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Pooling heterogeneous products for manufacturing environments

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Abstract

In a stochastic environment pooling naturally leads to economies of scale, but heterogeneity can also create variability. In the article, we investigate this trade-off in the case of a manufacturing environment. Pooling for queueing systems has been widely investigated in the literature on the design of service systems; however, much less attention has been given to manufacturing systems where jobs are given a due date upon arrival. In such systems it is not the elapsed time until the actual completion of the job that counts, but rather the due date lead time that can be promised to the customer in order to guarantee a high service level. The purpose of the article is to get a deeper understanding about how pooling strategies and lead-time decisions can be implemented to attain a high due-date performance. To this end, we develop a simulation and analytical study to determine the benefits of pooling manufacturing systems with heterogeneous demand streams. Our work allows managers to identify the characteristics of production systems such that a pooling strategy would be beneficial. Our results demonstrate that when a due-date setting and scheduling mechanism is implemented, heterogeneity does generally not lead to deterioration of performance, as previously observed in service environments. Our studies also reveal that the benefits of pooling in terms of the expected sojourn time obtained by a simple analytical treatment can serve as a good prediction of the benefits of pooling on the average due date lead time in a wide range of situations.

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Notes

  1. We restrict our attention to the case in which a manufacturer assigns a due date to the incoming order (as opposed to customer requested due dates).

  2. Given that the DDLT that can be promised is influenced by an order’s expected sojourn time, we implement the SEPT policy because it minimizes the expected sojourn time and its computation is analytically tractable.

References

  • Altendorfer K (2015) Influence of lot size and planned lead time on service level and inventory for a single-stage production system with advance demand information and random required lead times. Int J Prod Econ 170:478–488

    Article  Google Scholar 

  • Altendorfer K, Jodlbauer H (2011) An analytical model for service level and tardiness in a single machine MTO production system. Int J Prod Res 49(7):1827–1850

    Article  Google Scholar 

  • Altendorfer K, Minner S (2015) Influence of order acceptance policies on optimal capacity investment with stochastic customer required lead times. Eur J Oper Res 243(2):555–565

    Article  Google Scholar 

  • Azaron A, Fynes B, Modarres M (2011) Due date assignment in repetitive projects. Int J Prod Econ 129(1):79–85

    Article  Google Scholar 

  • Baker KR, Bertrand JWM (1982) A dynamic priority rule for scheduling against due-dates. J Oper Manag 3(1):37–42

    Article  Google Scholar 

  • Baker KR, Trietsch D (2009) Principles of sequencing and scheduling. Wiley, Hoboken (chap Appendix A: Practical Processing Time Distributions)

    Book  Google Scholar 

  • Barman S (1998) The impact of priority rule combinations on lateness and tardiness. IIE Trans 30(5):495–504

    Article  Google Scholar 

  • Bassamboo A, Randhawa RS, Van Mieghem JA (2010a) A little flexibility is all you need: asymptotic optimality of tailored chaining and pairing in queuing systems. Working paper, Northwestern University, Evanston, IL

  • Bassamboo A, Randhawa RS, Van Mieghem JA (2010b) Optimal flexibility configurations in newsvendor networks: Going beyond chaining and pairing. Manag Sci 56(8):1285–1303

    Article  Google Scholar 

  • Baykasoğlu A, Göçken M, Unutmaz ZD (2008) New approaches to due date assignment in job shops. Eur J Oper Res 187(1):31–45

    Article  Google Scholar 

  • Benjaafar S (1995) Performance bounds for the effectiveness of pooling in multi-processing systems. Eur J Oper Res 87(2):375–388

    Article  Google Scholar 

  • Benjaafar S, Cooper WL, Kim JS (2005) On the benefits of pooling in production-inventory systems. Manag Sci 51(4):548–565

    Article  Google Scholar 

  • Board of Governors of the Federal Reserve System (2015) Industrial production and capacity utilization-G 17. [statistical release]. http://www.federalreserve.gov/releases/g17/Current/. Accessed 28 Sept 2015

  • Bookbinder JH, Noor AI (1985) Setting job-shop due-dates with service-level constraints. J Oper Res Soc 36(11):1017–1026

    Article  Google Scholar 

  • Buzacott JA (1996) Commonalities in reengineered business processes: models and issues. Manag Sci 42(5):768–782

    Article  Google Scholar 

  • Chen B, Matis TI (2013) A flexible dispatching rule for minimizing tardiness in job shop scheduling. Int J Prod Econ 141(1):360–365

    Article  Google Scholar 

  • Cheng TCE, Gupta MC (1989) Survey of scheduling research involving due date determination decisions. Eur J Oper Res 38(2):156–166

    Article  Google Scholar 

  • Chevalier P, Lamas A, Lu L, Mlinar T (2015) Revenue management for operations with urgent orders. Eur J Oper Res 240(2):476–487

    Article  Google Scholar 

  • Cox DR, Smith WL (1961) Queues. Methuen Co. Ltd, London

    Google Scholar 

  • Duenyas I (1995) Single facility due date setting with multiple customer classes. Manag Sci 41(4):608–619

