Use of Goal Programming and Integer Programming for Water Quality Management—A Case Study of Gaza Strip

View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institutional Repository of the Islamic University of Gaza European Journal of Operational Research 174 (2006) 1991–1998 www.elsevier.com/locate/ejor O.R. Applications Use of goal programming and integer programming for water quality management—A case study of Gaza Strip Salah R. Agha * School of Industrial Engineering, P.O. Box 108, Islamic University-Gaza, Gaza Strip, Israel Received 13 September 2004; accepted 17 June 2005 Available online 24 August 2005 Abstract This paper describes a project dealing with achieving an optimum mix of water from different underground wells, each having different amounts of nitrates and chlorides. The amounts of chlorides and nitrates in each of the wells may be higher or lower than the World Health Organization (WHO) standards. Therefore, the optimum mix would be the one that meets WHO standard which is 250 mg/l for chlorides and 50 mg/l for nitrates. A goal programming model was developed to identify the combination of wells along with the amounts of water from each well that upon mixing would result in minimizing the deviation of the amounts of chlorides and nitrates from the standards set by WHO. The output of the goal programming model along with the coordinates of the wells identified above was then used for a second model that determines the locations of the mixing points ‘‘reservoirs’’ in such a way that minimizes the total weighted distances from the corresponding wells. Finally, an easy-to-use pumping schedule was developed using integer programming. Results indicate that for the case study, there exist several optima which make it easier for the decision maker to consider other intangible factors if there are any. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Goal programming; Water quality; Nitrates; Chlorides; Gaza 1. Introduction area is around 365 km2 and has a population around 1.1 million. In general, Gaza Strip is Gaza Strip is a narrow strip along the Mediter- known to have serious water problems ranging ranean sea as shown in Fig. 1. It is around 40 km from quality problems to expected shortage of long while its width varies from 6.4 to 9.6 km. Its water supplies not only for agricultural and industrial usage but also for drinking. It is to be noted here that groundwater is the only significant * Tel.: +972 8 2067577; fax: +972 8 2066477. source for water to meet the demand in Gaza E-mail address: [email protected] Strip. The common two problems with drinking 0377-2217/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.06.007 1992 S.R. Agha / European Journal of Operational Research 174 (2006) 1991–1998 Fig. 1. Location of Gaza Strip. water quality in Gaza Strip are the presence of of blue baby syndrome (methaemoglobinaemia) high amounts of both nitrates and chlorides. These [8]. two problems are mainly attributed to waste Moreover, high nitrates may have carcinogenic water, agricultural fertilizers, pesticides and indus- effects for adults [1]. While the presence of chlo- trial pollutants. These pollutants may directly pen- rides may not be as harmful as that of nitrates, etrate to the groundwater reservoir through pores the salinity it causes, makes the water unaccept- in rocks or indirectly by decomposition which in- able for drinking. Therefore, low level of chlorides creases the salts in the wells and thus deteriorates is critical for customer satisfaction. In general, water quality. when people in Gaza talk about ‘‘bad water’’, they In some wells, the level of nitrates in drinking mean high salinity water. Since the levels of ni- water may exceed 300 mg/l which is 6 times trates and chlorides are high in some wells and that allowed by (World Health Organization) low in others, the objective of this research is to WHO, while the level of chlorides may exceed achieve an optimum water mixing strategy in such the WHO standards by 4–5 times. According to a way that the amount of chlorides and nitrates are the literature, nitrates level in excess of 150 mg/l consistent with those approved by WHO. In other poses an extreme risk to infantsÕ health in the form words, mixing certain proportions of water from S.R. Agha / European Journal of Operational Research 174 (2006) 1991–1998 1993 certain wells with the result that the obtained mix- 2. Goal programming formulation ture satisfies the WHO standards for both chlorides and nitrates, wells capacity, and customers Assuming that