is the one with a small lead time. The software takes approximately 1654s to solve such instance.

  12. As an example, consider the production of small components of great precision (such as lenses for personal devices), requiring ultra precision and micro machining, or high expedition costs (Jáuregui et al. 2010).

References

  • Alfares HK (2007) Inventory model with stock-level dependent demand rate and variable holding cost. Int J Prod Econ 108(1–2):259–265

    Google Scholar 

  • Aloulou MA, Dolgui A, Kovalyov MY (2014) A bibliography of non-deterministic lot-sizing models. Int J Prod Econ 52(8):2293–2310

    Google Scholar 

  • Alp O, Erkip NK, Güllü R (2003) Optimal lot-sizing/vehicle-dispatching policies under stochastic lead times and stepwise fixed costs. Oper Res 51(1):160–166

    Google Scholar 

  • Azzamouri A, Baptiste P, Dessevre G, Pellerin R (2021) Demand driven material requirements planning (ddmrp): a systematic review and classification. J Ind Eng Manag 14(3):439–456

    Google Scholar 

  • Azzi A, Battini D, Faccio M, Persona A, Sgarbossa F (2014) Inventory holding costs measurement: a multi-case study. Int J Logist Manag

  • Bahu B, Bironneau L, Hovelaque V (2019) Compréhension du ddmrp et de son adoption: premiers éléments empiriques. Logist Manag 27(1):20–32

    Google Scholar 

  • Bayard S, Grimaud F (2018) Enjeux financiers de ddmrp: Une approche simulatoire. In: 12e Conférence Internationale de Modélisation, Optimisation et SIMulation-MOSIM’18

  • Brahimi N, Absi N, Dauzère-Pérès S, Nordli A (2017) Single-item dynamic lot-sizing problems: an updated survey. Eur J Oper Res 263(3):838–863

    Google Scholar 

  • Cannella S, Dominguez R, Ponte B, Framinan JM (2018) Capacity restrictions and supply chain performance: modelling and analysing load-dependent lead times. Int J Prod Econ 204:264–277

    Google Scholar 

  • Chen FY, Krass D (2001) Inventory models with minimal service level constraints. Eur J Oper Res 134(1):120–140

    Google Scholar 

  • Cobb BR, Rumí R, Salmerón A (2013) Inventory management with log-normal demand per unit time. Comput Oper Res 40(7):1842–1851

    Google Scholar 

  • Das C (1983) Inventory control for lognormal demand. Comput Oper Res 10(3):267–276

    Google Scholar 

  • Dessevre G, Martin G, Pierre B, Lamothe J, Lauras M (2019) Étude d’impact du paramétrage des temps de défilement sur la performance d’un déploiement de la méthode ddmrp. In: CIGI QUALITA 2019-13eme Conférence Internationale CIGI QUALITA

  • Eppen GD, Martin RK (1988) Determining safety stock in the presence of stochastic lead time and demand. Manag Sci 34(11):1380–1390

    Google Scholar 

  • Erraoui Y, Charkaoui A, Echchatbi A (2019) Demand driven drp: assessment of a new approach to distribution. Int J Supply Oper Manag 6(1):1–10

    Google Scholar 

  • Gardiner SC, Blackstone J Jr (1995) Setups and effective capacity: the impact of lot sizing techniques in an MRP environment. Prod Plan Control 6(1):26–38

    Google Scholar 

  • Goldratt EM (1990) Theory of constraints. North River Croton-on-Hudson

  • Hayya JC, Harrison TP, Chatfield DC (2009) A solution for the intractable inventory model when both demand and lead time are stochastic. Int J Prod Econ 122(2):595–605

    Google Scholar 

  • Hayya JC, Kim JG, Disney SM, Harrison TP, Chatfield D (2006) Estimation in supply chain inventory management. Int J Prod Res 44(7):1313–1330

