An Indian reservation irrigation project16 must decide how much water to release through the gate at the top of its main canal in each of the upcoming 4-hour periods t = 1,c, 18. Ideal canal outflows, rt , are known for each time period, and the total outflow over all 18 periods should equal or exceed the sum of these quantities.

However, period-to-period deviations may be needed to avoid flooding. The initial canal storage is 120 units, and the net effect of releases and outflows should never leave more than u units stored after any period. Within these limits, managers would like to minimize the total absolute deviation between desired demands rt and actual outflows. Formulate an LP model of this irrigation control problem using the decision variables 1t = 1,c, 182 xt ! gate release during period t st ! amount of water stored in the canal at the end of period t wt ! canal outflow during period t d1

+ ! over satisfaction of demand in period t d1

- ! undersatisfaction of demand in period t