    Article  Google Scholar 

  • Duenyas I, Hopp WJ (1995) Quoting customer lead times. Manag Sci 41(1):43–57

    Article  Google Scholar 

  • Easton FF, Moodie DR (1999) Pricing and lead time decisions for make-to-order firms with contingent orders. Eur J Oper Res 116(2):305–318

    Article  Google Scholar 

  • Enns ST, Grewal CS (2010) Lot size optimisation under pooled and unpooled scenarios in batch production system. Int J Prod Res 48(20):6085–6101

    Article  Google Scholar 

  • Gurumurth S, Benjaafar S (2004) Modeling and analysis of flexible queueing systems. Nav Res Logist 51(5):755–782

    Article  Google Scholar 

  • Hella Australia Pty Ltd (2007) Behr Hella service-bringing the world’s best thermal management products to the Australian automotive aftermarket. [press release]. http://www.hella.com/produktion/HellaAU/WebSite/Channels/Company/Press/National_Press/Company_News/BehrHellaPR.jsp. Accessed 15 Nov 2012

  • Hopp WJ, Spearman M (2008) Factory physiscs. McGraw-Hill, New-York

    Google Scholar 

  • Hopp WJ, Sturgis MLR (2000) Quoting manufacturing due dates subject to a service level constraint. IIE Trans 32(9):771–784

    Google Scholar 

  • Hübl A, Jodlbauer H, Altendorfer K (2013) Influence of dispatching rules on average production lead time for multi-stage production systems. Int J Prod Econ 144(2):479–484

    Article  Google Scholar 

  • Ivanescu CV, Fransoo JC, Bertrand JWM (2002) Makespan estimation and order acceptance in batch process industries when processing times are uncertain. OR Spectr 24(4):467–495

    Article  Google Scholar 

  • Ivănescu VC, Fransoo JC, Bertrand JWM (2006) A hybrid policy for order acceptance in batch process industries. OR Spectr 28(2):199–222

    Article  Google Scholar 

  • Iyer AV, Jain A (2004) Modeling the impact of merging capacity in production-inventory systems. Manag Sci 50(8):1082–1094

    Article  Google Scholar 

  • Jordan WC, Graves SC (1995) Principles on the benefits of manufacturing process flexibility. Manag Sci 41(4):577–594

    Article  Google Scholar 

  • Kaman C, Savasaneril S, Serin Y (2013) Production and lead time quotation under imperfect shop floor information. Int J Prod Econ 144(2):422–431

    Article  Google Scholar 

  • Kaminsky P, Lee ZH (2008) Effective on-line algorithms for reliable due date quotation and large-scale scheduling. J Sched 11(3):187–204

    Article  Google Scholar 

  • Kapuscinski R, Tayur S (2007) Reliable due-date setting in a capacitated MTO system with two customer classes. Oper Res 5(1):56–74

    Article  Google Scholar 

  • Kelly FP, Massoulié L, Walton NS (2009) Resource pooling in congested networks: proportional fairness and product form. Queue Syst Theory Appl 63(1–4):165–194

  • Keskinocak P, Tayur S (2004) Due-date management policies. In: Simchi-Levi D, Wu SD, Shen ZJM (eds) Handbook of quantitative supply chain analysis: modeling in the e-business era. International series in operations research and management science. Kluwer Academic Publishers, Norwell, pp 485–553

  • Keskinocak P, Ravi R, Tayur S (2001) Scheduling and reliable lead-time quotation for orders with availability intervals and leadtime sensitive revenues. Manag Sci 47(2):264–279

    Article  Google Scholar 

  • Law AM (2007) Simulation modeling and analysis. McGraw Hill, Boston

    Google Scholar 

  • Li L, Lee YS (1994) Pricing and delivery-time performance in a competitive environment. Manag Sci 40(5):633–646

    Article  Google Scholar 

  • Li M, Yang F, Wan H, Fowler JW (2015) Simulation-based experimental design and statistical modeling for lead time quotation. J Manuf Syst 37:362–374

    Article  Google Scholar 

  • Li X, Wang J, Sawhney R (2012) Reinforcement learning for joint pricing, lead-time and scheduling decisions in make-to-order systems. Eur J Oper Res 221(1):99–109

    Article  Google Scholar 

  • Mandelbaum A, Reiman MI (1998) On pooling in queueing networks. Manag Sci 44(7):971–981

    Article  Google Scholar 

  • Rothkopf MH, Rech P (1987) Perspectives on queues: combining queues is not always beneficial. Oper Res 35(6):906–909

    Article  Google Scholar 

  • Slotnik SA (2014) Lead-time quotation when customers are sensitive to reputation. Int J Prod Res 52(3):713–726

    Article  Google Scholar 

  • Smith DR, Whitt W (1981) Resource sharing for efficiency in traffic systems. Bell Syst Tech J 60(1):39–55

