AbstractWe analyze the expected time performance of two versions of the thinning algorithm of Lewis and Shedler for generating random variates with a given hazard rate on [0,∞]. For thinning with fixed dominating hazard rate g(x) = c for example, it is shown that the expected number of iterations is cE(X) where X is the random variate that is produced. For DHR distributions, we can use dynamic thinning by adjusting the dominating hazard rate as we proceed. With the aid of some inequalities, we show that this improves the performance dramatically. For example, the expected number of iterations is bounded by a constant plus E(log+(h(0)X)) (the logarithmic moment of X).
Naval Research Logistics QuarterlyVolume 33, Issue 1 p. 123-128 Article Scheduling n nonoverlapping jobs and two stochastic jobs in a flow shop R. D. Foley, R. D. Foley Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061Search for more papers by this authorS. Suresh, S. Suresh Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061Search for more papers by this author R. D. Foley, R. D. Foley Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061Search for more papers by this authorS. Suresh, S. Suresh Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061Search for more papers by this author First published: February 1986 https://doi.org/10.1002/nav.3800330111Citations: 5AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume33, Issue1February 1986Pages 123-128 RelatedInformation
AbstractAn optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision‐making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.
AbstractIn this article we propose a formal man‐machine interactive approach to multiple criteria optimization with multiple decision makers. The approach is based on some of our earlier research findings in multiple criteria decision making. A discrete decision space is assumed. The same framework may readily be used for multiple criteria mathematical programming problems. To test the approach two experiments were conducted using undergraduate Business School students as subjects in Finland and in the United States. The context was, respectively, a high‐level Finnish labor‐management problem and the management‐union collective bargaining game developed at the Krannert Graduate School of Management, Purdue University. The results of the experiments indicate that our approach is a potentially useful decision aid for group decision‐making and bargaining problems.
AbstractSingle‐ and multi‐facility location problems are often solved with iterative computational procedures. Although these procedures have proven to converage, in practice it is desirable to be able to compute a lower bound on the objective function at each iteration. This enables the user to stop the iterative process when the objective function is within a prespecified tolerance of the optimum value. In this article we generalize a new bounding method to include multi‐facility problems with lp distances. A proof is given that for Euclidean distance problems the new bounding procedure is superior to two other known methods. Numerical results are given for the three methods.
AbstractMinimum cardinality set covering problems (MCSCP) tend to be more difficult to solve than weighted set covering problems because the cost or weight associated with each variable is the same. Since MCSCP is NP‐complete, large problem instances are commonly solved using some form of a greedy heuristic. In this paper hybrid algorithms are developed and tested against two common forms of the greedy heuristic. Although all the algorithms tested have the same worst case bounds provided by Ho [7], empirical results for 60 large randomly generated problems indicate that one algorithm performed better than the others.
AbstractThis article concerns the scheduling of n jobs around a common due date, so as to minimize the average total earliness plus total lateness of the jobs. Optimality conditions for the problem are developed, based on its equivalence to an easy scheduling problem. It seems that this problem inherently has a huge number of optimal solutions and an algorithm is developed to find many of them. The model is extended to allow for the availability of multiple parallel processors and an efficient algorithm is developed for that problem. In this more general case also, the algorithm permits great flexibility in finding an optimal schedule.
AbstractMulti‐echelon logistic systems are essential parts of the service support function of high technology firms. The combination of technological developments and competitive pressures has led to the development of services systems with a unique set of characteristics. These characteristics include (1) low demand probabilities: (2) high cost items; (3) complex echelon structures; (4) existence of pooling mechanisms among stocking locations at the same echelon level; (5) high priority for service, which is often expressed in terms of response time service levels for product groups of items: (6) scrapping of failed parts; and (7) recycling of issued stock due to diagnostic use. This article develops a comprehensive model of a stochastic, multi‐echelon inventory system that takes account of the above characteristics. Solutions to the constrained optimization problem are found using a branch and bound procedure. The results of applying this procedure to a spare parts inventory system for a computer manufacturer have led to a number of important policy conclusions.
