A LINEAR ANALYSIS OF AN URBAN WATER SUPPLY SYSTEM1

The use of linear programming as a planning tool for determining the optimal long-range development of an urban water supply system was explored. A stochastic trace of water demand was synthesized and used as an input to the model. This permitted evaluating the feasibility of imposing demand restrictions as an effective cost reduction mechanism. The City of Lincoln, Nebraska, was used as the urban model. The fundamental problem was to allocate limited water supplies from several sources to an urban load center to minimize costs and comply with system constraints. The study period covered twenty years, and findings indicate the planning direction for stage development during this period. Sensitivity analyses were performed on cost coefficients and demands. Thirteen sources were included in the initial computations. Conclusions were that linear programming and generated demand traces are useful tools for both short- and long-term urban water supply planning. Lowering peak demands results in long-range development of fewer sources of supply and more economic and efficient use of the supplies developed.     

IRRIGATION WATER DELIVERY SYSTEM OPERATION VIA AGGREGATE STATE DYNAMIC PROGRAMMING1

ABSTRACT: A modified dynamic programming (DP) approach that is called aggregate state dynamic programming (ASDP) is presented to optimally operate irrigation water delivery systems. ASDP can be applied to multiple reservoir systems without encountering dimensionality problems. In addition, the random nature of water supply and consumptive crop demands can be incorporated into the technique. A case study is presented to display the application of ASDP. Using a sum-of-squared shortages objective, ASDP out performs a traditional separation technique and approaches the theoretical (ideal) optimum. Problem settings that are conducive to the use of ASDP and limitations of the technique are presented.     

THE IMPACT OF WATER QUALITY OBJECTIVES ON URBAN WATER SUPPLY PLANNING1

ABSTRACT: Optimal policies for supplying rapidly expanding urban centers with additional water supplies are shown to be dependent on water quality goals for the urban effluent. As effluents are required to meet increasingly stringent standards, the unit costs associated with adding capacity to existing wastewater treatment systems to renovate some waters for reuse are shown to substantially decrease. A nonlinear elimination algorithm is developed to delineate optimal policies. A model employing the technique was applied to the wastewater treatment system of a typical urban system and the water quality objectives varied. A comparison of costs with and without various levels of reuse were made and unit costs of reused water under these conditions determined.     

COMPARISON OF RESERVOIR LINEAR OPERATION RULES USING LINEAR AND DYNAMIC PROGRAMMING1

ABSTRACT: Mathematical optimization techniques are used to study the operation and design of a single, multi-purpose reservoir system. Optimal monthly release policies are derived for Hoover Reservoir, located in Central Ohio, using chance-constrained linear programming and dynamic programming-regression methodologies. Important characteristics of the former approach are derived, discussed, and graphically illustrated using Hoover Reservoir as a case example. Simulation procedures are used to examine and compare the overall performance of the optimal monthly reservoir release policies derived under the two approaches. Results indicate that, for the mean detention time and the corresponding safe yield target water supply release under existing design of Hoover Reservoir, the dynamic programming policies produce lower average annual losses (as defined by a two-sided quadratic loss function) while achieving at least as high reliability levels when compared to policies derived under the chance-constrained linear programming method. In making this comparison, the reservoir release policies, although not identical, are assumed to be linear. This restricted form of the release policy is necessary to make the chance-constrained programming method mathematically tractable.     

STOCHASTIC DYNAMIC PROGRAMMING FOR OPTIMUM RESERVOIR OPERATION1

ABSTRACT. For a multipurpose single reservoir a deterministic optimal operating policy can be readily devised by the dynamic programming method. However, this method can only be applied to sets of deterministic stream flows as might be used repetitively in a Monte Carlo study or possibly in a historical study. This paper reports a study in which an optimal operating policy for a multipurpose reservoir was determined, where the optimal operating policy is stated in terms of the state of the reservoir indicated by the storage volume and the river flow in the preceding month and uses a stochastic dynamic programming approach. Such a policy could be implemented in real time operation on a monthly basis or it could be used in a design study. As contrasted with deterministic dynamic programming, this method avoids the artificiality of using a single set of stream flows. The data for this study are the conditional probabilities of the stream flow in successive months, the physical features of the reservoir in question, and the return functions and constraints under which the system operates.     

