A digital microfluidic biochip (DMFB) is an attractive technology platform for automating laboratory procedures in biochemistry. However, today's DMFBs suffer from several limitations: (i) constraints on droplet size and the inability to vary droplet volume in a fine-grained manner; (ii) the lack of integrated sensors for real-time detection; (iii) the need for special fabrication processes and reliability/yield concerns. To overcome the above problems, DMFBs based on a micro-electrode-dot-array (MEDA) architecture have recently been demonstrated. However, due to the inherent differences between today's DMFBs and MEDA, existing synthesis solutions cannot be utilized for MEDA-based biochips. We present the first biochip synthesis approach that can be used for MEDA. The proposed synthesis method targets operation scheduling, module placement, routing of droplets of various sizes, and diagonal movement of droplets in a two-dimensional array. Simulation results using benchmarks and experimental results using a fabricated MEDA biochip demonstrate the effectiveness of the proposed co-optimization technique.