The wafer probing scheduling problem (WPSP) is a practical generalization of the classical parallel-machine scheduling problem, which has many real-world applications, particularly, in the integrated circuit (IC) manufacturing industry. In this paper, a case study on the WPSP is presented, which is taken from a wafer probing shop floor in an IC manufacturing factory. For the WPSP case investigated, the jobs are clustered by their product types, which are processed on groups of identical parallel machines and must be completed before the due dates. The job processing time depends on the product type, and the machine setup time is sequentially dependent on the orders of jobs processed. The objective in this case is to seek a probing job schedule with minimum total machine workload. Since the WPSP case investigated involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequentially dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. The WPSP is formulated as an integer programming problem and the problem solved using the powerful CPLEX with effective implementation strategies. An efficient solution procedure to solve the WPSP near-optimally is proposed.