#### Abstract

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.

#### Degree

MS

#### College and Department

Physical and Mathematical Sciences; Mathematics

#### Rights

http://lib.byu.edu/about/copyright/

#### BYU ScholarsArchive Citation

Burton, Christina Marie, "Quadratic Spline Approximation of the Newsvendor Problem Optimal Cost Function" (2012). *All Theses and Dissertations*. 3087.

http://scholarsarchive.byu.edu/etd/3087

#### Date Submitted

2012-03-10

#### Document Type

Thesis

#### Handle

http://hdl.lib.byu.edu/1877/etd5071

#### Keywords

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