Simulation-based GA Optimization
for Production Planning
Bioma 2014
September 13, 2014
Juan Esteban Díaz Leiva
Dr Julia Handl
Production Planning
Production
levels
Production Plan
Allocation of
resources
Business objectives
2
Production Planning
Experience
&
“Sixth sense”
Lack of
appropriate
instrument
Inappropriate methods
3
Simulation-based
Optimization
Simulation
Optimization
DES
GA
Aplicable solution
4
Objective
Support decision
making
Production
Planning
Feasibility
Simulation-based
optimization
Uncertainty
&
Real-life
complexity
Applicablility
Robustness
5
Simulation-based Optimization Model
6
Figure 1. Order processing subsystem for work centre 𝑙.
Simulation-based Optimization Model
Figure 2. Production subsystem for work centre 𝑙.
Figure 3. Repair service station of work centre 𝑙.
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Simulation-based Optimization Model
minimize:
1
𝑓 𝑥 =𝑐=
𝑛
𝑛
𝑐𝑚
(𝑚 = 1, 2, . . . , 𝑛)
𝑚=1
subject to :
𝑥𝑗 ∈ S
𝑥𝑗 ∈ ℤ≥
(𝑗 = 1, 2, . . . , 41)
(𝑗 = 1, 2, . . . , 41)
𝑛: number of replications
𝑓: fitness function value
𝑥: vector of decision variables 𝑥𝑗
𝑐 expected sum of backorders and inventory costs
8
Simulation-based Optimization Model
31
𝑐𝑚 =
𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦𝐶𝑜𝑠𝑡𝑘 + 𝐵𝑎𝑐𝑘𝑜𝑟𝑑𝑒𝑟𝐶𝑜𝑠𝑡𝑘
𝑘=1
where
𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦𝐶𝑜𝑠𝑡𝑘 =
𝑆𝑡𝑜𝑐𝑘𝑘 − 𝐷𝑘 × 𝐶𝑜𝑠𝑡𝑘
0
𝐵𝑎𝑐𝑘𝑜𝑟𝑑𝑒𝑟𝐶𝑜𝑠𝑡𝑘 =
𝐷𝑘 − 𝑆𝑡𝑜𝑐𝑘𝑘 × 𝑃𝑟𝑖𝑐𝑒𝑘
0
𝐷𝑘 : demand
if 𝑆𝑡𝑜𝑐𝑘𝑘 > 𝐷𝑘
if 𝑆𝑡𝑜𝑐𝑘𝑘 ≤ 𝐷𝑘
if 𝑆𝑡𝑜𝑐𝑘𝑘 < 𝐷𝑘
if 𝑆𝑡𝑜𝑐𝑘𝑘 ≥ 𝐷𝑘
9
Simulation-based Optimization Model
Requirement of sub-products
41
𝑎𝑖𝑗 × 𝑥𝑗 ≤ 𝑏𝑖
(𝑖 = 1,2, … , 4)
𝑗=1
𝑏𝑖 : quantity available of sub-product 𝑖
𝑎𝑖𝑗 : amount required of sub-product 𝑖 to produce one lot in process 𝑗
10
Simulation-based Optimization Model
GA (MI-LXPM) [2]
•
•
•
•
•
•
real coded
Laplace crossover
power mutation
tournament selection
truncation procedure for integer restrictions
parameter free penalty approach [1]
[1] K. Deb. An efficient constraint handling method for genetic algorithms. Computer methods in applied mechanics
and engineering, 186(2):311-338, 2000.
[2] K. Deep, K. P. Singh, M. Kansal, and C. Mohan. A real coded genetic algorithm for solving integer and mixed
integer optimization problems. Applied Mathematics and Computation, 212(2):505-518, 2009.
11
Results
Original model
Figure 4. Best, mean and worst fitness value of the population at each iteration.
12
Results
Model modifications
Figure 5. Order processing subsystem for work centre 𝑙.
13
Results
Model modifications
Figure 6. Production subsystem for work centre 𝑙.
14
Results
Profit maximization
15
Figure 7. Best, mean and worst fitness value of the population at each iteration (time: 8.17 h).
Results
ILP
CDF
deterministic
Stochastic
Simulation
Simulation-based
optimization
CDF
uncertainty
16
Results
Profit maximization
17
Figure 8. CDFs of profit obtained through stochastic simulation.
Conclusions
Production plan
• production levels and allocation of work centres
Process uncertainty
• delays
Real life complexity
• no complete analytic formulation
Better performance of solutions
• stochastic simulation
18
Post-doc Position
Constrained optimization
(applied in the area of protein structure prediction)
Start date: November 2014
in collaboration between:
Computer Sciences (Joshua Knowles),
Faculty of Life Sciences (Simon Lovell)
and MBS (Julia Handl).
Info: j.handl@manchester.ac.uk
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Q&A
20
Thank you
September 13, 2014
Juan Esteban Diaz Leiva
Dr Julia Handl
21