    Google Scholar 

  • Ihme M, Stratton R (2015) Evaluating demand driven mrp: a case based simulated study. In: International Conference of the European Operations Management Association, Neuchâtel, Switzerland

  • Jacobs FR, Chase RB, Lummus RR (2011) Operations and supply chain management. McGraw-Hill, New York

    Google Scholar 

  • Jáuregui AL, Siller HR, Rodríguez CA, Elías-Zúñiga A (2010) Evaluation of micromechanical manufacturing processes for microfluidic devices. Int J Adv Manuf Technol 48(9):963–972

    Google Scholar 

  • Jing F, Chao X (2021) A dynamic lot size model with perishable inventory and stockout. Omega 103:102421

    Google Scholar 

  • Jorion P (1996) Risk\(^2\): measuring the risk in value at risk. Financ Anal J 52(6):47–56

    Google Scholar 

  • Kaplan RS (1970) A dynamic inventory model with stochastic lead times. Manag Sci 16(7):491–507

    Google Scholar 

  • Kortabarria A, Apaolaza U, Lizarralde A, Amorrortu I (2018) Material management without forecasting: from MRP to demand driven MRP. J Ind Eng Manag 11(4):632–650

    Google Scholar 

  • Lee C-J, Rim S-C (2019) A mathematical safety stock model for ddmrp inventory replenishment. Math Probl Eng

  • McNeil AJ, Frey R, Embrechts P (2015) Quantitative risk management: concepts, techniques and tools-revised edition. Princeton University Press

    Google Scholar 

  • Miclo R (2016) Challenging the “Demand Driven MRP” promises: a Discrete Event Simulation Approach. PhD thesis, Ecole des Mines d’Albi-Carmaux

  • Miclo R, Fontanili F, Lauras M, Lamothe J, Milian B (2015) MRP vs. demand-driven MRP: towards an objective comparison. In: 2015 International Conference on Industrial Engineering and Systems Management (IESM), pp 1072–1080

  • Miclo R, Fontanili F, Lauras M, Lamothe J, Milian B (2016) An empirical comparison of mrpii and demand-driven MRP. IFAC-PapersOnLine 49(12):1725–1730

    Google Scholar 

  • Miclo R, Lauras M, Fontanili F, Lamothe J, Melnyk SA (2019) Demand driven MRP: assessment of a new approach to materials management. Int J Prod Res 57(1):166–181

    Google Scholar 

  • Mohammad FH, Benali M, Baptiste P (2022) An optimization model for demand-driven distribution resource planning dddrp. J Ind Eng Manag 15(2):338–349

    Google Scholar 

  • Orlicky JA (1974) Material requirements planning: the new way of life in production and inventory management. McGraw-Hill

    Google Scholar 

  • Orobia LA, Nakibuuka J, Bananuka J, Akisimire R (2020) Inventory management, managerial competence and financial performance of small businesses. J Account Emerg Econ

  • Orue A, Lizarralde A, Kortabarria A (2020) Demand driven MRP-the need to standardise an implementation process. Int J Prod Manag Eng 8(2):65–73

    Google Scholar 

  • Pekarčíková M, Trebuňa P, Kliment M, Trojan J (2019) Demand driven material requirements planning. some methodical and practical comments. Manag Prod Eng Rev 10:50–59

    Google Scholar 

  • Ptak C, Smith C (2016) Demand driven material requirements planning (DDMRP). Industrial Press

    Google Scholar 

  • Radasanu AC et al (2016) Inventory management, service level and safety stock. J Pub Adm Financ Law 9(09):145–153

    Google Scholar 

  • Ramasesh RV, Ord JK, Hayya JC, Pan A (1991) Sole versus dual sourcing in stochastic lead-time (s, q) inventory models. Manag Sci 37(4):428–443

    Google Scholar 

  • Robinson LW, Bradley JR (2008) Further improvements on base-stock approximations for independent stochastic lead times with order crossover. Manuf Serv Oper Manag 10(2):325–327

