Development and application of a multiperiod linear programming model for water management in the Willcox Basin, Arizona

Water for irrigation in the Willcox Basin, Arizona, is scarce and the water table is declining. Water pumping costs are increasing as a result of such a decline;The objectives of this study are: (1) to develop a multiperiod linear programming model; and (2) to apply the model to data from the area of study for the purposes of (a) providing a basis for allocating water in the area of study at the highest present value net returns over time, and (b) appraising selected policy options as means for achieving the above water allocation objective. The model consists of linear programming to optimize annual water pumping and of fortran to accomplish revisions and adjustments to accommodate the variables which change over time. The study period covers forty years starting from 1981 and ending in 2021 with optimum solutions at five year intervals;Four scenarios were developed as an inherent part of the analysis, consisting of (1) no-change scenario, meaning that price, cost, and yield remained constant over time at their 1981 levels of value; (2) cost-increase scenario, meaning that price and yield remained constant over time and cost increased by 3 percent annually; (3) price-, cost- and yield-increase scenario, meaning price, cost, and yield increased by an annual rate of 2, 3, and .7 percent, respectively; and (4) price- and yield-increase scenario, meaning that price and yield increased by an annual rate of 2 and .7 percent, respectively;Because the increase in pumping costs from 47.10 in 1981 to 97.34 in 2021, it was concluded that there would be little danger of exhausting the water supply for irrigation by 2021 but public policy may have to decide limitations on pumping each year within the range which extends from pumping only annual recharge (51,000 acre-feet of water) to unrestricted pumping. That is, public policy may have to provide choices between lower net returns and pumping limits and higher net returns and no pumping limits. If public interest favors present generations, its decision would be close to the unlimited pumping level. But if public interest favors future generations, the decision would be to limit pumping to the appropriate annual recharge. Taxes, quotas, and allotments would help in achieving the latter choice.