DYNAMIC PROGRAMMING FOR OPTIMUM CONJUNCTIVE USE1
Authors: Coahran Gilbert F. , Butcher William S. 
Published: June 2007

ABSTRACTThe Las Vegas, Nevada area like most semi‐arid basins, was developed through exploitation of available ground‐water resources. Area growth in this large valley has occurred in a scattered and sporadic manner with development both in incorporated areas and within the County. As a result, today there exist five major water suppliers which are: a water district, three municipalities, and a large corporation, in addition to numerous small water companies and thousands of domestic wells. In the past 20 years the area has grown from a population of less than 50,000 to over 300,000 today. The bulk of the water demand for this growth has been met from the ground‐water resource and as a result the basin is being severely mined. Current extractions are over three times the estimated annual replenishment. Rapidly declining water levels are increasing the costs of water and are creating water shortages during periods of peak demand. To meet both the current and anticipated water demands, the Southern Nevada Water Supply Project is being constructed to import additional water from nearby Lake Mead.Agriculture in the area is very limited, and primarily uses reclaimed waste water for irrigation. The chief water demands in the area are thus municipal and industrial, with the former predominating.This study was designed to determine how best the Las Vegas Valley Water District, supplier of 80 percent of the domestic water, might integrate the use of the existing ground water and anticipated imported surface water. Additionally the consequences of application of certain provisions in the Nevada Water Law were examined to determine their effects on the ground‐water system and costs of water.To achieve these objectives, a dynamic programming technique was utilized. The problem as formulated consists of a single decision variable, single state variable dynamic programming algorithm evaluated over a fifty‐year planning horizon at monthly intervals. Three alternative solutions, with different ground‐water law constraints are evaluated.In all solutions certain basic operating rules regarding ground‐water pumping distribution and use of surface‐water systems are kept constant.The problem is considered as deterministic in all respects. Recharge to ground water is assumed to equal the estimated average annual replenishment evenly distributed over the year and additionally is not considered to be a function of average basin ground water potential. The only surface supply, Lake Mead, is considered to operate at near constant elevation and not be subject to shortage conditions. In light of the size of Lake Mead, the Colorado River flow and the size of Nevada's allotment, 300,000 ac ft, the latter assumption is reasonable. Demand for water is considered as a known function of time.Optimization of conjunctive use for the Water District is based on the objective function of minimizing water production costs. Costs of distributing water are considered to be constant regardless of source, and so are not included. Also, fixed costs of amortizing the pipeline project and well fields are not considered.Results of the study are presented as a series of policy traces under each of the three alternatives considered. These traces describe the ground‐water basin response under optimal operating conditions, given an estimate as to the present worth of ground‐water pumping rights, and prescribe monthly water‐procurement schedules for the operation of the Water District.