An Optimal Network-Based Approach to Scheduling and Re-Rostering Continuous Heterogeneous Workforces

Abstract : This dissertation presents a mathematical programming approach to the personnel tour scheduling problem based upon a minimum cost network flow formulation with specialized side constraints. The linear program optimally solves the tour scheduling problem for industries with continuous (24-hour) operations and a heterogeneous workforce, such as fast food restaurants, hotels and resorts, university computer labs, nurses in large health care systems, and retail sales. The methodology allows for a workforce with varying availabilities, part and full-time employees, differing skill-sets and wage rates, and minimum and maximum shift requirements per week. Additionally, the formulation can quickly adjust an optimal schedule due to sickness, vacation, hiring or firing with the workforce, and minimize the number of deviations within the original schedule. A methodology that can optimally schedule both a continuous and a heterogeneous workforce in an insignificant amount of computational time is unique in the literature. In many instances, the linear program generates integral solutions to the tour-scheduling problem without branching, bounding, or cutting techniques. An interior-point method solves the formulation in less than 3 seconds for large problem instances of 80 employees scheduled to 420 distinct shifts. The efficiency of the formulation is presented for many test sets of problems as well as an application to the tour-scheduling problem of computer lab staffing at Arizona State University and nurses with the Banner Health network of heath care providers.