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1	The Multiple Retailer Inventory Routing Problem With Backorders Alisan, Onur 01 July 2008 (has links) (PDF) In this study we consider an inventory routing problem in which a supplier distributes a single product to multiple retailers in a finite planning horizon. Retailers should satisfy the deterministic and dynamic demands of end customers in the planning horizon, but the retailers can backorder the demands of end customers considering the supply chain costs. In each period the supplier decides the retailers to be visited, and the amount of products to be supplied to each retailer by a fleet of vehicles. The decision problems of the supplier are about when, to whom and how much to deliver products, and in which order to visit retailers while minimizing system-wide costs. We propose a mixed integer programming model and a Lagrangian relaxation based solution approach in which both upper and lower bounds are computed. We test our solution approach with test instances taken from the literature and provide our computational results. ZA Databases 4450-4460
2	Quadratic Spline Approximation of the Newsvendor Problem Optimal Cost Function Burton, Christina Marie 10 March 2012 (has links) (PDF) We consider a single-product dynamic inventory problem where the demand distributions in each period are known and independent but with density. We assume the lead time and the fixed cost for ordering are zero and that there are no capacity constraints. There is a holding cost and a backorder cost for unfulfilled demand, which is backlogged until it is filled by another order. The problem may be nonstationary, and in fact our approximation of the optimal cost function using splines is most advantageous when demand falls suddenly. In this case the myopic policy, which is most often used in practice to calculate optimal inventory level, would be very costly. Our algorithm uses quadratic splines to approximate the optimal cost function for this dynamic inventory problem and calculates the optimal inventory level and optimal cost. newsvendor problem single-product nonstationary discrete-time multi-period finite horizon independent demands no capacity constraints backordering optimal inventory level near optimal policy value function approximation quadratic splines Mathematics

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The Multiple Retailer Inventory Routing Problem With Backorders

Quadratic Spline Approximation of the Newsvendor Problem Optimal Cost Function