Suchergebnisse

AbstractIn the temporarily isolated situation in which a warship finds itself during a mission. not only spare parts, but also "spare" crewmen in various categories of specialization must he on board.Mathematical models for the probabilities of mission survival for personnel and for personnel and materiel jointly are proposed. A practical example is worked out: the optimal allocation of spare crewmen to different categories of specialization is calculated.

AbstractA new bivariate negative binomial distribution is derived by convoluting an existing bivariate geometric distribution; the probability function has six parameters and admits of positive or negative correlations and linear or nonlinear regressions. Given are the moments to order two and, for special cases, the regression function and a recursive formula for the probabilities. Purely numerical procedures are utilized in obtaining maximum likelihood estimates of the parameters. A data set with a nonlinear empirical regression function and another with negative sample correlation coefficient are discussed.

AbstractWe investigate a class of optimal stopping problems for dynamical systems described by one‐dimensional differential equations with an additive Poisson disturbance. The rate of the disturbance may depend upon the current state of the system. A dynamic programming equation for the optimal stopping cost is derived along with conditions which must be met at the boundary of the optimal stopping set. These boundary conditions depend upon whether or not the stopping set may be entered by smooth motion.

AbstractIn this paper the reliability function K = P(X < Y) has been estimated when X and Y follow gamma, exponential or bivariate exponential distributions. The paper is partly expository.

AbstractIn this paper we analyze optimal search strategies in an environment in which multiple, independent targets arrive and depart at random. The analysis revolves around a continuous time differential equation model which captures the time dependent nature of the search process. We explore the impact on optimal strategies of nonzero travel times between regions as well as differing target arrival rates. We derive simple closed form expressions for determining if only one region should be searched.

AbstractThis paper examines various models for maintenance of a machine operating subject to stochastic deterioration. Three alternative models are presented for the deterioration process. For each model, in addition to the replacement decision, the option exists of performing preventive maintenance. The effect of this maintenance is to "slow" the deterioration process. With an appropriate reward structure imposed on the processes, the models are formulated as continuous time Markov decision processes. the optimality criterion being the maximization of expected discounted reward earned over an infinite time horizon. For each model conditions are presented under which the optimal maintenance policy exhibits the following monotonic structure. First, there exists a control limit rule for replacement. That is, there exists a number i* such that if the state of machine deterioration exceeds i* the optimal policy replaces the machine by a new machine. Secondly, prior to replacement the optimal level of preventive maintenance is a nonincreasing function of the state of machine deterioration. The conditions which guarantee this result have a cost/benefit interpretation.

AbstractConsider a network G(N. A) with n nodes, where node 1 designates its source node and node n designates its sink node. The cuts (Zi, =), i= 1…, n ‐ 1 are called one‐node cuts if 1 ϵ Zi,. n q Zi, Z1‐− {1}, Zi ϵ Zi+1 and Zi and Zi+l differ by only one node. It is shown that these one‐node cuts decompose G into 1 m n/2 subnetworks with known minimal cuts. Under certain circumstances, the proposed one‐node decomposition can produce a minimal cut for G in 0(n2 ) machine operations. It is also shown that, under certain conditions, one‐node cuts produce no decomposition. An alternative procedure is also introduced to overcome this situation. It is shown that this alternative procedure has the computational complexity of 0(n3).

AbstractAnM/G/1 queueing system is studied in which the service time required by a customer is dependent on the interarrival time between his arrival and that of his predecessor Assuming the two variables are "associated," we prove that the expected delay in this system is less than or equal to than of a conventional M/G/1 queue This conclusion has been verified via simulation by Mitchell and Paulson [9] for a special class of dependent M/M/1 queue. Their model is a special case of the one we consider here. We also study another modified GI/G/1 queue. where the arrival process and/or the service process are individually "associated".

AbstractThe classical "Colonel Blotto" games of force allocation are generalized to include situations in which there are complementarities among the targets being defended. The complementarities are represented by means of a system "characteristic function," and a valuation technique from the theory of cooperative games is seen to indicate the optimal allocations of defense and attack forces. Cost trade‐offs between systems defense and alternative measures, such as the hardening of targets, are discussed, and a simple example is analyzed in order to indicate the potential of this approach.

AbstractFor the classical disposal model for selling an asset with unknown price distribution which is NWUE (new worse than used in expectation) with a given finite mean price, this note derives a policy which is maximin. The gain in using the maximin policy relative to the option of selling right away is convex decreasing in the continuation cost to mean price ratio. The relevant results of Derman, Lieberman and Ross also follow as a consequence of our analysis. Our theorem provides a practical justification of their main result on the cutoff bid for the disposal model subject to NWUE pricing.

AbstractThe classical Economic Order Quantity Model requires the parameters of the model to be constant. Some EOQ models allow a single parameter to change with time. We consider EOQ systems in which one or more of the cost or demand parameters will change at some time in the future. The system we examine has two distinct advantages over previous models. One obvious advantage is that a change in any of the costs is likely to affect the demand rate and we allow for this. The second advantage is that often, the times that prices will rise are fairly well known by announcement or previous experience. We present the optimal ordering policy for these inventory systems with anticipated changes and a simple method for computing the optimal policy. For cases where the changes are in the distant future we present a myopic policy that yields costs which are near‐optimal. In cases where the changes will occur in the relatively near future the optimal policy is significantly better than the myopic policy.

AbstractInventory systems with returns are systems in which there are units returned in a repairable state, as well as demands for units in a serviceable state, where the return and demand processes are independent. We begin by examining the control of a single item at a single location in which the stationary return rate is less than the stationary demand rate. This necessitates an occasional procurement of units from an outside source. We present a cost model of this system, which we assume is managed under a continuous review procurement policy, and develop a solution method for finding the policy parameter values. The key to the analysis is the use of a normally distributed random variable to approximate the steady‐state distribution of net inventory.Next, we study a single item, two echelon system in which a warehouse (the upper echelon) supports N(N ⩾ 1) retailers (the lower echelon). In this case, customers return units in a repairable state as well as demand units in a serviceable state at the retailer level only. We assume the constant system return rate is less than the constant system demand rate so that a procurement is required at certain times from an outside supplier. We develop a cost model of this two echelon system assuming that each location follows a continuous review procurement policy. We also present an algorithm for finding the policy parameter values at each location that is based on the method used to solve the single location problem.

AbstractThe operating characteristics of (s,S) inventory systems are often difficult to compute, making systems analysis a tedious and often expensive undertaking. Approximate expressions for operating characteristics are presented with a view towards simplified analysis of systems behavior.The operating characteristics under consideration are the expected values of: total cost per period, period‐end inventory, period‐end stockout quantity, replenishment cost per period, and backlog frequency. The approximations are obtained by a two step procedure. First, exact expressions for the operating characteristics are approximated by simplified functions. Then the approximations are used to design regression models which are fitted to the operating characteristics of a large number of inventory items with diverse parameter settings. Accuracy to within a few percent of actual values is typical for most of the approximations.

AbstractSufficient conditions are given for stochastic comparison of two alternating renewal processes based on the concept of uniformization. The result is used to compare component and system performance processes in maintained reliability systems.