16 research outputs found

Alternate Solutions Analysis For Transportation Problems

The constraint structure of the transportation problem is so important that the literature is filled with efforts to provide efficient algorithms for solving it.&nbsp; The intent of this work is to present various rules governing load distribution for alternate optimal solutions in transportation problems, a subject that has not attracted much attention in the current literature, with the result that the load assignment for an alternate optimal solution is left mostly at the discretion of the practitioner.&nbsp; Using the Shadow Price theory we illustrate the structure of alternate solutions in a transportation problem and provide a systematic analysis for allocating loads to obtain an alternate optimal solution.&nbsp; Numerical examples are presented to explain the proposed process

Note---An Improved Conditional Monte Carlo Technique for the Stochastic Shortest Path Problem

This paper describes a simulation procedure for estimating the distribution function of the shortest path length in a network with random arc lengths. The method extends the concept of conditional Monte Carlo utilizing special properties of the Uniformly Directed Cutsets and the unique arcs. The objective here is to reduce the sampling effort and utilize known probability information to derive multivariate integrals of lower dimension. The experimental results show that the proposed method is substantially cost effective and performs better than traditional Monte Carlo and conditional methods.stochastic networks, shortest path, Monte Carlo methods, variance reduction

On the fixed-charge transportation problem

In many distribution problems, the transportation cost consists of a fixed cost, independent of the amount transported and a variable cost, proportional to the amount shipped. In such fixed-charge transportation problems, is it possible to find a solution with less (or equal) cost than the optimal solution by shipping more units, under the condition that at least the same amount is shipped from each supply point and to each market? This question has not received any attention in the literature, and no algorithm (either analytical or heuristic) is known to address this problem. The more-for-less analysis could be useful for managers in decisions such as increasing warehouse/plant capacity, analyzing company acquisitions, mergers, consolidations or downsizing. In this paper we develop a quick sufficient condition to identify candidate markets and supply points to ship more for less in fixed-charge transportation problems.More-for-less paradox Fixed-charge Transportation problem Absolute point

A simple heuristic for solving small fixed-charge transportation problems

The fixed-charge transportation problem (FCTP) is an extension of the classical transportation problem in which a fixed cost is incurred, independent of the amount transported, along with a variable cost that is proportional to the amount shipped. The introduction of fixed costs in addition to variable costs results in the objective function being a step function. Therefore, fixed-charge problems are usually solved using sophisticated analytical or computer software. This paper deviates from that approach. It presents a simple heuristic algorithm for the solution of small fixed-charge problems. We present numerical examples to illustrate applications of the proposed method.Fixed-charge Transportation problem Heuristic algorithm

A note on the procedure MFL for a more-for-less solution in transportation problems

In a recent paper, Adlakha and Kowalski [A quick sufficient solution to the more-for-less paradox in the transportation problems. Omega, 1998;26:541-7] present a solution method for the more-for-less paradox for transportation problems. The method, though efficient, does not provide specific directions in some instances. In this note we modify the procedure to address issues raised by readers.More-for-less paradox Transportation problem

A quick sufficient solution to the More-for-Less paradox in the transportation problem

In a transportation problem, is it possible to find a solution with less (or equal) cost than the optimal solution by shipping more units under the condition that at least the same amount is shipped from each supply point and to each market? This more-for-less analysis could be useful for managers in decisions such as increasing warehouse/plant capacity, or advertising efforts to increase demand at certain markets. In this paper we develop a sufficient condition to identify candidate markets and supply points. The method is easy to apply and can serve as an effective tool for managers in solving the more-for-less paradox for large transportation problems, by providing the user with an insight into the problem. The procedure developed in this paper can also be used as an affective alternate solution algorithm for solving certain transportation problems.

Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities

In this paper, we consider a multi-index constrained transportation problem (CTP) of axial constraints with bounds on destination requirements, source availabilities, and multiple types of commodities. The specified problem is converted into a related transportation problem by adding a source, a destination, and a commodity, making it equivalent to a standard axial sum problem. This related problem is transformed into a multi-index transportation problem that can be solved easily. The provided solution method is very useful for transporting heterogeneous commodities. A transportation model may sometimes have various capacity constraints on the flow between pairs of origins and destinations. Moreover, budgetary, political, and emergency situations may impair or enhance the flow between origins and destinations, making it critical for a manager to reevaluate allocations. These considerations have motivated us to explore the multi-index CTP with impaired and enhanced flow. We present several numerical examples to demonstrate the proposed algorithms. Keywords: Classical transportation problem, Multi index, Impaired flow, Unbalanced, Optimal solutio