Yahya Fathi

A tabu search algorithm for the multi-stage parallel machine problem with limited buffer capacities

Abstract We investigate the problem of scheduling N jobs on parallel machines in L successive stages with limited buffer capacities between stages. The primary objective is to find a schedule that would minimize the makespan. This problem is shown to be NP -hard in the strong sense. We develop a tabu search algorithm for this problem in which the search is limited to the space of permutation vectors of size N . This vector represents the order in which the given set of jobs are performed in the first stage, and we propose a procedure to construct a complete schedule associated with every permutation vector. We conduct an extensive computational experiment using randomly generated instances with different structures and different buffer capacities. We also solve several specific instances of the problem from the open literature. All empirical evidence suggest that the proposed algorithm is an effective method for solving this problem.

A nonlinear programming approach to the parameter design problem

Abstract The problem of determining an optimal set of values for the parameters of a manufactured product (and/or a manufacturing process), from the point of view of its robustness against various sources of noise, is commonly referred to as the the parameter design problem . We propose an algorithmic strategy for solving the parameter design problem, and present a specific implementation of this strategy which we refer to as the Successive Quadratic Variance Approximation Method (SQVAM). SQVAM is based on conventional optimization techniques, and assumes that the functional relationship between the input parameters and the performance characteristic of interest is either known or could be well approximated. An illustrative numerical example, discussing the design of a Wheatstone bridge, is then presented. This is the same example used by Taguchi to illustrate the orthogonal array method.

Producer-Consumer Tolerances

The producers tolerance concept (in contrast to the consumers tolerance) follows naturally from the notion of continuous loss functions. Emerging producer tolerance methodology has proceeded without benefit of carefully defined assumptions. We rectify..

Exact and inexact methods for selecting views and indexes for OLAP performance improvement

In on-line analytical processing (OLAP), precomputing (materializing as views) and indexing auxiliary data aggregations is a common way of reducing query-evaluation time costs for important data-analysis queries. We consider an OLAP view- and index-selection problem stated as an optimization problem, where (i) the inputs include the data-warehouse schema, a set of data-analysis queries of interest, and a storage-limit constraint, and (ii) the output is a set of views and indexes that minimizes the costs of the input queries, subject to the storage limit. While greedy and other heuristic strategies for choosing views or indexes might help to some extent in improving the costs, it is highly nontrivial to arrive at a globally optimum solution, one that reduces the processing costs of typical OLAP queries as much as is theoretically possible. In fact, as observed in [17] and to the best of our knowledge, there is no known approximation algorithm for OLAP view or index selection with nontrivial performance guarantees. In this paper we propose a systematic study of the OLAP view- and index-selection problem. Our specific contributions are as follows: (1) We develop an algorithm that effectively and efficiently prunes the space of potentially beneficial views and indexes when given realistic-size instances of the problem. (2) We provide formal proofs that our pruning algorithm keeps at least one globally optimum solution in the search space, thus the resulting integer-programming model is guaranteed to find an optimal solution. (3) We develop a family of algorithms to further reduce the size of the search space, so that we are able to solve larger problem instances, although we no longer guarantee the global optimality of the resulting solution. (4) Finally, we present an experimental comparison of our proposed approaches with the state-of-the-art approaches of [2, 12]. Our experiments show that our approaches to view and index selection result in high-quality solutions --- in fact, in globally optimum solutions for many realistic-size problem instances. Thus, they compare favorably with the well-known OLAP-centered approach of [12] and provide for a winning combination with the end-to-end framework of [2] for generic view and index selection.

A formal model for the problem of view selection for aggregate queries

We present a formal analysis of the following view-selection problem: Given a set of queries and a database, return definitions of views that, when materialized in the database, would reduce the evaluation costs of the queries. Optimizing the layout of stored data using view selection has a direct impact on the performance of the entire database system. At the same time, the optimization problem is intractable, even under natural restrictions on the types of queries of interest. In this paper we use an integer-programming model to obtain optimal solutions to the problem of view selection for aggregate queries on data warehouses. We also report the results of the post-optimality analysis that we performed to determine/observe the impact of changing certain input characteristics on the optimal solution.

A mathematical model for loading the sequencers in a printed circuit pack manufacturing environment

A sequencing machine is a piece of equipment used in the electronics industry to produce sequenced reel-packaged tapes of axial leaded components for different types of printed circuit packs (PCPs). Due to the limited number of dispensing heads available on the sequencing machines, the relatively large number of component types competing for these heads, and the diversity of the component type requirements of different types of PCPs, efficient scheduling of these machines is usually not a simple task. In this paper we discuss a structured approach to the problem of scheduling the sequencers, and present a mathematical model, as well as a heuristic procedure, that can be used to resolve some of the difficulties involved.

A critical index algorithm for nearest point problems on simplicial cones

We consider the linear complementarity problem (q, M) in whichM is a positive definite symmetric matrix of ordern. This problem is equivalent to a nearest point problem [Γ; b] in whichΓ = {A.1,⋯, A.n} is a basis for Rn,b is a given point in Rn; and it is required to find the nearest point in the simplicial cone Pos(Γ) tob. We develop an algorithm for solving the linear complementarity problem (q, M) or the equivalent nearest point problem [Γ; b]. Computational experience in comparison with an existing algorithm is presented.

Heuristics for the Common Due Date Weighted Tardiness Problem

In this paper we consider the single machine “common due date weighted tardiness problem.” Initially the problem is related to other versions of the single machine total weighted tardiness problem. Several heuristics for the problem are discussed. Three “simple” heuristics are proposed and shown to have arbitrarily bad worst case performance. A fourth heuristic is then proposed and shown to have a worst case performance bound of 2.

A linear approximation model for the parameter design problem

Abstract We consider the problem of minimizing the variance of a nonlinear function of several random variables, where the decision variables are the mean values of these random variables. This problem arises in the context of robust design of manufactured products and/or manufacturing processes, where the decision variables are the set points for various design components. A nonlinear programming (NLP) model is developed to obtain approximate solutions for this problem. This model is based on a Taylor series expansion of the given function, up to its linear term. A case study pertaining to the design of a coil spring is discussed, and its corresponding NLP model is developed. Using this model, a non-inferior frontier curve is obtained that shows the trade-off between the minimum mass of the coil spring and the minimum variance of its performance characteristic. Results of applying the model to three other case studies are also presented.

A mathematical model and a heuristic procedure for the turbine balancing problem

Abstract We model the turbine balancing problem as a Quadratic Assignment Problem, and develop two heuristic procedures for solving it. We then compare and contrast the overall performance of these and other procedures on an empirical basis, and recommend a general strategy for solving this problem on the manufacturing floor.