A Column Generation Approach for Stochastic Optimization Problems: in the Applications of a Stochastic Generalized Assignment Problem and a Shift Planning and Scheduling Problem with Uncertain Demand

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.