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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 50 (1994), S. 319-337 
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we report on the use of combinatorial optimization techniques to design testing fixtures for Printed Circuit Boards (PCBs). For testing the functionality of a PCB, nail-like testing devices (probes) on the surface of a testing fixture are brought in contact with prespectified test points (pads) on the surface of the PCB. The two design decisions for the testing fixture are: (a) to select from an available set of pads the ones to test (this determines the location of the probes on the fixture) subject to the restriction that in prespecified subsets of the set of pads (these subsets are referred to as “nets”) and a priori determined number of pads have to be tested (this is referred to as the “net restriction”), and (b) to choose the probe size to be used for testing each pad (only two available sizes: a large (100 mil) and a small (50 mil)) subject to the considerations that larger size probes are more reliable for testing purposes and probes that are assigned to pads in close proximity should not come in physical contact with each other (it creates short circuits and erroneous test result). Thus, the problem the testing engineer faces is to assign the maximum number of 100 mil probes to an appropriately selected set of pads in a way that avoids the creation of short circuits and accounts for the “net restriction”. We develop an efficient algorithm to solve the problem using results from the vertex packing literature, which exploit the special structure of an appropriate geometric graph we can define in this application. The algorithm can handle the large size real problem within 2–3 minutes of real time on a microcomputer.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1572-9338
    Keywords: Data envelopment analysis ; efficient production frontier ; multiple input/output decision making ; production possibility set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we introduce a generalized Data Envelopment Analysis (DEA) model which unifies and extends most of the well-known DEA models developed over the past fifteen years and points the way to new models. By setting three binary parameters of this model to different values, we obtain subclasses of the DEA models with generalK cone andW cone descriptions to represent the evaluator's preferences for the Decision Making Units (DMU) and the input/output categories. We also show relationships among the various different subclasses of the generalized DEA model and give special attention to efficiency definitions and solutions. Furthermore, we state and rigorously prove the equivalence between DEA efficiency and the nondominated solutions of a corresponding multi-objective program. This latter result is especially important for understanding and interpreting the concept of efficiency. Detailed examples are also presented to demonstrate the functions ofK cone andW cone, as well as their characteristics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of productivity analysis 6 (1995), S. 171-186 
    ISSN: 1573-0441
    Keywords: Data Envelopment Analysis (DEA) ; Frontier Estimation ; Goal Programming (GP) ; Discriminant Function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract This paper describes a new frontier estimation procedure which relies on results obtained from Data Envelopment Analysis (DEA). The paper reviews some of the earlier works in this area and points out potential difficulties with them. It further suggests ways to validate such developments. A procedure is constructed on the basis of a Goal Programming (GP)-Discriminant Function model developed in stages during the 1980s. A numerical example is used to illustrate the proposed procedure. Then, an extensive simulation in which the GP-based procedure is compared to three regression-based techniques is presented. The simulation results clearly indicate the superiority of the proposed technique over the regression alternatives.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    IIE transactions 32 (2000), S. 181-193 
    ISSN: 1573-9724
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, the irregular operations problem is approached for the first time in a way that allows an airline to provide for schedule recovery with minimal deviations from the original aircraft routings. A network model with side constraints is presented in which delays and cancellations are used to deal with aircraft shortages in a way that ensures a significant portion of the original aircraft routings remain intact. The model is flexible, allowing user preferences in the objective, and thereby reflecting the immediate concerns of the decision-maker in the recovery schedule. The model can be tailored by airline operations personnel to emphasize differing solution characteristics. Fleet data provided by Continental Airlines are used to demonstrate the approach. Extensive testing indicates that optimal or near-optimal solutions are routinely obtained from the LP relaxation of the network formulation. When integrality is not achieved, a rounding heuristic is provided that finds feasible solutions within a small fraction of the optimum.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of combinatorial optimization 1 (1997), S. 151-164 
    ISSN: 1573-2886
    Keywords: local optimality ; approximation algorithms ; combinatorial optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a graph G = (V,E), we define the locally optimal independent sets asfollows. Let S be an independent set and T be a subset of V such that S ∩ T = ∅ and Γ(S) $$ \subseteq $$ T, where Γ(S) is defined as the neighbor set of S. A minimum dominating set of S in T is defined as TD(S) $$ \subseteq $$ T such that every vertex of S is adjacent to a vertex inTD(S) and TD(S) has minimum cardinality. An independent setI is called r-locally optimal if it is maximal and there exists noindependent set S $$ \subseteq $$ V\I with |ID (S)| ≤ r such that|S| 〉|I ∩ Γ(S)|.In this paper, we demonstrate that for k-claw free graphs ther-locally optimal independent sets is found in polynomial timeand the worst case is bounded by $$\left| {I*} \right| \leqslant \frac{1}{2}\left[ {\frac{1}{{\sum _{i = 1}^r (k - 2)^{i - 1} }} + k - 1} \right]\left| I \right|$$ , where I and I* are a locally optimal and an optimal independent set,respectively. This improves the best published bound by Hochbaum (1983) bynearly a factor of two. The bound is proved by LP duality and complementaryslackness. We provide an efficientO(|V|r+3) algorithm to find an independent set which is notnecessarily r-locally optimal but is guarantteed with the above bound. Wealso present an algorithm to find a r-locally optimal independent set inO(|V|r(k-1)+3) time.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of combinatorial optimization 1 (1997), S. 209-210 
    ISSN: 1573-2886
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of combinatorial optimization 1 (1997), S. 211-228 
    ISSN: 1573-2886
    Keywords: GRASP ; airline scheduling ; real-time control ; irregular operations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a greedy randomized adaptive search procedure (GRASP) to reconstruct aircraft routings in response to groundings and delays experienced over the course of the day. Whenever the schedule is disrupted, the immediate objective of the airlines is to minimize the cost of reassigning aircraft to flights taking into account available resources and other system constraints. Associated costs are measured by flight delays and cancellations. In the procedure, the neighbors of an incumbent solution are generated and evaluated, and the most desirable are placed on a restricted candidate list. One is selected randomly and becomes the incumbent. The heuristic is polynomial with respect to the number of flights and aircraft. This is reflected in our computational experience with data provided by Continental Airlines. Empirical results demonstrate the ability of the GRASP to quickly explore a wide range of scenarios and, in most cases, to produce an optimal or near-optimal solution.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of combinatorial optimization 1 (1997), S. 305-321 
    ISSN: 1573-2886
    Keywords: Real-time decision support ; crew management ; multi-commodity network flow ; heuristics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Airline irregular operations have long been a realm where human experience and judgement are the most important tools to utilize. Crew management during irregular operations is usually the bottleneck of the whole system-recovering process due to complicated crew schedules and restrictive crew legalities as well as the size and scope of the hub-and-spoke networks adopted by major carriers. A system-wide multi-commodity integer network flow model and a heuristic search algorithm for the above purpose are presented and discussed in this paper. The computational experiences show that the algorithm is efficient enough to solve problems of realistic size and also has the flexibility to accommodate practical business requirements.
    Type of Medium: Electronic Resource
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