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.

QED driven QAOA for network-flow optimization

We present a general framework for modifying quantum approximate optimization algorithms (QAOA) to solve constrained network flow problems. By exploiting an analogy between flow-constraints and Gauss' law for electromagnetism, we design lattice quantum electrodynamics (QED)- inspired mixing Hamiltonians that preserve flow constraints throughout the QAOA process. This results in an exponential reduction in the size of the configuration space that needs to be explored, which we show through numerical simulations, yields higher quality approximate solutions compared to the original QAOA routine. We outline a specific implementation for edge-disjoint path (EDP) problems related to traffic congestion minimization, numerically analyze the effect of initial state choice, and explore trade-offs between circuit complexity and qubit resources via a particle-vortex duality mapping. Comparing the effect of initial states reveals that starting with an ergodic (unbiased) superposition of solutions yields better performance than beginning with the mixer ground-state, suggesting a departure from the ``short-cut to adiabaticity" mechanism often used to motivate QAOA.

Unit Commitment-Security Constraints Using the Priority List-Genetic Algorithm Method in the IEEE 6 Bus and IEEE 14 BUS Case Studies

<p><strong>Unit commitment (UC) is the scheduling of on-off operation of a power plant unit to meet the demand for electrical power over a certain period of time in order to obtain an economical total cost of generation The PL method is used for scheduling and the AG is optimized using DOE for ED problems. The results obtained from the research that there are still improvements in the calculation of ED problems using load flow constraints and can be corrected. The results of the comparison of the total percentage cost of IEEE 6 buses used in ED problems without considering the load flow constraints with those considering this problem amounted to 26.30%. The result of the comparison of the total percentage cost of IEEE 14 buses used in ED problems without considering load flow constraints with those considering this problem is 11.55%. The load flow calculation using Newton-Rapshon uses a smaller number of iterations and a shorter time than Gauss-Seidel.</strong></p><p><strong><br /></strong></p>

Examining the determinants and consequences of financial constraints faced by Micro, Small and Medium Enterprises' owners

PurposeThe Micro, Small and Medium Enterprises (MSMEs) counter numerous financial obstacles concerning business financing and cash flow management. The study, therefore, intends to examine the level of perceived severity of financial constraints on the business growth of enterprises, in terms of sales, profitability and asset growth. An attempt is made to study the influence of owner and firm attributes as the determinants of financial constraints faced by MSMEs.Design/methodology/approachThe data were collected from MSME owners of Northern India through a self-administered questionnaire. In total, 213 responses were analysed using partial least squares-structural equation modelling (PLS-SEM) technique through SmartPLSv2.FindingsThe findings advocate the role of owner and firm attributes in the severity of financial constraints experienced by the MSME owners. Most importantly, the study establishes a strong link between owner and firm attributes and cash flow constraints. Further, the paper confirms the negative influence of financing and cash flow problems on the growth of the firm.Research limitations/implicationsThe evaluation and categorisation of perceived financial challenges into meaningful dimensions generate value to the problematic area of MSME operations. Thus, the findings are useful for the policymakers and researchers to contemplate the financial vulnerability of MSMEs.Originality/valueThe empirical findings of the present study add worth to the limited evidence of the relationship between owner and firm attributes and severity of cash flow constraints faced by the Indian MSME owners.