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.

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.

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.

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.

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.

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.

We consider a bilinear optimal control problem for a von Kármán plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. We first state the existence of solutions for the von Kármán equation and then derive optimality conditions for a given objective functional. Finally, we show the uniqueness of the optimal control.

We analyse the steady-state operation of a continuous flow bioreactor in which the biochemical reaction is governed by noncompetitive substrate inhibition (Andrews kinetics). A generalized reactor model is used in which the well-stirred bioreactor and the idealized membrane bioreactor are special cases. As generic properties of systems subject to substrate inhibition have been obtained by other authors, we discuss reaction engineering features specific to Andrews kinetics.

Steady water infiltration in homogeneous soils is governed by the Richards equation. This equation can be studied more conveniently by transforming to a type of Helmholtz equation. In this study, a dual-reciprocity boundary element method (DRBEM) is employed to solve the Helmholtz equation numerically. Using the solutions obtained, numerical values of the suction potential are then computed. The proposed method is tested on problems involving infiltration from different types of periodic channels in a homogeneous soil. Moreover, the method is also examined using infiltration from periodic trapezoidal channels in three different types of homogeneous soil.

This paper presents an integrated guidance and control (IGC) design method for an unmanned aerial vehicle with static stability which is described by a nonlinear six-degree-of-freedom (6-DOF) model. The model is linearized by using small disturbance linearization. The dynamic characteristics of pitching mode, rolling mode and Dutch rolling mode are obtained by analysing the linearized model. Furthermore, an IGC design procedure is also proposed in conjunction with a proportional–integral–derivative (PID) control method and fuzzy control method. A PID controller is applied in the control loop of the elevator and aileron, and the attitude angle and attitude angular velocity are used as compensation feedback, giving a simple and low-order control law. A fuzzy control method is applied to perform the cross-coupling control of rolling and yawing. Finally, the 6-DOF simulation shows the effectiveness of the developed method.

In the performance measurement using tools such as data envelopment analysis (DEA), datawithout explicit inputs has attracted considerable attention among researchers. In suchstudies the problem of production planning in the next production season is an importantand interesting subject. Because of the uncertain nature of the future, decision makersneed to provide robust procedures in order to examine alternative courses of action andtheir implications. The purpose of this paper is to develop an approach to productionplanning problem in production processes without explicit inputs that typically appears incentralized decision making environment. Application of the proposed approach isillustrated empirically using a real case.

We consider multistage bidding models where two types of risky assets (shares) are tradedbetween two agents that have different information on the liquidation prices of tradedassets. These prices are random integer variables that are determined by the initialchance move according to a probability distribution p over thetwo-dimensional integer lattice that is known to both players. Player 1 is informed on theprices of both types of shares, but Player 2 is not. The bids may take any integer values.The model of n-stage bidding is reduced to a zero-sum repeated game withlack of information on one side. We show that, if liquidation prices of shares have finitevariances, then the sequence of values of n-step games is bounded. This makes itreasonable to consider the bidding of unlimited duration that is reduced to the infinitegame G∞(p). We give the solutions for thesegames. Optimal strategies of Player 1 generate random walks of transaction prices. Butunlike the case of one-type assets, the symmetry of these random walks is broken at thefinal stages of the game.

To model the dynamics of discrete deterministic systems, we extend the Petri netsframework by a priority relation between conflicting transitions, which is encoded byorienting the edges of a transition conflict graph. The aim of this paper is to gain someinsight into the structure of this conflict graph and to characterize a class of suitableorientations by an analysis in the context of hypergraph theory.

In this paper, we show that the direct semidefinite programming (SDP) bound for thenonconvex quadratic optimization problem over ℓ1 unit ball(QPL1) is equivalent to the optimal d.c. (difference between convex) bound for thestandard quadratic programming reformulation of QPL1. Then we disprove a conjecture aboutthe tightness of the direct SDP bound. Finally, as an extension of QPL1, we study therelaxation problem of the sparse principal component analysis, denoted by QPL2L1. We showthat the existing direct SDP bound for QPL2L1 is equivalent to the doubly nonnegativerelaxation for variable-splitting reformulation of QPL2L1.

One-fund theorem states that an efficient portfolio in a Mean-Variance (M-V) portfolioselection problem for a set of some risky assets and a riskless asset can be representedby a combination of a unique risky fund (tangency portfolio) and the riskless asset. Inthis paper, we introduce a method for which the tangency portfolio can be produced as acorner portfolio. So, the tangency portfolio can be computed easily and fast by anyalgorithm designed for tracing out the M-V efficient frontier via computing the cornerportfolios. Moreover, we show that how this method can be used for tracing out the M-Vefficient frontier when problem contains a riskless asset in which the borrowing is notallowed.

Usual periodic scheduling problems deal with precedence constraints having non-negativelatencies. This seems a natural way for modelling scheduling problems, since task delaysare generally non-negative quantities. However, in some cases, we need to consider edgeslatencies that do not only model task latencies, but model other precedence constraints.For instance in register optimisation problems devoted to optimising compilation, ageneric machine or processor model can allow considering access delays into/fromregisters. Edge latencies may be then non-positive leading to a difficult schedulingproblem in presence of resources constraints. This research result is related to theproblem of periodic scheduling with storage requirement optimisation; its aims is to solvethe practical problem of register optimisation in optimising compilation. We show thatpre-conditioning a data dependence graph (DDG) to satisfy register constraints beforeperiodic scheduling under resources constraints may create circuits with non-positivedistances, resulted from the acceptance of non-positive edge latencies. As a compilerconstruction strategy, it is forbidden to allow the creation of circuits with non-positivedistances during the compilation flow, because such DDG circuits do not guarantee theexistence of a valid instruction schedule under resource constraints. We study twosolutions to avoid the creation of these problematic circuits. A first solution isreactive, it tolerates the creation of non-positive circuit in a first step, and ifdetected in a further check step, makes a backtrack to eliminate them. A second solutionis proactive, it prevents the creation of non-positive circuits in the DDG during theregister optimisation process. It is based on shortest path equations which define anecessary and sufficient condition to free any DDG from these problematic circuits. Thenwe deduce a linear program accordingly. We have implemented our solutions and we presentsuccessful experimental results.

In matricial analysis, the theorem of Eckart and Young provides a best approximation ofan arbitrary matrix by a matrix of rank at most r. In variationalanalysis or optimization, the Moreau envelopes are appropriate ways of approximating orregularizing the rank function. We prove here that we can go forwards and backwardsbetween the two procedures, thereby showing that they carry essentially the sameinformation.