The shipowner is usually bound by the master’s signature to a bill of lading, unless the master, in signing the bill of lading, exceeds his authority.
Per Kerr LJ in Navigation Company Panama SA v Anonima Petroli Italiana SpA (The Olympic Brilliance)  2 Lloyd’s Rep 205, at p.209:
… the ascertainment of any short delivery after a normal voyage is notoriously difficult in the bulk carriage of oil. It depends on complex calculations comparing the quantity apparently loaded with the quantity apparently discharged, with some additional allowances for undischargeable quantities of sediment and for oil remaining in the ship’s lines, and also possibly for apparent losses due to evaporation. At the end of the day, as in the present case, there may remain an apparent, but inexplicable, short delivery.