“…Where umb1 i,t , umb2 i,t , umb3 p,t , umb4 p,t , umb5 p,t , umb6 are dual variables corresponding to original mass-balance constraints (11), (12), (13), (14), (15), and (10), respectively. Similarly, vcp1 i,p,t , vcp2 p,m,t , vcp3 p,t , vcp4 m,t , vcp5 t are dual variables corresponding to original capacity constraints (16), (17), (18), (19), and (20), respectively.…”