Approximation Algorithms for Stochastic Optimization Problems in Operations Management

Abstract

This article provides an introduction to approximation algorithms in stochastic optimization models arising in various application domains, including central areas of operations management, such as scheduling, facility location, vehicle routing problems, inventory and supply chain management, and revenue management. Unfortunately, these models are very hard to solve to optimality in both theory and practice. We will survey recent development on approximation algorithms for these stochastic optimization models and their performance analysis techniques with worst‐case performance guarantees.

A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems

“…This is problematic, as a survey which goes into considerable mathematical depth on a particular new methodology can be instrumental in moving an academic field forward, by providing a reference which can quickly introduce researchers to the key ideas and techniques needed to apply those ideas to other problems. Among the aforementioned surveys, it seems that some of the very few attempting such a presentation recently are Levi (2010) and Shi (2011), for the myopic balancing approximation algorithm methodology pioneered by Levi and co‐authors; and Chen (2017), for the use of convexity and related methodologies in inventory problems.…”

“…This general approach has by now led to a vast literature on mathematical inventory problems. For example, the following is a (non-comprehensive) list of surveys done on various aspects of mathematical inventory control in the past 60 years: Veinott (1966a), Clark (1972), Aggarwal (1974), Silver (1981), Nahmias (1982), Aksoy and Erenguc (1988), Porteus (1990), Raafat (1991), Kleijn and Dekker (1999), Petruzzi and Dada (1999), Kennedy et al (2002), Minner (2003), Elmaghraby and Keskinocak (2003), Chan et al (2004), Urban (2005), Williams and Tokar (2008), Syntetos et al (2009), Levi (2010), Dror and Hartman (2011), Bijvank and Vis (2011), Winands et al (2011), Fiestras-Janeiro et al (2011, Shi (2011), Krishnamoorthy et al (2011), Bakker et al (2012), Chen and Simchi-Levi (2012), Coelho et al (2013), Brahimi et al (2017), Yao and Minner (2017), Atan et al (2017), Chen (2017), Duong et al (2018), along with at least one survey of surveys (Bushuev et al 2015), and several textbooks (Porteus 2002, Simchi-Levi et al 2005, Zipkin 2000).…”