A simple idea used in many combinatorial algorithms is the idea ofpivoting. Originally, it comes from the method proposed by Gauss in the19th century for solving systems of linear equations. This method had been extended in1947 by Dantzig for the famous simplex algorithm used for solving linear programs. Fromsince, a pivoting algorithm is a method exploring subsets of a ground set and going fromone subset σ to a new one σ′ by deleting anelement inside σ and adding an element outside σ:σ′ = σ\ { v}  ∪  {u},with v ∈ σ and u ∉ σ.This simple principle combined with other ideas appears to be quite powerful for manyproblems. This present paper is a survey on algorithms in operations research and discretemathematics using pivots. We give also examples where this principle allows not only tocompute but also to prove some theorems in a constructive way. A formalisation isdescribed, mainly based on ideas by Michael J. Todd.

This paper broadens the exponential utility function commonly used by risk-averse investors to the linear plus double exponential utility function, which is applicable in most cases. Thus it is of essential and supreme significance to conduct a research on its optimal investment portfolio in securities investment. This paper, by means of the non-difference curve method, carries out a research into the optimal portfolio decision-making by investors who have this type of utility function. The optimal decision-making and the ratio of optimal portfolio investment are derived. Finally, an actual case is given to verify the relevant results.

Analysis of empirical sales data lead us to consider newsboy model for four practicalmarket conditions arising from the presence/absence of stochastic lead time and exogenouslinear temporal decline in selling price when distribution of the stochastic demanddepends upon initial selling price. Viability of the solutions is discussed for threestrategies of obtaining optimal initial selling price and/or ordering quantity. Numericalstudies are conducted to assess the effects of lead time and price decline.

The rising car usage deriving from growth in jobs and residential population causes airpollution, energy waste and consumption of people’s time. Public transport cannot be theonly answer to this increasing transport demand. Carpooling, which is based on the ideathat sets of car owners pick up colleagues while driving to or from the workplace, hasemerged to be a viable possibility for reducing private car usage in congested areas. Itsactual practice requires a suitable information system support and, the most important,the capability of effectively solving the underlying combinatorial optimization problem.This paper describes an ant colony algorithm based hybrid approach (HAC) for solving themulti-destination carpooling problem. Experiments have been performed to confirm theefficiency and the effectiveness of the approach.

The paper addresses a multi-item, multi-plant lot-sizing problem with transfer costs andcapacity constraints. The problem is reformulated according to a multi-commodity flowformalism, and decomposed, through Lagrangean relaxation, into a master facility locationproblem and a slave minimal cost multi-commodity flow problem. The decomposition frameworkgives rise in a natural way to designing a Lagrangean based heuristic. Numericalexperiments showing the efficiency of the proposed approach are reported.

This paper aims at developing efficient solving methods for an original service networkdesign problem imbued with sustainable issues. Indeed the network has to be designed forshort and local supply chain and for fresh food products. The original features of theproblem are the seasonality of supply, the limitation of transshipments for a product andno possibility of storage between consecutive periods. Decisions at strategic and tacticallevel are (1) decisions on a subset of hubs to open among a given set of potentiallocations, (2) transportation services to open between the actors and (3) flow quantitiesfor the fresh food products. We propose for this problem a Mixed Integer Programmingformulation and two solving techniques: Benders Decomposition and Dynamic Slope ScalingProcedure. These techniques are adapted to the problem and some experimental tests areconducted in order to compare the approaches on large-scale instances.

In this paper we present a robust real-time optimization method for the online linear oilblending process. The blending process consists in determining the optimal mix ofcomponents so that the final product satisfies a set of specifications. We examinedifferent sources of uncertainty inherent to the blending process and show how to addressthis uncertainty applying the Robust Optimization techniques. The polytopal structure ofour problem permits a simplified robust approach. Our method is intended to avoidreblending and we measure its performance in terms of the blend quality giveaway andfeedstocks prices. The difference between the nominal and the robust optimal values (theprice of robustness) provides a benchmark for the cost of reblending which is difficult toestimate in practice. This new information can be used to adjust the level of conservatismin the model. We analyze the feasibility of a blend to be produced from a set offeedstocks when the heel of a previous blend is used in the composition of the new blend.Additional critical information for the control system is then produced.

This paper presents a heuristic approach combining constraint satisfaction, local searchand a constructive optimization algorithm for a large-scale energy management andmaintenance scheduling problem. The methodology shows how to successfully combine andorchestrate different types of algorithms and to produce competitive results. We alsopropose an efficient way to scale the method for huge instances. A large part of thepresented work was done to compete in the ROADEF/EURO Challenge 2010, organized jointly bythe ROADEF, EURO and Électricité de France. The numerical results obtained on officialcompetition instances testify about the quality of the approach. The method achieves 3 outof 15 possible best results.