Centralization and ROP

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# Centralization and ROP - PowerPoint PPT Presentation

Centralization and ROP. A key component has a cost c = 10, holding cost h (for the period) = 1, salvage value v = 10, and sales price p = 19. What is the optimal target inventory level at each WH? What is the total inventory?. Warehouse A. Warehouse B. Demand N~(100,10^2).

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Presentation Transcript
Centralization and ROP
• A key component has a cost c = 10, holding cost h (for the period) = 1, salvage value v = 10, and sales price p = 19.
• What is the optimal target inventory level at each WH?
• What is the total inventory?

Warehouse A

Warehouse B

Demand N~(100,10^2)

Demand N~(100,10^2)

Central Warehouse
• What is the optimal target inventory level at CWH?

Central Warehouse

Demand N~(100,10^2)

Demand N~(100,10^2)

Physical Centralization
• Physical Centralization: the firm consolidates all its warehouses in one location from which is can serve all customers.
• Example: Two warehouses. Demand in the two ware houses are independent.
• Both warehouses have the same distribution for their lead time demand.
• LTD1: N(LTD, σLTD )LTD2: N(LTD, σLTD )

Both warehouses have identical service levels

To provide desired SL, each location must carry Isafety = zσLTD

z is determined by the desired service level

The total safety inventory in the decentralized system is

Independent Lead time demands at two locations

Decrease in safety inventory by a factor of

LTDC = LTD1 + LTD2 LTDC = LTD + LTD = 2 LTD

Centralization reduced the safety inventory by a factor of 1/√2

GE lighting operating 7 warehouses. A warehouse with average lead time demand of 20,000 units with a standard deviation of 5,000 units and a 95% service level needs to carry a safety inventory of

Isafety = 1.65×5000= 8250

independent Lead time demands at N locations

Independent demand in N locations: Total safety inventory to provide a specific SL increases not by N but by √N

Centralization of N locations:

If centralization of stocks reduces inventory, why doesn’t everybody do it?

• Longer response time
• Higher shipping cost
• Less understanding of customer needs
• Less understanding of cultural, linguistics, and regulatory barriers

These disadvantages my reduce the demand.

Dependent Demand
• Does centralization offer similar benefits when demands in multiple locations are correlated?
• LTD1 and LTD2are statistically identically distributed but correlated with a correlation coefficient of ρ .

No Correlation: ρ close to 0

+ Correlation, + Perfect Correlation

Positive Correlation: ρ close to 1

Perfect Positive Correlation: ρ = +1

Negative Correlation: ρ close to -1

Perfect Negative Correlation: ρ = -1

The safety inventory in the two-location decentralized system is larger than in the centralized system by a factor of

Correlation

If demand is positively fully correlated, ρ = 1, centralization offers no benefits in the reduction of safety inventory

Benefits of centralization increases as the demand on the two locations become negatively correlated. The best case is  = -1, where we do not need safety inventory at all

Principle of Aggregation and Pooling Inventory
• Inventory benefits  due to principle of aggregation.
• Statistics: Standard deviation of sum of random variables is less than the sum of the individual standard deviations.
• Physical consolidation is not essential, as long as available inventory is shared among various locations  Pooling Inventory
• Virtual Centralization
• Specialization
• Component Commonality
• Delayed Differentiation
• Product Substitution
Virtual Centralization

Virtual Centralization: inventory pooling in a network of locations is facilitated using information regarding availability of goods and subsequent transshipment of goods between locations to satisfy demand.

• Location A
• Exceeds Available stock

Location B

Less than Available stock

1. Information about product demand and availability must be available at both locations

2. Shipping the product from one location to a customer at another location must be fast and cost effective

Pooling is achieved by keeping the inventories at decentralized locations.

Specialization, Substitution
• Demand for both products exist in both locations. But a large portion of demand for P1 is in location A, while a large portion of demand for P2 is in location B.

Location B

Product P2

Location A

Product P1

Both locations keep average inventory.

Safety inventory is kept only in the specialized warehouse

One other possibility to deal with variability is product substitution.

Component Commonality
• Up to now we have discussed aggregating demand across various geographic locations, either physical or virtual
• Aggregating demand across various products has the same benefits.
• Computer manufacturers: offer a wide range of models, but few components, CPU, RMA, HD, CD/DVD drive, are used across product lines.
• Replace Make-to-stock with make Make-to-Order
• Commonality + MTO:
• Commonality: Safety inventory of the common components much less than safety inventory of unique components stored separately.
• MTO: Inventory cost is computed in terms of WIP cost not in terms of finished good cost (which is higher).
Postponement (Delayed Differentiation)
• Forecasting Characteristic: Forecasts further into the future tends to be less accurate than those of more imminent events.
• Since shorter-range forecasts are more accurate, operational decisions will be more effective if supply is postponed closer to the point of actual demand.
• Two Alternative processes (each activity takes one week)
• Alternative A: (1) Coloring the fabric, (2) assembling T-shirts
• Alternative B: (1) Assembling T-shirts, (2) coloring the fabric
• No changes in flow time. Alternative B postponed the color difference until one week closer to the time of sale. Takes advantage of the forecasting characteristic: short-Range forecast more accurate.
Postponement (Delayed Differentiation)