Formulation Of Transportation Problem Research Articles

A decentralized approach towards resolving transmission grid congestion in Germany using vehicle-to-grid technology

The increasing penetration of renewable generation in electricity markets as well as the rising number of electric vehicles pose new challenges for transmission grids. Additional demand and regionally clustered generation force system operators to consider costly expansion plans and employ expensive redispatch measures in the meantime. In this paper, we assess the ability of the expanded German transmission grid to cope with the additional demand of uncoordinated electric vehicle charging using a transportation problem formulation. We then propose local flexibility markets for electric vehicle owners to relieve the grid of congestion and to provide a heuristic that finds feasible solutions. We test our models on empirical data from the German electricity system of 2016. We find that the currently proposed expansion of the German electricity grid will not suffice to cope with increased electricity demand from uncoordinated electric vehicle charging. However, with coordination, electric vehicles can support transmission grid balancing and local flexibility markets can provide reasonable remuneration for electric vehicle owners.

Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint?

AbstractThe Lattice Boltzmann Method (LBM) has established itself as a popular numerical method in computational fluid dynamics. Several advancements have been recently made in LBM, which include multiple-relaxation-time LBM to simulate anisotropic advection-diffusion processes. Because of the importance of LBM simulations for transport problems in subsurface and reactive flows, one needs to study the accuracy and structure preserving properties of numerical solutions under the LBM. The solutions to advective-diffusive systems are known to satisfy maximum principles, comparison principles, the non-negative constraint, and the decay property. In this paper, using several numerical experiments, it will be shown that current single- and multiple-relaxation-time lattice Boltzmann methodsfailto preserve these mathematical properties for transient diffusion-type equations. We will also show that these violations may not be removed by simply refining the discretization parameters. More importantly, it will be shown that meeting stability conditions alone does not guarantee the preservation of the aforementioned mathematical principles and physical constraints in the discrete setting. A discussion on the source of these violations and possible approaches to avoid them is included. A condition to guarantee the non-negativity of concentration under LBM in the case of isotropic diffusion is also derived. The impact of this research is twofold.First, the study poses several outstanding research problems, which should guide researchers to develop LBM-based formulations for transport problems that respect important mathematical properties and physical constraints in the discrete setting. This paper can also serve as a good source of benchmark problems for such future research endeavors.Second, this study cautions the practitioners of the LBM for transport problems with the associated numerical deficiencies of the LBM, and provides guidelines for performing predictive simulations of advective-diffusive processes using the LBM.

Allocation of Returned Products among Different Recovery Options through an Opportunity Cost–Based Dynamic Approach*

ABSTRACTIn a make‐to‐order product recovery environment, we consider the allocation decision for returned products decision under stochastic demand of a firm with three options: refurbishing to resell, parts harvesting, and recycling. We formulate the problem as a multiperiod Markov decision process (MDP) and present a linear programming (LP) approximation that provides an upper bound on the optimal objective function value of the MDP model. We then present two solution approaches to the MDP using the LP solution: a static approach that uses the LP solution directly and a dynamic approach that adopts a revenue management perspective and employs bid‐price controls technique where the LP is resolved after each demand arrival. We calculate the bid prices based on the shadow price interpretation of the dual variables for the inventory constraints and accept a demand if the marginal value is higher than the bid price. Since the need for solving the LP at each demand arrival requires a very efficient solution procedure, we present a transportation problem formulation of the LP via variable redefinitions and develop a one‐pass optimal solution procedure for it. We carry out an extensive numerical analysis to compare the two approaches and find that the dynamic approach provides better performance in all of the tested scenarios. Furthermore, the solutions obtained are within 2% of the upper bound on the optimal objective function value of the MDP model.

Discontinuous subgrid formulations for transport problems

In this paper we develop two discontinuous Galerkin formulations within the framework of the two-scale subgrid method for solving advection–diffusion-reaction equations. We reformulate, using broken spaces, the nonlinear subgrid scale (NSGS) finite element model in which a nonlinear eddy viscosity term is introduced only to the subgrid scales of a finite element mesh. Here, two new subgrid formulations are built by introducing subgrid stabilized terms either at the element level or on the edges by means of the residual of the approximated resolved scale solution inside each element and the jump of the subgrid solution across interelement edges. The amount of subgrid viscosity is scaled by the resolved scale solution at the element level, yielding a self adaptive method so that no additional stabilization parameter is required. Numerical experiments are conducted in order to demonstrate the behavior of the proposed methodology in comparison with some discontinuous Galerkin methods.

