Shop scheduling with availability constraints

Scheduling Theory studies planning and timetabling of various industrial and human activities and, therefore, is of constant scientific interest. Being a branch of Operational Research, Theory of Scheduling mostly deals with problems of practical interest which can be easily (from a mathematical point of view) solved by full enumeration and at the same time usually require enormous time to be solved optimally. Therefore, one attempts to develop algorithms for finding optimal or near optimal solutions of the problems under consideration in reasonable time. If the output of an algorithm is not always an optimal solution then the worst-case analysis of this algorithm is undertaken in order to estimate either a relative error or an absolute error that holds for any given instance of the problem. Scheduling problems which are usually considered in the literature assume that the processing facilities are constantly available throughout the planning period. However, in practice, the processing facility, e.g. a machine, a labour, etc. can become non-available due to various reasons, e.g. breakdowns, lunch breaks, holidays, maintenance work, etc. All these facts stimulate research in the area of scheduling with non-availability constraints. This branch of Scheduling Theory has recently received a lot of attention and a considerable number of research papers have been published. This thesis is fully dedicated to scheduling with non-availability constraints under various assumptions on the structure of the processing system and on the types of non-availability intervals

Job-shop scheduling with approximate methods

Imperial Users onl

Algorithms for two-stage flow-shop with a shared machine in stage one and two parallel machines in stage two

Scheduling problems may be encountered in many situations in everyday life. Organizing daily activities and planning a travel itinerary are both examples of small optimization problems that we try to solve every day without realizing it. However, when these problems take on larger instances, their resolution becomes a difficult task to handle due to prohibitive computations that generated. This dissertation deals with the Two-Stage Flow-shop problem that consists of three machines and in which we have two sets of jobs. The first set has to be processed, in this order, by machine M± and then by machine M2. Whereas, the second set of jobs has to be processed, in this order, by machine M± and then by machine M3. As we can see, machine M1 is a shared machine, and the other two machines are dedicated to each of the two subsets of jobs. This problem is known to be strongly NP-Hard. This means there is a little hope that it can be solved by an exact method in polynomial time. So, special cases, heuristic, and meta-heuristic methods are well justified for its resolution. We thus started in this thesis to present special cases of the considered problem and showed their resolution in polynomial time. In the approximation front, we solved the considered problem with heuristic and meta-heuristic algorithms. In the former approach, we designed two heuristic algorithms. The first one is based on Johnson's rule, whereas the second one is based on Nawez, Enscore, and Ham algorithm. The experimental study we have undertaken shows that the efficiency and the quality of the solutions produced by these two heuristic algorithms are high. In the latter approach, we designed a Particle Swarm Optimization algorithm. This method is known to be popular because of its easy implementation. However, this algorithm has many natural shortcomings. We thus combined it with the tabu search algorithm to compensate the negative effects. The experimental study shows that the new hybrid algorithm outperforms by far not only the standard Particle Swarm Optimization, but also the tabu search method we also designed for this problem

Generalized Descent Methods for Asymmetric Systems of Equations and Variational Inequalities

We consider generalizations of the steepest descent algorithm for solving asymmetric systems of equations. We first show that if the system is linear and is defined by a matrix M, then the method converges if M2 is positive definite. We also establish easy to verify conditions on the matrix M that ensure that M is positive definite, and develop a scaling procedure that extends the class of matrices that satisfy the convergence conditions. In addition, we establish a local convergence result for nonlinear systems defined by uniformly monotone maps, and discuss a class of general descent methods. Finally, we show that a variant of the Frank-Wolfe method will solve a certain class of variational inequality problems. All of the methods that we consider reduce to standard nonlinear programming algorithms for equivalent optimization problems when the Jacobian of the underlying problem map is symmetric. We interpret the convergence conditions for the generalized steepest descent algorithms as restricting the degree of asymmetry of the problem map

