The planning of semiconductor manufacturing presents formidable challenges for the successful app... more The planning of semiconductor manufacturing presents formidable challenges for the successful application of mathematical optimization. Formulation techniques are described that precisely model noninteger flow times, time-phased capacity consumption by reentrant process flows, proper horizon behavior, multiple priority classes of demands and multiple objectives, binning and substitution in product structures, and arbitrary distributions of initial work in process. We also formulate exact capacity analyses of nonhomogeneous resources, machine arrangement constraints, and alternative combinations of resources necessary to execute manufacturing operations. Brief histories are provided of key modeling contributions and of optimization applications to production planning in the industry.
We study trends in worldwide semiconductor fabrication capacity, measured in quadrillions of elec... more We study trends in worldwide semiconductor fabrication capacity, measured in quadrillions of electrical functions that could be produced per month. We estimate this capacity for 1,175 fabs worldwide based on each fab's minimum feature size, wafer size and wafer output capacity, assuming each function of each integrated circuit on each wafer could be produced with minimum feature size. The data for the 1,175 fabs comes from the "International Fabs on Disk" spreadsheet marketed by Semiconductor Equipment and Materials International, plus our own updates and estimates of historical progressions through feature sizes. At the start of 1998, world fabrication capacity amounted to about 1,100 quadrillion electrical functions per month. Since the late 1980s, worldwide fabrication capacity has grown fairly steadily at an average of 32 percent per year, with the notable exception of 1995, during which it grew by 55 percent. Extrapolating the stable 32 percent per year growth pat...
Important aspects of a company-wide production-planning system implemented at Harris corporation ... more Important aspects of a company-wide production-planning system implemented at Harris corporation semiconductor sector are discussed. At the heart of the system is an optimization-based production-planning system known as the Berkeley planning system (BPS), developed at the University of California at Berkeley. The system utilizes mathematical optimization techniques to establish worldwide factory production plans and product-availability schedules supporting the on-line quotation of delivery dates. This paper focuses on the choice of an objective function for planning decisions made by BPS. It is shown that overall demands for each product must be broken into classes such as on-hand customer orders, safety-stock rebuilds, reliable-demand forecasts, uncertain-demand forecasts, etc., in order to properly reflect business objectives. An approach somewhat similar to goal programming is utilized in which successive mathematical optimization calculations are performed to incrementally loa...
ABSTRACT The resource leveling problem for a construction system producing a stream of output uni... more ABSTRACT The resource leveling problem for a construction system producing a stream of output units is considered. The system is modeled using a critical-path-analysis activity network, from which an extended network is developed for an integrated planning effort of all output units. Activity intensity variables are defined which measure activity demand rates for resources and consequent activity durations for the production of each output unit. A heuristic approach consisting of an iterative nonlinear programming procedure is presented which computes activity durations (intensities) for the minimization of resource capacity costs subject to meeting construction due dates. The application to a major ship overhaul project is described, in which the procedure was used to level workloads of the various labor–trade shops.
IEEE Transactions on Semiconductor Manufacturing, 2003
Page 1. 2 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 16, NO. 1, FEBRUARY 2003 Stochas... more Page 1. 2 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 16, NO. 1, FEBRUARY 2003 Stochastic Wafer Fabrication Scheduling Youxun Shen and Robert C. Leachman AbstractTo meet the challenge ...
