Evaluation of an integrated supplier-buyer quality-control system

In this article, a quality-control design framework that employs information for the supplier-buyer system is modeled. Significant operational savings may be obtained by using the integrated plans developed under this framework. This is especially true when the cost of a defective is high, and the variable sampling and rework costs are low. Analysis of the interaction of defective, rework, and variable sampling costs reveals that the savings are the result of a shift of control effort from the process-control to the lot-acceptance stage, which is the consequence of tradeoffs involving both stages. The managerial impact of adopting integrated plans is discussed.     

The continuous multiple-modular design problem

In this article we extend our previous work on the continuous single-module design problem to the multiple-module case. It is assumed that there is a fixed cost associated with each additional module used. The Kuhn–Tucker conditions characterize local optima among which there is a global optimum. Modules are associated with partitions and a special class, guillotine partitions, are characterized. Branch-and-bound, partial enumeration, and heuristic procedures for finding optimum or good guillotine partitions are discussed and illustrated with examples.     

Variables inspection for SPC‐quarantined production

When a control chart signals an out‐of‐control condition for a production process, it may be desirable to “quarantine” all units produced since the last in‐control SPC sample. This paper presents an efficient procedure for variables inspection of such “SPC quarantined” product. A Bayesian sequential inspection procedure is developed which determines whether the out of control production is of acceptable quality. By inspecting the units in reverse of the order in which they were produced, the procedure is also capable of detecting the point at which the process went out of control, thus eliminating the need to inspect units produced prior to the onset of the out of control condition. Numerical examples are presented, and the performance characteristics of the procedure are demonstrated using Monte Carlo simulation. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 159–171, 2001     

Capacitated selection problem

Optimizing the selection of resources to accomplish a set of tasks involves evaluating the tradeoffs between the cost of maintaining the resources necessary to accomplish the tasks and the penalty cost associated with unfinished tasks. We consider the case where resources are categorized into types, and limits (capacity) are imposed on the number of each type that can be selected. The objective is to minimize the sum of penalty costs and resource costs. This problem has several practical applications including production planning, new product design, menu selection and inventory management. We develop a branch‐and‐bound algorithm to find exact solutions to the problem. To generate bounds, we utilize a dual ascent procedure which exploits the special structure of the problem. Information from the dual and recovered primal solutions are used to select branching variables. We generate strong valid inequalities and use them to fix other variables at each branching step. Results of tests performed on reasonably sized problems are presented. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 19–37, 1999     

Combination setwise-Bonferroni-type bounds

We consider three classes of lower bounds to P(c) = P (X₁ ≤ c₁,…, X_n ≤ c); Bonferroni-type bounds, product-type bounds and setwise bounds. Setwise probability inequalities are shown to be a compromise between product-type and Bonferroni-type probability inequalities. Bonferroni-type inequalities always hold. Product-type inequalities require positive dependence conditions, but are superior to the Bonferroni-type and setwise bounds when these conditions are satisfied. Setwise inequalities require less stringent positive dependence bound conditions than the product-type bounds. Neither setwise nor Bonferroni-type bounds dominate the other. Optimized setwise bounds are developed. Results pertaining to the nesting of setwise bounds are obtained. Combination setwise-Bonferroni-type bounds are developed in which high dimensional setwise bounds are applied and second and third order Bonferroni-type bounds are applied within each subvector of the setwise bounds. These new combination bounds, which are applicable for associated random variables, are shown to be superior to Bonferroni-type and setwise bounds for moving averages and runs probabilities. Recently proposed upper bounds to P(c) are reviewed. The lower and upper bounds are tabulated for various classes of multivariate normal distributions with banded covariance matrices. The bounds are shown to be surprisingly accurate and are much easier to compute than the inclusion-exclusion bounds. A strategy for employing the bounds is developed. © 1996 John Wiley & Sons, Inc.     

Partitioning and balancing for the assembly of nozzle guide vanes in gas turbine engines

The gas turbine engine is used to power many different types of commercial and military aircraft. During the scheduled maintenance of these engines, many of the turbine components are replaced. Of particular importance to us is the replacement of nozzle guide vanes in the nozzle assembly section of the engine. Individual vanes are selected from inventory to make up sets, and each set must meet certain characteristics in order to be feasible. The vanes in each set must then be sequenced in order to meet additional criteria. In this article, we give heuristics for the above partitioning and sequencing problems. Empirical analyses, using actual data from a branch of the armed services and a major engine manufacturer, are used to evaluate the proposed heuristics. The results of these analyses indicate that the heuristics are effective.