Optimization-based order release planning Hubert Missbauer - - PowerPoint PPT Presentation

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 1

Optimization-based order release planning

Hubert Missbauer

Department of Information Systems, Production and Logistics Management University of Innsbruck A-6020 Innsbruck, Austria

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 2

Contents

1. Manufacturing planning and control systems, workload control and order release algorithms 2. Order release planning vs. traditional order release mechanisms 3. Order release planning models with fixed lead times 4. Clearing function models 5. Clearing functions – a critical assessment 6. Iterative approach (FLT order release – lead time updating) 7. Conclusions

Intro | Trad. ORR | FLT models | Clearing function models | CF assessment | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 3

Hierarchical structure of a typical manufacturing planning and control system

Top level (“Goods flow control”, “Supply Chain Operations Planning”): Planning and control of the material flow through the entire logistic chain, including capacity planning, at an appropriate level of aggregation. Base level (“Production unit control”): Detailed scheduling of the orders within the production units, usually performed at the shop floor level and for each production unit separately. Interface:

• Order release decisions
• requires anticipation of flow times – lead times for order release planning

⇒ Controlling flow times by controlling WIP => Workload control (WLC) concept ⇒ Great importance of order release function ⇒ Algorithms for determining order releases are essential research topic!

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 4

Order release planning in hierarchical MPC systems

Order release planning performs

• material coordination
• control of the state of the production units (WIP, avg. flow times, output)

=> “mesoscopic” modeling level (Chen and Mandelbaum 1994)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 5

Algorithms for determining order release times/periods considering lead times

• Traditional order review/release mechanisms (rule-based approach)

Variants of a “basic release procedure” (Land 2004), e.g.,

• CONWIP (Spearman et al. 1989, 1990)
• Lancaster University Management School (LUMS) approach (Hendry/Kingsman

1991; Stevenson/Hendry 2006)

• Load-oriented order release (Wiendahl 1995)
• Starvation Avoidance (Glassey and Resende 1988)
• …

Interaction order release – dispatching is discussed in this community.

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 6

Algorithms for determining order release times/periods considering lead times Cont’d

• Multi-period order release models
• Fixed lead times (based on Input/Output Control: Belt 1976, Wight 1974;

with fixed time-lags: Hackman/Leachman 1989)

• Load-dependent lead times
• Clearing function models (Karmarkar 1989, Missbauer 1998, 2002,

Asmundsson et al. 2006, 2009)

• Lead time estimation without referring to WIP evolution

(e.g., Voss/Woodruff 2006)

• Iterative approaches (Hung/Leachman 1996, Riaño 2006, Kim/Kim 2001)

Essential differences of the two basic order release concepts:

• Decomposition vs. integration of medium-term planning and short-term order

release

• Capability to utilize foreknowledge of demand

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 7

Order release planning models for one production unit: generic structure

• Production unit is represented as a network of work centers.
• Network flow model with continuous flows in discrete time

(e.g., Johnson/ Montgomery 1975).

• Capacities of the work centers are represented appropriately, depending on the

manufacturing system.

• Variables: Releases Rjt, Production Xjmt, WIP Wjmt, FGI Ijt for each product j in (or at

the end of, resp.) period t, measured in units or hours of work.

• Flow times (congestion effects) are modelled by additional constraints
• internal to the model,
• external to the model (by simulation or queueing; iterative solution).
• Only the releases Rjt are actually executed.

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 8

Model of a production unit with a single (bottleneck) work center: Fixed lead time v, lag before

• 1
• 1

Min! Subject to +

• 1, ...,

+ X - 1, ..., 1, ..., 1, ..., , , , 1, ...,

t t t t t t t t t t t t t t t t v t t t t t t

hW l I W W R X t T I I D t T X R t T X C t T I R W X t T

−

+ → = = = = = = ≤ = ≥ =

∑ ∑

Symbols (all measured in hours of work):

t

W WIP at the end of period t

t

R Work released in period t

t

X Output (actual production) in period t

t

I Finished goods inventory at the end of period t

t

D Demand in period t (parameter) Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 9

Model of a production unit with a single (bottleneck) work center: Pre-determined backward lead time (distribution)

(see also Hung/Leachman 1996; analogous Riaño 2003)

• 1
• 1

,

Min! Subject to +

• 1, ...,

+ X - 1, ..., 1, ..., 1, ..., , , , 1, ...,

t t t t t t t t t t t t t t T b t t t t t t t t t

hW l I W W R X t T I I D t T R X w t T X C t T I R W X t T

τ τ τ τ − =

+ → = = = = = = ≤ = ≥ =

∑ ∑ ∑

Additional Symbol

, b t

w

τ

Fraction of the output in period t that must be released in period t τ − (in order to be finished in period t)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 10

Model of a production unit with a single (bottleneck) work center: Fixed lead time v, Input/Output control

(see Pürgstaller/Missbauer 2012, de Kok/Fransoo 2003)

