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This paper treats the optimal location of nuclear-power plants in the Pacific Northwest with respect to capital-construction, operating, and transmission costs. It presents a mathematical formulation of this two-product (peak and energy power) plant-location problem, using the simplex method in conjunction with a branch-and-bound process, and indicates a check procedure using Vogel's approximation method in conjunction with an algorithm for solving the transportation problem and a branch-and-bound process. The paper gives results for demand-growth rates of 4, 5, 6 and 7 percent and alternative designs and their costs. It also discusses the stability of the optimal solution. [ABSTRACT FROM AUTHOR]

In this paper the dual method and the poly-ω technique are specialized for the generalized transportation problem. A simple procedure is obtained for solving the parametric version of this problem, i.e. for passing from a solution optimal for given values of the parameters, to solutions optimal for other values of the parameters. This procedure is then extended to the case when not only the parameters change, but additional constraints appear. Finally, the procedure may be used as a general method for solving the usual (non-parametric) generalized transportation problem, and for this case a way is described for finding an initial (dual-feasible) solution. [ABSTRACT FROM AUTHOR]

This paper describes the use of a general purpose electronic analogue computer for locating a distribution centre, or in general for solving the problem of link-length minimization in networks (for example, when it is required to locate a set of supply points, such that the overall cost of transportation is minimized). Analogue programmes for solving the problem with one or two distribution centres are given and the extension of the method to cover the case of m distribution centres is indicated. Examples for systems with one and two distribution centres are solved and results are compared with those obtained analytically. The method can be extended to cover the case where costs are a non-linear function of distance. [ABSTRACT FROM AUTHOR]

The article presents a paper, which shows how to determine the optimal number and routings of containers used to move mail among several cities. This paper extends the above system to more than two cities, with different schedules on different days and with transfer of containers permitted throughout the system. A mathematical formulation is developed that can be readily solved by known linear programming techniques. Critical assumptions are (a) periodic demand patterns and linear transportation costs between each city-pair, and (b) constant fixed cost per container in the system. The optimization problem is transformed into a network flow linear program for which efficient solution methods are known. The researchers have investigated a system where containerized mail would be sent between two cities. The problem solved in reference was that of determining the best number of containers to be sent each day between the two cities, based on (a) the distribution of mail volumes going between the cities each day and (b) the costs for sending containers, full or empty, and for sending mail by other means in case of container shortage. Thus the original convex programming problem has been converted to an especially tractable type of linear program, namely the optimization of a network flow.

The model in this paper is intended to explain the choice of transport made by shippers, as well as their total demand for transportation services. The optimal choice of mode is shown to involve a trade-off among freight rates, speed, dependability (variance in speed) and en-route lossage. It is shown that faster, more dependable service simply reduces the shipper's or receiver's inventories, including his safety stock and his inventory in transit. Hence inventory theory makes possible a direct comparison of the four attribute on which mode selection is based and leads to a model of rational choice in transport demand. The resulting model is suitable for statistical estimation given adequate data. [ABSTRACT FROM AUTHOR]

In this paper we apply the following general scheme to determine toll patterns for multiclass-user transportation networks: we modify the travel cost as perceived by the individual traveler by charging him a 'toll.' Then we try to determine the toll pattern in such a way that the system-optimizing flow pattern becomes at the same time user- optimizing. We discuss two toll policies: (a) Tolls are collected on a link basis. (b) Tolls are collected on a path basis. The study shows that there is a degree of freedom in the path-toll collection policy. Alternative criteria are proposed for the exploitation of the degree of freedom such as: (i) that the tolls collected be nonnegative; (ii) that the personal cost of travelers, before and after the imposition of tolls, remains the same; (iii) that certain classes are treated discriminately in order to attain some social good. [ABSTRACT FROM AUTHOR]

Various versions of the Weber problem deal with the location of facilities in a system with fixed destinations or customers. The object is to minimize the sum of transportation costs, which is represented as the sum of the weighted distances in the system. This paper finds the optimum location for facilities where the object is to minimize the maximum weighted distance in the system. Rectangular distances, which are more appropriate for urban transportation than straight line distances, are used in the model. Optimization is achieved through parametric linear programming. [ABSTRACT FROM AUTHOR]

