Michele E. Pfund

Heuristic scheduling of jobs on parallel batch machines with incompatible job families and unequal ready times

This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication, where the machines can be modeled as parallel batch processors. We attempt to minimize total weighted tardiness on parallel batch machines with incompatible job families and unequal ready times of the jobs. Given that the problem is NP-hard, we propose two different decomposition approaches. The first approach forms fixed batches, then assigns these batches to the machines using a genetic algorithm (GA), and finally sequences the batches on individual machines. The second approach first assigns jobs to machines using a GA, then forms batches on each machine for the jobs assigned to it, and finally sequences these batches. Dispatching and scheduling rules are used for the batching phase and the sequencing phase of the two approaches. In addition, as part of the second decomposition approach, we develop variations of a time window heuristic based on a decision theory approach for forming and sequencing the batches on a single machine.

Genetic algorithm based scheduling of parallel batch machines with incompatible job families to minimize total weighted tardiness

This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication, where the machines can be modelled as parallel batch processors. We attempt to minimize total weighted tardiness on parallel batch machines with incompatible job families. Given that the problem is NP-hard, we propose two different versions of a genetic algorithm (GA), each consisting of three different phases. The first version forms fixed batches, then assigns batches to the machines using a GA, and finally sequences the batches on individual machines. The second version assigns jobs to machines using a GA, then forms batches on each machine for the jobs assigned to it, and finally sequences these batches. Heuristics are used for the batching phase and the sequencing phase. For both these versions an additional fourth phase can be included wherein the sequenced batches are modified using pairwise swapping techniques. Using stochastically generated test data we show that algorithms of the first version of the GA outperform (1) traditional dispatching rules with respect to solution quality and (2) the algorithms of the second version with respect to both solution quality and computation time.

Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems

This research compares the performance of various heuristics and one metaheuristic for unrelated parallel machine scheduling problems. The objective functions to be minimized are makespan, total weighted completion time, and total weighted tardiness. We use the least significant difference (LSD) test to identify robust heuristics that perform significantly better than others for a variety of parallel machine environments with these three performance measures. Computational results show that the proposed metaheuristic outperforms other existing heuristics for each of the three objectives when run with a parameter setting appropriate for the objective.

A SURVEY OF ALGORITHMS FOR SINGLE AND MULTI-OBJECTIVE UNRELATED PARALLEL-MACHINE DETERMINISTIC SCHEDULING PROBLEMS

ABSTRACT This paper surveys the literature related to solving traditional unrelated parallel-machine scheduling problems. It compiles algorithms for the makespan, total weighted sum of completion times, maximum tardiness, total tardiness, total earliness and tardiness, and multiple criteria performance measures. The review of the existing algorithms is restricted to the deterministic problems without setups, preemptions, or side conditions on the problem. Even for such traditional problems, this survey reveals that while makespan minimization has been fairly widely studied, problems that include processing characteristics such as release times, sequence dependent setups, and preemptions remain largely unstudied. Research in solving unrelated parallel-machine scheduling problems involving the minimization of the number of tardy jobs, weighted number of tardy jobs, total tardiness, and total weighted tardiness is quite limited.

Scheduling interfering job sets on parallel machines

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT-LPT-SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy - based on the properties of a non-dominated solution - to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.

Semiconductor Manufacturing Scheduling and Dispatching

This chapter discusses scheduling and dispatching in one of the most complex manufacturing environments — wafer fabrication facilities. These facilities represent the most costly and time-consuming portion of the semiconductor manufacturing process. After a brief introduction to wafer fabrication operations, the results of a survey of semiconductor manufacturers that focused on the current state of the practice and future needs are presented. Then the chapter presents a review of some recent dispatching approaches and finally an overview of a recent deterministic scheduling approach is provided.

THE INCLUSION OF FUTURE ARRIVALS AND DOWNSTREAM SETUPS INTO WAFER FABRICATION BATCH PROCESSING DECISIONS

This paper presents a new batch machine dispatching policy that incorporates knowledge about future arrivals and the status of critical machines in subsequent (downstream) processing into the batch processing decision process. The intent is to create a methodology that balances the time lots spend waiting at a batch machine with the time spent in setup, thus improving the overall cycle time. Using discrete-event simulation, this heuristic is compared to existing heuristics that do not consider downstream operations to evaluate their impact on the cycle time both for a small three-machine system and a semiconductor manufacturing facility model. The results showed considerable improvement in cycle times for the small three-machine system. Results for the semiconductor-manufacturing model with downstream batching indicate that the new heuristic is robust but produces results consistent with the current standard heuristic; however, with further modifications, this heuristic may be capable of producing significantly better results.

Multiple-objective heuristics for scheduling unrelated parallel machines

This research proposes two heuristics and a Genetic Algorithm (GA) to find non-dominated solutions to multiple-objective unrelated parallel machine scheduling problems. Three criteria are of interest, namely: makespan, total weighted completion time, and total weighted tardiness. Each heuristic seeks to simultaneously minimize a pair of these criteria; the GA seeks to simultaneously minimize all three. The computational results show that the proposed heuristics are computationally efficient and provide solutions of reasonable quality. The proposed GA outperforms other algorithms in terms of the number of non-dominated solutions and the quality of its solutions.

Impact of permutation enforcement when minimizing total weighted tardiness in dynamic flowshops with uncertain processing times

This paper is motivated by the problem of meeting due dates in a flowshop production environment with jobs with different weights and uncertain processing times. Enforcement of a permutation schedule to varying degrees for dynamic flowshops is investigated with the goal of minimizing total weighted tardiness (TWT). The approaches studied are categorized as follows: (1) pure permutation scheduling (2) shift-based scheduling (3) pure dispatching (which leads to non-permutation sequences). A simulation-based experimental study was carried out to study the performance of the above methods with respect to minimizing TWT when new jobs arrive to the flowshop at every shift change. Results indicate significant gains in performance are possible when the permutation requirement is relaxed and shift-based scheduling is allowed. Shift-based scheduling yields competitive results with respect to the pure dispatching approach, even though dispatching has the advantage of a full relaxation of the permutation requirement.

Evaluating the impacts of reticle requirements in semiconductor wafer fabrication

Photolithography is generally the most constraining workstation in a semiconductor fabrication facility. Up to this point, much of the research and analysis in this area has not included the inherent system requirements created by reticle masks, but the fact remains that in order to process a job in the photolithography station, the job must be ready, the machine must be idle, and the reticle must be inspected and setup on the idle machine. To better understand the impacts of the reticle requirements in the production environment, a discrete-event simulation model of the photolithography station has been created and coupled with a network flow optimization model that optimizes the location of all reticles at 6-h intervals. All other production processes are modeled using a generic stochastic processing delay. Using this framework and a 2/sup 6/ full factorial-designed experiment, we have identified when optimal reticle management processes positively impact the productivity of the overall facility the most. These results were then used to derive and test new dispatching policies for the photolithography workstation.