IEEE Transactions on Semiconductor Manufacturing, 1993
Demonstrates a methodology which uses the information of future work-in-process (WIP) arrivals to... more Demonstrates a methodology which uses the information of future work-in-process (WIP) arrivals to minimize the average number of lots in the queue at a workstation which is capable of processing multiple lots simultaneously as a single batch. This kind of batch-process workstation is common in semiconductor manufacturing; an example is furnace tubes used for deposition operations. The proposed heuristic seeks
ABSTRACT We introduce an optimization-based production planning tool for the biotechnology indust... more ABSTRACT We introduce an optimization-based production planning tool for the biotechnology industry. The industry’s planning problem is unusually challenging because the entire production process is regulated by multiple external agencies – such as the US Food and Drug Administration – representing countries where the biopharmaceutical is to be sold. The model is structured to precisely capture the constraints imposed by current and projected regulatory approvals of processes and facilities, as well as capturing the outcomes of quality testing and processing options, facility capacities and initial status of work-in-process. The result is a supply chain “Planning Engine” that generates capacity-feasible batch processing schedules for each production facility within the biomanufacturing supply chain and an availability schedule for finished product against a known set of demands and regulations. Developing the formulation based on distinct time grids tailored for each facility, planning problems with more than 27,000 boolean variables, more than 130,000 linear variables and more than 80,000 constraints are automatically formulated and solved within a few hours. The Planning Engine’s development and implementation at Bayer Healthcare’s Berkeley, CA manufacturing site is described.
ABSTRACT A new heuristic approach is presented for scheduling economic lots in a multi-product si... more ABSTRACT A new heuristic approach is presented for scheduling economic lots in a multi-product single-machine environment. Given a pre-defined master sequence of product setups, an integer linear programming formulation is developed which finds an optimal subsequence and optimal economic lots. The model takes explicit account of initial inventories, setup times and allows setups to be scheduled at arbitrary epochs in continuous time, rather than restricting setups to a discrete time grid. We approximate the objective function of the model and solve to obtain an optimal capacity feasible schedule for the approximate objective. The approach was tested on a set of randomly generated problems, generating solutions that are on average 2.5% above a lower bound on the optimal cost. We also extend the approach to allow shortages.
The planning of semiconductor manufacturing presents formidable challenges for the successful app... more The planning of semiconductor manufacturing presents formidable challenges for the successful application of mathematical optimization. Formulation techniques are described that precisely model noninteger flow times, time-phased capacity consumption by reentrant process flows, proper horizon behavior, multiple priority classes of demands and multiple objectives, binning and substitution in product structures, and arbitrary distributions of initial work in process. We also formulate exact capacity analyses of nonhomogeneous resources, machine arrangement constraints, and alternative combinations of resources necessary to execute manufacturing operations. Brief histories are provided of key modeling contributions and of optimization applications to production planning in the industry.
We study trends in worldwide semiconductor fabrication capacity, measured in quadrillions of elec... more We study trends in worldwide semiconductor fabrication capacity, measured in quadrillions of electrical functions that could be produced per month. We estimate this capacity for 1,175 fabs worldwide based on each fab's minimum feature size, wafer size and wafer output capacity, assuming each function of each integrated circuit on each wafer could be produced with minimum feature size. The data for the 1,175 fabs comes from the "International Fabs on Disk" spreadsheet marketed by Semiconductor Equipment and Materials International, plus our own updates and estimates of historical progressions through feature sizes. At the start of 1998, world fabrication capacity amounted to about 1,100 quadrillion electrical functions per month. Since the late 1980s, worldwide fabrication capacity has grown fairly steadily at an average of 32 percent per year, with the notable exception of 1995, during which it grew by 55 percent. Extrapolating the stable 32 percent per year growth pat...
Important aspects of a company-wide production-planning system implemented at Harris corporation ... more Important aspects of a company-wide production-planning system implemented at Harris corporation semiconductor sector are discussed. At the heart of the system is an optimization-based production-planning system known as the Berkeley planning system (BPS), developed at the University of California at Berkeley. The system utilizes mathematical optimization techniques to establish worldwide factory production plans and product-availability schedules supporting the on-line quotation of delivery dates. This paper focuses on the choice of an objective function for planning decisions made by BPS. It is shown that overall demands for each product must be broken into classes such as on-hand customer orders, safety-stock rebuilds, reliable-demand forecasts, uncertain-demand forecasts, etc., in order to properly reflect business objectives. An approach somewhat similar to goal programming is utilized in which successive mathematical optimization calculations are performed to incrementally loa...