MULTICRITERIA PROGRAMMING OF WATER SUPPLY SYSTEMS FOR RURAL AREAS1

ABSTRACT: The aim of this paper is to present a multicriteria methodology for decision aid at the stage of programming a water supply system (WSS) for a rural area. The programming stage is an intermediate one between planning and designing water supply facilities, and can be decomposed into two problems: (a) setting up a priority order of water users, taking into account socio-economic criteria; and (b) choosing the best technical variant of the WSS. Among the criteria considered for the latter problem, there is a criterion of distance between the socio-economic priorities of users and the precedence orders of users according to the technical programming, which plays a coordinating role between problems (a) and (b). All steps of the presented methodology are illustrated by a real case study.     

WATER SUPPLY AND URBAN GROWTH PLANNING: A PARTNERSHIP1

ABSTRACT As urban expansion outstrips water supplies, the usual solution is to build pipelines to bring in water from sources farther afield. Such water supplies may act as either a leader of urban development or as a follower. In either case, this engineering approach to the provision of water has fostered less than optimal utilization of regional water and land resources for urban growth. More efficient utilization of these resources is achieved when water supply development and urban growth planning are conjoint activities. Water supply planners and land use planners, working together, are able to generate and evaluate the full range of urban development options, including water demand management through conservation. Preferred regional growth plans are achieved using the best mix of water supply and urban growth. The result is a reduced rate of water supply development and a reduction of urban expansion on prime lands. This partnership approach is demonstrated for the Calgary Region under two levels of water conservation.     

A STOCHASTIC DYNAMIC PROGRAMMING BASED APPROACH TO THE OPERATION OF A MULTI-RESERVOIR SYSTEM1

ABSTRACT: An heuristic iterative technique based upon stochastic dynamic programming is presented for the analysis of the operation of a three reservoir ‘Y’ shaped hydroelectric system. The technique is initiated using historical inflow data for the downstream reservoir. At each iteration the optimal policies for the downstream hydroelectric generating unit are used to provide relative weightings or targets for operation of upstream reservoirs. New input inflows to the downstream reservoir are then obtained by running the historical streamflow record through the optimal policies for the upstream reservoirs. These flows are then used to develop a new operating policy for the downstream reservoir and hence new targets for the upstream reservoirs. The process is continued until the operating policies for each reservoir provide the same overall system benefit for two successive iterations. Results obtained from the procedure are compared to the results obtained by historical operation of the system. The procedure is shown to develop operating policies which give benefits which are as close to the historical benefits as can be expected given the choice of the number of storage state variables.     

EFFICIENT MANAGEMENT POLICIES FOR URBAN WATER SUPPLY1

ABSTRACT .This paper attempts to spell out the difficult conditions faced by urban water supply managers in achieving overall efficiency. Based upon these conditions, and changes that are likely in the next decade, it then tries to suggest strategies that would lead to even higher levels of efficiency in the future. A blending of political and economic concepts is used to make what is hoped to be a realistic analysis. What do we mean by “efficient”? The usual welfare economics definition is attainable only under a very special and highly unrealistic set of institutional arrangements. As soon as we delegate responsibility to a specialized agency we provide the opportunity, indeed we make it imperative that, in a social sense, a sub-optimization will take place. From the specifics of the indictment of this sub-optimization we can learn something about the opportunities for more efficient management in the future. In general there is an under-exploitation of multiple-function, multiple-objective opportunities. The pressures for sub-optimization hinge very directly on the sources of support and opposition to the water supply agency. A change requires the creation of a broader political base. The search for regional solutions is largely a political problem, and probably the development of flexible, responsive regional agency, so long sought, is still the answer.     

OPTIMAL ALLOCATION OF ARTIFICIAL AERATION ALONG A POLLUTED STREAM USING DYNAMIC PROGRAMMING1

ABSTRACT: When a series of aerators are used to raise the level of dissolved oxygen in a polluted stream through instream artificial aeration augmentation, the system is governed by the basic dissolved oxygen mass balance equation with the existence of artificial aeration as its boundary conditions. A mathematical model is formulated for the optimization of the allocation of aeration capacity to each of the series of aerators subject to a limitation on total available aeration capacity. The objective function is the minimization of the sum of the squares of the aeration costs and the costs incurred by damaging or unnecessarily improving the system. The original constrained allocation problem is simplified by converting it to an unconstrained one via the use of Lagrange multiplier. A discretized dynamic programming algorithm is formulated for finding the optimal allocation policy. A typical optimal aeration capacity allocation policy and its corresponding dissolved oxygen sag profile for the illustrated numerical example is presented, and the relationship between the total available aeration capacity and Lagrange multiplier is also developed treating weighting factors as parameters.     

