Your SlideShare is downloading. ×
0
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
A P I C  P A P E R 7
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

A P I C P A P E R 7

250

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
250
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
3
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. PRESENTERS:
    AKSHAY BHARDWAJ
    KSHITIJ PADHYE
    SRIKANTH CHADA
    4/16/2009
    On the Interactions Between Routing andInventory-Management Policies in a One-WarehouseN-Retailer Distribution System
    Leroy B. Schwarz, James E. Ward, Xin Zhai
    Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana
    MANUFACTURING & SERVICE
    OPERATIONS MANAGEMENT
    Vol. 8, No. 3, Summer 2006, pp. 253–272
    issn 1523-4614 eissn 1526-5498 06 0803 025
  • 2. 4/16/2009
    GOAL
    This paper examines the interactions between routing and inventory-management decisions in a two-level
    supply chain consisting of a cross-docking warehouse and N retailers.
    The authors’ goal is to determine a combined system inventory-replenishment, routing, and inventory allocation
    policy that minimizes the total expected cost/period of the system over an infinite time horizon.
  • 3. 4/16/2009
    INTRODUCTION
    Due to increasing competition in retailing, high availability and low-average inventory levels are imperative.
    One of the ways suggested by the authors to achieve this is by:
    • Dynamic Routing of Inventory
    • 4. Dynamic Allocation of Inventory.
    Thanks to advancements in technology (e.g. RFID at Wal-Mart and dynamic truck routing by Schneider Trucking), the above can be implemented.
  • 5. PROCEDURE
    The authors demonstrated that the optimal static route is not the shortest-total-distance (TSP) route, but depends on the variance of customer demands, and, if in-transit inventory-holding costs are charged, also on mean customer demands.
    We then examine dynamic-routing policies, i.e., policies that can change the route from one system-replenishment-allocation cycle to another, based on the status of the retailers’ inventories.
    Next, the performance of a change-revert heuristic policy is examined. Although its routing decisions are not fully dynamic, but determined and fixed for a given cycle at the time of each system replenishment, simulation tests with N = 2 and N = 6 retailers indicate that its use can substantially reduce system inventory-related costs even if most of the time the chosen route is the optimal static route.
    4/16/2009
  • 6. PROPOSED MODEL
    The model examined by the authors consists of a single cross-docking warehouse, N retailers, one un-capacitated
    vehicle, and a single item (SKU). This supply chain is centrally managed, using a periodic-review system.
    Each retailer i experiences normally distributed customer demand each time period. Demand realizations are independent across time and across retailers. Excess demand is backordered at cost $p/unit-period, and a holding cost of $h/unit-period is charged on system (i.e., on-vehicle or at-retailer) inventory. Transportation times between system sites are fixed and known.
    4/16/2009
  • 7. ASSUMPTIONS
    Three major assumptions are made to facilitate our Analysis.
    The Allocation Assumption
    The Returns-Without-Penalty-Assumption
    The Last-Period Backorders Assumption
    4/16/2009
  • 8. MODEL
    The total cost assigned to a single cycle that starts in period t0, and whose retailers’ allocation cycles have known arbitrary starting and ending periods, is
    4/16/2009
    where Et is the system total net inventory, si t are the
    backorders at retailer i in period t, and e[i ]is the
    end period in retailer i’s allocation cycle.
    H is the holding cost and p is the penalty for back-orders.
  • 9. MODEL
    4/16/2009
  • 10. MODEL
    While Y ∗, K∗, µ1c and σ1c are identical under the two cost structures,
    4/16/2009
    Retailer-only holding costs: A sufficient condition to visit the closest retailer first is for the closest retailer to also have the largest variance. Otherwise, the choice of the optimal static route depends on a trade-off
    between travel times (i.e., a TSP-oriented parameter) and per-period demand variance (i.e., an inventory management
    parameter).
    System based holding costs: Hence, when holding costs are also charged on the vehicle inventory, the retailers’ average demands affect the choice of the route.
  • 11. DYNAMIC ROUTING POLICIES
    Dynamic Routing introduces two types of uncertainties, neither of which is present under a fixed routing policy: (1) “UAL uncertainty,” i.e., uncertainty in each retailer’s delivery lead time, and (2) “UPD uncertainty,” i.e., uncertainty in the number of periods of customer demand each retailer’s allocation is to supply.
    A management decision to adopt a dynamic-routing policy should be viewed as a tradeoff between reducing expected inventory-related costs, in exchange for increased logistics-related (e.g., transportation) cost.
    In a symmetric system for any given inventory-allocation policy, least-inventory first (LIF) is an optimal dynamic routing policy.
    4/16/2009
  • 12. The heuristic’s decision rule is applied before the vehicle leaves the warehouse, and yields one of two decisions: (a) use the default route in the current replenishment cycle or (b) choose another route.
    The decision rule then chooses the route with the smallest
    value of C∗, where
    C* =Z* +(p+h)SP
    Where z* is the single-cycle cost
    Sp is the expected shortages of retailer in its last allocation cycle.
    4/16/2009
    CHANGE REVERT HEURISTIC
  • 13. CONCLUSION
    The authors used simulation to examine the impact of the major assumptions used to develop the analytical model. The results indicate: that these assumptions are seldom violated; and, second, even when they are, the insights provided by the analytical model—in particular, the model’s estimates of cost/period and the desirability of changing routes—appear to be insensitive to them.
    In particular, the simulation results provide evidence that the change revert heuristic provides statistically significant and managerially meaningful savings for multi retailer systems.
    4/16/2009
  • 14. SCOPE FOR RESEARCH
    Finally, the authors deliberately leave two questions open for future research:
    First is an examination of fully dynamic-routing policy. This form of dynamic routing would decide which retailer to visit next as part of the allocation decision made at every retailer (except the last) in each replenishment cycle.
    Second is a closer examination of change-revert routing
    policies. Perhaps the most interesting question here is
    “What is the best default route?” We arbitrarily chose
    the optimal static route to be the default route, but,
    given a change-revert policy, it is certainly possible
    that a different default route would provide even better
    results.
    4/16/2009

×