we have ‘‘n’’ wells, the amount demand at the least cost. Using water mixing of chlorides in the ith well is ‘‘CLi’’ mg/l and the would outperform desalination which is known amount of nitrates is ‘‘Ni’’ mg/l. Moreover, the 3 to reject up to 60% of the input water amount as ith well can discharge the amount of Si (m /year) brine water and this would result in serious at a given operational level. Since the levels of ni- environmental problems as cited by [2]. Another trates and chlorides are high in some wells and low draw back of desalination is the high costs in others, it is known that mixing certain propor- involved. tions from certain wells will achieve the required Most of the research performed in this area is of objective. It is also assumed that there are ‘‘m’’ res- a qualitative nature or at best descriptive and still ervoirs (destinations) each of which can accommo- tends to be more of a data-gathering type of re- date a certain amount of water that satisfies the search. This research is an attempt to quantify demand of the specific region. Let Dj represent and model the data that is scattered in the litera- the demand required for reservoir ‘‘j’’. Moreover, 3 ture to come up with tangible, economically feasi- Xij is the amount of water (m /year) discharged ble and easily applicable solutions to some of the from well ‘‘i’’ to reservoir ‘‘j’’. The maximum al- problems related to drinking water quality in Gaza lowed amount of chlorides per liter (WHO stan- city. Some studies have focused only on chlorides dard) is CLmax, while the maximum allowed alone without considering the nitrates. Reports amount of nitrates according to WHO standards of harmful effects for human health have been re- is Nmax. ported only for nitrates. Therefore, reducing ni- Therefore, the constraints can be grouped as trates level below the specifications of WHO may follows: yield ‘‘healthy’’ water. On the other hand, high chlorides level may render the water undrinkable • Well capacity constraints due to its salinity. In other words, focusing on Xj¼m chlorides only would not solve the problem since X 6 S ði ¼ 1; ...; nÞ. ð1Þ people would rather drink non-salty water than ij i j¼1 water with high level of nitrates which is proved to be dangerous in terms of health. This research • Reservoirs capacity and demand constraints considers both nitrates and chlorides using goal Xi¼n programming, which provides a way of striving to- X ij P Dj ðj ¼ 1; ...; mÞ. ð2Þ ward more than one objective function simulta- i¼1 neously. It seeks to establish a specific numeric Chlorides balance constraints goal for each of the objectives, and then seeks • for a solution that minimizes the weighted sum Xi¼n Xi¼n þ À 6 of deviations of objective functions from their cor- X ijCLi À X ijCLmax À Y jCL þ Y jCL 0 responding goals [4]. The goal programming ap- i¼1 i¼1 proach is used to seek the amounts of waters ðj ¼ 1; ...; mÞ. ð3Þ from different wells to be mixed in such a way that the deviations from the objective functions are • Nitrates balance constraints minimized. The use of goal programming or multi- Xi¼n Xi¼n objective programming is very common when þ À X ijNi À X ijNmax À Y jN þ Y jN dealing with environmental issues where there are i¼1 i¼1 normally more than one objective. The following 6 0 ðj ¼ 1; ...; mÞ. ð4Þ section shows the formulation of the problem as a goal programming problem. All variables are >= 0, 1994 S.R. Agha / European Journal of Operational Research 174 (2006) 1991–1998 þ where Y jCL is the excess of chlorides from the reasonable assumption given the topography of À WHO standard in reservoir ‘‘j’’; Y jCL is the amount Gaza city. by which chlorides in reservoir ‘‘j’’ is below the Xn Xn þ WHO standard; Y jN is the excess of nitrates from Minf ðxÞ¼ vjkdðX j; X kÞ À j¼1 k¼1 the WHO standard in reservoir ‘‘j’’; Y jN is the amount by which nitrates in reservoir ‘‘j’’ is below Xn Xm the WHO standard. þ wjidðX j; P kÞ; Finally the objective function can be written as j¼1 i¼1 follows: where Xj =(xj, yj) location of new facility j, j =1,2,..., n; P =(a , b ) location of existing facil- Xj¼m Xj¼m i i þ þ ity i, i =1,2,..., m; Vjk cost per unit distance tra- Minz1 ¼ Y jN þ Y jCL. j¼1 j¼1 vel between new facilities j and k; Wjk cost per unit distance travel between j and i; d(Xj, Xk) distance The set of constraints in Eq. (1) guarantees that between j and k; d(Xj, Pk) distance between j and the total amount of the discharged water from cer- i with rectilinear distance tain wells does not exceed the capacity these wells.

Load more