Benders Decomposition: A Humanitarian Operation with Stochastic Programming Framework

Jyotirmoy Dalal () and Faiz Hamid ()
Additional contact information
Jyotirmoy Dalal: Sheffield University Management School (University of Sheffield)
Faiz Hamid: Indian Institute of Technology Kanpur

Chapter Chapter 8 in Optimization Essentials, 2024, pp 257-277 from Springer

Abstract: Abstract Benders Decomposition (BD) is a popular large-scale optimization technique. Within an iterative framework, it attempts to solve difficult problems by fixing complicating variables. Researchers have successfully applied this exact method to a variety of challenging, large-scale optimization problems in diverse domains such as telecommunication, transportation and logistics, emergency management, sustainable energy management, healthcare, etc. Although this decomposition framework is quite general, the structural aspect of the two-stage stochastic programming (SP) models that represent data uncertainties by scenarios makes this class of problem particularly amenable to BD. The wide popularity of SP as an optimization tool for decision-making under uncertainties and the possibility of successfully applying BD to solve large-scale instances makes this technique attractive. This chapter begins with a mathematical foundation for the BD framework, followed by a step-by-step guide to iteratively solve a mixed-integer programming model by decomposing the same into a relaxed master problem and one or more subproblems. We demonstrate an application of this well-known large-scale optimization technique in stochastic settings and illustrate the concept through an example inspired by a research problem. We conclude the chapter by discussing a variety of implementation-related challenges and some contemporary implementation strategies utilizing the state-of-the-art CPLEX solver.

Keywords: Large-scale optimization; Exact algorithm; Benders decomposition; Stochastic programming; Uncertainty; Nonprofit operations (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-981-99-5491-9_8

Ordering information: This item can be ordered from
http://www.springer.com/9789819954919

DOI: 10.1007/978-981-99-5491-9_8

Access Statistics for this chapter

More chapters in International Series in Operations Research & Management Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().