Abstract
The order release models described in this volume rely heavily on the functional relationship between the expected output of a production resource and its expected workload which, as discussed in Chap. 2 for the case of steady-state queues, is related to the expected cycle time by Littleās Law. This relationship is significantly affected by various decision rules used within the PPC system, such as scheduling policies on the shop floor. Lot sizing, the decision as to how much of a product to produce each time a machine is set up for the product, is of particular importance in this respect. For a given production quantity, determined by the master production schedule, the lot sizes influence capacity utilization (via the amount of setup time required on the resource in a planning period), the mean and variance of the interarrival times (via the number and size of production lots), and the mean and variance of the service times (via the lot sizes). Following the discussion in Chap. 2, we begin this section with insights from simple queueing models, and then show how these can be used to develop a system of multivariate clearing functions to address a dynamic lot-sizing problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anli OM, Caramanis M, Paschalidis IC (2007) Tractable supply chain production planning modeling non-linear lead time and quality of service constraints. J Manuf Syst 26(2):116ā134
Benjaafar S (1996) On production batches, transfer batches and lead times. IIE Trans 28:357ā362
Billington PJ, Mcclain JO, Thomas JL (1983) Mathematical programming approaches to capacity-constrained MRP systems: review, formulation and problem reduction. Manag Sci 29:1126ā1141
Brahimi N, Dauzere-Peres S, Najid NM, Nordli A (2006) Single-item lot sizing problems. Eur J Oper Res 168:1ā16
Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems. Prentice-Hall, Englewood Cliffs
Cheng M, Mukherjee NJ, Sarin SC (2013) A review of lot streaming. Int J Prod Res 51(23/24):7023ā7046
DeGraeve Z, Jans R (2007) A new Dantzig-Wolfe reformulation and branch and price algorithm for the capacitated lot sizing problem with setup times. Oper Res 55(5):909ā920
Desaulniers G, Desrosiers J, Solomon MM (2005) Column generation. Springer, Berlin
Drexl A, Kimms A (1997) Lot sizing and schedulingāsurvey and extensions. Eur J Oper Res 99:221ā235
Erenguc SS, Mercan M (1990) A multifamily dynamic lot-sizing model with coordinated replenishments. Nav Res Logist 37:539ā558
Harris FW (1915) Operations and cost. In: Factory management series. A. W. Shaw Co, Chicago
Hopp WJ, Spearman ML (2008) Factory physics: foundations of manufacturing management. Irwin/McGraw-Hill, Boston
Jen Huei C, Huan Neng C (2005) A comprehensive review of lot streaming. Int J Prod Res 43(8):1515ā1536
Jutz S (2017) Lot sizing in a two-stage production-inventory systemāa flow time oriented perspective. Department of Information systems, production and logistics management. PhD, University of Innsbruck, Innsbruck, p 194
Kang Y, Albey E, Uzsoy R (2011) A column generation approach for multiple product dynamic lot-sizing with congestion. Raleigh, NC 27695-7906, Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University
Kang Y, Albey E, Hwang S, Uzsoy R (2014) The impact of lot-sizing in multiple product environments with congestion. J Manuf Syst 33(3):436ā444
Kang Y, Albey E, Uzsoy R (2018) Rounding heuristics for multiple product dynamic lot-sizing in the presence of queueing behavior. Comput Oper Res 100:54ā65
Karmarkar US (1987) Lot sizes, lead times and in-process inventories. Manag Sci 33(3):409ā418
Karmarkar US (1989) Capacity loading and release planning with work-in-progress (WIP) and lead-times. J Manuf Oper Manag 2(1):105ā123
Karmarkar US, Kekre S, Kekre S (1992) Multi-item batching heuristics for minimization of queues. Eur J Oper Res 58:99ā111
Lasdon LS (1970) Optimization theory for large systems. Macmillan, New York
Lasdon LS, Terjung RC (1971) An efficient algorithm for multi-item scheduling. Oper Res 19(4):946ā969
Medhi J (1991) Stochastic models in queuing theory. Academic, Cambridge
Missbauer H (2002) Lot sizing in workload control systems. Prod Plan Control 13:649ā664
Missbauer H, Jutz S (2018) A flow time oriented lot sizing model for a serial two-stage production-inventory system: analytical approximation and simulation-based optimization. In: Twentieth international working seminar on production economics, Innsbruck, Austria
Pochet Y, Wolsey LA (2006) Production planning by mixed integer programming. Springer, New York
Quadt D, Kuhn H (2008) Capacitated lot sizing with extensions: a review. 4OR Q J Oper Res 6:61ā83
Schneeweiss C (2003) Distributed decision making. Springer, Berlin
Sƶhner V, Schneeweiss C (1995) Hierarchically integrated lot size optimization. Eur J Oper Res 86(1):73ā90
Trigeiro WW, Thomas LJ, McClain JO (1989) Capacitated lot sizing with setup times. Manag Sci 35:353ā366
Vaughan TS (2006) Lot size effects on process lead time, lead time demand, and safety stock. Int J Prod Econ 100:1ā9
Wijngaard J (1989) Timing and lot-sizing in production control. J Manuf Oper Manag 2:35ā51
Zipkin PH (1986) Models for design and control of stochastic, multi-item batch production systems. Oper Res 34(1):91ā104
Author information
Authors and Affiliations
Rights and permissions
Copyright information
Ā© 2020 Springer Science+Business Media, LLC, part of Springer Nature
About this chapter
Cite this chapter
Missbauer, H., Uzsoy, R. (2020). Lot-Sizing Models Using Multi-dimensional Clearing Functions. In: Production Planning with Capacitated Resources and Congestion. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0354-3_9
Download citation
DOI: https://doi.org/10.1007/978-1-0716-0354-3_9
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-0716-0352-9
Online ISBN: 978-1-0716-0354-3
eBook Packages: Business and ManagementBusiness and Management (R0)