Search

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.

This paper describes an algorithm for a ship scheduling problem, obtained from a Swedish ship-owning company. The algorithm uses the Dantzig-Wolfe decomposition method for linear programming. The subprograms are simple network flow problems that are solved by dynamic programming. The master program in the decomposition algorithm is an LP problem with only zero-one elements in the matrix and the right-hand side. Integer solutions are not guaranteed, but generation and solution of a large number of problems indicates that the frequency of fractional solutions is as small as 1-2 per cent. Problems with about 40 ships and 50 cargoes are solved in about 2.5 minutes on an IBM 7090. In order to resolve the fractional cases, some integer programming experiments have been made. The results will be reported in a forthcoming paper. [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

The Dantzig and Fulkerson Tanker Scheduling Problem is concerned with the determination of the minimum size and optimal routing of a fleet of homogeneous tankers needed to meet a prescribed schedule of deliveries. This problem has been formulated as a network flow problem. Later formulations consider an existing nonhomogeneous tanker fleet and relax the fixed shipping schedule. These problems are treated as multicommodity minimal cost flow problems. This paper further extends the problem to consider differing carrying capabilities of the vehicles and formulates a mixed integer linear program that permits partially loaded tankers. A branch-and-bound enumerative scheme in conjunction with a decomposed linear program with network sub-problem is presented. [ABSTRACT FROM AUTHOR]

The paper discusses the computer construction of the lists of weeks of work that form the basis of the rotating roster for crews operating buses for a transit system. There are two construction phases; the first consists of making a day-off pattern and the second consists of placing daily shifts in the lists under the constraint of the day-off pattern. Techniques used to attain objectives include integer linear programming and optimal assignment. [ABSTRACT FROM AUTHOR]