Mobile Cable-Driven Parallel Robots (MCDPRs) are special type of Reconfigurable Cable Driven Parallel Robots (RCD-PRs) with the ability of undergoing an autonomous change in their geometric architecture. MCDPRs consists of a classical Cable-Driven Parallel Robot (CDPR) carried by multiple Mobile Bases (MBs). Generally MCDPRs are kinematically redundant due to the additional mobilities generated by the motion of the MBs. As a consequence, this paper introduces a methodology that aims to determine the best kinematic redundancy scheme of Planar MCDPRs (PMCDPRs) with one degree of kinematic redundancy for pick-and-place operations. This paper also discusses the Static Equilibrium (SE) constraints of the PMCDPR MBs that are needed to be respected during the task. A case study of a PMCDPR with two MBs, four cables and a three degree-of-freedom (DoF) Moving Platform (MP) is considered.