OR Spectrum

pp 1–32 | Cite as

Optimizing case-pack sizes in the bricks-and-mortar retail trade

  • Thomas Wensing
  • Michael G. Sternbeck
  • Heinrich Kuhn
Regular Article


Before reaching the store, products generally flow through the retail distribution system as larger bundles, the so-called case packs (CP). In several studies these case packs have been identified as having a significant impact on distribution logistics efficiency. In this paper we develop a quantitative model and solution approach determining optimal case-pack sizes for non-perishable products in grocery retailing. The model captures the relevant operative cost drivers along the internal supply chain of a large bricks-and-mortar retailer. It explicitly represents each day of the retailer’s business week, where the replenishment doctrine considered generalizes the well-known periodic review reorder point (rsnq) policy as a stationary cyclic version. Exact and approximate methods are developed to evaluate the costs of a model instance. In addition, an optimization procedure is outlined that uses either exact or approximate methods to identify optimal and near-optimal CP sizes for a single store as well as for a network of multiple stores to be operated with one common CP. Applied to real-world examples of a large European retail chain, the methods reveal average cost improvement potential of more than 20% by adjusting the CP sizes that are currently in use. The approach presented is thus shown to be a valuable addition to any integrative retail supply chain planning system. Its results are directly applicable to retail practice.


