In this paper we study a Monte Carlo simulation--based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates, stopping rules, and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem.

/pdf/the-sample-average-approximation-method-for-stochastic-58q5cyf5zb.pdf

The Sample Average Approximation Method for Stochastic Discrete Optimization

https://homepages.fhv.at/hgb/New-Papers/CMAME07_BS07b.pdf

Robust Optimization - A Comprehensive Survey

https://ira.lib.polyu.edu.hk/bitstream/10397/1269/1/SetupSurvey-2006%28June-19%29.pdf

A survey of scheduling problems with setup times or costs

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Predictive Control for Linear and Hybrid Systems

http://www.optimization-online.org/DB_FILE/2003/06/670.pdf

A stochastic programming approach for supply chain network design under uncertainty

Cell formation has received much attention from academicians and practitioners because of its strategic importance to modern manufacturing practices. Existing research on cell formation problems using integer programming (IP) has achieved the target of solving problems that simultaneously optimise: (a) cell formation, (b) machine-cell allocation, and (c) part-machine allocation.

/pdf/fuzzy-extensions-to-integer-programming-models-of-cell-49wy5onmf3.pdf

Fuzzy extensions to Integer Programming models of cell-formation problems in machine scheduling

This paper presents two new heuristics for the vehicle routing problem on tree-like road networks. These networks occur, for example, in rural road systems where the supply (or delivery) nodes are located on rural roads leading off from a few highways which form the 'trunks' of a tree-like network. The heuristics have the conventional objective of minimising the total distance travelled by the vehicles. The development of the heuristics takes advantage of the tree-like structure of the network. These two new heuristics and two other heuristics from the published literature are applied to some test problems and computational results are presented. The computational experience indicates that one of the new heuristics provides superior solutions to the existing heuristics and in reasonable computing time. It therefore appears suitable for large-scale practical routing problems.

Heuristics for vehicle routing on tree-like networks

Decision support systems have become widespread in recent years. However, most of these systems are not carefully validated and this has led in some cases to serious errors. One of the principal reasons for the lack of validity is the lack of an operationalised validation methodology. A simplified validity framework has already been developed by the authors as the first part of a 3-phase approach towards devising a practical validation methodology. This paper describes the second phase, reporting as it does on a survey that has been undertaken to unearth the contingency factors that influence how the process of validation, employing the validity framework, will be carried out for a particular kind of decision support system—one involving a spreadsheet model.

John M. Wilson

Papers

Fuzzy extensions to Integer Programming models of cell-formation problems in machine scheduling

Heuristics for vehicle routing on tree-like networks

A survey of contingency factors affecting the validation of end-user spreadsheet-based decision support systems

Elite guided steady-state genetic algorithm for minimizing total tardiness in flowshops

The role of OR specialists in ‘do it yourself’ spreadsheet development