Optimization Models and Algorithms for Workforce Scheduling with Uncertain Demand

Abstract

A workforce plan states the number of workers required at any point in time. Efficient workforce plans can help companies achieve their organizational goals while keeping costs low. In ever increasing globalized work market, companies need a competitive edge over their competitors. A competitive edge can be achieved by lowering costs. Labour costs can be one of the significant costs faced by the companies. Efficient workforce plans can provide companies with a competitive edge by finding low cost options to meet customer demand. This thesis studies the problem of determining the required number of workers when there are two categories of workers. Workers belonging to the first category are trained to work on one type of task (called Specialized Workers); whereas, workers in the second category are trained to work in all the tasks (called Flexible Workers). This thesis makes the following three main contributions. First, it addresses this problem when the demand is deterministic and stochastic. Two different models for deterministic demand cases have been proposed. To study the effects of uncertain demand, techniques of Robust Optimization and Robust Mathemat- ical Programming were used. The thesis also investigates methods to solve large instances of this problem; some of the instances we considered have more than 600,000 variables and constraints. As most of the variables are integer, and objective function is nonlinear, a commercial solver was not able to solve the problem in one day. Initially, we tried to solve the problem by using Lagrangian relaxation and Outer approximation techniques but these approaches were not successful. Although effective in solving small problems, these tools were not able to generate a bound within run time limit for the large data set. A number of heuristics were proposed using projection techniques. Finally this thesis develops a genetic algorithm to solve large instances of this prob- lem. For the tested population, the genetic algorithm delivered results within 2-3% of optimal solution.