Showing papers on "Assignment problem published in 1972"

A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem

Abstract: A general procedure is presented for computing the best, 2nd best,…, Kth best solutions to a given discrete optimization problem. If the number of computational steps required to find an optimal solution to a problem with n(0, 1) variables is c(n), then the amount of computation required to obtain the if best solutions is O(Knc(n)). The procedure specializes to published procedures of Murty and of Yen for the assignment problem and the shortest path problem, respectively. A method is presented for reducing the required amount of storage by a factor of n, compared with the algorithms of Murty and of Yen. It is shown how the K shortest (loopless) paths in an n-node network with positive and negative arcs can be computed with an amount of computation which is O(Kn3). This represents an improvement by a factor of n, compared with Yen's algorithm.

The Traffic Assignment Problem for Multiclass-User Transportation Networks

Abstract: In a recent paper a traffic assignment model has been constructed in which the cost on a link may depend not only on its load, but also on the loads on other links of the network. In this paper it is shown that this model is also capable of handling the case of several classes of users in the same transportation network each of which has an individual cost function and, at the same time, contributes to its own and other classes' cost functions in an individual way. Typical applications arise not only in street networks where vehicles of different types share the same roads (e.g., trucks and passenger cars) but also in other types of transportation networks (e.g., telephone networks). An algorithm is constructed for finding the system-optimizing flow pattern for such a multiclass-user transportation network.

An analysis of the stable marriage assignment algorithm

Abstract: An algorithm for assigning the members of two disjoint equal sets to each other under the criterion of Stable Marriage is analysed and the results compared to the experimental results obtained on a computer The number of comparisons is shown to be of ordern logn (wheren is the size of the sets) which is better than that achieved by algorithms for solving the Classical Assignment Problem

Technical Note—Bounds for the Travelling-Salesman Problem

Abstract: This paper concerns finding a tight lower bound to the travelling-salesman problem, with the hope that all the different branch-and-bound algorithms for this problem can benefit from it. The bound is calculated by an iterative procedure with guaranteed convergence and is shown to require a computation time only about 9 per cent greater than the time required to solve an equivalent assignment problem. This new bound was tested on 14 sample problems and, on the average, found to be only 4.7 per cent below the optimum for symmetrical, and 3.8 per cent below the optimum for asymmetrical problems.

Asymptotic Optimal Policies for the Stochastic Sequential Assignment Problem

Abstract: Certain sets of numbers {ain}, i = 0,..., n, n = 1, 2,..., are known characterize an optimal sequential assignment policy. In this paper the limiting behavior as n → ∞ of the ain's is studied.

The quadratic assignment problem: a note

Abstract: Results of the Koopmans-Beckmann (K-B) analysis of the quadratic assignment problem [3] have perplexed many location theorists. K-B hold that indivisibilities of plant, in the presence of minimal interaction between spatially separated plants (namely, the shipment of intermediate goods at positive transportation rates), preclude the existence of a system of rents which will sustain an integral assignment, optimal or otherwise [3, p. 69]. Earlier in their paper K-B show that a sustaining price system does exist when the transportation of intermediate products is excluded; however, it is the presence of such interaction that leads to the more interesting quadratic assignment problem and the pessimistic conclusion reported above. The authors first present the quadratic assignment problem in a "permutation search" format, and then construct an equivalent linear programming problem which allows fractional assignments to be optimal without forfeiting any integral (one whole plant to each location) solutions that might exist:

On a Ramp-Flow Assignment Problem

Abstract: The formulation of ramp-flow assignment problem in the operations of controlled expressways during the rush-hour period is presented here. In order to discuss the problem on a quantitative basis, a simple unidirectional expressway system with multiple entrance-ramps has been selected as the model. When the flow throughout the system can be maintained below the bottleneck capacity of the expressway, the condition of steady flow prevails, and the model may be regarded as a dynamic process in the direction of flow. The ramp-flow regulation problem in an expressway system is then formulated as a multistage decision process by considering the ramp-flows as decision variables. Various criteria for selecting the optimum ramp-flow assignment are discussed and their implications in the regulation of rush-hour traffic are illustrated through a simple example. In the example, the technique of dynamic programming was used successfully to determine the optimum policy that minimizes the system congestion period and the...

Recursive simplification of pole-assignment problem in multi-input systems†

Abstract: It is shown in this paper that the pole-assignment problem for a linear time-invariant system of order (n) having (p) number of inputs can be solved by seeking the solution of the same problem for a similar system of order (n−p−r) [where 1≤r≤p] having (r 1) [with r1≤r] number of inputs. This operation can be repeated to simplify the pole-assignment problem in a recursive manner. Another contribution of this paper is that it shows that the asymptotic state-estimator problem for a linear time-invariant system of order (n) having (q) number of outputs can be solved by using the solution to the pole assignment problem of a similar system of order (n−q) having (q1 ) [with q1≤q] number of inputs.