ABSTRACT The resource leveling problem for a construction system producing a stream of output uni... more ABSTRACT The resource leveling problem for a construction system producing a stream of output units is considered. The system is modeled using a critical-path-analysis activity network, from which an extended network is developed for an integrated planning effort of all output units. Activity intensity variables are defined which measure activity demand rates for resources and consequent activity durations for the production of each output unit. A heuristic approach consisting of an iterative nonlinear programming procedure is presented which computes activity durations (intensities) for the minimization of resource capacity costs subject to meeting construction due dates. The application to a major ship overhaul project is described, in which the procedure was used to level workloads of the various labor–trade shops.
IEEE Transactions on Semiconductor Manufacturing, 2003
Page 1. 2 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 16, NO. 1, FEBRUARY 2003 Stochas... more Page 1. 2 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 16, NO. 1, FEBRUARY 2003 Stochastic Wafer Fabrication Scheduling Youxun Shen and Robert C. Leachman AbstractTo meet the challenge ...
IEEE Transactions on Semiconductor Manufacturing, 1993
Demonstrates a methodology which uses the information of future work-in-process (WIP) arrivals to... more Demonstrates a methodology which uses the information of future work-in-process (WIP) arrivals to minimize the average number of lots in the queue at a workstation which is capable of processing multiple lots simultaneously as a single batch. This kind of batch-process workstation is common in semiconductor manufacturing; an example is furnace tubes used for deposition operations. The proposed heuristic seeks
ABSTRACT We introduce an optimization-based production planning tool for the biotechnology indust... more ABSTRACT We introduce an optimization-based production planning tool for the biotechnology industry. The industry’s planning problem is unusually challenging because the entire production process is regulated by multiple external agencies – such as the US Food and Drug Administration – representing countries where the biopharmaceutical is to be sold. The model is structured to precisely capture the constraints imposed by current and projected regulatory approvals of processes and facilities, as well as capturing the outcomes of quality testing and processing options, facility capacities and initial status of work-in-process. The result is a supply chain “Planning Engine” that generates capacity-feasible batch processing schedules for each production facility within the biomanufacturing supply chain and an availability schedule for finished product against a known set of demands and regulations. Developing the formulation based on distinct time grids tailored for each facility, planning problems with more than 27,000 boolean variables, more than 130,000 linear variables and more than 80,000 constraints are automatically formulated and solved within a few hours. The Planning Engine’s development and implementation at Bayer Healthcare’s Berkeley, CA manufacturing site is described.
ABSTRACT A new heuristic approach is presented for scheduling economic lots in a multi-product si... more ABSTRACT A new heuristic approach is presented for scheduling economic lots in a multi-product single-machine environment. Given a pre-defined master sequence of product setups, an integer linear programming formulation is developed which finds an optimal subsequence and optimal economic lots. The model takes explicit account of initial inventories, setup times and allows setups to be scheduled at arbitrary epochs in continuous time, rather than restricting setups to a discrete time grid. We approximate the objective function of the model and solve to obtain an optimal capacity feasible schedule for the approximate objective. The approach was tested on a set of randomly generated problems, generating solutions that are on average 2.5% above a lower bound on the optimal cost. We also extend the approach to allow shortages.
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process flows, proper horizon behavior, multiple priority classes of demands and multiple objectives, binning and substitution in product structures, and arbitrary distributions of initial work in process. We also formulate exact capacity analyses of nonhomogeneous resources,
machine arrangement constraints, and alternative combinations of resources necessary to execute manufacturing operations. Brief histories are provided of key modeling contributions and of optimization applications to production planning in the industry.
process flows, proper horizon behavior, multiple priority classes of demands and multiple objectives, binning and substitution in product structures, and arbitrary distributions of initial work in process. We also formulate exact capacity analyses of nonhomogeneous resources,
machine arrangement constraints, and alternative combinations of resources necessary to execute manufacturing operations. Brief histories are provided of key modeling contributions and of optimization applications to production planning in the industry.