A Review on the Performance of Linear and Mixed Integer Two-Stage Stochastic Programming Software

Abstract

This paper presents a tutorial on the state-of-the-art software for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classified according to the decomposition alternatives and the types of the variables in the problem. We review the fundamentals of Benders decomposition, dual decomposition and progressive hedging, as well as possible improvements and variants. We also present extensive numerical results to underline the properties and performance of each algorithm using software implementations, including DECIS, FORTSP, PySP, and DSP. Finally, we discuss the strengths and weaknesses of each methodology and propose future research directions.

A mathematical modeling approach for supply chain management under disruption and operational uncertainty

“…Algorithms such as logic‐based Benders decomposition, 65 specialized branch and bound techniques, 66 and the dual decomposition strategy 67 are applicable in this case. We direct interested readers to Torres et al 68 and Kücükyavuz and Sen, 26 for further information on these algorithms. Furthermore, we have assumed once an entity is disrupted, the full capacity is lost, this assumption can also be relaxed in future and the degree of disruption can be determined.…”

“…Algorithms such as logic-based Benders decomposition, 65 specialized branch and bound techniques, 66 and the dual decomposition strategy 67 are applicable in this case. We direct interested readers to Torres et al 68 and F I G U R E 7 Implemented cost for the rolling horizon. The text on each bar (det = deterministic mode, and sto = stochastic model) Kücükyavuz and Sen, 26 for further information on these algorithms.…”

A Practical and Sustainable Approach to Determining the Deployment Priorities of Automatic Vehicle Identification Sensors

“…The solution methods for stochastic programming models are divided into three groups: exact methods, approximate methods, and heuristic methods [26,27]. A heuristic method is a generally used algorithm that can find the optimal solutions to common problems, whereas it cannot guarantee global optimality.…”