A new look at the traffic assignment problem

Abstract: TRAFFIC ASSIGNMENT MODELS IN USE PRESENTLY ASSUME THAT THE COST OF USING A LINK IN A NETWORK IS THE SAME TO ALL THE USERS OF THE LINK. THERE IS NO DOUBT THAT THIS ASSUMPTION DOES NOT CORRECTLY DESCRIBE THE ACTUAL SITUATION. FOR EXAMPLE, THE VALUE OF TIME AND THE OPERATING COST OF THE VEHICLE, TWO OF THE COMPONENTS OF THE COST OF TRAVEL, ARE NOT THE SAME TO ALL THE USERS. THE EXISTENCE OF TRAFFIC ASSIGNMENTS WHEN THE ABOVE ASSUMPTION IS NOT MADE IS EXAMINED FOR SOME VERY SIMPLE NETWORKS. WE SHOW THAT STABLE TRAFFIC ASSIGNMENTS EXIST AND THAT THESE ASSIGNMENTS ARE QUITE DIFFERENT FROM THE ASSIGNMENTS OBTAINED WITH THE PRESENT MODELS. (A)

Using the Out-of-Kilter Algorithm to Solve a Complex Assignment Problem

Abstract: The out-of-kilter algorithm is used to solve a complex assignment problem involving interacting and conflicting personal choices subject to interacting resource constraints. An example of successful use is given and extensions into the corporate and social planning fields are suggested.

An extension of the (szwarc) truck assignment problem

Abstract: IN THIS JOURNAL IN 1967, SZWARE PRESENTED AN ALGORITHM FOR THE OPTIMAL ROUTING OF A COMMON VEHICLE FLEET BETWEEN M SOURCES AND N SINKS WITH P DIFFERENT TYPES OF COMMODITIES. THE MAIN PREMISE OF THE FORMULATION IS THAT A TRUCK MAY CARRY ONLY ONE COMMODITY AT A TIME AND MUST DELIVER THE ENTIRE LOAD TO ONE DEMAND AREA. THIS ELIMINATES THE PROBLEM OF ROUTING VEHICLES BETWEEN SOURCES OR BETWEEN SINKS AND LIMITS THE PROBLEM TO THE ROUTING OF LOADED TRUCKS BETWEEN SOURCES AND SINKS AND EMPTY TRUCKS MAKING THE RETURN TRIP. SZWARE CONSIDERED ONLY THE TRANSPORTATION ASPECT OF THE PROBLEM (I.E., NO INTERMEDIATE POINTS) AND PRESENTED A VERY EFFICIENT ALGORITHM FOR SOLUTION OF THE CASE HE DESCRIBED. IF THE TOTAL SUPPLY IS GREATER THAN THE TOTAL DEMAND, SZWARE SHOWS THAT THE PROBLEM IS EQUIVALENT TO A (MP + N) BY (NP + M) HITCHCOCK TRANSPORTATION PROBLEM. DIGITAL COMPUTER CODES FOR THIS ALGORITHM REQUIRE RAPID ACCESS STORAGE FOR A MATRIX OF SIZE (MP + N) BY (NP + M); THERFORE, COMPUTER STORAGE REQUIRED GROWS PROPORTIONALLY TO P SQUARED. THIS PAPER OFFERS AN EXTENSION OF HIS WORK TO A MORE GENERAL FORM: A TRANSSHIPMENT NETWORK WITH CAPACITY CONSTRAINTS ON ALL ARCS AND FACILITIES. THE PROBLEM IS SHOWN TO BE SOLVABLE DIRECTLY BY FULKERSON'S OUT-OF-KILTER ALGORITHM. DIGITAL COMPUTER CODES FOR THIS FORMULATION REQUIRE RAPID ACCESS STORAGE PROPORTIONAL TO P INSTEAD OF P SQUARED. COMPUTATIONAL RESULTS INDICATE THAT, IN ADDITION TO HANDLING THE EXTENSIONS, THE OUT-OF-KILTER ALGORITHM IS MORE EFFICIENT IN THE SOLUTION OF THE ORIGINAL PROBLEM WHEN THERE IS A MODERATE NUMBER OF COMMODITIES AND A COMPUTER OF LIMITED STORAGE CAPACITY. /AUTHOR/

Development of Generalized Network Flow Algorithms for Solving the Personnel Assignment Problem.

Abstract: : The report describes research designed to develop efficient solution approaches applicable to the personnel assignment problem. The research resulted in methodological enhancements to primal-dual network flow algorithms -- enhancements which provide a manyfold increase in efficiency. The enhanced solution methodology is described in detail. Benchmarks are included to demonstrate the increased efficiency of the enhanced algorithms over original versions of the Ford-Fulkerson algorithms. Although the enhanced algorithms are hardware independent their efficiency is still somewhat dependent on the basic computational speed and instructional repertoire of the hardware used. Benchmarks are provided to compare the relative efficiency of the enhanced algorithms on large, scientific computers manufactured by IBM, CDC and UNIVAC. (Author)

The Choice Behavior of Transportation Mode

Abstract: So far some economists have studied the pattern of traffic assignment theoretically and empirically. But it seems that there are few proper stochastic or statistical models for analyzing the traffic assignment problem on the base of an economic theory. The purpose of this paper is to formulate the economic behavior of traffic assignment and to derive some statistical models which seem useful for empirical study or the prediction of the future course.Three diffirent models for traffic assignment were developed. The first is similar to Quandt-Baumol model (1966) by which they analyzed the social traffic demand in California. In that model it is suggested that individual will choose the transportation modes so as to minimize his loss prescribed by traffic time and cost of each mode. However in deriving the social demand function from individual's one, we have had no consistent procedure concerning aggregation.The second model was developed by a stochastic approach to overcome the difficulty in the aspect of aggregation of the first model. The traffic time and cost are main factors to assign the modes in that model too.The thrid model was proposed for prediction in the future course so that model always satisfys the condition that the sum of predicted values of each assignment ratio be strictly unity.Finally some empirical applications on the basis of the second and thrid model were attempted. It seems that such applcations were rather succesful.