In order to investigate more realistic group scheduling problems with position-dependent effects,the model of general position-dependent group scheduling is proposed,where the actual group setup times and actual processing times are described by general functions of the normal group setup time and position in the sequence.These general functions are not assumed to have specific function structures,and are not restricted to be monotone.By mathematical analysis and proof,each considered problem is decomposed into a group scheduling process and a job scheduling process,and each scheduling process is transferred into the classic assignment problem or the classic single-machine sequence problem,and then the computational complexity to solve the considered problem is analyzed.Analysis results show that,even with general position-dependent job processing times,both the single machine makespan minimization group scheduling problems and the parallel-machine total load minimization group scheduling problems remain polynomially solvable.
Based on the assumption that the customer is time and price sensitive and price is a piecewise function of the delivery time, a service delivery time guarantee decision model is proposed, and the existence of the optimal service delivery time guarantee L^＊ is proved. Furthermore, the impact of the correlation parameters on the optimal L^＊ is analyzed. It is revealed that if the optimal L^＊ is smaller than the industry level L0, the service provider with low cost should quote a shorter delivery time, and the service provider should increase the delivery time guarantee under the conditions of the decrease in customer time sensitivity or the increase in the difference of the customer reservation payment. When L^＊ 〉 L0, the service provider should quote a longer delivery time guarantee and should increase the delivery time guarantee and reduce the price under the conditions of the increase in the customer price sensitivity or the decrease in the mean customer reservation payment.
