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A new customer order scheduling problem on a single-machine with job setup times
(2014) Akkocaoğlu Çatmakaş, Hale
In this study, we consider a relatively new class of the customer order scheduling (COS) problem where each order consists of one or more individual jobs. All jobs in the same customer order are processed successively and delivered at the same time to the customer. Thus, the completion time of the last job processed in each customer order defines the completion time of the order. A sequence independent setup is required before the processing of each job in a customer order. However, no setup is necessary before the processing of the first job of a customer order if this first job is the same as the last job of the immediately preceding customer order. We investigate the single-machine problem for two cases in which the makespan, which is the time to complete all customer orders, is minimized in the first case while the total completion time, which is the sum of the completion time of the orders, is minimized in the second case. For some special cases of both problems, we derive the properties of the optimal solution, which can be obtained by priority rules. We show that the makespan problem is polynomially solvable. For the total completion time problem, we develop a mixed integer programming model capable of solving small-sized problem instances optimally and propose a constructive heuristic algorithm that obtains optimal and near-optimal solutions for medium and large sized problem instances. Computational experiments are done to evaluate the performance of our solution approaches in terms of both quality and time. The results show that the mixed integer linear programming model does not seem to be a useful alternative, especially for large-sized problem instances. However, the proposed heuristic algorithms find near-optimal solutions in very short time
Unrelated parallel machines scheduling under machine availability and eligibility constraints
(2012) Kurt, Atıl
In the literature of the parallel machines scheduling, it is generally assumed that all machines are continuously available for processing jobs and each job can be processed by any machine. However, these assumptions become unrealistic in some industrial environments. In this study, we consider the problem of scheduling n independent jobs on m unrelated parallel machines subject to machine availability and eligibility constraints, given the maximum continuous working time before the maintenance of each machine and the maintenance time. Our objective is to minimize the makespan, which is the time to complete the processing of all jobs. We consider both resumable and non-resumable jobs, and develop mathematical models and heuristic algorithm that obtain exact and near-optimal solutions, respectively, for both cases with multiple machine unavailability periods. Computational experiments are done to evaluate the performance of our solution methods in terms of both quality and time. The results show that the proposed heuristic algorithm finds near-optimal solutions in very short time

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