Robust minimum cost flow problem under consistent flow constraints

The robust minimum cost flow problem under consistent flow constraints (RobMCF$$\equiv $$ ≡ ) is a new extension of the minimum cost flow (MCF) problem. In the RobMCF$$\equiv $$ ≡ problem, we consider demand and supply that are subject to uncertainty. For all demand realizations, however, we require that the flow value on an arc needs to be equal if it is included in the predetermined arc set given. The objective is to find feasible flows that satisfy the equal flow requirements while minimizing the maximum occurring cost among all demand realizations. In the case of a finite discrete set of scenarios, we derive structural results which point out the differences with the polynomial time solvable MCF problem in networks with integral demands, supplies, and capacities. In particular, the Integral Flow Theorem of Dantzig and Fulkerson does not hold. For this reason, we require integral flows in the entire paper. We show that the RobMCF$$\equiv $$ ≡ problem is strongly $$\mathcal {NP}$$ NP -hard on acyclic digraphs by a reduction from the (3, B2)-Sat problem. Further, we demonstrate that the RobMCF$$\equiv $$ ≡ problem is weakly $$\mathcal {NP}$$ NP -hard on series-parallel digraphs by providing a reduction from Partition. If in addition the number of scenarios is constant, we propose a pseudo-polynomial algorithm based on dynamic programming. Finally, we present a special case on series-parallel digraphs for which we can solve the RobMCF$$\equiv $$ ≡ problem in polynomial time.

Developing a Parametric Cash Flow Forecasting Model for Complex Infrastructure Projects: A Comparative Study

Forecasting the cash flow for infrastructure projects has not received much attention in the existing models. Moreover, disregarding the cost flow behaviour and proposing models that entail a relatively high dimensionality of inputs have been the main drawbacks of the existing models. This study proposes a heuristic cash flow forecasting (CFF) model for infrastructure projects, and it explores the underlying behaviour of the cost flow. The proposed model was validated by adopting a case study approach,the actual cost flow datasets were mined from a verified data system. The results invalidated the employment of a dominant heuristic rule with regard to a cost-flow-time relationship in infrastructure projects. On the other hand, a mathematical parameter-based comparison between the trends analysed from previous studies revealed that the cost flows of infrastructure projects procured through a design-bid-build (D-B-B) route behaved in a similar manner to building projects procured through a construction management route. This research contributes to the body of knowledge providing a method to enable infrastructure contractors to accurately forecast the required working capital through adding a new dimension for project classification by coining the term “the quaternary flow percentage”. In addition, this study indicates the importance of identifying the impact of root risks on the individual cost flow components rather than on the aggregated cost flow, which is a recommendation for future research.

Maximal concurrent minimal cost flow problems on extended multi-cost multi-commodity networks

The graph is a great mathematical tool, which has been effectively applied to many fields such as economy, informatics, communication, transportation, etc. It can be seen that in an ordinary graph the weights of edges and vertexes are taken into account independently where the length of a path is the sum of weights of the edges and the vertexes on this path. Nevertheless, in many practical problems, weights at vertexes are not equal for all paths going through these vertexes, but are depending on coming and leaving edges. Moreover, on a network, the capacities of edges and vertexes are shared by many goods with different costs. Therefore, it is necessary to study networks with multiple weights. Models of extended multi-cost multi-commodity networks can be applied to modelize many practical problems more exactly and effectively. The presented article studies the maximal concurrent minimal cost flow problems on multi-cost and multi-commodity networks, which are modelized as optimization problems. On the base of the algorithm to find maximal concurrent flow and the algorithm to find maximal concurrent limited cost flow, an effective polynomial approximate procedure is developed to find a good solution.

Efficient Algorithms for Identifying Loop Formation and Computing θ Value for Solving Minimum Cost Flow Network Problems

While the minimum cost flow (MCF) problems have been well documented in many publications, due to its broad applications, little or no effort have been devoted to explaining the algorithms for identifying loop formation and computing the θ value needed to solve MCF network problems. This paper proposes efficient algorithms, and MATLAB computer implementation, for solving MCF problems. Several academic and real-life network problems have been solved to validate the proposed algorithms; the numerical results obtained by the developed MCF code have been compared and matched with the built-in MATLAB function Linprog() (Simplex algorithm) for further validation.