Postoptimization of the model of water supply for urban and industrial agglomeration

Abstract

A case study of the tools used by an analyst of the economic aspects of the operation of the water supply network has been undertaken in this paper. All issues discussed here are formulated by using degenerated linear programming models ( PL ). Below, it is noted that the linear dependence of binding constraints ( CO ) distorts standard postoptimization procedures in PL. This observed fact makes postoptimization analysis mostly unhelpful for an average analyst due to problems with the int erpretation of ambiguous sensitivity reports which are obtained from popular computer packages. In standard postoptimization methods, changes to single parameters of the right-hand vector CO are analyzed or referred to parametric linear programming that unfortunately requires prior knowledge of mathematically and economically justified vectors of changes of right-hand sides CO. Therefore, it is suggested that modifications are introduced to some of the postoptimization procedures in this work. For issues in the field of hydrology, the following were presented: interpretation and methods of generating justified vectors of changes of right-hand sides of limiting conditions. And so, the procedure of generating infinitely many solutions of the dual issue based on certain vectors orthogonal to the vector of right-hand sides of constraint conditions was demonstrated. Furthermore, the same orthogonal vectors were used to obtain nodal solutions of the dua0l model and the corresponding vectors of changes of the entire right-hand sides of the constraint conditions. Then, managerial interpretation was applied to this way of proceeding. The methods presented in the work serve to improve the functioning of the system of water supply.

Selected problems of ambiguity of the dual price of water in the post-optimization analysis of the water supply system

“…Numerous studies [26, 29-30, 40, 48, 55-58] indicate the necessity of caution when using LP methods. This is mainly due to the ambiguity of sensitivity reports containing dual price vectors [55][56][57][58]. In this work, it is noted that the ambiguity of dual price vectors is a consequence of the linear dependence of the row vectors of the parameters of the left-hand sides binding the constraint conditions of the LP model.…”

“…The authors note that the dubiousness in the literature on the usefulness of dual prices that can be seen so far is probably related to both the lack of knowledge about their ambiguity and the lack of practical methods for utilising this fact. The works [24,[55][56][57][58] may be an exception here. In section 2, on a simple example of a water supply network with infinitely many dual price vectors, it is suggested how to propose the framework for alternative modernization scenarios of a previously optimized network.…”

“…∆ . Thus, it generalises the importance of vectors balancing in the transport model and orthogonal to b and allows for generalization of the dual price matrix method [24,[55][56][57][58] for models with inequality constraint conditions. The methodology presented above can be directly adapted to 6.…”

“…Models of reliability, readiness and safety in connection with linear programming are useful in the identification and prediction of reliability, readiness and safety of complex technical systems as well as in the optimization and analysis of the operating costs of these systems [28,[32][33]66]. The uncertainty of the parameters of a typical linear programming model indicated here requires, in addition to an optimization procedure, easy access to post-optimization procedures [56,58].…”

“…The fact that there are infinitely many solutions to the dual model [55][56] makes a sensitivity report most often unhelpful for an average analyst due to problems with the interpretation of ambiguous reports obtained. So far, this last problem has been described only partially and only in individual cases of transport models [57][58]. The transport models presented there are a special case of sensitivity analysis with the functional dependence of the parameters of the right-hand sides of constraint conditions [23].…”