Standard Transportation Problem Research Articles

Algorithm of the Generalized Method of Potentials for the Problem of Optimal Linear Synthesis of a Communication Network

A new efficient algorithm for solving the linear separable problem of the synthesis of a communication network called the generalized method of potentials is considered and justified. It is a generalization of the known method of potentials for solving the standard transportation problem. The finiteness of the proposed algorithm is proved.

A model for optimization of transport infrastructure for some homogeneous goods markets

The optimization problem studied in this paper generalizes the standard transportation problem and turns out to be NP-hard under the positive fixed costs of the transmission lines expansion. For a market with a tree-type network, a method for the supply-demand balances transfer to its root node is proposed. The method is based on the Welfare Theorem, and it proceeds from a solution to an auxiliary convex optimization problem with zero fixed costs for the lines expansion. The complexity of the method for the auxiliary problem is proven to be quadratic with respect to the number of nodes. Also, the proposed method is modified to obtain an approximate solution to the original problem and to estimate the welfare loss corresponding to this solution.

Sensor management based on fisher information gain

Multi-sensor system is becoming increasingly important in a variety of military and civilian applications. In general, single sensor system can only provide partial information about environment while multi-sensor system provides a synergistic effect, which improves the quality and availability of information. Data fusion techniques can effectively combine this environmental information from similar and/or dissimilar sensors. Sensor management, aiming at improving data fusion performance by controlling sensor behavior, plays an important role in a data fusion process. This paper presents a method using fisher information gain based sensor effectiveness metric for sensor assignment in multi-sensor and multi-target tracking applications. The fisher information gain is computed for every sensor-target pairing on each scan. The advantage for this metric over other ones is that the fisher information gain for the target obtained by multi-sensors is equal to the sum of ones obtained by the individual sensor, so standard transportation problem formulation can be used to solve this problem without importing the concept of pseudo sensor. The simulation results show the effectiveness of the method.

The Transportation Problem with Objective of Simultaneous Minimization of Total Transportation Cost and Transportation Time to Each Destination

For the Vector Minimization Problem (VMP) of simultaneous minimization of total transportation cost and transportation time to each destination two algorithms are proposed, which give a sequence of strictly non-dominated solutions (SNDS) by constructing suitable cost function involving penalty weights in the framework of a sequence of standard transportation problems and solving them sequentially. Whenever multiple optima are confronted in this procedure to the standard transportation problem, a second algorithm branching off from the main algorithm, tests the optimal feasible solution for dominence to the VMP, and if it is dominated, yields a non-dominated solution, which is a member of the sequence of SNDS. Apart from their reduced number as compared to the number of non-dominated solutions, the SNDS introduce a well-defined preference order in the solution as one goes up in the sequence. Thus, SNDS constitute a superior class of dominated solutions and render the task of choosing a preferred solution by the Decision-maker less difficult. Several special cases, in which the proposed algorithms can be applied are briefly described to highlight their usefulness to real-life problems.

Solving the transportation problem with mixed constraints

Variants of the standard transportation problem in which availability or requirement constraints are specified as inequalities can be solved by means of related standard transportation problems. In this paper we show that to each transportation problem with mixed constraints a standard transportation problem with two additional constraints can be related. The method of solution proposed also applies to the case that a lexicographic optimization is to be performed.

Equalities in transportation problems and characterizations of optimal solutions

This paper considers the classical finite linear transportation Problem (I) and two relaxations, (II) and (III), of it based on papers by Kantorovich and Rubinstein, and Kretschmer. Pseudo-metric type conditions on the cost matrix are given under which Problems (I) and (II) have common optimal value, and a proper subset of these conditions is sufficient for Problems (II) and (III) to have common optimal value. The relationships between the three problems provide a proof of Kantorovich's original characterization of optimal solutions to the standard transportation problem having as many origins as destinations. The result are extended to problems having cost matrices which are nonnegative row-column equivalent.

A Linear Time Algorithm for a $2 \times n$ Transportation Problem

This paper considers a special case of the standard transportation problem obtained by restricting the number of origins to two. Necessary and sufficient conditions are established which lead to a direct construction of the optimal solution. Using an extension of a recent selection algorithm, an algorithm is developed to solve this special case of the transportation problem in $O(n)$ time in the worst case. The algorithm applies to both capacitated as well as uncapacitated problems.

The Transportation Problem with Mixed Constraints

A generalization of the standard transportation model in which the origin and destination constraints consist not only of equality but also inequality constraints is considered. It is shown that the model is equivalent to a standard transportation problem having only one additional origin and destination.

A Variant of the Transportation Problem in Which the Constraints are of Mixed Type

An algorithm is presented for solving a variant of the transportation problem with a mixture of equality and inequality requirement and availability constraints. The method involves a simple transformation to the solution of a standard transportation problem. Proof is given of the optimality of the solution obtained.

An Algorithm for Assigning Uses to Sources in a Special Class of Transportation Problems

This paper considers a special class of transportation problems in which the needs of each user are to be supplied entirely by one of the available sources. We first show that an optimum solution to this special transportation problem is a basic feasible solution to a slightly different standard transportation problem. A branch-and-bound solution procedure for finding the desired solution to the latter is then presented and illustrated with an example. We then consider an extension of this problem by allowing the possibility of increasing (at a cost) the source capacities. The problem formulation is shown to provide a generalization to the well known assignment problem. The solution procedure appears to be relatively more efficient when the number of uses greatly exceeds the number of sources.

The Transportation Problem with Penalty Costs

Abstract The transportation problem with excess total demand and varying penalty costs for not meeting the individual demands is converted to a standard transportation problem.

A Linear Location Model

AbstractThe paper describes research work carried out in Czechoslovakia concerning the location and size of mills, with particular reference to the lumber industry. Two models are presented, the first being a relatively simple linear model (a generalization of an algorithm for solving the standard transportation problem), and the second a more realistic mixed integer location model.