The Problem of Scheduling a Single Machine by Considering Variable Priorities and Release Times

In recent years, with the competitive environment, the importance of on time delivery and customer satisfaction is crucial. The objective functions, such as minimizing the number of tardy jobs, have attracted an increasing attention. This study aims to schedule the operations by minimizing the number of weighted tardy jobs in two modes of delay with a financial penalty and delay with lost sales. In this paper, the start time of operation is a decision variable. Furthermore, the operations can be only pursued one time, but the time of their availability is considered uncertain. In addition, the completion time of each operation is variable in two intervals; At the beginning of the interval, the delivery time of the task is considered without any penalty while at the end of the interval, the delivery time is determined with a penalty. As another innovation, this research examines the priority of variables so that by approaching the due dates and deadlines as well as the degree of customer urgency. It is updated based on some factors including the weight of the product order and the remaining processing time. In this paper, first the mathematical problem formulation is established and then a heuristic algorithm is used to solve the proposed model and find near-optimal solutions. To accomplish that, 2700 sample problems are generated and each is solved by GAMS software and the mentioned heuristic algorithm. The obtained results show the satisfactory performance of the heuristic algorithm in obtaining the near-optimal solution in a reasonable time.