The last two decades have seen many efficient algorithms and architectures for the design of low-complexity bit-parallel Multiple Constant Multiplications (MCM) operation, that dominates the complexity of Digital Signal Processing (DSP) systems. On the other hand, digit-serial architectures offer alternative low-complexity designs, since digit-serial operators occupy less area and are independent of the data wordlength. This paper introduces the problem of designing a digit-serial MCM operation with minimal area at gate-level and presents the exact formalization of the area optimization problem as a 0-1 Integer Linear Programming (ILP) problem. Experimental results show the efficiency of the proposed algorithm and digit- serial MCM designs in terms of area at gate-level.