Multi-stage scheduling for banks by mathematical programming

Despite moves toward electronic funds transfer systems, the United States banking industry must continue to cope with the paper processing requirements associated with a payments system still heavily reliant upon checks. Through the development of MICR (magnetic ink character recognition), computers have been utilized to sort documents and post customer accounts. However, a labor intensive key encoding function is required to prepare documents for processing. An attempt to eliminate the labor intensity is the recent development of optical scanning capture equipment which 'reads' printed or hand-written documents and inscribes them with MICR characters. However, the utilization of optical scanning technology requires the scheduling and coordination of five processing activities. A mathematical programming model has been developed which minimizes the combination of payroll and float costs while recognizing machine capacity constraints in the scheduling of optical capture systems. The formulation was specifically designed to respond to the bank check processing scheduling problem. However, with minor modifications, the model is directly transferable to any multi-echelon processing system where penalties are incurred when the units of output fail to meet prespecified deadlines.