    Google Scholar 

  • Román Cuadra R et al. (2017) Estudio del ddmrp (demand-driven materials requirement planning). Master’s thesis, Universidad de Valladolid

  • Schroeder RG, Linderman K, Liedtke C, Choo AS (2008) Six sigma: definition and underlying theory. J Oper Manag 26(4):536–554

    Google Scholar 

  • Schwartz SC, Yeh Y-S (1982) On the distribution function and moments of power sums with log-normal components. Bell Syst Tech J 61(7):1441–1462

    Google Scholar 

  • Shofa MJ, Widyarto WO (2017) Effective production control in an automotive industry: MRP vs. demand-driven mrp. In: AIP Conference Proceedings. AIP Publishing

  • Slack N, Chambers S, Johnston R (2010) Operations management. Pearson

    Google Scholar 

  • Smith D, Smith C (2013) Becoming demand driven: how to change from push and promote to position and pull. Strateg Financ 95(5):37–46

    Google Scholar 

  • Smith D, Smith C (2013) Demand driven performance. McGraw Hill

    Google Scholar 

  • So KC, Zheng X (2003) Impact of supplier’s lead time and forecast demand updating on retailer’s order quantity variability in a two-level supply chain. Int J Prod Econ 86(2):169–179

    Google Scholar 

  • Sodhi MS (2005) Managing demand risk in tactical supply chain planning for a global consumer electronics company. Prod Oper Manag 14(1):69–79

    Google Scholar 

  • Sox CR (1997) Dynamic lot sizing with random demand and non-stationary costs. Oper Res Lett 20(4):155–164

    Google Scholar 

  • Srivastav A, Agrawal S (2020) On a single item single stage mixture inventory models with independent stochastic lead times. Oper Res 20(4):2189–2227

    Google Scholar 

  • Sugimori Y, Kusunoki K, Cho F, Uchikawa S (1977) Toyota production system and Kanban system materialization of just-in-time and respect-for-human system. Int J Prod Res 15(6):553–564

    Google Scholar 

  • Tadikamalla PR (1984) A comparison of several approximations to the lead time demand distribution. Omega 12(6):575–581

    Google Scholar 

  • Tempelmeier H (2007) On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints. Eur J Oper Res 181(1):184–194

    Google Scholar 

  • Tempelmeier H (2013) Stochastic lot sizing problems. Handbook of stochastic models and analysis of manufacturing system operations. Springer, pp 313–344

    Google Scholar 

  • Thürer M, Fernandes NO, Stevenson M (2020) Production planning and control in multi-stage assembly systems: an assessment of Kanban, MRP, opt (dbr) and ddmrp by simulation. Int J Prod Res, pp 1–15

  • Villa Hincapie V (2018) Application of demand driven material requirement planning (DDMRP) methodology for components inventory management in a company of automotive industry. PhD thesis, Politecnico di Torino

  • Zipkin P (1986) Stochastic leadtimes in continuous-time inventory models. Nav Res Logist Q 33(4):763–774

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management, Università Ca’ Foscari Venezia, Fondamenta San Giobbe 873, Cannaregio, 30121, Venice, Italy

    Daniela Favaretto, Alessandro Marin & Marco Tolotti

  2. Qantica S.r.l., Padua, Italy

    Alessandro Marin

Authors
  1. Daniela Favaretto
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Alessandro Marin
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Marco Tolotti
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Marco Tolotti.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors acknowledge financial support by Qantica S.r.l.; they thank Raffaele Pesenti for insipring discussions and three anonymous reviewers for their valuable comments on an earlier version of the paper.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Favaretto, D., Marin, A. & Tolotti, M. A theoretical validation of the DDMRP reorder policy. Comput Manag Sci 20, 8 (2023). https://doi.org/10.1007/s10287-023-00443-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10287-023-00443-5

Keywords