1 / 29

Evaluation of case-pack sizes in grocery retailing using a Markov Chain approach

This study explores the impact of case pack sizes on logistics costs in grocery retailing and proposes an optimization approach based on a Markov Chain model. The results of a numerical study are presented, along with conclusions and suggestions for future research.

naron
Download Presentation

Evaluation of case-pack sizes in grocery retailing using a Markov Chain approach

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Evaluation of case-pack sizes in grocery retailing using a Markov Chain approach Heinrich KuhnThomas Wensing Michael Sternbeck SMMSO 2015, Volos, Greece Department of Operations Catholic University Eichstätt-Ingolstadt Auf der Schanz 49, 85049 Ingolstadt, Germany

  2. Optimizingcase-pack sizesin grocery retailing using a Markov Chain approach Heinrich KuhnThomas Wensing Michael Sternbeck SMMSO 2015, Volos, Greece Department of Operations Catholic University Eichstätt-Ingolstadt Auf der Schanz 49, 85049 Ingolstadt, Germany

  3. Agenda • INTRODUCTION • MODEL DEVELOPMENT • OPTIMIZATION APPROACH • NUMERICAL STUDY • CONCLUSIONS AND FUTURE RESEARCH

  4. Agenda • INTRODUCTION • MODEL DEVELOPMENT • OPTIMIZATION APPROACH • NUMERICAL STUDY • CONCLUSIONS AND FUTURE RESEARCH

  5. 1. Introduction Logistics costs distribution in retail chains Warehousing28% In-store Logistics48% (secondary) Transportation 24% Retail system Distribution Transportation Store Consumer center see Kuhn/Sternbeck (2013, OMR)

  6. 1. Introduction Case-Pack Size DC Store Case-pack size of a product Products delivered to stores are generally combined in case packs that are used as order and distribution unit Case-pack sizes influence in-store processes How to dimension the Case Pack (CP) fromanin-store operations perspective?

  7. 1. Introduction Instore Activities Filling the shelf Backroom store Product delivery Storing overflow inventory SKU 2 SKU 1 Opening case pack Single unit Case pack Shelf on sales floor SKU 1 SKU 2 Refilling when shelf space becomes available

  8. 1. Introduction Introductory Example Status quoq= 12 Simulated scenarioq= 6 Shelf Size = 14 Shelf Size = 14 Number of units that have to be stored in the backroom was reduced substantially by 79.5% ̶ total instore logistics costs for this SKU were reduced by almost 48 % see Sternbeck (2014, JBE)

  9. 1. Introduction Two main research questions arise: • How does case-pack size (q) influence instore logistics costs ? • What is the optimumcase-pack size (qopt) ? Assuming an (r,s,nq) inventory policy … and a given replenishment /delivery pattern qopt s q 2q r

  10. 1. Introduction Litrature Relevance of Case-Pack Size in Retail Trade van derLaan, Joost W.,Optimal Case-pack Quantity of FMCG products, Retail Economics, September 2011, http://retaileconomics.com/case-pack-quantity/ Kuhn, H., Sternbeck M.G., Integrative retail logistics: An exploratory study, Operations Management Research, Vol. 6, No. 1, 2013, pp. 2-18. (r,s,nq) Inventory Policy Tempelmeier, H., Fischer, L., Approximation of the probability distribution of the customer waiting time under an (r, s, q) inventory policy in discrete time. IJPR 48 (21), 2010, 6275–6291. Shang, K. H., Zhou, S. X.,Optimal and heuristic echelon (r, nq, t) policies in serial inventory systems with fixed costs. Operations Research 58 (2), 2010, pp. 414–427. Zheng, Y.-S., Chen, F., Inventory policies with quantized ordering. Naval Research Logistics Quarterly 39, 1992, pp. 285–305. Optimum Case-Pack Size Models Sternbeck, M.G., A store-oriented approach to determine order packaging quantities in grocery retailing, forthcoming in: Journal of Business Economics, 2015 Wen, N., Graves, St.C., Ren, Z.J., Ship-pack optimization in a two-echelon distribution system, European Journal of Operational Research, Vol. 220, No. 3, 2012, pp. 777-785

  11. Agenda • INTRODUCTION • MODEL DEVELOPMENT • OPTIMIZATION APPROACH • NUMERICAL STUDY • CONCLUSIONS AND FUTURE RESEARCH

  12. 2. Model Development Inventory Model – Control • Stochastic demand • Length of period = one day • Lost sales • Deterministic lead time (l) • Replenishment policy:Generalization of the (r, s, nq) inventory policy: • On certain days of the week (e.g., Mo, We, Sa) • check the inventory position (IP) and place an order • if IP is equal to or lower than the reorder level (s) for the particular weekday. s 14 12 10 supply demand Shelf Size 16 Display Stock 8