APPLICATION OF A SINGLE RESERVOIR OPERATION POLICY TO A RAIN WATER CISTERN SYSTEM1

The operation policy for a single reservoir is applied to a rain water cistern system because the functions of a cistern are similar to a simple single reservoir. Since the cistern is a closed system, water loss is negligible. In this study, a dynamic programming analysis has been made to study the effects of the probable weekly rainfall and the water storage in the cistern towards the water consumption policy. The result of this study indicates that the water consumption rate should be adjusted into a lower rate when the water storage in the cistern is low and/or when the expected probable weekly rainfall is low if the owner of the cistern does not want to risk the chance of an empty cistern. The demand for a reliable method for forecasting weekly rainfall is evident in this study.     

WATER SUPPLY IMPACTS OF NUCLEAR FALL1

ABSTRACT: “Nuclear winter,” more properly called “nuclear fall,” could be caused by injection of large amounts of dust into the atmosphere. Besides causing a decrease in temperature, it could be accompanied by “nuclear drought,” a catastrophic decrease in precipitation. Dry land agriculture would then be impossible, and municipal, industrial, and irrigation water supplies would be diminished. It has been argued that nuclear winter/fall poses a much greater threat to human survival than do fall out or the direct impacts of a conflict. However, this does not appear to be true, at least for the U.S. Even under the unprecedented drought that could result from nuclear fall, water supplies would be available for many essential activities. For the most part, ground water supplies would be relatively invulnerable to nuclear drought, and adequate surface supplies would be available for potable uses. This assumes that conveyance facilities and power supplies survive a conflict largely intact or can be repaired.     

THE OPTIMALITY OF CAPACITY SHARING IN STOCHASTIC DYNAMIC PROGRAMMING PROBLEMS OF SHARED RESERVOIR OPERATION1

ABSTRACT: This paper is concerned with finding an optimal allocation of water entitlements for each of two users of water who share a reservoir. Two instruments of allocation are considered. The first, release sharing, involves sharing the releases from the reservoir; the second, capacity sharing, is concerned with allocating to each user of water a share of inflows, reservoir capacity and leakage and evaporation losses. Stochastic dynamic programming problems of reservoir operation under each type of sharing arrangement are formulated. It is shown that the maximum discounted expected profit from reservoir operation over the life of the storage using capacity sharing is at least as large as that obtained using release sharing and that release sharing is not Pareto efficient.     

IDENTIFICATION OF MONTHLY TRENDS IN URBAN WATER USE1

ABSTRACT: Monthly water use for the period 1960–1984 for the Columbus, Ohio, metropolitan area is analyzed to identify differential monthly trends in growth of water use. By associating water use activities with the identified trend months, inferences may be made as to the possible underlying causes of the observed trend in overall water use. Three methods were found useful in determining monthly trends: 1) regression analysis on the monthly percentage of annual use, 2) regression analysis on the monthly water use data itself, and 3) analysis of the slope of the monthly water use regression line. Agreement between the three methods is strong, but each provides some insight not found in the others. All three should be used in drawing final conclusions. For the case study, usage in the Winter months January-April has grown considerably relative to the other months, while the Summer-Fall months of June, August, September, and October show a relative decline. A possible explanation for the trend is aging of the distribution system, with consequent general leakage and increased water main breakage caused by freeze/thaw conditions. More research needs to be carried out linking water use activities to particular months or groups of months.     

MUNICIPAL WATER SUPPLY RESTRICTIONS AS URBAN GROWTH CONSTRAINTS1

ABSTRACT: Municipal water supply restrictions and/or conservation policies are widely believed to affect urban growth, at least in Western states. An analysis of this issue, drawing upon a wide array of empirical water use research, casts doubt upon the presumed connection. Water availability seems likely to have little effect upon the amenities which draw newcomers to Western cities. It also seems to have little effect upon the locational decisions of industries which affect growth by creating new jobs. Consequently, there is little reason to oppose municipal water restrictions as prejudicial to urban growth or to favor such restrictions in the hope of constraining growth.     

