We describe the development of a fully automatic and programmable microfluidic cell culture array that integrates on-chip generation of drug concentrations and pair-wise combinations with parallel culture of cells for drug candidate screening applications. The device has 64 individually addressable cell culture chambers in which cells can be cultured and exposed either sequentially or simultaneously to 64 pair-wise concentration combinations of two drugs. For sequential exposure, a simple microfluidic diffusive mixer is used to generate different concentrations of drugs from two inputs. For generation of 64 pair-wise combinations from two drug inputs, a novel time dependent variable concentration scheme is used in conjunction with the simple diffusive mixer to generate the desired combinations without the need for complex multi-layer structures or continuous medium perfusion. The generation of drug combinations and exposure to specific cell culture chambers are controlled using a LabVIEW interface capable of automatically running a multi-day drug screening experiment. Our cell array does not require continuous perfusion for keeping cells exposed to concentration gradients, minimizing the amount of drug used per experiment, and cells cultured in the chamber are not exposed to significant shear stress continuously. The utility of this platform is demonstrated for inducing loss of viability of PC3 prostate cancer cells using combinations of either doxorubicin or mitoxantrone with TRAIL (TNF-alpha Related Apoptosis Inducing Ligand) either in a sequential or simultaneous format. Our results demonstrate that the device can capture the synergy between different sensitizer drugs and TRAIL and demonstrate the potential of the microfluidic cell array for screening and optimizing combinatorial drug treatments for cancer therapy.