Dennis L. Bricker

Profit Incentives and Technical Efficiency in the Production of Nursing Home Care

In recent years, nursing home care expenditures have approached one percent of GNP. Their growth is a major contributor to the escalating costs of health care. In this article, the authors analyze a sample of nursing homes from Wisconsin to determine the characteristics of the efficiently operated nursing homes. Data envelopment analysis is used to calculate efficiency scores for the various nursing homes in the sample. The authors then use regression analysis to investigate the determinants of efficiency, holding constant the characteristics of the output. They find that for-profit firms have significantly higher efficiency scores. Copyright 1989 by MIT Press.

Genetic algorithms for reliability design problems

Abstract This paper presents genetic algorithms for solving various reliability design problems, which include series systems, series–parallel systems and complex (bridge) systems. The objective is to maximize the system reliability, while maintaining feasibility with respect to three nonlinear constraints, namely, cost and weight constraints, and constraints on the products of volume and weight. In this paper, mixed-integer reliability problems are studied. Numerical examples show that genetic algorithms perform well for all the reliability problems considered in this paper. In particular, as reported, some solutions obtained by genetic algorithms are better than previously best-known solutions.

Effectiveness of a geometric programming algorithm for optimization of machining economics models

Machining economics problems usually contain highly non-linear equations which may present difficulties for some non-linear programming algorithms. An earlier article by Duffuaa et al. [1] compared the performance of several non-linear programming algorithms, including a geometric programming algorithm, applied to five machining economics problems. Those authors concluded that the Generalized Reduced Gradient (GRG) algorithm is the most suitable method for solving such problems. In this paper, we point out shortcomings in that conclusion and demonstrate the effectiveness of the Geometric Programming technique in such problems compared with the results of GRG which were presented.

Solving Posynomial Geometric Programming Problems via Generalized Linear Programming

This paper revisits an efficient procedure for solving posynomial geometric programming (GP) problems, which was initially developed by Avriel et al. The procedure, which used the concept of condensation, was embedded within an algorithm for the more general (signomial) GP problem. It is shown here that a computationally equivalent dual-based algorithm may be independently derived based on some more recent work where the GP primal-dual pair was reformulated as a set of inexact linear programs. The constraint structure of the reformulation provides insight into why the algorithm is successful in avoiding all of the computational problems traditionally associated with dual-based algorithms. Test results indicate that the algorithm can be used to successfully solve large-scale geometric programming problems on a desktop computer.

Scheduling linearly deteriorating jobs on multiple machines

Abstract This paper investigates the scheduling problems in which the job processing times do not remain constant but are increasing linear functions of their starting times. Two deteriorating scheduling models, Model 1 and Model 2, for multiple machines are considered, with the goal being to minimize the makespan. In this paper, we propose an efficient heuristic for Model 1 and prove that the ratio of the makespan obtained by the heuristic to the optimal makespan is bounded. For Model 2, three heuristics, including a probabilistic heuristic, are proposed for minimizing the makespan. Numerical results are provided to show the efficiency of the approaches in this paper.

Polynomial geometric programming as a special case of semi-infinite linear programming

This paper develops a wholly linear formulation of the posynomial geometric programming problem. It is shown that the primal geometric programming problem is equivalent to a semi-infinite linear program, and the dual problem is equivalent to a generalized linear program. Furthermore, the duality results that are available for the traditionally defined primal-dual pair are readily obtained from the duality theory for semi-infinite linear programs. It is also shown that two efficient algorithms (one primal based and the other dual based) for geometric programming actually operate on the semi-infinite linear program and its dual.

A Dynamic Programming Algorithm for Scheduling In-Vehicle Messages

In-vehicle information systems (IVISs) can enhance or compromise driving safety. Such systems present an array of messages that range from collision warnings and navigation instructions to tire pressure and e-mail alerts. If these messages are not properly managed, the IVIS might fail to provide the driver with critical information, which could undermine safety. In addition, if the IVIS simultaneously presents multiple messages, the driver may fail to attend to the most critical information. To date, only simple algorithms that use priority-based filters have been developed to address this problem. This paper presents a dynamic programming model that goes beyond the immediate relevance and urgency parameters of the current Society of Automotive Engineers (SAE) message scheduling algorithm. The resulting algorithm considers the variation of message value over time, which extends the planning horizon and creates a more valuable stream of messages than that based only on the instantaneous message priority. This method has the potential to improve road safety because the most relevant information is displayed to drivers across time and not just the highest priority at any given instant. Applying this algorithm to message sets shows that scheduling that considers the time-based message value, in addition to priority, results in substantially different and potentially better message sequences compared with those based only on message priority. This method can be extended to manage driver workload by adjusting message timing relative to demanding driving maneuvers.

ANALYSIS OF A MARKOV CHAIN MODEL OF A MULTISTAGE MANUFACTURING SYSTEM WITH INSPECTION, REJECTION, AND REWORK

The authors present an informative application of Markov Chain Analysis to a multistage manufacturing problem. They also point out an error in the literature which has remained undetected for many years. Edward A. Silver, Department Editor Absorption analysis is applied to a Markov chain model of a multistage manufacturing process with inspection and reworking.

Sequencing of imperfect inspection operations subject to constraints on the quality of accepted and rejected units

Abstract Several imperfect inspection operations are available in a discrete production environment. A decision regarding acceptance or rejection of the produced items needs to be made without exceeding specified limits for the probabilities of accepted units being non-conforming and rejected units conforming to quality specifications. A branch and bound approach is used to find the inspection sequence resulting in least expected total inspection cost. Following the heuristic construction of a trial solution, a dominance relationship is applied to search the tree of possible sequences for the optimal sequence. A numerical example is included.

Investigation of path-following algorithms for signomial geometric programming problems

This paper considers signomial geometric programming (GP) dual problems, a class of nonconvex nonlinear programming problems possessing multiple locally optimal solutions. The primary purpose of this paper is to investigate the quality of solutions found by use of a path-following algorithm. The path-following method may be applied to either the original nonconvex problem, or to each of a sequence of convex posynomial GP problems approximating the original problem. For each test problem, the algorithms were initiated with thousands of different starting points. It was determined that, when the stopping criterion was relaxed for early posynomial GP problems in the sequence, the ultimate solution tended to be of better quality, and more frequently globally optimal.