NETWORK MODEL FOR DECISIONSUPPORT IN MUNICIPAL RAW WATER SUPPLY1

ABSTRACT: A water supply network optimization model called MODSIM3 is presented as a decision-support tool for aiding city staff in determining how best to utilize and exchange existing and potential water supplies with other users in a river basin. The model is applied to the City of Fort Collins, Colorado, water supply system as a means of determining optimum ways the City can utilize direct flow rights, storage rights, and exchangeable waters from various sources. Results clearly confirm both the benefits of the use of exchanges and the value of MODSIM3 as a water supply planning and management tool.     

ASSESSMENT ANALYSIS FOR WATER SUPPLY ALTERNATIVES1

ABSTRACT Providing adequate water supplies of good quality is becoming a serious problem in many areas of the United States. Some of the alternatives proposed for meeting the growing shortage of clean-water or cheap-water are reallocation, reuse, and importation. This paper outlines a methodology to assess all of these water supply alternatives by examining the amount and time-staging for development of water sources. In conceptualizing the problem, sources of supply are classified in three categories: primary or base supplies, secondary or effluent supplies, and supplementary or imported supplies. A model of the water system is formulated as a “transportation problem” in linear programming depicting the possible sources of supply which can be used to satisfy the requirements of various water users. The optimizing objective in the model is to minimize the cost of water under various assumptions for operating the system. A case study of the Salt Lake Qty, Utah, area is used to illustrate the application of the model in obtaining optimal water supply allocations for projected future demands. Assessment of alternatives in the study include redistribution of supplies, time-staging of supplies and related treatment facilities, and sensitivity of allocations to changes in costs.     

COST MINIMIZATION OF NUTRIENT REDUCTION IN WATERSHED MANAGEMENT USING LINEAR PROGRAMMING1

ABSTRACT: Linear programming is applied to identify the least cost strategy for reaching politically specified phosphorus and total suspended solids reduction targets for the Fox-Wolf river basin in Northeast Wisconsin. The programming model uses data collected on annualized unit reduction costs associated with five categories of sources of phosphorus and total suspended solids discharge in each of the 41 sub-watersheds in the basin to determine the least cost management strategy. Results indicate that: (1) cost-effective nutrient reduction requires careful selection of geographic areas and source categories to address throughout the watershed; (2) agricultural sources are the most cost-effective to address in the basin; and (3) care should be exercised in setting nutrient reduction targets, given that there are likely to be significantly increasing marginal costs of nutrient reduction; the model predicts that lowering the most restrictive target by 33 percent would cut reduction expenditures by about 75 percent. Policy implications of the model include support for the investigation and potential development of institutional arrangements that enable cost-effective nutrient reduction activities to occur, such as the creation of an agency with authority over a given watershed, coordinated watershed management activities, or nutrient trading programs.     

OPTIMAL CAPACITIES OF WATER SUPPLY RESERVOIRS IN SERIES AND PARALLEL1

ABSTRACT: The planning of water supply reservoirs has traditionally been based on the Rippl or sequent peak analysis which applies to the design of a single reservoir. This paper incorporates the sequent peak method as the central feature in establishing a procedure for determining the sizes of several potential reservoirs located in a system of one or more rivers. Separate algorithms are developed for sites on parallel streams and for sites on the same stream. In both cases the approach is to find the combination of reservoirs which can satisfy a given constant monthly demand at a minimum total construction cost. It is shown that both problems can be cast in the form of a dynamic programming problem. A more complex system is then a combination of reservoirs in parallel and in series. An extension is given if the monthly demand is not constant but each reservoir satisfies a constant fraction of the monthly demand.     

PRACTICAL IMPLICATIONS IN THE USE OF STOCHASTIC DYNAMIC PROGRAMMING FOR RESERVOIR OPERATION1

ABSTRACT: A stochastic dynamic programming model is applied to a small hydroelectric system. The variation in number of stage iterations and the computer time required to reach steady state conditions with changes in the number of storage states is investigated. The increase in computer time required to develop the storage probability distributions with increase in the number of storage states is reviewed. It is found that for an average of seven inflow states, the largest number of storage states for which it is computationally feasible to develop the storage probability distributions is nine. It is shown that use of the dynamic program results based on a small number of storage states results in unrealistically skewed storage probability distributions. These skewed distributions are attributed to “trapping” states at the low end of the storage range.