A technique which combines modified pattern search methods with composite designs and polynomial constraints to solve constrained optimization problems

This paper presents a method of selecting design parameters which optimizes a specific measure (aircraft design example: minimum weight, maximum mission effectiveness) and guarantees designated levels of response in specified areas (such as combal ceiling, acceleration time). The method employs direct search optimization applied to a nonlinear functional constrained by nonlinear surfaces. The composite design technique is combined with regression methods to determine adequate surface representations with a minimum of required data points. A sensitivity analysis is conducted at the optimum set of design parameters to test for uniqueness.     

On the assignment and sequencing of operations on a crew-served project

This paper is concerned with assigning and sequencing a set of activities for some or all members of a crew of operators so that the completion time of all such operations is minimized. It is assumed that each of the operators in the crew possesses, initially, certain tasks that only he can perform. A branch-and-bound scheme is proposed to treat the problem, and suitable computational experience is provided.     

The effect of correlated exponential service times on single server tandem queues

An investigation via simulation of system performance of two stage queues in series (single server, first-come, first-served) under the assumption of correlated exponential service times indicates that the system's behavior is quite sensitive to departures from the traditional assumption of mutually independent service times, especially at higher utilizations. That service times at the various stages of a tandem queueing system for a given customer should be correlated is intuitively appealing and apparently not at all atypical. Since tandem queues occur frequently, e.g. production lines and the logistics therewith associated, it is incumbent on both the practitioner and the theoretician that they be aware of the marked effects that may be induced by correlated service times. For the case of infinite interstage storage, system performance is improved by positive correlation and impaired by negative correlation. This change in system performance is reversed however for zero interstage storage and depends on the value of the utilization rate for the case where interstage storage equals unity. The effect due to correlation is shown to be statistically significant using spectral analytic techniques. For correlation equal unity and infinite interstage storage, results are provided for two through twenty-five stages in series to suggest how adding stages affects system performance for ρ>0. In this extreme case of correlation, adding stages has an effect on system performance which depends markedly on the utilization rate. Recursive formulae for the waiting time per customer for the cases of zero, one, and infinite interstage storage are derived.     

Nature of renyi's entropy and associated divergence function

Nature of Renyi's entropy and associated divergence function is discussed in terms of concave (convex) and pseudoconcave (pseudoconvex) functions.     

Minimizing quality control costs for laboratory instruments using information delays

This paper proposes the use of a cost-based statistical process control system for monitoring the quality of an unreliable analytical machine. In this environment the accuracy of the process cannot be determined by inspecting the output, but must be verified by analyzing standards of known values. The results demonstrate that a significant cost savings can be obtained if analytical results are placed in a “buffer” and their release delayed until the accuracy of the test can be assured. Results suggest the approach not only dramatically improves the quality of results reported but also significantly reduces the expected total cost of testing. © 1996 John Wiley & Sons, Inc.     

Algorithms for the constrained maximum-weight connected graph problem

Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph (MCG) problem is to find a connected subgraph with R vertices that maximizes the sum of the weights. The MCG problem is strongly NP-complete, and we study a special case of it: the constrained MCG (CMCG) problem, which is the MCG problem with a constraint of having a predetermined vertex included in the solution. We first show that the Steiner tree problem is a special case of the CMCG problem. Then we present three optimization algorithms for the CMCG problem. The first two algorithms deal with special graphs (tree and layered graphs) and employ different dynamic programming techniques, solving the CMCG problem in polynomial times. The third one deals with a general graph and uses a variant of the Balas additive method with an imbedded connectivity test and a pruning method. We also present a heuristic algorithm for the CMCG problem with a general graph and its bound analysis. We combine the two algorithms, heuristic and optimization, and present a practical solution method to the CMCG problem. Computational results are reported and future research issues are discussed. © 1996 John Wiley & Sons, Inc.     

Multiple-attribute decision making with partial information: The expected-value criterion

We consider the multiple-attribute decision problem with finite action set and additive utility function. We suppose that the decision maker cannot specify nonnegative weights for the various attributes which would resolve the problem, but that he/she supplies ordinal information about these weights which can be translated into a set of linear constraints restricting their values. A bounded polytope W of feasible weight vectors is thus determined. Supposing that each element of W has the same chance of being the “appropriate one,” we compute the expected utility value of each action. The computation method uses a combination of numerical integration and Monte Carlo simulation and is equivalent to finding the center of mass of the bounded polytope W . Comparisons are made with another criterion already presented, the comparative hyper-volume criterion, and two small examples are presented.     

Optimal state-dependent pricing policies for a class of stochastic multiunit service systems

This paper models a k-unit service system (e.g., a repair, maintenance, or rental facility) with Poisson arrivals, exponential service times, and no queue. If we denote the number of units that are busy as the state of the system, the state-dependent pricing model formalizes the intuitive notion that when most units are idle, the price (i.e., the service charge per unit time) should be low, and when most units are busy, the price should be higher than the average. A computationally efficient algorithm based on a nonlinear programming formulation of the problem is provided for determination of the optimal state-dependent prices. The procedure ultimately reduces to the search on a single variable in an interval to determine the unique intersection point of a concave increasing function and a linear decreasing function. The algorithm takes, on the average, only about 1/2 second per problem on the IBM 360/65 (FORTRAN G Compiler). A discrete optimal-control approach to the problem is shown to result in essentially the same procedure as the nonlinear-programming formulation. Several properties of the optimal state-dependent prices are given. Comparisons of the optimal values of the objective function for the state-dependent and state-independent pricing policies show that the former is on the average, only about 0.7% better than the latter, which may explain partly why state-dependent pricing is not prevalent in many service systems. Potential generalizations of the model are discussed.