Column Generation Approach For Stochastic Optimization Problems

Understanding how uncertainty effects the dynamics §and behavior of an organization is a critical aspect §of system design. Models and methods that take §uncertainty into account can lead to significant §reductions in cost. This book investigates the use §of stochastic optimization models for a generalized §assignment problem (GAP) with uncertain resource §capacity and a shift planning and scheduling problem §(SPSP) with unknown demand. For the GAP, the first §stage decisions correspond to an assignment of jobs §to agents. Penalties are incurred when the §assignments do not permit all demand to be §satisfied. For the SPSP, the number of full-time and §part-time employees, as well as the number of full-§time shifts by type, must be specified before the §demand is known. In the second stage, feasibility is §addressed by allocating overtime and calling in §temporary workers to handle spikes in the mail §volume. This book contains the development and §analysis of stochastic integer models for the GAP §and the SPSP and the estimation of the demand §distributions from historical data. To solve the §associated stochastic integer problems, the column §generation algorithms are developed.