This paper proposes a dynamic programming approach targeted to solve a natural resource problem of water storage management for irrigation in an environmentally and socially sustainable way. The problem we examine in our formulation, which deals with the control of water storage in tanks, incorporates assumptions that are milder compared to those previously discussed in the literature concerning similar approaches. Specifically, we consider a time periodic optimal control problem whose performance functional to be maximized merely satisfies a contraction assumption (in the sense of Boyd and Wong) weaker than the one usually considered in the pertinent literature. By using an appropriate fixed point theorem, a time periodic value function can be constructed to enable the definition of optimal feedback control strategies. After showing the insufficiency of Banach contraction frameworks, and proving the underlying auxiliary mathematical results, we show our main result under conditions that are weaker than the previous related ones. Simulation results illustrate the performance of our approach.