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Inventory Management  &  Risk Pooling
Introduction ,[object Object],[object Object],[object Object],[object Object],Response:- Inventory Management in Supply Chain
Goals of Inventory Management  ,[object Object],[object Object],[object Object],[object Object],Reduce Cost, Improve Service Inventory Levels Financial Investment  Operational Need
Inventory ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Functions of Inventory ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Factors Affecting Inventory Policy ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Economic Order Quantity Model Assuming demand certainty Trade-offs between setup costs and inventory holding costs,  but ignores issues such as demand uncertainty and forecasting . 1000 2000 3000 4000 5000 6000 0 50 100 150 200 250 300 350 Ordering (Acquisition)Costs Holding or Carrying Costs Total Costs Economic Order Quantity
Single Period Model Without Initial Inventory
Case: Swimsuit Production ,[object Object],[object Object],[object Object],[object Object]
Demand forecast forecast averages about 13,000 ,[object Object]
Swimsuit Costs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Swimsuit Two Scenarios ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Swimsuit Best Questions ? ,[object Object],[object Object]
How much to Make? ,[object Object],[object Object],[object Object],[object Object]
Swimsuit Expected Profit
Swimsuit : Important Observations ,[object Object],[object Object],[object Object],[object Object]
Swimsuit Expected Profit
Case: Swimsuit Production ,[object Object],[object Object]
Probability of Outcomes
Key Points from this Case ,[object Object],[object Object],[object Object],[object Object]
Single Period Model With Initial Inventory
Initial Inventory ,[object Object],[object Object],[object Object],[object Object],[object Object]
Initial Inventory and Profit The case motivates a powerful ( s , S ) inventory policy (or a  min max  policy):  s  is the reorder point and  S  is the order-up-to-level
Multi-Order Opportunities under Uncertainties
Inventory Policies ,[object Object],[object Object],[object Object],[object Object]
Variable Demand with a Fixed ROP Reorder point,  R Q LT Time LT Inventory level 0 Result of uncertainty
Reorder Point with a Safety Stock The amount of safety stock needed is based on the degree of uncertainty in the lead time demand and desired customer service level Reorder point,  R Q LT Time LT Inventory level 0 Safety Stock
Determinants of the Reorder Point ,[object Object],[object Object],[object Object],[object Object]
Continuous Review Policy ,[object Object],[object Object],[object Object],[object Object],[object Object],p =shortage cost
Continuous Review Policy ,[object Object],[object Object]
Continuous Review Policy –Variable demand & fixed lead time ,[object Object],[object Object],[object Object],[object Object],[object Object]
Continuous Review Policy –Variable demand & fixed lead time ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],Continuous Review Policy –Variable demand & lead time
Periodic Review Policy ,[object Object],[object Object],[object Object]
Periodic Review Policy ,[object Object],[object Object],[object Object]
Periodic Review Policy ,[object Object],[object Object],[object Object],[object Object]
RISK POOLING
Risk Pooling ,[object Object],Questions:  Q1: For the same service level, which system will require more inventory? Q2: For the same total inventory level, which system will have better service?  Market Two Supplier Warehouse One Warehouse Two Market One Market Two Supplier Warehouse Market One
What is Risk Pooling? ,[object Object],[object Object],[object Object],[object Object],[object Object]
Lead Time Pooling Supplier 8-week lead time
Lead Time Pooling Supplier 8-week lead time Retail DC 1-week lead time
Capacity Pooling  3 Links – no flexibility
Capacity Pooling  9 Links – Total Flexibility
Advantages / Disadvantages  large costs to have flexibility accommodate demand uncertainty Capacity Pooling   reduce inventory investment   additional transportation costs keep inventory closer to customer   extra costs of operating distribution center decrease lead time  Lead Time Pooling   better performance in terms of matching supply and demand   potentially degrades product functionality reduction in demand variability Product Pooling   reduce expected inventory investment needed to achieve a target service level   creates distance between inventory and customers  reduce demand variability Location Pooling Disadvantages Advantages
Summary Risk Pooling ,[object Object],[object Object],[object Object]
Example Decentralized system: total SS = 47.88 total avg. invent. = 179 Safety Stock SS = z   · STD  · Reorder Point R =  AVG · L +  SS Order Quantity Q = sqrt(2* C 0 *AVG/h ) Order-up-to-level R + Q Average Inventory    SS + Q/2 Service Level:97%  k=1.88 Lead Time= 1 week Q/2+SS AVG STD SS R Q Order- up-to Level Average Inventory Warehouse 1 39.3 13.2 25.08 65 132 197 91 Warehouse 2 38.6 12.0 22.8 62 131 193 88 Centralized Warehouse 77.9 20.7 39.35 118 186 304 132
Risk Pooling –  Effect of Correlation   ,[object Object]
Warehouse Market 1 Market 2 D 1 +D 2 : (  ,   2 ) Calculating demand variability of centralized system Conclusions:  1. Stdev of aggregated demand is  less than the sum of stdev of individual  demands 2. If demands are independent or negatively correlated,  the std of  aggregated demand is much less 1. If D 1 , D 2  positively correlated,    > 0 2. If D 1 , D 2  are independent,    = 0 3. If D 1 , D 2  negatively correlated,    < 0    =   1  +   2    = ?? ,[object Object],[object Object],Warehouse 1 Warehouse 2 Market 1 Market 2 D 1 : (  1 ,   1 2 ) D 2 : (  2 ,   2 2 )  2  =   1 2  +   2 2  + 2  1  2 ,  where -1          1  :  correlation coefficient of D 1 , D 2        1 +   2    1 +  2 1 0 -1 P.C. N.C. Ind.
