1 / 33

Presented by: Y. LEVENT KOÇAĞA

A Model for Assessing the Value of Warehouse Risk Pooling: Risk Pooling Over Outside-Supplier Leadtimes. Presented by: Y. LEVENT KOÇAĞA. THE MODEL. A multi-echelon inventory model A high service level system Highlights warehouse risk-pooling Two alternative configurations.

lynton
Download Presentation

Presented by: Y. LEVENT KOÇAĞA

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. A Model for Assessing the Value of Warehouse Risk Pooling: Risk Pooling Over Outside-Supplier Leadtimes Presented by: Y. LEVENT KOÇAĞA

  2. THE MODEL • A multi-echelon inventory model • A high service level system • Highlights warehouse risk-pooling • Two alternative configurations

  3. Alternative system configurations Outside supplier Outside supplier Leadtime = (LS+LTW ) Warehouse Leadtime = (Ls +Ltr ) Leadtime = (Ltr+LPW ) 1 2 3 1 2 3 Retailers Retailers System1: Direct shipment to Retailers System2: Shipment through Warehouse

  4. Assumptions • Retailers supply a normal identical demand • Periodic-review demand replenishment • Fixed lead times • IT system to track inventory(at order time) • No interchange of goods between retailers

  5. Assumptions( specific to system2) • Warehouse does not hold inventory • Arriving orders are allocated at warehouse • Allocation only at the order receipt • Equalization of retailers` inventory • Cost of allocation avoided

  6. Key differences • Time of order allocation • Additional lead time (Ltw + Lpw) in system2 • Pipeline inventory in system 2

  7. Comparison of two systems System 1 100 100 30 40 40 30 H H -Ls-Ltr 0 -Ls-Ltr 0 System 2 100 100 30 40 33 37 54 50 -Lpw-Ltr -Lpw-Ltr H H -Ls-Ltw-Lpw-Ltr 0 0 -Ls-Ltw-Lpw-Ltr

  8. Scope of the Study • Derive expressions for means and variances • Formulate the performance measures • Analysis to find breakeven lead times • Sensitivity analysis • Conclusions and managerial insights • Further extensions

  9. Two alternative systems • N identical retailers • Identical demand is N~(μ, σ) • Drawings are independent(iid) • Review period is H (system cycle) • Order up to S0i every H periods, i=1,2

  10. Analysis of system 1 • System order up to level is S01 • Order placed (Ls +Ltr ) periods before period 1 • Then retailer end-of-period k net inventory is: t=k Ikl = S01/N -∑Dt , k=1,…,H t=-(Ls +Ltr )

  11. Analysis of system 1 • E(Ikl)= S01/N –(k+ Ls +Ltr) μ , k=1,…H • Var(Ikl)= (k+ Ls +Ltr) σ2 , k=1,…H

  12. Analysis of system 2 • System order up to level is S02 • Order placed at (Ls +Ltw + Lpw + Ltr )periods before period 1 • Then retailer end-of-period k net inventory is: j=Nt=-(Lpw + Ltr+1)t=k Ikl = {S02 - ∑ ∑ }/N - ∑ Dt , k=1,…,H j=1t=-(Ls +Ltw + Lpw + Ltr ) t= (Lpw + Ltr)

  13. Analysis of system 2 • E(Ik2)=S02/N –(k+ Ls +Ltw + Lpw + Ltr )μ,k=1,…H • Var(Ik2)=[k+ Ls/N+(Ltw/N+Lpw) + Ltr] σ2, k=1,…H

  14. Service level measures • Retailer expected end-of-period backorders is : EUBki = √var(Iki) . G[ E(Iki) / √Var(Iki)] , k=1,...H • P = EUBki /(Hμ) • Observe that P = 1 – fill rate

  15. Risk pooling: incentive quantified • Warehouse serves to pool risk over outside-supplier leadtime • The incentive is reduced overall variance of inventory process • RPI = Var(Ik1)- Var(Ik2) • RPI = [(N-1) Ls – Ltw – NLpw)]σ2/ N

  16. SS Breakeven Leadtimes • How large can (Ltw ,Lpw) be given that • Retailers have the same safety stock • Both systems provide the same service level • This yields: Ltw + N.Lpw = (N-1).Ls

  17. Inventory cost breakeven leadtimes • System 2 incurs pipeline stock due to its internal lead time (Lpw + Ltr) • Change the question to address this issue: How large can (Ltw ,Lpw) be given that • Both systems provide the same service level • The same safety holding cost ( plus pipeline holding cost for System 2)

  18. Inventory cost breakeven leadtimes • Given an inventoryholding cost h, the safety stock holding cost for system1 per cycle is: • Whereas the safety stock plus pipeline inventory holding cost for system 1 is:

  19. Inventory cost breakeven leadtimes • Equating the holding costs gives

  20. Inventory cost breakeven leadtimes • Average cycle inventories ignored • Safety stocks approximated by end-of-period expected on-hand inventory • System 2 retailer stock is set to system 1 retailer stock less the retailer pipeline inventory • Determination of breakeven points trades the reduction in variance against this reduction

  21. Computational studies • Holding cost breakeven (Ltw ,Lpw) lead times for representative sets • Ls used as a scale parameter to assess the breakevens • H is set to 1

  22. Case1: Ltw and Ltr both set to zero • If transportation / receiving times are set to zero RPI = [(N-1) Ls – NLpw)]σ2/ N • system 2’s pipeline inv. hldng. cost is LpwNμHh

  23. Holding cost breakeven Lpw values

  24. Holding cost breakeven Lpw values

  25. Case2: Ltw and Ltr both positive

  26. Case3: (Ltw,Lpw)-Lines • Lpw incurs pipeline inventory holding cost of LpwNμHh per system cycle • System does not pool risk over Lpw • Therefore holding cost breakeven Lpw’s will be smaller than h. Cost breakeven Ltw’s • As Ltr increases both should decrease

  27. Case3: (Ltw,Lpw)-Lines

  28. Case3: (Ltw,Lpw)-Lines

  29. Conclusions • Overall value of using System to pool risk critically depends on System 2’s pipeline stock • Holding cost breakeven (Lpw,Ltw) values: Very small values of Lpw but larger for Ltw

  30. Conclusions • Breakeven values decrease • as N decreases, • as Ltr increases, • as σ/μ decreases, • as H increases.

  31. Managerial Interpretations • If System 2 is to outperform System 1 • Lpw must be quite small compared to Ls • Ltw may be considerably larger than Ls • Limited to high service level systems due to the allocation assumption

  32. Possible extensions • Goods “enter” each system • More complex cost structure • Generalizing transpotation/receiving leadtime • Different H values for different systems

  33. Q & A

More Related