STOCHASTICS SEMINAR :: Inventory Control in a Build-to-Order Environment

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Today, most manufacturers are forced to offer a greater variety to meet customer expectations and maintain a competitive edge. The number of models and options offering by auto manufacturers for example has increased tremendously: BMW offers 10 to the 17th power variations of its 7-series alone. Build-to-Order offers a way to convert the problem of managing the essentially infinite number of end products to one of managing demand for the few thousand components that go into making a vehicle. While auto manufacturers produce the same number of vehicles each day, day-to-day usage of parts can vary significantly since each plant typically makes different models -often on the same line- and demand for option parts varies with customer preferences. At the same time growing reliance on suppliers in lower cost countries like Mexico and China has compounded the complexity of supply. We look at the challenges and solution strategies of employing build-to-order (BTO) in the context of global supply. We introduce a new shipping policy, "Ship-to-Average", which prescribes sending a fixed quantity, based on the long term average forecast, with each shipment and making adjustments only if the inventory strays outside a prescribed range. We provide theoretical support for the observed performance of this type of policy by addressing a Brownian control problem whose objective is to find the right balance between holding costs and the operational costs involved in adjusting the shipment sizes. We consider an inventory whose content fluctuates as a Brownian motion in the absence of control. A linear holding cost is incurred continuously. At any moment a controller can adjust the inventory level by any positive or negative quantity at a fixed plus proportional cost. We show that the optimal policy in this theoretical abstraction of the original supply problem is of a simple form called control band policies. In fact, Ship-to-Average policies are a practical implementation of Control Band policies in the industrial setting which includes delivery delays. To reflect the realities of the problem, as an extension to the Brownian model we introduce constraints on available inventory space and expediting/curtailing quantities. Employing techniques based on methods of Lagrangian relaxation, we show that control band policy is optimal even with constraints on the size of adjustments and on the maximum inventory level.


  • Workflow Status: Published
  • Created By: Barbara Christopher
  • Created: 10/08/2010
  • Modified By: Fletcher Moore
  • Modified: 10/07/2016


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