Single CNC machine scheduling with controllable processing times and multiple due dates

In order to reflect the characteristics of a modern manufacturing environment, elements of customer satisfaction and the competition between firms should be considered simultaneously. Manufacturers should be careful on deciding which orders to accept, and should pay attention on the weighted earliness and tardiness penalties they will be due, while considering the priorities of the customers. Customers that want to minimize the risk of deviation from a delivery date, offer multiple due dates to the manufacturer, each coming with a distinct price for the order that is decreasing as the date gets later. Manufacturers that use flexible manufacturing systems have the capability to control the processing times of jobs, by changing the machining conditions at the expense of tooling costs. In this study, we consider the problem of scheduling a set of jobs on a single CNC machine, while maximizing the total profit that is composed of sum of prices of scheduled jobs less the sum of total weighted earliness/tardiness cost, tooling cost and machining cost. This problem is NP-hard since the total weighted tardiness problem is NP-hard alone. Furthermore, because of the nature of the tooling cost, the problem is nonlinear. We propose a number of ranking rules and scheduling algorithms. Using these rules and algorithms, we construct a single-pass heuristic algorithm that determines the processing times for each job and schedules them simultaneously, to maximize the overall profit.