Professor Merve Bodur presented “Stochastic integer programming in staffing and scheduling problems under uncertainty” at the UT-ITE seminar on September 21, 2018.
Stochastic integer programming is a useful tool for decision making under uncertainty in optimization problems. One of the applications of this tool is solving staffing and scheduling problems when customer demand is uncertain.
Previous studies of this problem first identify staffing level, and then, determine schedules for the staff that cover these levels. Professor Bodur collaborated with Professor James R. Luedtke of University of Wisconsin-Madison and together, they proposed a novel stochastic integer programming formulation that integrates these staffing and scheduling decisions. They also developed an optimization technique to solve the problem efficiently.
Using data from a bank call centre, they implemented their model and found that savings of up to 5% could be achieved compared to considering staffing and scheduling separately.
Their study was published in Management Science in 2016 as “Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty.”
Stochastic integer programming has numerous applications in transportation, such as transit timetable development and vehicle/crew scheduling. Professor Bodur is now collaborating with Professor Amer Shalaby to apply stochasticity to transfer optimization work.
Professor Bodur has generously shared her presentation slides here.
To watch a video of the presentation, please click on the image below:
Abstract
Many practical planning, design and operational problems involve making decisions under uncertainty. Also, most of them include some integer decisions. Stochastic integer programming (SIP) is a useful tool for dealing with uncertainty and integrality requirements in optimization problems.
We consider server scheduling in multiclass service systems under uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels, and then determine schedules for the servers that cover these levels.
We propose a new SIP model that integrates these two decisions, which can yield lower scheduling costs by exploiting the presence of alternative server configurations that yield similar quality-of-service.
As the model is computationally very challenging, we develop an improved Benders decomposition algorithm for its solution. Numerical examples illustrate the computational efficiency of the proposed approach and the potential benefit of solving the integrated model compared to considering the staffing and scheduling problems separately.
This is joint work with Jim Luedtke from University of Wisconsin-Madison.
Short Biography
Merve Bodur is an Assistant Professor in the Department of Mechanical and Industrial Engineering at the University of Toronto. She also holds a Dean’s Spark Professorship in the Faculty of Applied Science and Engineering. She obtained her PhD from University of Wisconsin-Madison and did a postdoc at the Georgia Institute of Technology. She received her BS in Industrial Engineering and BA in Mathematics from Bogazici University, Turkey. Her research interests include theory and applications of stochastic programming, integer programming, multiobjective integer programming and combinatorial optimization.