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Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem Gary D. EPPEN Management Science Vol 2

Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem Gary D. EPPEN Management Science Vol 25 No.5 1979. Salih ÖZTOP 20202801 26.03.2003. Context. Introduction Derived Expression for expected holding and penalty cost

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Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem Gary D. EPPEN Management Science Vol 2

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  1. Effects of Centralization on Expected Costs in a Multi-Location Newsboy ProblemGary D. EPPENManagement Science Vol 25 No.5 1979 Salih ÖZTOP 20202801 26.03.2003

  2. Context • Introduction • Derived Expression for expected holding and penalty cost • Comparison of Centralized and Decentralized systems using the derived expression • Effect of Correlation of demands on the saving amount • Relationship between cost and number of consolidated demand centers Effects of Centralization on Expected Costs.. Eppen

  3. 1. Introduction • Aim of the paper:To show the cost saving using a centralized system rather than a decentralized system • Single-Period, Single-Product inventory model with N individual sources of demand Effects of Centralization on Expected Costs.. Eppen

  4. Decentralized System Seperate inventory is kept to satisfy the demand at each source of demand Manufacturer DC 1 Inv. DC 2 Inv. DC N Inv. . . . . . . . DC 1 Demand DC 2 Demand DC N Demand Effects of Centralization on Expected Costs.. Eppen

  5. Centralized System All demands are satisfied from one central warehouse Manufacturer Central Warehouse . . . . . . . DC 1 Demand DC 2 Demand DC N Demand Effects of Centralization on Expected Costs.. Eppen

  6. Some Definitions :Demand at distribution center i • Normality is assumed because it has frequent aplicability and gives simple analytic results :Covariance of and :Correlation Coefficient of and Positive Correlation Negative Correlation Effects of Centralization on Expected Costs.. Eppen

  7. Holding Cost when Penalty Cost when Holding and Penalty Cost Holding and Penalty Costs are assumed to be linear and constant for over all sources of demand. • Expected holding and penalty cost at source i when yitems are on hand at the beginning of the period: :Demand at distribution center :Density function of normaly distributed demand , Effects of Centralization on Expected Costs.. Eppen

  8. 2.Derivation 1 2 3 4 1’ 1’’ 2’ 2’’ Effects of Centralization on Expected Costs.. Eppen

  9. 2.Derivation 1+1’ 2+2’ 3+ 1’’ 4+ 2’’ Effects of Centralization on Expected Costs.. Eppen

  10. 2.Derivation Right-hand unit normal linear loss inegral Density Function of Normal distribution Result: Effects of Centralization on Expected Costs.. Eppen

  11. 2.Derivation • To minimize the expected holding and penalty cost at source i; start the period with smallest on hand inventory, y, such that: :Cumulative distribution function : Fractile point of optimal initial inventory at source i Effects of Centralization on Expected Costs.. Eppen

  12. 2.Derivation • Then z is the (p/p+h)th fractile of the standard normal distribution Put that value into our result Effects of Centralization on Expected Costs.. Eppen

  13. 2.Derivation K Final result: Effects of Centralization on Expected Costs.. Eppen

  14. 3.Comparison of Centralized and Decentralized Systems a) Decentralized: for all i Effects of Centralization on Expected Costs.. Eppen

  15. 3.Comparison of Centralized and Decentralized Systems b) Centralized: Covariance Effects of Centralization on Expected Costs.. Eppen

  16. 3.Comparison of Centralized and Decentralized Systems b) Centralized: covariance Effects of Centralization on Expected Costs.. Eppen

  17. 3.Comparison of Centralized and Decentralized Systems b) Centralized: correlation For easy comparison Effects of Centralization on Expected Costs.. Eppen

  18. 3.Comparison of Centralized and Decentralized Systems Result 1: Effects of Centralization on Expected Costs.. Eppen

  19. 4.Effect of Correlation of demands on the saving amount Result 2: Since Effects of Centralization on Expected Costs.. Eppen

  20. 5. Relationship between cost and number of demand centers When demands are uncorrelated Effects of Centralization on Expected Costs.. Eppen

  21. 5. Relationship between cost and number of demand centers Assumption: is constant over all locations. Say Then, Result 3: Effects of Centralization on Expected Costs.. Eppen

  22. References • Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem - Gary D. EPPENManagement Science Vol 25 No.5 1979 • Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem – Miao Sheng CHEN,Chin Tsai LINThe Journal of Operational Research Society Vol 40 No.6 1989 Effects of Centralization on Expected Costs.. Eppen

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