O.R. ApplicationsOptimal installation policies of additional water supply facilities for a growing population
Introduction
The design of a water supply system is aimed to meet the needs of the population for a specific period in future. The future population and the amount of water required by the people must be estimated keeping in view the industrial and commercial growth of the area. An estimation of the future population of a town or city helps the management to decide the time and size of enhancing the level of water supply system. The problem considered in this paper is concerned with the optimal installation of additional facilities in water supply system of a rapidly growing industrial area.
Dynamic programming has been found to be a very useful tool for water supply and distribution system analysis (see [1]). In this paper dynamic programming is used to find out the optimal installation times of additional facilities and the optimal number of such facilities in a given time period. It may be observed that the problem of vehicle dispatching considered by Sharma et al. [2] has certain resemblance with the problem of water supply installations. In fact, this observation led to the idea of the solution of the problem considered in this paper.
Section snippets
Statement of the problem
In a town with a rapidly growing population, the water supply management is required to construct additional facilities from time-to-time. The additional facilities include new reservoirs to provide increased storage capacity, enlargement of various treatment units, and extension of distribution network system. As the extra facilities involve a considerable expenditure, such facilities are to be provided in steps over a given time period. The decisions for installation of additional water
Formulation of the problem
Let [t0,T] be the interval of time in which additional water supply services are to be installed. We assume that the increase in water supply system will be done in n steps.
For j=1,2,…,n, define tj as time when the jth additional facility is installed; xj the number of persons not getting service at time tj (after the jth installation); vj the number of persons being provided service at time tj (after the jth installation); uj the installed capacity of the jth installation, i.e., number of
Solution of the problem
The solution consists in finding (i) the optimal installation times of t1,t2,…,tn as well as the installed capacities u1,u2,…,un when n, the total number of installations, is given, and (ii) the optimal number of installations.
Computational aspects
The values of p(t) and x(t) at any time t, as well as the values of xj, uj, and vj, are all nonnegative integers. It will be convenient if t0 and T are also taken as integers. We divide the interval [t0,T] into equal subintervals of length h and estimate the population at times t0+h,t0+2h,…,T. The value of p(t) at any time t can be obtained by standard interpolation formulas. However, for the sake of simplicity, we may assume that p(t) is linear on each subinterval [t0+(m−1)h,t0+mh], m=1,2,…
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Cited by (1)
Container berth expansion planning with dynamic programming and fuzzy set theory
2006, 2006 IEEE International Conference on Service Operations and Logistics, and Informatics, SOLI 2006