  13. 2. Model Development Inventory Model – Cost Drivers • What are the crucialinstore logistics cost drivers? • Physical Inventory • Display Stock Undershoot • Backroom Activity • Backroom Inventory • Case Pack Handling (3,4) (3) (1) (2) (5) supply demand Shelf Size: 16 Display Stock: 8

  14. 2. Model Development Inventory Model – Cost Drivers • How do cost drivers develop with increasing case-pack size (q) • Physical Inventory ↑ • Display Stock Undershoot ↓ • Backroom Activity ↑ ↓ • Backroom Inventory ↑ • Case Pack Handling ↓ (3,4) (3) (1) (2) (5) supply demand Shelf Size: 16 Display Stock: 8

  15. 2. Model Development Inventory Model – Cost Function • 1) Physical Inventory : I • 2) Display Stock (DS) Undershoot (U )U := MAX(0, DS – I ) • 3) Backstore Activity (B1) B1:= 1 if B1>0 and A*>0B1 := 0 otherwise • BackstoreInventory (B2)B2 := MAX(0, I – SP**) • Case Pack Handling (H) H := A/q • * New Arrivals (A) • ** Shelf Size (SP)

  16. 2. Model Development Inventory Model – States and Transitions w : Mo, Tu, We, Th, Fr, Sasw = ( 14, - , 12, - , - , 10) Day w_x, i, nor 0 w_y, max(0,i–d), nand 0, respectively Case 1: w_y is neitherorder issue nororder arrival period P(d=D) Phys. inventory w_x, i, 0 w_y, max(0,i–d), n* P(d=D) Case 2: w_y is order issue periodn* = min(n|n*q ≥s-max(0, i – d)) w_x, i, n w_y, i*,0 Open order of size n*q Case 3: w_y is order arrival period i*= max(0, i – d+n*q) P(d=D) Note: For a clearer presentation, we assume that only one order can be outstanding and order issue periods cannot be equal to arrival periods.

  17. 2. Model Development Analytical Model - Approach • Markov Chain • State defined by • weekday (w) • inventory level (I) • arriving or outstandingcase packs (n) • Transitions follow from deterministic arrivals and stochastic demands Solid arrows refer to transition probability 0.5, dotted arrows to certain transition.

  18. Agenda • INTRODUCTION • MODEL DEVELOPMENT • OPTIMIZATION APPROACH • NUMERICAL STUDY • CONCLUSIONS AND FUTURE RESEARCH

  19. 3. Optimization Approach Optimization Approach Total Cost Function Optimization Procedure • In-store logistic costs ↑↓ when case pack size qincrease • Physical Inventory ↑ • Display Stock Undershoot ↓ • Backroom Activity ↑ ↓ • Backroom Inventory ↑ • Case Pack Handling ↓ Declining cost function (dec) Increasing cost function (inc)

  20. 3. Optimization Approach Optimization Approach

  21. Agenda • INTRODUCTION • MODEL DEVELOPMENT • OPTIMIZATION APPROACH • NUMERICAL STUDY • CONCLUSIONS AND FUTURE RESEARCH

  22. 4. Numerical Study Numerical Study – Cases Products (1, 2, … , 6) Stores (A, B, … , H) Changes of current CP sizes when optimal CP sizes are applied

  23. 4. Numerical Study Numerical Study – Product 1, Store H Cost functions

  24. 4. Numerical Study Numerical Study – Product 1, Store H q = 32 Shelf Size = 23 qopt = 11 Shelf Size = 23

  25. 4. Numerical Study Numerical Study – One-Size-for-all-Stores

  26. Agenda • INTRODUCTION • MODEL DEVELOPMENT • OPTIMIZATION APPROACH • NUMERICAL STUDY • CONCLUSIONS AND FUTURE RESEARCH

  27. 5. Conclusions and Future Research Contribution, current status and further research Optimizing case pack size Areas for further research • The presented model fills a gapin literature and opens the opportunity to evaluate case-pack-sizes in respect to retailin-store logistics costs. • Relevantin-storecost drivers are considered, i.e., physical inventory, display stock undershoot, backroom inventory, backroom activity, case pack handling. • Numerical analyses of a real case study show that case-pack sizes should be reduced for some products as well as increased for other products. • Integration of unpacking and/or packing costs in the DC • Integration of case pack size related picking costs in the DC • Synchronization of case pack sizes acrossstores • Agreements with fast moving consumer goods companies in respect of “optimal” case-pack sizes

  28. …many thanks for your attention

More Related