A Mathematical Model for the Capacity Expansion Problem of Inter-regional Water Supply Facilities

This paper concerns the capacity expansion problem of inter-regional water supply facilities, and presents a mathematical model to analyze the problem. The model postulates such an inter-regional water supply system that is managed by a body which is independent of municipalites ; and provides water to municipalities by conveying purified water to distribution reserviors in the municipalities through conduits laid between them. The formulated model, which belongs to a nonlinear programming, is solved by both an enumeration method and dynamic programming. A case study was conducted by applying the model to the capacity expansion problem in the region consisting of Takasago, Kakogawa and Akashi Cities in Hyogo Prefecture The calculated results show that such a management system as is presumed in the model, is economically effective mainly because joint expansion for the increased supply in several municipalities will save associated costs, provided that unnecessarily excessive expansion is avoided

A System Analysis for the Planning of Facilities in Inter-basin Water Distribution Problems

With a high increase in water demands in urbanized areas, there has been a growing concern about inter-basin water distribution problems. The primary objective of this study is to present a mathematical model which may serve as an available tool of system analysis for this kind of problem. In the proposed model are incorporated three functions, namely a choice of alternatives in dam planning, a choice of alternatives in channel planning and the integrating process of the above-mentioned two functions. To dissect the incorporated functions in terms of mathematics, the decomposition principle is employed in solving the model. The applicability and validity of the model are evidenced by a case study conducted for the water distribution problem in Hyogo Prefecture

Modeling Multi-Objective, Interbasin, Surface Water Development System with Supplementary Use of Reclamation System

This paper centers on the multi-objective, interbasin, surface water development system, whereby, if necessary, the conjunctive use of reclamation system is assumed to be available. The major objectives of the paper include (i) analysis of the quality of industrial waters blended with renovated waters ; (ii) identification of the relation between the blended water demand and its blending ratio and (iii) modeling and analysis of the coordinated attainments of multiple goals involved in the stated system. A case study is conducted at the interbasin system of the southern part of Hyogo Prefecture and some informative results obtained point to the need of this kind of alternative water utilization systems. The major findings of the study include : (1) The reclamation system is required to be implemented on a certain scale to supplement the industrial water supply. (2) In cases where the permitted-levels of the collection goals related to each river basin are set to be relatively higher, the total amounts of water supply that must be covered by the reclamation systems should be allocated to the system of each basin roughly in proportion to the amounts of its industrial water demand. (3) The increased attainments of the amounts of collection, and in consequence, the increased attainments of the improvement in the blended water quality are achievable only at the sacrifice of economic efficiency. (4) The attainments of the goals are seen to be well-balanced and not biased to any of them, chiefly owing to the L-type utility function underlying the model