Essays on optimization and incentive contracts

Includes bibliographical references (p. 167-176).Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.(cont.) In the second part of the thesis, we focus on the design and analysis of simple, possibly non-coordinating contracts in a single-supplier, multi-retailer supply chain where retailers make both pricing and inventory decisions. Specifically, we introduce a buy-back menu contract to improve supply chain efficiency, and compare two systems, one in which the retailers compete against each other, and another in which the retailers coordinate their decisions to maximize total expected retailer profit. In a linear additive demand setting, we show that for either retailer configuration, the proposed buy-back menu guarantees the supplier, and hence the supply chain, at least 50% of the optimal global supply chain profit. In particular, in a coordinated retailers system, the contract guarantees the supply chain at least 75% of the optimal global supply chain profit. We also analyze the impact of retail price caps on supply chain performance in this setting.In this thesis, we study important facets of two problems in methodological and applied operations research. In the first part of the thesis, motivated by optimization problems that arise in the context of Internet advertising, we explore the performance of the greedy algorithm in solving submodular set function maximization problems over various constraint structures. Most classic results about the greedy algorithm assume the existence of an optimal polynomial-time incremental oracle that identifies in any iteration, an element of maximum incremental value to the solution at hand. In the presence of only an approximate incremental oracle, we generalize the performance bounds of the greedy algorithm in maximizing nondecreasing submodular functions over special classes of matroids and independence systems. Subsequently, we unify and improve on various results in the literature for problems that are specific instances of maximizing nondecreasing submodular functions in the presence of an approximate incremental oracle. We also propose a randomized algorithm that improves upon the previous best-known 2-approximation result for the problem of maximizing a submodular function over a partition matroid.by Pranava Raja Goundan.Ph.D

Electrical Characterization of Intrinsic and Induced Deep Level Defects in Hexagonal SiC

Deep level defects in hexagonal SiC were studied using digital deep level transient spectroscopy (DLTS) methods over the temperature range of 100 to 800 deg K. New centers were found in bulk and epitaxial 6H-SiC with ionization energies between 0.38 to 1.3 eV, and levels from 0.2 to 0.856 eV were identified in 4H-SiC epitaxy. Direct correlation between inequivalent lattice sites was identified for energetic pairs associated with both vanadium and ion implanted Mg impurities. Nonradioative carrier capture mechanisms were studied and deep level trapping was found to proceed via lattice relaxation multi-phonon emission, indicating efficient electronic lattice coupling in the wide bandgap material. Junction transport characteristics of 4H-SiC p+/n bipolar devices were observed to be dominated by deep level defects in the epitaxial layers. Significant tunneling conduction in both forward and reverse bias conditions was directly correlated to deep level centers in these devices

Managing temporal uncertainty under limited communication : a formal model of tight and loose team coordination

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (leaves 155-157).In the future, groups of autonomous robots will cooperate in large networks in order to achieve a common goal. These multi-agent systems will need to be able to execute cooperative temporal plans in the presence of temporal uncertainty and communication limitations. The duration of many planned activities will not be under direct control of the robots. In addition, robots will often not be able to communicate during plan execution. In order for the robots to robustly execute a cooperative plan, they will need to guarantee that a successful execution strategy exists, and provide a means to reactively compensate for the uncertainty in real-time. This thesis presents a multi-agent executive that enables groups of distributed autonomous robots to dynamically schedule temporally flexible plans that contain both temporal uncertainty under communication limitations. Previous work has presented controllability algorithms that compile the simple temporal networks with uncertainty, STNUs, into a form suitable for execution. This thesis extends the previous controllability algorithms to operate on two-layer plans that specify group level coordination at the highest level and agent level coordination at a lower level. We introduce a Hierarchical Reformulation (HR) algorithm that reformulates the two-layer plan in order to enable agents to dynamically adapt to uncertainty within each group plan and use a static execution strategy between groups in order to compensate for communication limitations. Formally, the HR algorithm ensures that the two-layer plan is strongly controllable at the highest level and dynamically controllable at the lower level. Furthermore, we introduce a new fast dynamic controllability algorithm that has been empirically shown to run in O(N³)(cont.) The Hierarchical Reformulation algorithm has been validated on a set of hand coded examples. The speed of the new fast dynamic controllability algorithm has been tested using a set of randomly generated problems.by John L. Stedl.S.M