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

Logical relations occur frequently in integer programming problems and are modelled by introducing binary variables in association with linear expressions. Applications requiring constraints involving precedence, exclusion, implication and other conditions give rise to the logical relations OR and IMPLIES in the models. These relations will be considered in this paper from a modelling point of view and formulations investigated for situations where the logical variables link sets of integer variables. Valid inequalities (cuts) that can be added to a model will be developed for a number of the formulations and the computational benefits of these cuts will be considered from an experimental point of view by considering the performance of sets of problem instances. New formulations and combinations of older established formulations will be considered. It will be contended that tight formulations may not always be the most successful.

Modelling either-or relations in integer programming

Tributes have been paid from around the world to Russell Ackoff who died in October 2009. It is appropriate that this journal should also mark the influence of Ackoff on OR in the UK. Ackoff had a major influence on OR in this country in a number of ways. First he was the author or joint-author of many books, two of which from the 1960s (Ackoff and Rivett, 1963; Ackoff and Sasieni, 1968) played an important role as standard references for training of OR practitioners on short courses and of MSc programmes at a time of growth in OR education. These books provided a background to the techniques of OR. Such books were very much of their time, providing a way to solve OR problems arising in a number of different contexts by use of standard modelling procedures. Second, Ackoff had a personal influence on one of the key lively figures in British OR, Pat Rivett, and through him influenced the development of OR education in Britain. University programmes developed in the US by Ackoff and his colleagues impressed Rivett and he sought to mimic them in programmes in Britain for training practitioners and later in university programmes that were developing in the ‘new’ universities of the 1960s in Britain. It is easy to see with hindsight how OR educators could be seduced by a technical approach to OR. Linear programming appeared to offer a revelation as a tool, with its promise of optimal policies and precise mathematical explanation of fundamental concepts of economics such as price and value of resources. However, Rivett and others in Britain soon realised the limitations of a purely technical approach to OR. The neglect of the personal and managerial dimension was a major defect. Simultaneously while UK OR was moving away from a technical underpinning, Ackoff was developing views of a softer systems approach, which harmonised with expectations in OR circles in Britain. Ackoff was a regular visitor to the UK in these years and gave many presentations of these new views that touched chords. (I was privileged to hear him talk as part of the seminar programme Pat Rivett organised for MSc students in the early 1970s and, like many eager students, was impressed by this visiting guru figure.) It was to be in Britain that Ackoff articulated aspects of his new vision of OR, that was to have dramatic effect in the later 1970s. A third key aspect of Ackoff’s influence in Britain was the delivery of talks at the ORS Conference of 1978, and the subsequent publication of them in this journal, which illuminated his new vision and led to two papers appearing in JORS (Ackoff, 1979a,b). In these papers Ackoff was critical of the way OR had developed, and was continuing to develop, and made a plea for a new way forward. These two papers have had a far-reaching influence on OR worldwide. Although views of a US expert, they have had considerable influence on the development of a particularly ‘British view’ of OR. The loss of Ackoff as a challenging voice of reason in OR will be mourned worldwide.

Russell L Ackoff

A bookmobile is a specially adapted bus or van used as part of the outreach operations of public library systems. Bookmobiles play a significant part in the service of the public library system in Buskerud County, Norway. They are used to deliver and collect library materials (printed books, audio books, periodicals, and music) to and from borrower groups throughout the County, many in remote areas. The question of how best to utilise the County’s bookmobile resources can be modelled as an interesting variation of one of the classical models of operational research — the travelling salesman problem. The combination of the features that make this scenario non-standard include multiple depots, simultaneous cost minimisation and prize collection objectives, differing customer service levels, time windows, route start time flexibility for some routes, multiple route duration restrictions, route lunch breaks, and overnight stays on certain routes. We report on models for the bookmobile problem, and the outcome of its application to the Buskerud County bookmobile system.

Integer Programming Models of Bookmobile Routing

The k-sequential generalized assignment problem (GAPkSeq) is a problem of allocating tasks to time periods, where each of n tasks must be assigned to k sequential time periods out of a total of m. Using standard mathematical programming software, GAPkSeq becomes intractable for relatively small values of k, m and n; hence there is a need for heuristic algorithms to solve such problems. It is shown how a heuristic combining both divide-and-conquer and a linear programming-based heuristic developed previously for the generalized assignment problem with special ordered sets can be modified and extended to solve GAPkSeq. Encouraging results in terms of speed and accuracy are described.

An LP-based metaheuristic procedure for the k-sequential generalized assignment problem

Patients with cystic fibrosis (CF) and suitable genotypes are now able to access gene-potentiating therapy that improves lung function, weight gain, and prolongs the time between pulmonary exacerbations. We report the case of a 74 year old woman who had CF with a R117H gating mutation. Lung function had declined to 38% predicted normal FEV1 and there was progressive bronchiectasis evident on CT scanning. After treatment with ivacaftor over 12 months, lung function has improved to FEV1 of 50% predicted normal. Repeat CF scanning showed marked improvement of bronchiectasis. This case report demonstrated that gene-potentiating therapy may be beneficial in CF patients with advancing age and that structural improvement may occur on treatment.

John M. Wilson

Papers

Modelling either-or relations in integer programming

Russell L Ackoff

Integer Programming Models of Bookmobile Routing

An LP-based metaheuristic procedure for the k-sequential generalized assignment problem

Apparent Improvement of Airway Injury after Gene-Potentiating Therapy in Cystic Fibrosis