“…Parameters ca,g,i,r costs of consumption at node i in region r for group g in period a c_stori costs of storage at node i d_maxa,g,i maximum demand at node i for group g in period a d_mina,g,i minimum demand at node i for group g in period a d_refa,g,i known reference demand at node i for group g in period a evapa,i evaporation at node i in period a f _maxi,j maximum flow on arc(i,j) f _mini,j minimum flow on arc(i,j) ma,g,i slope of linear demand function at node i for group g in period a na,g,i prohibitive price at node i for group g in period a preca,i precipitation at node i in period a p_refg,i known reference price at node i for group g returng return flow factor for group g stor_maxi maximum storage capacity at node i ηg price elasticity of demand for group g Variables da,g,i,r demand at node i in region r for group g in period a d_areaa,g,i,r area below demand function at node i in region r for group g in period a f lowa,i,j flow on arc(i,j) in period a stor_ina,i,r incoming storage controlled by region r at node i in period a stor_outa,i,r outgoing storage controlled by region r at node i in period a z welfare VIII 9 APPENDIX Kavvas, et al (2011), Kolars (1994, Sener (2007), and Shahin(1989).…”