We analyze degeneracy characterizations for two classical problems: the transportation paradox in linear transportation problems and the pure constant fixed charge transportation problem. Solving the pure constant fixed charge problem is equivalent to finding a basic tree solution with maximum degree of degeneracy. Problems possess degenerate solutions if the equal subsum property is satisfied ...

The fixed charge (fixed cost) may present the cost of renting a vehicle, landing fees in an airport, setup cost for machines in a manufacturing environment, etc. In this paper, we discuss fixed charge capacitated in a non-linear transportation problem. Thereby, we establish local optimum condition of this problem. Next we establish an algorithm for solving this transportation problem. Also, we ...

Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in a distribution network so that they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) studied in this paper captures a core structure encountered in many of these environments. We model the FCTPwB as ...

We consider a class of fixed-charge transportation problems over graphs. We show that this problem is strongly NP-hard, but solvable in pseudo-polynomial time over trees using dynamic programming. We also show that the LP formulation associated to the dynamic program can be obtained from extended formulations of single-node flow polytopes. Given these results, we present a unary expansion-based...

In this paper, the transportation problem under the carbon emission trading program ismodelled by mathematical programming and genetic algorithm. Since green supply chain issuesbecome important and new legislations are taken into account, carbon emissions costs are included inthe total costs of the supply chain. The optimisation model has the ability to minimise the total costsand provides the ...

The bi-criteria fixed charge transportation problem is an extension of the classical transportation problem. The bi-criteria fixed charge transportation problem in a crisp environment is, often, not effective in dealing with imprecision or vagueness in the values of the problem parameters. To deal with such situations, it has been proposed that the parameters should be represented as fuzzy numb...

A cost driven traffic assignment model is proposed to maximise the global benefit of transportation network users. A decentralised primal-dual time synchronised approach is used to solve for the optimal traffic rates subjecting the objective function to the bounds of the network tolerable costs. For a successful operation of the transportation network, the affordable upper bounds on the costs h...

The main insulation system in high-voltage direct current (HVDC) transformer consists of oil-paper insulation. The formation of space charge in insulation paper is crucial for the dielectric strength. Unfortunately, space charge behavior changes because of the corrosive sulfur substance in oil. This paper presents the space charge behavior in insulation paper induced by copper sulfide generated...

The single-sink fixed-charge transportation problem (SSFCTP) consists in finding a minimum cost flow from a number of nodes to a single sink. Beside a cost proportional to the amount shipped, the flow cost encompass a fixed charge. The SSFCTP is an important subproblem of the well-known fixed-charge transportation problem. Nevertheless, just a few methods for solving this problem have been prop...