Andreas Klemmt

Scheduling jobs with time constraints between consecutive process steps in semiconductor manufacturing

In this paper, we consider flow shop scheduling problems for jobs with time constraints between consecutive process steps. We start by analyzing different types of time constraints that arise in semiconductor wafer fabrication facilities. A simple heuristic that sequentially schedules the jobs in a list scheduling manner is proposed. Moreover, a decomposition approach based on mixed integer programming is developed. The two approaches are compared by means of randomly generated problem instances.

Scheduling preventive maintenance tasks with synchronization constraints for human resources by a CP modeling approach

This paper presents an approach for scheduling different types of preventive maintenances (PMs) for a work center of a semiconductor manufacturing facility. The PM scheduling problem includes time-dependent synchronization constraints and is implemented in a constraint programming model. A mix of periodic and workload-specific maintenances is scheduled considering the synchronization to available engineers which have individual shift schedules and skills that define the range of feasible maintenances. This also comprises maintenances having process durations covering multiple shifts, which requires a continuous availability of sufficiently skilled engineers. Additionally to the PMs, also handling and maintaining of unscheduled downs is considered in the model. Multiple objectives are investigated and used for optimization and tested on realistic data. To compare the results an additional simulation model is built up.

Product mix optimization for a semiconductor fab

For optimizing a semiconductor fab we are aiming to match the production capabilities and capacities with the demand in the most profitable way. In this paper we address a linear programming model of the product mix problem considering product dependent demand limits (obligations and demand forecast) and profits while respecting the capacity bounds of the production facility. Since the capacity consumption is highly depended on choosing from different production alternatives we are implicitly solving a static capacity planning problem for each product mix. This kind of planning approach is supported by the fluid flow concept of complete resource pooling in high traffic. We propose a general model that considers a wide range of objectives and we introduce a decomposition heuristic. The computational study of the approaches is based on real world data and on randomly generated instances.

Advanced secondary resource control in semiconductor lithography areas: from theory to practice

Semiconductor frontend fabs are very complex manufacturing systems. Typically, the bottleneck of such a fab is the photolithography area because of its highly expensive equipment and the huge number of required secondary resources - the so called reticles. A reticle (mask) is needed to structure different layers of integrated circuits on the wafers. The reticles can be moved between the equipment with regard to several constraints. This paper examines the benefits of a solver-based reticle allocation in comparison to a classical rule-based heuristic. In a first part, several simulation experiments are performed on the basis of representative test data. The second part presents results from real world application. Thereby it is shown, that the new approach shows significant improvements of different key performance indicators (KPIs).

Improving flow line scheduling by upstream mixed integer resource allocation in a wafer test facility

The effort for scheduling real manufacturing systems is generally very high for mathematical as well as for simulation-based methods. Combining both methods is the key for solving complex scheduling problems. The paper introduces a special approach, where at first a static resource allocation problem is solved by mixed integer programming (MIP). Based on the resulting reduced dedication matrices, feasible schedules are then generated by a discrete event simulation (DES). Possible applications can be found in many parts of the semiconductor manufacturing process, for example in the wafer test. The investigated wafer test consists of two pronounced bottlenecks; each of it is formed as a workcenter with its own dedication matrix. After testing the method with practice oriented benchmarks, the benefits of the approach are shown on data derived directly from the semiconductor manufacturing process.

Product mix optimization for a semiconductor fab: modeling approaches and decomposition techniques

For optimizing a semiconductor fab we are aiming to match the production capabilities and capacities with the demand in the most profitable way. In this paper we address a linear programming model of the product mix problem considering product dependent demand limits (obligations and demand forecast) and profits while respecting the capacity bounds of the production facility. Since the capacity consumption is highly depended on choosing from different production alternatives we are implicitly solving a static capacity planning problem for each product mix. This kind of planning approach is supported by the fluid flow concept of complete resource pooling in high traffic. We propose a general model that considers a wide range of objectives and we introduce a decomposition heuristic. The computational study of the approaches is based on real world data and on randomly generated instances.

Yield integrated scheduling using machine condition parameter

Currently machines in a parallel work center in semiconductor manufactory are assumed uniform in terms of impact on yield for most logic to dispatch schedule this machine set. But in reality machines are different even though they are allowed for the same products. In some layer forming areas machines can get a so called health parameter which describes the current condition of the machine. A high health value means, that defects produced with a machine are less probable. Also the products, which are processed at this work center, differ in their complexity and wafer area used for one chip. The goal is to schedule products with a high complexity and a larger chip size to those machines with the best health value. Doing so will minimize defect wafer area. For this, different dispatching rules and a mixed integer programming approach are compared within a simulation model for practical test data.

Scheduling maintenance tasks with time-dependent synchronization constraints by a CP modeling approach

Ensuring a high uptime for manufacturing machines is crucial for efficient and cost-effective production. In opposite, preventive maintenance tasks (PMs) are necessary to assure the reliability of manufacturing processes. This also prevents serious and unpredictable machine crashes, which affect uptime and process scheduling. However, PM tasks themselves lower the uptime and are to be smartly scheduled within their given domain considering some requirements as ensuring the availability of a sufficient number of qualified engineers for the concerning period. This work investigates a PM scheduling problem with time-dependent synchronization constraints for a lithography work center. For this, a constraint programming (CP) modeling approach including decomposition is used. Multiple objectives are considered. For example, the minimization of crew backup violations or scheduling PMs according to the work in process (WIP) for embedding upcoming PMs smoothly into the system work load. This minimizes negative effects on throughput and tardiness.

A CP approach for planning lot release dates in a supply chain of semiconductor manufacturing

In this paper a constraint programming (CP) approach for calculating release dates for lots within a supply chain environment is investigated. The lot start times are verified by a simulation model using different dispatching rules focusing on tardiness. To test the presented CP approach a simple fab model is constructed. The fab model consists of parallel batch machines as well as work centers and single machines. The investigated objectives are tardiness, earliness and cycle time. Due to the high complexity decomposition methods for the CP approach are tested. The results from the CP method are lot start dates which are verified by a downstream simulation run. The results show that the presented CP approach could outperform the simulation for all objectives. The content of this paper could be used as a first investigation for new scheduling methods within a supply chain management.

One solver for all - a generic allocation concept for planning and shop floor control

This paper gives an overview of several optimization solutions for semiconductor problems using mixed integer programming (MIP). The single solutions presented in former papers are not key of the publication. We rather focus on the generic portion within each solution and the approach of building a unique MIP model. This allows us to reduce complexity in different applications. The universal model enables the use in a wide range of problems for different optimization stages mapped to static allocation problems. The model itself is a kit of constraints that can be activated according to the problem needs. The underlying data layer is an abstract database model that can be fed by different data sources. The paper describes the advantages of the consistent technical embedding of database, different solvers and generic MIP models in the MES environment.