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.

Scheduling algorithms for the broadcast delivery of digital products

We provide scheduling algorithms that attempt to maximize the profits of a broadcast-based electronic delivery service for digital products purchased, for example, at e-commerce sites on the World Wide Web. Examples of such products include multimedia objects such as CDs and DVDs. Other examples include software and, with increasing popularity, electronic books as well. We consider two separate alternatives, depending in part on the sophistication of the set-top box receiving the product at the customer end. The first, more restrictive option, assumes that the atomic unit of transmission of the product is the entire object, which must be transmitted in order from start to finish. We provide a solution based in part on a transportation problem formulation for this so-called noncyclic scheduling problem. The second alternative, which is less restrictive, assumes that the product may be transmitted cyclically in smaller segments, starting from an arbitrary point in the object. Three heuristics are provided for this difficult cyclic scheduling problem. Both scenarios assume that the broadcasts of the same digital product to multiple customers can be batched. We examine the effectiveness of these algorithms via simulation experiments under varying parametric assumptions. Each of the three cyclic scheduling algorithms perform better than the noncyclic algorithm. Moreover, one of the cyclic scheduling algorithms emerges as the clear winner.

Simplifying teaching the transportation problem

An algorithm to find optimal routeing for distribution‐related problems is presented. Usually these problems are formulated as transportation problems (TP) and solved using the stepping‐stone (SS) technique. In practice, however, the SS algorithm encounters major obstacles including difficulties in identifying an initial basic feasible solution, resolving SS degeneracy, and enumerating SS paths. The proposed algorithm solves the linear programming (LP) formulation of TP in a novel way and, unlike simplex or dual simplex methods, does not require artificial or slack/surplus variables. A general‐purpose algorithm is proposed which not only solves the classical TP, but also can effectively handle an unbalanced condition and additional side‐constraints on the routes. The proposed algorithm uses only the Gauss Jordan row operation, as used in the simplex method. As such, it is much easier to understand and apply, and can serve as an effective tool for teaching TP. Numerical examples are presented to illustrate applications of the proposed method. It is assumed that the reader is familiar with simplex terminology.

A transportation problem formulation for the MAC Airlift Planning problem

The Military Airlift Command (MAC) is responsible for planning the allocation of airlift resources for the movement of cargo and passengers. A heuristic algorithm, the Airlift Planning Algorithm (APA), has recently been developed under subcontract to the Oak Ridge National Laboratory to assist MAC in scheduling airlift resources. In this paper, we present a transportation problem formulation which can be used as a preprocessor to the APA or as an estimator for the APA. This paper examines the robustness and sensitivity of the transportation problem formulation. In particular, the performance of the APA improves by approximately 10% when the transportation problem is used as a preprocessor for two hypothetical problems and improves by up to 50% for derived airlift constrained problems.

Formulation of transportation problems

Algorithm developers commonly work in terms of equations and inequalities or matrices. Much of the literature is expressed in these terms. However, formulators commonly formulate models in terms of activities and constraints on the activities.

Chance Constrained Programming of the Machine Loading Problem with Stochastic Processing Times

The statistical model of a chance constrained variable which is the sum of stochastically independent random variables is considered, using the machine loading problem as an expository case. The resulting chance constrained statement, Pr {∑ni=1∑xik=0aik ≥ H} ≤ β, is shown to be different in substance from the classical case, Pr{∑ni=1 a′ixi ≤ H} ≥ β, where xi denotes the variable of the program and aik and a′i denote the random variables. A formal mathematical analysis is carried out on the deterministic equivalent nonlinear problem with solutions over a set that may be nonconvex. The mathematical results are then used in stating and evaluating a linear approximation, thus enabling one to state the problem using a generalized transportation problem formulation.