Retail operations Case-pack size Inventory Distribution system 


  1. Abbott H, Palekar US (2008) Retail replenishment models with display-space elastic demand. Eur J Oper Res 186(2):586–607CrossRefGoogle Scholar
  2. Atan Z, Erkip N (2015) Note on “The backroom effect in retail operations”. Prod Oper Manag 24:1833–1834CrossRefGoogle Scholar
  3. Axsäter S (2006) Inventory control, 2nd edn. Vol. 90 of International series in operations research and management science. Springer, BostonGoogle Scholar
  4. Broekmeulen RACM, van Donselaar KH (2009) A heuristic to manage perishable inventory with batch ordering, positive lead-times, and time-varying demand. Comput Oper Res 36(11):3013–3018CrossRefGoogle Scholar
  5. Broekmeulen RACM, Sternbeck MG, van Donselaar KH, Kuhn H (2017) Decision support for selecting the optimal product unpacking location in a retail supply chain. Eur J Oper Res 259(1):84–99CrossRefGoogle Scholar
  6. de Koster R, Le-Duc T, Roodbergen KJ (2007) Design and control of warehouse order picking: a literature review. Eur J Oper Res 182(2):481–501CrossRefGoogle Scholar
  7. DeHoratius N, Raman A (2008) Inventory record inaccuracy: an empirical analysis. Manag Sci 54(4):627–641CrossRefGoogle Scholar
  8. DeHoratius N, Ton Z (2015) The role of execution in managing product availability. In: Agrawal N, Smith SA (eds) Retail supply chain management, 2nd edn. Springer, New York, pp 53–77Google Scholar
  9. Ehrenthal JCF, Stölzle W (2013) An examination of the causes for retail stockouts. Int J Phys Distrib Logist Manag 43(1):54–69CrossRefGoogle Scholar
  10. Eroglu C, Williams BD, Waller MA (2013) The backroom effect in retail operations. Prod Oper Manag 22(4):915–923CrossRefGoogle Scholar
  11. Fernie J, Sparks L, McKinnon AC (2010) Retail logistics in the UK: past, present and future. Int J Retail Distrib Manag 38(11/12):894–914CrossRefGoogle Scholar
  12. Fleischmann B (2016) The impact of the number of parallel warehouses on total inventory. OR Spectrum 38:899–920CrossRefGoogle Scholar
  13. Gámez Albán HM, Soto Cardona OC, Mejía Argueta C, Sarmiento AT (2015) A cost-efficient method to optimize package size in emerging markets. Eur J Oper Res 241(3):917–926CrossRefGoogle Scholar
  14. Gruen TW, Corsten DS, Bharadwaj S (2002) Retail out-of-stocks: a worldwide examination of extent, causes and consumer response. Washington, DCGoogle Scholar
  15. Hadley G, Whitin T (1963) Analysis of inventory systems. Prentice Hall, Englewood CliffsGoogle Scholar
  16. Holzapfel A, Hübner A, Kuhn H, Sternbeck MG (2016) Delivery pattern and transportation planning in grocery retailing. Eur J Oper Res 252(1):54–68CrossRefGoogle Scholar
  17. Hübner A, Kuhn H, Sternbeck MG (2013) Demand and supply chain planning in grocery retail: an operations planning framework. Int J Retail Distrib Manag 41(7):512–530CrossRefGoogle Scholar
  18. Ketzenberg M, Metters R, Vargas V (2002) Quantifying the benefits of breaking bulk in retail operations. Int J Prod Econ 80(3):249–263CrossRefGoogle Scholar
  19. Kiesmüller G, de Kok A (2006) The customer waiting time in an (r, s, q) inventory system. Int J Prod Econ 104(2):354–364CrossRefGoogle Scholar
  20. Kuhn H, Sternbeck M (2013) Integrative retail logistics—an exploratory study. Oper Manag Res 6(1):2–18CrossRefGoogle Scholar
  21. Larsen C, Kiesmüller G (2007) Developing a closed-form cost expression for an policy where the demand process is compound generalized erlang. Oper Res Lett 35(5):567–572CrossRefGoogle Scholar
  22. McCarthy-Byrne TM, Mentzer JT (2011) Integrating supply chain infrastructure and process to create joint value. Int J Phys Distrib Logist Manag 41(2):135–161CrossRefGoogle Scholar
  23. Raman A, DeHoratius N, Ton Z (2001a) The Achilles’ heel of supply chain management. Harvard Bus Rev 79(5):25–28Google Scholar
  24. Raman A, DeHoratius N, Ton Z (2001b) Execution: the missing link in retail operations. Calif Manag Rev 43(3):136–152CrossRefGoogle Scholar
  25. Reiner G, Teller C, Kotzab H (2012) Analyzing the efficient execution on in-store logistics processes in grocery retailing—the case of dairy products. Prod Oper Manag 22(4):924–939CrossRefGoogle Scholar
  26. Rouwenhorst B, Reuter B, Stockrahm V, van Houtum GJ, Mantel RJ, Zijm MWH (2000) Warehouse design and control: framework and literature review. Eur J Oper Res 122(3):515–533CrossRefGoogle Scholar
  27. Shang KH, Zhou SX (2010) Optimal and heuristic echelon (r, nq, t) policies in serial inventory systems with fixed costs. Oper Res 58(2):414–427CrossRefGoogle Scholar
  28. Simons D, Francis M, Jones DT (2005) Food value chain analysis. In: Doukidis GJ, Vrechopoulos AP (eds) Consumer driven electronic transformation. Springer, Berlin, pp 179–192CrossRefGoogle Scholar
  29. Sternbeck MG (2015) A store-oriented approach to determine order packaging quantities in grocery retailing. J Bus Econ 85(5):569–596CrossRefGoogle Scholar
  30. Sternbeck MG, Kuhn H (2014) An integrative approach to determine store delivery patterns in grocery retailing. Transp Res Part E 70:205–224CrossRefGoogle Scholar
  31. Tempelmeier H (2011) Inventory management in supply networks: problems, models, solutions, 2nd edn. Books on Demand, NorderstedtGoogle Scholar
  32. Tempelmeier H, Fischer L (2010) Approximation of the probability distribution of the customer waiting time under an (r, s, q) inventory policy in discrete time. Int J Prod Res 48(21):6275–6291CrossRefGoogle Scholar
  33. van den Berg JP, Sharp GP, Gademann AJRM, Pochet Y (1998) Forward-reserve allocation in a warehouse with unit-load replenishments. Eur J Oper Res 111(1):98–113CrossRefGoogle Scholar
  34. van Donselaar KH, Broekmeulen RACM (2008) Static versus dynamic safety stocks in a retail environment with weekly sales patterns. BETA working papers series, 262Google Scholar
  35. van Zelst S, van Donselaar KH, van Woensel T, Broekmeulen RACM, Fransoo J (2009) Logistics drivers for shelf stacking in grocery retail stores: potential for efficiency improvement. Int J Prod Econ 121(2):620–632CrossRefGoogle Scholar
  36. Wen N, Graves SC, Ren ZJ (2012) Ship-pack optimization in a two-echelon distribution system. Eur J Oper Res 220(3):777–785CrossRefGoogle Scholar
  37. Zheng Y-S, Chen F (1992) Inventory policies with quantized ordering. Naval Res Logist Q 39:285–305CrossRefGoogle Scholar
  38. Zipkin PH (2000) Foundations of inventory management, 1st edn. McGraw-Hill/Irwin, LondonGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Thomas Wensing
    • 1
  • Michael G. Sternbeck
    • 1
  • Heinrich Kuhn
    • 1
  1. 1.Department of OperationsCatholic University of Eichstätt-IngolstadtIngolstadtGermany

Personalised recommendations