摘要:

AbstractThis paper considers a group ofSidentical aircraft, each of which is partitioned intoKparts which fail exponentially. The only way in which a failed aircraft can be repaired is by cannibalizing its out‐of‐commission parts from other failed aircraft. The evolution of the number of good aircraft over time is governed by the transient behavior of an absorbing Markov chain. We can therefore study this behavior by matrix multiplication although the computational problem grows large forK≥ 3. Some numerical results and some approximations are also pro

ISSN:0028-1441    

DOI:10.1002/nav.3800170202

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractAccording to “interference theory” of reliability, a component fails if the maximum stress exceeds the component's strength. Assuming that both these quantities are random and their distributions are normal, we obtain in this paper some point and interval estimates of reliability when the stress distribution is known and a few observations exist on component streng

ISSN:0028-1441    

DOI:10.1002/nav.3800170203

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractThe subject of this paper is the utilization of the “infant mortality” or decreasing failure rate effect to improve the reliability of repairable devices. Decreasing failure rate implies the possibility that devices which exhibit it can be improved by “burn‐in testing” of each unit. Such a test serves to accumulate operating time while shielded from the full costs and consequences of failure. A general formulation of the burn‐in test decision for repairable devices is presented and some special cases are solved. A class of models, indexed by the degree of partial replacement present in the repair process, is considered and numerical results for the optimal policy are given for several members of that class. A comparison of those results reveals the profitability of testing increases with the complexity of the repair

ISSN:0028-1441    

DOI:10.1002/nav.3800170204

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800170205

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractA model is developed for planning optimal production and employment levels in multi‐product, multistage production systems. The market requirements for each product over the planning period are given. Backorders and/or shortages are permitted. Backorders and shortages must be considered in order to determine the amount of each product's demand that should be filled, backlogged, or go unsatisfied if the production capacity is insufficient to fill all market requirements. Backorders and shortages, on the other hand, are desirable under certain dynamic market condition

ISSN:0028-1441    

DOI:10.1002/nav.3800170206

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractA new primal‐dual linear programming algorithm is exhibited. A proof is given that optimal solutions to both primal and dual problems (when such solutions exist) are found in a finite number of steps by this algorithm. A numerical example is included to illustrate the metho

ISSN:0028-1441    

DOI:10.1002/nav.3800170207

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractThis paper presents an algorithm for determining where to place intercepting units in order to maximize the probability of preventing an opposing force from proceeding from one particular node in an undirected network to another.The usual gaming assumptions are invoked; namely, the strategy for placing the units is known to the opponent and he will choose a path through the network which, based on this knowledge, maximizes his probability of successful traverse. As given quantities, the model requires a list of the arcs and nodes of the network, the number of intercepting units available to stop the opposing force, and the probabilities for stopping the opposition at the arcs and nodes as functions of the number of intercepting units placed there. From these quantities, the algorithm calculates the probabilities for placing the unit at the arcs and nodes when one intercepting unit is available, and the expected numbers of units to place at the arcs and nodes when multiple intercepting units are available.

ISSN:0028-1441    

DOI:10.1002/nav.3800170208

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractThe fixed charge problem is a nonlinear programming problem of practical interest in business and industry. Yet, until now no computationally feasible exact method of solution for large problems had been developed.In this paper an exact algorithm is presented which is computationally feasible for large problems. The algorithm is based upon a branch and bound approach, with the additional feature that the amount of computer storage required remains constant throughout (for a problem of any given size).Also presented are three suboptimal heuristic algorithms which are of interest because, although they do not guarantee that the true optimal solution will be found, they usually yield very good solutions and are extremely rapid techniques.Computational results are described for several of the heuristic methods and for the branch and bound algorithm.

ISSN:0028-1441    

DOI:10.1002/nav.3800170209

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractThe discounted return associated with a finite state Markov chainX1,X2… is given byg(X1)+ αg(X2) + α2g(X3) + …, whereg(x) represents the immediate return from statex. Knowing the transition matrix of the chain, it is desired to compute the expected discounted return (present worth) given the initial state. This type of problem arises in inventory theory, dynamic programming, and elsewhere.Usually the solution is approximated by solving the system of linear equations characterizing the expected return. These equations can be solved by a variety of well‐known methods. This paper describes yet another method, which is a slight modification of the classical iterative scheme. The method gives sequences of upper and lower bounds which converge mono‐tonely to the solution. Hence, the method is relatively free of error control problems.Computational experiments were conducted which suggest that for problems with a large number of states, the method is quite efficient. The amount of computation required to obtain the solution increases much slower with an increase in the number of states,N, than with the conventional methods. In fact, computational time is more nearly proportional toN2,

ISSN:0028-1441    

DOI:10.1002/nav.3800170210

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the determination of explicit expressions for economic order quantities and reorder levels, such that the cost of ordering and holding inventory is minimized for specific backorder constraints. Holding costs are applied either to inventory position or on‐hand inventory, and the backorder constraint is considered in terms of the total number of backorders per year or the average number of backorders at any point in time. Through the substitution of a new probability density function in place of the normal p.d.f., explicit expressions are determined for the economic order quantities and the reorder points. The resulting economic order quantities are independent of all backorder constraints. It is also concluded that under certain conditions, the minimization of ordering costs and inventory holding costs (applied to inventory position), subject to a backorder constraint, is equivalent in terms of reorder levels to minimization of the safety level dollar investment subject to the same backorder constrain

ISSN:0028-1441    

DOI:10.1002/nav.3800170211

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1970

数据来源: WILEY