AbstractThis paper formulates a problem of continuous quality production and maintenance of a machine. Quality is assumed to be a known function of the machine's (Markov diffusion process) degradation states. Applications to a specific quality function are used to obtain analytical solutions to an open‐loop and feedback stochastic control maintenance problem.
AbstractA system receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. The system fails when the accumulated damage exceeds a fixed threshold. Upon failure the system is replaced by a new one. The damage process is controlled by means of a maintenance policy. There are M possible maintenance actions. Given that a maintenance action m is employed, then the cumulative damage decreases at rate rm. Replacement costs and maintenance costs are considered. The objective is to determine an optimal maintenance policy under the following optimality criteria: (1) long‐run average cost; (2) total expected discounted cost over an infinite horizon. For a diffusion approximation, we show that the optimal maintenance expenditure rate is monotonically increasing in the cumulative damage level.
AbstractIn this paper we consider the single‐facility and multifacility problems of the minisum type of locating facilities on the plane. Both demand locations and the facilities to be located are assumed to have circular shapes, and demand and service is assumed to have a uniform probability density inside each shape. The expected distance between two facilities is calculated. Euclidean and squared‐Euclidean distances are discussed.
AbstractSimple criteria are found for reducing the computational effort in multistage Bayesian acceptance sampling. Regions of optimality are given for both terminal actions accept and reject. Also, criteria are presented for detecting nonoptimality of sets of sample sizes. Finally, nearly optimal (z,c−,c+)‐sampling plans are constructed by restricting attention to a small subset of sample sizes.
AbstractThe effects of environmental stochasticity in a Lanchester‐type model of combat are investigated. The methodology is based on a study of stochastic differential equations with random parameters characterized by dichotomous Markov processes. Exact expressions for the Laplace transforms of the time evolution of the first‐ and second‐order moments of the system are obtained. A special case when the fluctuations in the parameters occur with great rapidity in comparison with the natural time scale of the system is also analyzed. The stochastic stability in the mean‐square sense is discussed by using the Routh–Hurwitz criterion and it is found that the stochastic perturbations tend to destabilize the system.
AbstractA large sample test based on normal approximation for the traffic intensity parameter ρ in the cases of single and multiple‐server queues has been proposed. The test procedure is developed without imposing steady‐state assumptions and is applicable to queueing systems with general interarrival and service‐time distributions.
AbstractCharacteristics of supply performance at the top echelon of an optimally managed multiechelon supply system are investigated; insights are developed which are useful in devising coordinated single‐echelon policies which can approximate the benefits derived from multiechelon management.
A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.
This paper presents a specialized algorithm for the transshipment along a single road problem. The problem is a specially structured network flow problem. For larger problems, the specialized algorithm is in excess of a hundred times faster than the primal simplex method on a graph.
AbstractA probabilistic model is developed that applies to military bombardment, advertising for a mass audience, and other kinds of situations in which striking a target means that less of it is left to strike. The model provides the basis for decision analysis based on marginal gain in such circumstances. Heterogneous resources are considered as well as composite targets. All expenditures are quantized. The model has been developed as part of a computer‐based military expert system, to replace a large complex set of expert opinions. In that application it sharply improves efficiency, yet conforms to major tenets of tactical doctrine.
AbstractTolerance limits which control both tails of the normal distribution so that there is no more than a proportion β1 in one tail and no more than β2 in the other tail with probability γ may be computed for any size sample. They are computed from X̄ ‐ k1S and X̄ ‐ k2S, where X̄ and S are the usual sample mean and standard deviation and k1 and k2 are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X̄ – k1S) and (X̄ + k2S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.
AbstractThe concept of maximum entropy has been applied to specify the probabilistic model of consumer purchase behavior. This article is concerned with the marketing structure analysis based on entropy model when a new brand has pushed into the existing two‐brand market. A comparison between the proposed model and the initial three‐brand model is attempted based on their marketing structures. An optimal price decision maximizing the sales is also discussed.
