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The wafer probing scheduling problem (WPSP) is a variation of the parallel-machine problem, which carries with the objective to minimize the total workload to enhance the utilization rate of machine capacity. However, to minimize the maximum completion time for the wafer probing scheduling problem (WPSP) is very important for equally utilizing the capacity of parallel-machine, while satisfying the requirements of product types, product family, sequence dependent setup time, product-type dependent processing time, due dates of jobs, and capacities of machines. To solve such a complicated problem efficiently and effectively, we adopt the hybrid genetic algorithm approach, which generates initial population with the insertion and savings algorithms for WPSP and provide a new crossover operator to generate better solutions. Considering the disturbance of due dates of jobs in scheduling, we design a new crossover which makes each machine keep the critical sub-schedule in the generation of offspring. The performance of the proposed hybrid genetic algorithm is evaluated by two real-world problems and the solution quality of the proposed approach is analyzed under five levels of mutation rates and four levels of number of generations. Computational results reveal that the hybrid genetic algorithm can efficiently solve the considered problem and the reduction of makespan is related to the mutation rates and the number of generations.

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This paper proposed a quantity-based integrated model to coordinate inventory replenishment and outbound shipment consolidation for vendor-managed inventory system. An analytical model is developed to derive the optimum replenishment quantity and economic shipment quantity simultaneously. The quantity-based integrated model is a more effective integration of the different logistical activities. It results in a total cost less than that of the time-based integrated model. In the vendor-managed inventory (VMI) system we developed, a supplier can simultaneously reduce the logistical costs and provide a high customer service level. This result can help a supplier to obtain substantial benefits from the integrated model.