    Article  Google Scholar 

  • Sridharan V, Li X (2008) Improving delivery reliability by a new due-date setting rule. Eur J Oper Res 186(3):1201–1211

    Article  Google Scholar 

  • Stidham S Jr (1970) On the optimality of single-server queueing systems. Oper Res 18(4):708–732

    Article  Google Scholar 

  • Swinnen J, Van Herck K (2011) Poland, Bulgaria and Romania: social impact of discount and organized food retail formats on remote regions. Report series 16, FAO Investment Centre/EBRD Cooperation Programme, Licos

  • Tekin E, Hopp WJ, Van Oyen MP (2009) Pooling strategies for call center agent cross-training. IIE Trans 41(6):546–561

    Article  Google Scholar 

  • van Dijk NM, van der Sluis E (2008) To pool or not to pool in call centers. Prod Oper Manag 17(3):296–305

    Article  Google Scholar 

  • Veral EA (2001) Computer simulation of due-date setting in multi-machine job shops. Comput Ind Eng 41(1):77–94

    Article  Google Scholar 

  • Vinod V, Sridharan R (2011) Simulation modeling and analysis of due-date assignment methods and scheduling decision rules in a dynamic job shop production system. Int J Prod Econ 129(1):127–146

    Article  Google Scholar 

  • Watanapa B, Techanitisawad A (1999) Simultaneous price and due date settings for multiple customer classes. Eur J Oper Res 166(2):351–368

    Article  Google Scholar 

  • Wein LM (1991) Due-date setting and priority sequencing in a multiclass M/G/1 queue. Manag Sci 37(7):834–850

    Article  Google Scholar 

  • Wein LM, Chevalier PB (1992) A broader view of the job-shop scheduling problem. Manag Sci 38(7):1018–1033

    Article  Google Scholar 

  • Yu DZ, Zhao X, Sun D (2013) Optimal pricing and capacity investment for delay-sensitive demand. IEEE Trans Eng Manag 60(1):124–136

    Article  Google Scholar 

  • Zhang ZG, Kim I, Springer M, Cai GG, Yu Y (2013) Dynamic pooling of make-to-stock and make-to-order operations. Int J Prod Econ 144(1):44–56

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. IÉSEG School of Management (LEM-CNRS), Socle de la Grande Arche, 1 Parvis de La Défense, 92044, Paris La Défense Cedex, France

    Tanja Mlinar

  2. Louvain School of Management, Center for Operations Research and Econometrics, Université catholique de Louvain, Place des Doyens 1, 1348, Louvain-la-Neuve, Belgium

    Philippe Chevalier

Authors
  1. Tanja Mlinar
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Corresponding author

Correspondence to Tanja Mlinar.

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Funding

Research that the authors conducted at Center for Operations Research and Econometrics, Université catholique de Louvain was partially supported by the ARC project Managing Shared Resources in Supply Chains [ARC 08-13-008].

Conflicts of interest

The authors declare that they have no conflict of interest.

Appendix

Appendix

For the comparison of the production configurations with different number of order types, we add an additional superscript n to the appropriate notation. In order to show that \(\varepsilon (E\left[ S_g^{n}\right] )\le \varepsilon (E\left[ S_g^{n+1}\right] )\), it is sufficient that \(E\left[ S_g^{d,n}\right] \le E\left[ S_g^{d,n+1}\right] \) and \(E\left[ S_g^{p,n}\right] \ge E\left[ S_g^{p,n+1}\right] \).

The inequality \(E\left[ S_g^{d,n}\right] \le E\left[ S_g^{d,n+1}\right] \) can be written as follows:

$$\begin{aligned} \dfrac{n}{n+1}\le \dfrac{\sum _{i=1}^n k^{\tfrac{i-1}{n-1}}}{\sum _{i=1}^{n+1} k^{\tfrac{i-1}{n}}}. \end{aligned}$$
(18)

The right side of inequality (18) is an increasing function of k and it achieves the minimum (i.e. \(\dfrac{n}{n+1}\)) when \(k=1\). Then, the inequality is satisfied for any value of \(k\ge 1\).

Based on Eqs. (11) and (12), the global expected sojourn time for system p with n order types can be expressed as:

$$\begin{aligned} E\left[ S_g^{p,n}\right] =\rho \tau _1 k \sum ^n_{i=1} \left[ k^{\frac{i-1}{n-1}}(n-i\rho )(n-(i-1)\rho )\right] ^{-1}+\tau _1 k\left[ \sum ^n_{i=1} k^{\frac{i-1}{n-1}}\right] ^{-1}. \end{aligned}$$
(19)

Equation (19) shows that increasing the number of order types between the order types with the minimum and maximum expected processing times will decrease the variance of the processing times of the pooled facility and will consequently lead to a decrease in the global expected sojourn time. Therefore, \(E\left[ S_g^{p,n}\right] \) is decreasing in n.

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Mlinar, T., Chevalier, P. Pooling heterogeneous products for manufacturing environments. 4OR-Q J Oper Res 14, 173–200 (2016). https://doi.org/10.1007/s10288-016-0307-1

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