1. Echelon Reorder Points, Installations Reorder Points, and the Value of Centralized Demand Information By; Fangruo Chen Presented by; Justin Johnson Dr. Edmonds

2. Outline of Article

• Introduction

• Preliminaries

• Echelon Reorder Points

• Installation Reorder Points

• Numerical Experimental Data

• Class Discussion and Questions

3. Why bother understanding?

• The value of information is a central issue in inventory management.

• Benefits of timely placement orders due to the availability of echelon-stock information- Defined as inventory position of a subsystem consisting of the stage itself and all downstream stages.

• Demand info and inventory are substitutes for one another.

• • Example- Advanced warnings from customers of their orders reduces inventory. Leads to Better communication b/t customers & suppliers as well as supply-chain members.

4. 1. Introduction Section

• • Each serial inventory system has N stages

• • • Materials flow in from outside suppliers

• • • • • Proceeds to stage N 1. and finally to stage 1(Customer Demand arises.)

• • Inv. Transferred in Batches

• • Each stage replenishes a stage-specific inventory position according to a stage-specific reorder point / order quantity policy.

• • Based on numerical equations/ Lemmas and Theorems

• These algorithms allow one to conduct an extensive computational study to assess the value of centralized demand information and to understand how this value depends on several key system parameters, i.e., the number of stages, lead-times, batch sizes, demand variability, and the desired level of customer service.

5. 2 variations of reorder pt

• 2 policies are said to be identical if they result in the same ordering procedure.

• Echelon stock- inventory position of the subsystem consisting of the stage itself and all downstream stages.

• • • To or - Echelon reorder pt- order placed

• • • Demand info at stage 1 real time basis and has centralized demand info.

• Installation Stock- (local) inventory position

• • • To or - Installation reorder pt- order placed

• • • Requires only local inventory information

6. 2. Preliminaries

• Each serial inventory system has N stages. 1 from 2, 2 from 3 etc.

• Each stage N orders from an outside supplier with unlimited stock. (outside supplier is called stage N + 1.)

• Each stage represents a stocking point in a production system, distribution system, or hybrid one.

• When stage 1 runs out of stock- demand is backlogged.

• Holding costs are associated.

• Idea; minimize the long-run avg. total cost in the sys.

7. Continued

• Echelon stock must be continuously monitored and accessible to information at stage 1 at a real time basis.

• Replenishment Policy- when inventory falls to or below a reorder point R the stage given must order a minimum integer multiple of Q ( base quantity) to + inventory position above R .

• If the supplier does not have sufficient inventory on hand shipment is sent and the rest of the order is backlogged.

• • (base qt. are assumed as fixed, reorder pts are only decision variables throughout paper)

• • Various equations determine replenishment policy

• • • All determine when and how much to order at every stage.

8. 3. Echelon Reorder Points

• Efficient Algorithms are developed for determining optimal echelon reorder points.

• Echelon stock

• Based on observation that in a steady state each stage is seen as essentially the echelon inventory position at each stage is equal to the inventory of a single stage.

• Through satisfying these simple equations lead times, delays, reorder points, long run/back order costs, inventories can all be laid out for everyone involved in the supply chain & production processes minimizing confusions and costs associated.

• Communication through fun math/ discrete time models.

9. 4.Installation Reorder Points

• Installation Stock

• Inventory level of an item which signals the need for placement of a replenishment order, taking into account the consumption of the item during order lead time and the quantity required for the safety stock.

• Considered to be Computationally infeasible for some problem instances, especially those with many stages involved.

• Bounds presented on the optimal installation reorder points.

• These are used to search for an optimal solution based on numerical data.

• These solutions ultimately give us the installation reorder points that have the lowest long run average costs.

• Saves time, confusion, and most importantly money

10. 5.) Numerical Examples

• This section reports an extensive computational study designed to test the best optimal algorithm developed in the previous section (installation reorder points) and assesses centralized demand information.

• In this study a pool of 1,536 examples, it was found that the value of information tends to increase when the number of stages, batches, and lead-times involved increases.

• The value of information, and levels of customer service tend to increase in value.

11. The math is so hard it confuses Excel

12. Class Discussion

• Bases on the ZERO questions I received I am assuming you were all already experts on the topic.

• Questions?

• Thank you!