A Glass Float Line Simulation: Modeling Methodology and Applications Scott R. Schultz - Mercer University, Macon, GA.

Outline – Glass Float Line Simulation Glass Float Line Introduction Problem Statement Modeling Issues Selected Application - Typical Scheduling Session -Comparison of Sequencing Algorithms - Design for New Float Line

Glass Float Line Introduction Top View – Glass Float Line

Glass Float Line Introduction Cutting and Scoring Process 1 – Continuous Ribbon of Glass 2 – Streams of Glass 3 – Individual Brackets Conveyors Pull gaps (speedup conveyors) Spurline speed dependent on number of panels in light tilt-down conveyors conveyor control rules

Glass Float Line Introduction Mainline Scrap Generation conveyor immediately downstream from furnace cannot stop all other mainline conveyor sections will stop until spurline clears Cutting Algorithms up to 2 routes per spurline sequential –vs- dynamic

Operational Issues: Inefficient cutting schedules (generates mainline scrap, requires too much manpower) Cutting algorithms (which route to cut when, impacts mainline scrap) Issues / Problems Design Issues: Upstream or downstream mainline scrap cullet 4 –vs- 5 spurlines

Operational Issues: Evaluate cutting schedules (used on a daily basis) Evaluate and develop alternative cutting algorithms Design Issues (future float line): Evaluate effect of having an upstream –vs- downstream mainline scrap cullet Evaluate the impact of 4 –vs- 5 spurlines Simulation Goals

Process is initially continuous (ribbon of glass), then becomes discrete (lights, followed by panels). Gaps between “streams” and “brackets” must be precisely modeled due to impact on controlling conveyor zones. Modeling Issues

Continuous-discrete Process: Furnace produces continuous ribbon of glass 24 hours a day, but continuous ribbon turns into discrete “streams” at the slant cutter. Approach: ignore continuous portion. Start model at the slant cutters. Discrete entity – “stream” of glass Time between entity arrivals is a function of the “stream” length and the mainline conveyor speed. “Stream” length varies as a function of the cutting algorithm and cutting schedule. “Stream” of glass generates multiple entities at spurline snap roller. Modeling Issues

Controlling gaps between “streams” and “brackets” and conveyor control: gaps are generated as a function of the difference in speeds between the upstream conveyor and downstream speedup conveyor. zone control for tilt down conveyors - only one covey (streams for same spurline) per conveyor section. Modeling Issues

29 resources 74 conveyors 123 stations 600 parameters (mostly associated with cutting schedule) Model Summary

Analysis of Cutting Schedules Example cutting schedule entered by user.

Analysis of Cutting Schedules Example float line operating paramters.

Analysis of Cutting Schedules Results using previous cutting schedule and operating parameters.

Analysis of Cutting Schedules Analyst decided to reduce the number of active routes to from 11 to 8. Efficiency increased from 37.2% to 69.2%.

Analysis of Cutting Schedules Analyst decided to further reduce the number of active routes to 6. Utilization fell from 69.2 to 50.4%, and 35.9% scrapped at mainline cullet.

Comparing Cutting Algorithms Sequential: 1. Cut streams for all active routes, in order from spurline 7 to spurline Repeat steps 1 to 2. Dynamic: 1. Initialize a clock for every active spurline to 0. These clocks increment one unit for every elapsed second. 2. Find the spurline with the greatest clock value and cut all active routes for that spurline. 3. Reset the clock for the spurline chosen in step 2 to minus the stream removal time 1 for that spur. 4. Repeat steps 2 to 4. 1 Stream removal time - {(rm i + rt i )*n i } rm i - standard time to remove panel i rt i - time to rotate panel i n i - number of panels per stream i i - an element of the set of active routes for the stream.

Comparing Cutting Algorithms Modified-Dynamic: 1. Initialize a counter for every active spurline to Find the active spurline with the smallest counter value and cut all active routes for that spurline. 3. Increase the counter for the spurline chosen in step 2 by the stream removal time 1 for that spur. 4. Repeat steps 2 to 4.

Comparing Cutting Algorithms

Comparison of Results: Modified-Dynamic significantly outperforms both the sequential and dynamic in both mainline scrap reduction and balanced spurline utilization.

Comparison of 4 –vs- 5 Spurlines Approach Spurlines functional 90% of time (downtime associated with scheduled and unscheduled maintenance) 64 day cutting schedule simulated using 5, 4, 3, 2, or 1 spurline respectively to determine percent mainline scrap generated. Using Binomial function, and the 90% uptime estimate, probability of having 5,4,3,2,1, or 0 (or 4,3,2,1 or 0) spurlines active is calculated. Probabilities used in conjunction with simulation of scrap generation used to calculate expected scrap amount. Results Expected Mainline Scrap 4 Spurlines % 5 Spurlines -0.62%

Comparison of Upstream –vs- Downstream Mainline Cullet Approach Same 64 day cutting schedule and approach used to compare 4 –vs- 5 spurlines. For upstream cullet, when spurline gate is occupied, the glass will stop on the previous mainline conveyor section. Glass may continue to backup to mainline cullet. With downstream cullet, when spurline gate is occupied, glass destined for that spurline will pass over the spurline and will scrap at downstream location. Results Expected Mainline Scrap UpstreamDownstream 4 Spurlines %2.46% 5 Spurlines -0.62%0.47%

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