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121.
The authors extend the generalized von Neumann model they developed (with J. G. Kemeny) in 1956 to an open model by assuming that there are exogeneously determined export and import prices and that any amount can be exported or imported at these prices. The open model is then characterized by means of seven axioms. It is shown, by applying the theory of linear programming, that if four economically reasonable assumptions hold, the open model has at least one solution in which at least one good with positive export price is exported and at least one good with positive import price is imported. It is also shown that, in general, a continuum of expansion rates can be achieved by varying certain control variables. The choice of these expansion rates gives indirectly the choice of a suitable sub-economy and also determines the exports and imports of the economy. Other results and examples are discussed. 相似文献
122.
Robert R. Read 《海军后勤学研究》1969,16(4):555-572
The paper treats the output process of a service center that has a large number of independent exponential channels in parallel. Initially all channels are working and there is a fixed backlog of items awaiting service. The moments are derived and central limit theorems are developed. Problems of computation are discussed and suitable formulae are developed. The joint distribution of the output of the center with the center's total busy time and total idle time are derived. Normal approximations to these distributions are presented. 相似文献
123.
This paper gives a new organization of the theoretical results of the Generalized Transportation Problem with capacity constraints. A graph-theoretic approach is utilized to define the basis as a one-forest consisting of one-trees (a tree with an extra edge). Algorithmic development of the pivot-step is presented by the representation of a two-tree (a tree with two extra edges). Constructive procedures and proofs leading to an efficient computer code are provided. The basic definition of an operator theory which leads to the discussion of various operators is also given. In later papers we will present additional results on the operator theory for the generalized transportation problem based on the results in the present paper. 相似文献
124.
A modified generalized programming procedure is presented for solving concave programming problems with equality constraints. The procedure constructs convenient linear approximations of the gradient of the dual and finds points where the approximating functions vanish. In the quadratic programming case, the procedure is finitely convergent. Global convergence is established for the non-quadratic case. Illustrative numerical examples are included. 相似文献
125.
A method is presented to locate and allocate p new facilities in relation to n existing facilities. Each of the n existing facilities has a requirement flow which must be supplied by the new facilities. Rectangular distances are assumed to exist between all facilities. The algorithm proceeds in two stages. In the first stage a set of all possible optimal new facility locations is determined by a set reduction algorithm. The resultant problem is shown to be equivalent to finding the p-median of a weighted connected graph. In the second stage the optimal locations and allocations are obtained by using a technique for solving the p-median problem. 相似文献
126.
James G. Taylor 《海军后勤学研究》1975,22(4):617-650
The treatment of force-level constraints in time-sequential combat optimization problems is illustrated by further studying the fire-programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire-distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjoint variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire-programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time-sequential combat optimization problems can be handled, and a more systematic solution procedure is developed. 相似文献
127.
Paul S. Dwyer 《海军后勤学研究》1975,22(4):751-775
The general solution process of the Hitchcock transportation problem resulting from the application of the method of reduced matrices may give solutions with some negative xij values. This paper is devoted to a review of the reduced matrices method, an examination of suitable interpretation of sets of xij which include some negative values, and ways of interpreting these values in useful modifications of the Hitchcock problem. Such modifications include a) the reshipment problem, b) the overshipment problem, and c) the transshipment problem. Techniques are developed for determining and eliminating cij which are not optimal. These techniques and results are useful in solving the problems indicated above. The natural applicability of the simple and general method of reduced matrices is emphasized. 相似文献
128.
A pseudo-monotonic interval program is a problem of maximizing f(x) subject to x ε X = {x ε Rn | a < Ax < b, a, b ε Rm} where f is a pseudomonotonic function on X, the set defined by the linear interval constraints. In this paper, an algorithm to solve the above program is proposed. The algorithm is based on solving a finite number of linear interval programs whose solutions techniques are well known. These optimal solutions then yield an optimal solution of the proposed pseudo-monotonic interval program. 相似文献
129.
John A. Muckstadt 《海军后勤学研究》1978,25(3):377-394
The optimization problem as formulated in the METRIC model takes the form of minimizing the expected number of total system backorders in a two-echelon inventory system subject to a budget constraint. The system contains recoverable items – items subject to repair when they fail. To solve this problem, one needs to find the optimal Lagrangian multiplier associated with the given budget constraint. For any large-scale inventory system, this task is computationally not trivial. Fox and Landi proposed one method that was a significant improvement over the original METRIC algorithm. In this report we first develop a method for estimating the value of the optimal Lagrangian multiplier used in the Fox-Landi algorithm, present alternative ways for determining stock levels, and compare these proposed approaches with the Fox-Landi algorithm, using two hypothetical inventory systems – one having 3 bases and 75 items, the other 5 bases and 125 items. The comparison shows that the computational time can be reduced by nearly 50 percent. Another factor that contributes to the higher requirement for computational time in obtaining the solution to two-echelon inventory systems is that it has to allocate stock optimally to the depot as well as to bases for a given total-system stock level. This essentially requires the evaluation of every possible combination of depot and base stock levels – a time-consuming process for many practical inventory problems with a sizable system stock level. This report also suggests a simple approximation method for estimating the optimal depot stock level. When this method was applied to the same two hypotetical inventory systems indicated above, it was found that the estimate of optimal depot stock is quite close to the optimal value in all cases. Furthermore, the increase in expected system backorders using the estimated depot stock levels rather than the optimal levels is generally small. 相似文献
130.
A. Victor Cabot 《海军后勤学研究》1978,25(3):473-481
In this paper we consider the problem of maximizing the sum of certain quasi-concave functions over a convex set. The functions considered belong to the classes of functions which are known as nonlinear fractional and binonlinear functions. Each individual function is quasi-concave but the sum is not. We show that this nonconvex programming problem can be solved using Generalized Benders Decomposition as developed by Geoffrion. 相似文献