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Background:STELIA (formerly Composites Atlantic) builds composite airplane parts mostly from carbon fiber. These parts contain a resin that under high pressure and heat binds the different layers. This high pressure and heat are applied to the parts with the use of autoclaves in the curing centre (See Figure 1). Once the parts are cured, they proceed to demoulding where the part is separated from the mould and then continue on to other downstream processes like trimming, drilling, painting, and assembly.
The curing centre is the bottleneck of the entire operation and contains very complicated processes. Although it currently operates well, there are significant opportunities for improvement through optimization and standardization of these processes. The first process to be improves it the building of cure-sets, which are a set of parts that can go together into the autoclave (Bin Packing Problem). The second process is the scheduling of these cure-sets across the planning horizon (Scheduling Problem).
Pains:● Pain 1: Manually building cure-sets
○ Time consuming○ Sub-optimal (but “pretty good”)
● Pain 2: Manually scheduling cure-sets○ Time consuming○ Complex constraints
Pains are exacerbated by a growing company. These problems grow exponentially and thus become even harder to solve.
Solution:Solve the Bin Packing Problem first, then the Scheduling Problem with the results from the BPP. Doing so on Amazon Web Services it was possible to use Gurobi Cloud, thus allowing a per hour fee instead of an expensive license purchase.
Bin Packing Problem (BPP)- How to optimally pack parts into an autoclave to respect the following constraints:
● Recipe constraints (heat+pressure profile)
● Thermocouple constraint● Volume constraints● Length constraints● Tool constraints● Customer-specific constraints
Objectives: 1. Minimize cost
a. Number of curesb. Use preferred autoclave for parts
2. Level out load for autoclaves
BPP Solution- Use a modified version of the hill-climbing algorithm (Lewis, 2009). Implemented with use of Python, solved on Amazon Web Services server.
Scheduling Problem- How to best schedule bin packings to minimize cost, maintain schedule flexibility, and meet the following constraints:
● Meet demand● Bin packings can only go on certain
autoclaves● Autoclave utilization constraints● Tool recycling time constraints● Blackout period constraints● Layup room manpower constraints
Objectives:1. Minimize cost
a. Overtimeb. Peak Power
2. Maintain schedule flexibility3. Maintain schedule usability for upstream
processes
Scheduling Solution- Use of Mixed-Integer-Programming to create a mathematical model. Model is outlined below and solved using Gurobi Optimization on the cloud (see Figure 3).
Expected Implementation: June 2015Expected Results:
Tools Used:● Amazon Web Services
○ API● Pyomo● Gurobi Cloud● SSH● Python
Autoclave Packing and SchedulingBy: Andres Collart | [email protected] | www.andrescollart.com
Kit Cutting Layup Curing Centre Demolding Downstream Processes
Figure 1: General Workflow of Plant Processes
Mold clean-upMold Mold
LocalMachine
AP
I Cal
l +
files
1. Get Inputs for week. Encode
2. Start Linux and send problem
3. Solve BPP with Heuristic
4. Create Scheduling MIP problem
5. Start Gurobi + send problem
AP
I Cal
l +
prob
lem
6. Solve + send back
Sol
utio
n
“I’m
don
e”
7. Download solution, decode, display
Sol
utio
n
Gurobi Cloud Server(AWS)
Linux Server(AWS)
How do you fit parts in the autoclave most
efficiently?
UNMOLD
carbon fiber airplane parts
layered parts cured in autoclave (big oven)
PRO
CES
S
How do you optimize scheduling of cures for
the autoclaves?
Decreased Peak Power
DecreasedPower
Consumption
Increased Schedule Flexibility
Decreased WeekendOvertime
Long term capacity planning
Figure 2: Large autoclave at STELIA (STELIA, 2015)
PAIN
SB
IN
PAC
KIN
GPR
OB
LEM
RESULTSEfficient Bin Packing
Optimized scheduling
SOLU
TIO
N
SCH
EDU
LIN
GPR
OB
LEM
lower cost png
Reduce Cost
Level out Autoclave Load
DecreasedPower
Consumption
Objectives:
Constraints:
Heat Profile(Recipe)
Volume +
Length
Mold(Tool)
Other Customer Specific
Reduce Cost
Objectives:
Constraints:
Schedule Flexibility
Balance Input Process
Preferences
Part-Autoclave compatibility
Mold Recycle
Time
Scheduled Downtime
Resource Capacity
(Autoclaves)
Other
Bin Packing Problem: ● Modified Hill-Climbing Heuristic
Scheduling Problem: ● Discrete-Time MIP with Rolling Time Horizon
=
Pains:●
●
Pains are exacerbated by a growing company. These problems grow exponentially and thus become even harder to solve.
Manually building cure-sets○ Time consuming○ Sub-optimal use of
autoclaves
Manually scheduling cure-sets○ Time consuming○ Complex constraints○ High energy cost
Thermos