Scheduling jobs with agreeable processing times and due dates on a single batch processing machine

AbstractIn this paper we study the problems of scheduling jobs with agreeable processing times and due dates on a single batch processing machine to minimize total tardiness, and weighted number of tardy jobs. We prove that the problem of minimizing total tardiness is NP-hard even if the machine capacity is two jobs and we develop a pseudo-polynomial-time algorithm for an NP-hard special case of this problem. We also develop a pseudo-polynomial-time algorithm for the NP-hard problem of minimizing weighted number of tardy jobs, which suggests that this problem cannot be strongly NP-hard unless P=NP

Stronger Lagrangian bounds by use of slack variables: applications to machine scheduling problems

Lagrangian relaxation is a powerful bounding technique that has been applied successfully to manyNP-hard combinatorial optimization problems. The basic idea is to see anNP-hard problem as an easy-to-solve problem complicated by a number of nasty side constraints. We show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds. The trick is widely applicable, but we focus on a broad class of machine scheduling problems for which it is particularly useful. We provide promising computational results for three problems belonging to this class for which Lagrangian bounds have appeared in the literature: the single-machine problem of minimizing total weighted completion time subject to precedence constraints, the two-machine flow-shop problem of minimizing total completion time, and the single-machine problem of minimizing total weighted tardiness

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines. We then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for the TWT and TWET problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm for solving the preemptive relaxation formulated as a mixed integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines, and then we exploit recent advances in solving the non-preemptive single machine TWT and TWET problems for constructing non-preemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances up to 5 machines and 200 jobs

Scheduling with controllable processing times in a CNC environment

Cataloged from PDF version of article.Flexible manufacturing systems give a manufacturer some capabilities to consider and solve different manufacturing problems simultaneously instead of one by one in a sequential manner. Using those makes her more competitive in the market. One of those capabilities is controllable processing times. By using this capability, the due date requirements of customers can be satisfied much more effectively. Processing times of the jobs in a CNC machine can be easily controlled via machining conditions such that they can be increased or decreased at the expense of tooling cost. In this study, we consider the problem of scheduling a set of jobs by minimizing the sum of total weighted tardiness, tooling and machining costs on a single CNC machine. This problem is NP-hard since the total weighted tardiness problem is NP-hard alone. Moreover, the problem is non-linear because of the nature of the tooling cost. We proposed a DP-based heuristic to solve the problem for a given sequence and designed a local search algorithm that uses it as a base heuristic.İlhan, TaylanM.S

A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem

In this paper, we study the job shop scheduling problem with the objective of minimizing the total weighted tardiness. We propose a hybrid shifting bottleneck - tabu search (SB-TS) algorithm by replacing the reoptimization step in the shifting bottleneck (SB) algorithm by a tabu search (TS). In terms of the shifting bottleneck heuristic, the proposed tabu search optimizes the total weighted tardiness for partial schedules in which some machines are currently assumed to have infinite capacity. In the context of tabu search, the shifting bottleneck heuristic features a long-term memory which helps to diversify the local search. We exploit this synergy to develop a state-of-the-art algorithm for the job shop total weighted tardiness problem (JS-TWT). The computational effectiveness of the algorithm is demonstrated on standard benchmark instances from the literature