Risk Pooling –  Effect of Coefficient of Variation ,[object Object],[object Object]
Decentralized Centralized Inbound transportation cost (from factories to warehouses) Facility/Labor cost Outbound transportation cost (from warehouses to retailers) Safety Stock Responsiveness to customers (lead time) Centralized vs. Decentralized Overhead Costs Service Level
Case Study ,[object Object],[object Object],[object Object],(Adapted from Simchi-Levi, Chen, and Bramel,  The Logic of Logistics , Springer, 2004) PART 1 DALLAS ($260) 15 7 8 PART 2 CHARLESTON ($7) 14 PART 4 BALTIMORE   ($220) 5 PART 3 AUSTIN ($2) 14 6 8 5 PART 5 CHICAGO ($155) 45 PART 7 CHARLESTON   ($30) 14 PART 6 CHARLESTON ($2) 32 8 0 14 55 14 45 14 32
A Pure Pull System ,[object Object],[object Object],[object Object],PART 1 DALLAS ($260) 15 7 8 PART 2 CHARLESTON ($7) 14 PART 4 BALTIMORE   ($220) 5 PART 3 AUSTIN ($2) 14 6 8 5 PART 5 CHICAGO ($155) 45 PART 7 CHARLESTON   ($30) 14 PART 6 CHARLESTON ($2) 32 8 77 14 55 14 45 14 32
A Pure Push System ,[object Object],[object Object],[object Object],PART 1 DALLAS ($260) 15 7 8 PART 2 CHARLESTON ($7) 14 PART 4 BALTIMORE   ($220) 5 PART 3 AUSTIN ($2) 14 6 8 5 PART 5 CHICAGO ($155) 45 PART 7 CHARLESTON   ($30) 14 PART 6 CHARLESTON ($2) 32 8 0 14 55 14 45 14 32
A Hybrid Push-Pull System ,[object Object],[object Object],PART 1 DALLAS ($260) 15 7 8 PART 2 CHARLESTON ($7) 14 PART 4 BALTIMORE   ($220) 5 PART 3 AUSTIN ($2) 14 6 8 5 PART 5 CHICAGO ($155) 45 PART 7 CHARLESTON   ($30) 14 PART 6 CHARLESTON ($2) 32 8 30 7 8 9 45 14 32 push/pull boundary
CST vs. Inventory Cost Push System Pull System Push-Pull System
Echelon Inventory System Supplier Warehouse Retailers Warehouse  echelon inventory Warehouse  echelon lead  time
Managing Inventory in the Supply Chain ,[object Object],[object Object],[object Object],[object Object]
Forecasting ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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3 Inventory Management And Risk Pooling

  • 1. Inventory Management & Risk Pooling
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7. Economic Order Quantity Model Assuming demand certainty Trade-offs between setup costs and inventory holding costs, but ignores issues such as demand uncertainty and forecasting . 1000 2000 3000 4000 5000 6000 0 50 100 150 200 250 300 350 Ordering (Acquisition)Costs Holding or Carrying Costs Total Costs Economic Order Quantity
  • 8. Single Period Model Without Initial Inventory
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 16.
  • 18.
  • 20.
  • 21. Single Period Model With Initial Inventory
  • 22.
  • 23. Initial Inventory and Profit The case motivates a powerful ( s , S ) inventory policy (or a min max policy): s is the reorder point and S is the order-up-to-level
  • 25.
  • 26. Variable Demand with a Fixed ROP Reorder point, R Q LT Time LT Inventory level 0 Result of uncertainty
  • 27. Reorder Point with a Safety Stock The amount of safety stock needed is based on the degree of uncertainty in the lead time demand and desired customer service level Reorder point, R Q LT Time LT Inventory level 0 Safety Stock
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 38.
  • 39.
  • 40. Lead Time Pooling Supplier 8-week lead time
  • 41. Lead Time Pooling Supplier 8-week lead time Retail DC 1-week lead time
  • 42. Capacity Pooling 3 Links – no flexibility
  • 43. Capacity Pooling 9 Links – Total Flexibility
  • 44. Advantages / Disadvantages large costs to have flexibility accommodate demand uncertainty Capacity Pooling   reduce inventory investment   additional transportation costs keep inventory closer to customer   extra costs of operating distribution center decrease lead time Lead Time Pooling   better performance in terms of matching supply and demand   potentially degrades product functionality reduction in demand variability Product Pooling   reduce expected inventory investment needed to achieve a target service level   creates distance between inventory and customers reduce demand variability Location Pooling Disadvantages Advantages
  • 45.
  • 46. Example Decentralized system: total SS = 47.88 total avg. invent. = 179 Safety Stock SS = z · STD · Reorder Point R = AVG · L + SS Order Quantity Q = sqrt(2* C 0 *AVG/h ) Order-up-to-level R + Q Average Inventory  SS + Q/2 Service Level:97% k=1.88 Lead Time= 1 week Q/2+SS AVG STD SS R Q Order- up-to Level Average Inventory Warehouse 1 39.3 13.2 25.08 65 132 197 91 Warehouse 2 38.6 12.0 22.8 62 131 193 88 Centralized Warehouse 77.9 20.7 39.35 118 186 304 132
  • 47.
  • 48.
  • 49.
  • 50. Decentralized Centralized Inbound transportation cost (from factories to warehouses) Facility/Labor cost Outbound transportation cost (from warehouses to retailers) Safety Stock Responsiveness to customers (lead time) Centralized vs. Decentralized Overhead Costs Service Level
  • 51.
  • 52.
  • 53.
  • 54.
  • 55. CST vs. Inventory Cost Push System Pull System Push-Pull System
  • 56. Echelon Inventory System Supplier Warehouse Retailers Warehouse echelon inventory Warehouse echelon lead time
  • 57.
  • 58.