The article focuses on models of fleet routing and scheduling problems for transportation systems, which are formulated as integer linear programs with 0-1 variables. The topics discussed in this paper are concerned with important operational problems confronting the management of the competitive air transportation system. Some of these problems are significant for other transportation systems, including those with public-service rather than profit objectives. The problems are those connected with fleet utilization, fleet size, routing, and scheduling. Work that is related to some of these problems has been carried out by operations researchers and has been limited because, when optimal solutions were sought, computation times were excessive. The principal method of attack has been dynamic programming, which usually involves a very large state space for any real-life transportation system. The basic models are of the discrete-time rather than of the continuous-time variety. This property permits the formulation of the optimization problems as integer linear programs. The aim is to formulate a realistic model and to obtain its optimal solution

This paper presents a method for developing efficient timetables for the operation of fixed schedule common-carrier passenger transportation systems. The ability to compute such timetables is needed in the consideration of planning alternatives for future transportation systems and/or the efficient operation of existing systems. Here, time- table optimization is accomplished by maximizing an objective function consisting of three basic components: operating costs, revenues, and traveler benefits. Traveler benefits are computed using a consumer preference model that specifies a traveler's willingness to pay for alternative trips, based on the scheduling of those trips. The optimization is based on successive iterations of a dynamic programming algorithm that develops timetables for each vehicle in the system. Solutions are termed optimal to within a 'first-order passenger exchange! Examples are presented to illustrate the utilization of the methodology for computing information relevant to the development of system operating policies and to the consideration of planning alternatives. [ABSTRACT FROM AUTHOR]

A problem which exists in a large research laboratory is the allocation of professional people to work on research projects. Each department manager must allocate his personnel so that effectiveness, value of a given man to a given project, is maximized. Computationally, the transportation technique maybe used to solve the problem if it is possible to determine the individual coefficients (or effectiveness values) giving the relative value of the ith man to the jth project, for all i, j. This paper describes a technique for determining these effectiveness values. The effectiveness values are subjective, and reflect the value judgments of the department manager and of those who assign projects. The philosophy used in producing the effectiveness values is to simplify the manager's decisionmaking task in expressing his value judgments to comparing only two alternatives with respect to a single criterion at one time. The results of the ratings taken are reduced to produce a set of normalized effectiveness values. The use of the technique in a model allocation problem is shown. The application of the technique need not be confined to a personnel allocation problem, but can be applied to any resource allocation problem where the objective is to optimize a subjective measure. [ABSTRACT FROM AUTHOR]

A transportation queueing process in which taxis arrive in a Poisson process and customers arrive as a renewal process independent of taxi-arrival process is controlled by calling extra taxis whenever the total number of customers lost to the system reaches a certain predetermined number. Transient and steady state behavior of this process is studied using renewal theoretic arguments. The optimum value of the control variable is also obtained so as to minimize the total cost to the system due to the waiting taxis and lost customers. [ABSTRACT FROM AUTHOR]

A class of scheduling problems involving deferral costs has been formulated by McNaughton, who has described a simple method of solution for the linear, single-processor case. In this report dynamic programming and linear programming techniques are applied to nonlinear and multiple-processor problems. A dynamic programming solution of the nonlinear, single processor problem is possible, provided the number of jobs is small. Transportation methods of linear programming can be used to solve large nonlinear, multiple-processor problems, provided the processing times for the jobs are equal. Approximate and/or partial solutions are possible for other cases. [ABSTRACT FROM AUTHOR]

The article discusses the "transportation problem," which is a class of linear programming problems involving the selection of the most economical shipping routes for a commodity from given sources to given destinations. The transportation problem has been typically approached either as a specialized type of linear programming problem or as a method of representation of some combinatorial problems. The author asserts that a third method is possible, which is applicable for the determination of optimum linked paths over a series of points, or "transhipment." The transhipment problem is more complex than shipping an item from one point to another, because points can now be both origins and destinations. The question resembles a combinatorial problem but may be solved by linear programming.