1. /faculteit technologie management Modelling Imperfect Advance Demand Information and Analysis of Optimal Inventory Policies Tarkan Tan Technische Universiteit Eindhoven October 23, 2007 Forecasting and Inventory Management: Bridging the Gap EPSRC project Meeting - London

2. /faculteit technologie management OUTLINE INTRODUCTION - CONTRIBUTIONS ENVIRONMENT MODELING IMPERFECT ADI DESCRIPTION OF THE INV. MODEL CHARACTERIZATION OF THE OPTIMAL POLICY VALUE OF ADI CONCLUSION AND FUTURE RESEARCH

3. /faculteit technologie management INTRODUCTION DEVELOPMENTS IN INFORMATION TECHNOLOGIES Decreasing demand variability Decreasing lead times New forms of information IMPERFECT ADVANCE DEMAND INFORMATION (ADI) Internet Retailing  Number of visits to a commercial web site  Filtered information  Shopping carts, wish lists, price watch B2B Applications  Vendor Managed Inventories  Collaborative Planning, Forecasting and Replenishment Traditional Retailing  Sales representatives

4. /faculteit technologie management CONTRIBUTIONS Probabilistic representation of imperfect advance demand information. Relating imperfect ADI with production/inventory decisions – structural properties. Measurement – Benefits of employing imperfect ADI

5. /faculteit technologie management ENVIRONMENT Production/Inventory System  Demand is stochastic.  All unmet demand is backlogged.  Linear holding, backorder, unit production costs.  Finite-horizon model  L – supply lead-time  l – demand lead-time (customers order ahead of time)   = ( L - l ) effective lead-time

6. /faculteit technologie management MODELING IMPERFECT ADI M n – size of the ADI (rv) in period n. Assumed to be i.i.d. with K n – potential customers in period n. p – probability that demand is realized r – probability that customer waits q = 1-p-r – probability that customer leaves.

7. /faculteit technologie management MODELING IMPERFECT ADI

8. /faculteit technologie management MODELING IMPERFECT ADI Demand in period n is a function of total ADI size available at period n. Hence, demands are not i.i.d. (unless r = 0) W n (k) effective lead-time demand given k at period n.

9. /faculteit technologie management MODELING IMPERFECT ADI Effective lead-time demand can be computed by following each ADI and “counting” possible realizations. where

10. /faculteit technologie management DESCRIPTION OF THE PROD/INV. MODEL

11. /faculteit technologie management DESCRIPTION OF THE PROD/INV. MODEL Stochastic DP –  Write out the state variable: current inventory and stock of ADI.  Form DP recursive equations.  Ending conditions.

12. /faculteit technologie management CHARACTERIZATION OF THE OPTIMAL POLICY RESULTS – 4 Theorems State-dependent order up-to policy Results regarding the relation between order- up-to levels given ADI of different periods – computationally important. Results regarding size of ADI and order-up-to level – computationally important.

13. /faculteit technologie management VALUE OF ADI Compare two systems – one utilizing ADI, the other not. –System not utilizing ADI uses expected and variance of lead-time demand distribution. –System utilizing ADI uses the observation of the available ADI stock, k. Myopic Problem (single decision epoch) – Analytical Results (costs evaluated under normal app.)

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15. VALUE OF ADI General case – computations made under Poisson distributed K.  Distribution of effective lead-time demand, W, under ADI is convolution of Binomial and Poisson.  Distribution of W under no-ADI is Poisson.

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17. CONCLUSION AND FUTURE RESEARCH Source segmentation. p=1 corresponds to perfect information. Incorporation of “regular” demand and rationing. Extension to configured-demand cases.