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A smoothing replenishment policy with endogenous lead times.

By Robert Boute, SM Disney, Marc Lambrecht and B Van Houdt

Abstract

We consider a two echelon supply chain consisting of a single retailer and a single manufacturer. Inventory control policies at the retailer level often transmit customer demand variability to the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). When the manufacturer produces in a make-to-order fashion though, he prefers a smooth order pattern. But dampening the variability in orders inflates the retailer's safety stock due to the increased variance of the retailers inventory levels. We can turn this issue of conflicting objectives into a win-win situation for both supply chain echelons when we treat the lead time as an endogenous variable. A less variable order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer's safety stock. We show that by including endogenous lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels.Bullwhip effect; Demand; endogenous lead times; Fashion; Inventory; Inventory control; Markov processes; Order; Policy; Queueing; Research; Safety stock; Smoothing; Supply chain; Supply chain management; Time; Variability; Variance;

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  1. (2004). 3-moments matching with minimal, positive acyclic phase-type distributions. Research report.
  2. (1983). A ¯rst course in bulk queues.
  3. (2005). A heuristic to control integrated multi-product multi-machine production-inventory systems with job shop routings and stochastic arrival, set-up and processing times.
  4. (1967). A linear production-inventory control rule.
  5. (2002). A new algorithm for computing the rate matrix of
  6. (1999). A single-item inventory model for a nonstationary demand process.
  7. (1986). A variance bounds test of the linear quadratic inventory model.
  8. (2003). Acyclic discrete phase type distributions: Properties and a parameter estimation algorithm.
  9. (2004). An analytical investigation of the bullwhip e®ect.
  10. (2004). An exact analytical solution to the production inventory problem.
  11. (1955). Application of discrete variable servo theory to inventory control.
  12. (1986). Balancing production level variations and inventory variations in complex production systems.
  13. (1986). Can the production smoothing model of inventory behavior be saved?.
  14. (1976). Coordinating control of production-inventory systems.
  15. (2004). Coordinating supply chains by controlling upstream variability propagation.
  16. (1997). Do inventories moderate °uctuations in output?.
  17. (1982). Dynamic analysis of an inventory and order based production control system.
  18. (2001). Factory Physics. 2nd edn.
  19. (2000). Foundations of Inventory Management.
  20. (1956). Guides to inventory control, part II. Harvard Business Review,
  21. (1961). Industrial Dynamics.
  22. (1997). Information distortion in a supply chain: The bullwhip e®ect.
  23. (1999). Introduction to Matrix Analytic Methods and stochastic modeling.
  24. (1998). Inventory Management and Production Planning and Scheduling. 3rd edn.
  25. (1993). Manufacturing lead times, order release and capacity loading. in
  26. (2002). Matching moments for acyclic discrete and continuous phase-type distributions of second order.
  27. (1981). Matrix-Geometric Solutions in Stochastic Models, An Algorithmic Approach.
  28. (2003). Measuring and avoiding the bullwhip e®ect: A control theoretic approach.
  29. (2000). Minimal coe±cient of variation of discrete phase type distributions.
  30. (1999). Modeling supply chain contracts: A review.
  31. (1988). Nonlinear matrix equations in applied probability - solution techniques and open problems.
  32. (1952). On the application of servomechanism theory in the study of production control.
  33. (2003). On the bullwhip and inventory variance produced by an ordering policy.
  34. (2005). On variance ampli¯cation in a three-echelon supply chain with minimum mean square error forecasting.
  35. (2003). Order ¯ll rate, leadtime variability, and advance demand information in an assemble-to-order system.
  36. (1999). Order-ful¯llment performance measures in an assemble-to-order system with stochastic lead times.
  37. (2002). Performance analysis and optimization of assemble-to-order systems with random lead times.
  38. (2004). Periodic review base-stock replenishment policy with endogenous lead times.
  39. (2002). PhFit: A general phase-type ¯tting tool.
  40. (1995). Probability, Stochastic Processes, and Queueing Theory.
  41. (2002). Production and inventory control; the variability trade-o®.
  42. (1958). Production Planning and Inventory Control.
  43. (1991). Production smoothing evidence from physical-product date.
  44. (2002). Production-inventory system controller design and supply chain dynamics.
  45. (1979). Production-Inventory Systems: Planning and Control. 3rd edn.
  46. (2000). Quantifying the bullwhip e®ect in a simple supply chain: The impact of forecasting, lead times, and information.
  47. (2005). Quantifying the bullwhip e®ect in a supply chain with stochastic lead time. European Journal of operational research,
  48. (1988). Seasonality, cost shocks, and the production smoothing model of inventories.
  49. (1989). Structured Stochastic Matrices of M/G/1 type and their applications.
  50. (2006). Taming bullwhip whilst watching customer service in a single supply chain echelon.
  51. (1997). The bullwhip e®ect in supply chains.
  52. (1996). The joint e®ect on leadtime variance and lot size in a parallel processing environment.
  53. (1983). The production and inventory behavior of the american automobile industry.
  54. (1989). The production smoothing model is alive and well. Cowles Foundation Discussion Papers 896. Cowles Foundation,
  55. (2004). The scale factor: a new degree of freedom in phase type approximation. Performance Evaluation,
  56. (1966). The status of mathematical inventory theory.

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