A simple idea used in many combinatorial algorithms is the idea of pivoting. Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset σ to a new one σ′ by deleting an element 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 many problems. This present paper is a survey on algorithms in operations research and discrete mathematics using pivots. We give also examples where this principle allows not only to compute but also to prove some theorems in a constructive way. A formalisation is described, 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 practical market conditions arising from the presence/absence of stochastic lead time and exogenous linear temporal decline in selling price when distribution of the stochastic demand depends upon initial selling price. Viability of the solutions is discussed for three strategies of obtaining optimal initial selling price and/or ordering quantity. Numerical studies 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 air pollution, energy waste and consumption of people’s time. Public transport cannot be the only answer to this increasing transport demand. Carpooling, which is based on the idea that sets of car owners pick up colleagues while driving to or from the workplace, has emerged to be a viable possibility for reducing private car usage in congested areas. Its actual 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 the multi-destination carpooling problem. Experiments have been performed to confirm the efficiency and the effectiveness of the approach.

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

This paper aims at developing efficient solving methods for an original service network design problem imbued with sustainable issues. Indeed the network has to be designed for short and local supply chain and for fresh food products. The original features of the problem are the seasonality of supply, the limitation of transshipments for a product and no possibility of storage between consecutive periods. Decisions at strategic and tactical level are (1) decisions on a subset of hubs to open among a given set of potential locations, (2) transportation services to open between the actors and (3) flow quantities for the fresh food products. We propose for this problem a Mixed Integer Programming formulation and two solving techniques: Benders Decomposition and Dynamic Slope Scaling Procedure. These techniques are adapted to the problem and some experimental tests are conducted 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 oil blending process. The blending process consists in determining the optimal mix of components so that the final product satisfies a set of specifications. We examine different sources of uncertainty inherent to the blending process and show how to address this uncertainty applying the Robust Optimization techniques. The polytopal structure of our problem permits a simplified robust approach. Our method is intended to avoid reblending and we measure its performance in terms of the blend quality giveaway and feedstocks prices. The difference between the nominal and the robust optimal values (the price of robustness) provides a benchmark for the cost of reblending which is difficult to estimate in practice. This new information can be used to adjust the level of conservatism in the model. We analyze the feasibility of a blend to be produced from a set of feedstocks 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 search and a constructive optimization algorithm for a large-scale energy management and maintenance scheduling problem. The methodology shows how to successfully combine and orchestrate different types of algorithms and to produce competitive results. We also propose an efficient way to scale the method for huge instances. A large part of the presented work was done to compete in the ROADEF/EURO Challenge 2010, organized jointly by the ROADEF, EURO and Électricité de France. The numerical results obtained on official competition instances testify about the quality of the approach. The method achieves 3 out of 15 possible best results.