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A smoothing replenishment policy with endogenous lead times.

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


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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  19. (2000). Foundations of Inventory Management.
  20. (1956). Guides to inventory control, part II. Harvard Business Review,
  21. (1961). Industrial Dynamics.
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  32. (1952). On the application of servomechanism theory in the study of production control.
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  42. (1958). Production Planning and Inventory Control.
  43. (1991). Production smoothing evidence from physical-product date.
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  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.
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