• 1
• 1
• 1

1

Min! Subject to +

• 1, ...,
• 1, ...,
• 1, ...,

1, ...,

b a t t t t t t t t t t t t t t t t t v t t t v t t v t k k t t t

h W h F l I W W R X t T F F X R t T I I R D t T W X t T X C

− − + = +

+ + → = = = + = = + = ≤ = ≤

∑ ∑ ∑ ∑

1, ..., , , , , 1, ...,

t t t t t

t T I R W X F t T = ≥ = Additional Symbol

t

F

WIP inventory of product j after the work center at the end of period t

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 11

Simulation model of optical storage media production

24 products, rolling horizon setting Experimental factors: demand pattern, product mix, forecast accuracy

Final product inventory Raw material Production

CD DVD

Printing Packing

SD KOD MOD V1 V3 V2 V4

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 12

Simulation results for traditional release mechanism (tradRM) and Input/Output control (IOC) with perfect demand forecasts (Pürgstaller/Missbauer 2012)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 13

Simulation results for Input/Output control (IOC) for different settings of demand predictability

(Pürgstaller/Missbauer 2012)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 14

Fixed lead time order release planning models - assessment

• Largely mature for practical applications, facilitate material coordination
• Input/Output control is superior to traditional order review/release mechanisms,

even for inaccurate demand forecasts

• Input/Output control accurately models the smoothing capability of WIP, models

with fixed positioning of time-lag do not.

• Fixed lead time is a constraint – no adaptation to demand variations.
• Lead time setting and adaptation is critical.

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 15

Clearing function model of a production unit with a single (bottleneck) work center

( )

, , -1 , -1 , -1

Min! Subject to +

• ,

+ X

• ,

+ , ; 1,...,

jt jt jt jt j t t j t jt j t jt jt jt j t jt jt jt j t jt jt jt j j jt j kt

h W l I W W R X j t I I D j t W R j t X f t X f k J + → = ∀ = ∀ Λ = ∀   ≤ Λ ∀     ≤ Λ =

∑∑ ∑∑ ∑ ∑

, , , , ,

jt jt jt jt

j t I R W X j t ∀ ≥ ∀

jt

Λ

Load (available work) in period t

Intro | Trad. ORR | FLT models | Clearing function models | shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 16

Clearing Function (CF) - formulations

• Basic definition of a clearing function for work center i: Xit = fi(WIPit)
• Linear CF (Graves 1986): Xit = αi(Wi,t-1+Rit)
• Saturating CF with load (available work) as WIP measure (Karmarkar 1989):

Xit = fi(Wi,t-1+Rit; Cit)

5 1 1 5 2 2 5 3 Wt 1 Rt 2 4 6 8 1 Xt

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 17

Allocated Clearing function (ACF) model of a production unit with a single (bottleneck) work center (see Asmundsson et al. 2006)

, -1 , -1 , -1

Min! Subject to +

• ,

+ X

• ,

+ , 1

jt jt jt jt j t j t jt j t jt jt jt j t jt jt jt j t jt jt jt jt jt jt j

h W l I W W R X j t I I D j t W R j t X Z f t Z Z + → = ∀ = ∀ Λ = ∀   Λ ≤ ∀       =

∑∑ ∑∑ ∑

, , , , ,

jt jt jt jt jt

t I R W X Z j t ∀ ≥ ∀

Additional Symbol

jt

Z

Fraction of the maximum possible output allocated to product i in period t

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 18

Simulation results for IOC and ACF for constant total demand measured in units (Häussler et al. 2015)

Constant total demand

Constant product mix

Variable product mix WIP FGI TI RR TI SSAP WIP FGI TI RR TI SSAP IOCIPR

18.78 86.85 105.63 100% 54.28 35.42 84.2 119.62 98.05% 94.74

IOCSRD

18.78 31.89 50.67 98.18% 48.92

• ACF

18.85 31.89 50.67 98.18% 48.92 31.72 43.18 74.90 84.42% 89.32

Diff.

0.00 0.00 0.00 0.00 0.00 3.70* 41.02* 44.72* 5.42*

*significant difference (t-test, α=5%)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 19

Simulation results for IOC and ACF for seasonal total demand measured in units (Häussler et al. 2015)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Seasonal total demand

Constant product mix

Variable product mix WIP FGI TI RR TI SSAP WIP FGI TI RR TI SSAP IOCIPR

49.22 72.97 122.19 90.75% 274.44 70.03 71.76 141.64 83.26% 348.60

IOCSRD

30.59 34.74 65.33 88.21% 273.31 35.74 30.45 66.19 74.46% 332.65

ACF

56.66 40.47 97.13 81.13% 271.89 60.79 48.42 109.21 76.17% 321.14

Diff.

• 26.07*
• 5.73
• 31.8*

1.42*

• 25.05*
• 17.97*

43.02* 11.51*

*significant difference (t-test, α=5%)

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 20

Clearing functions – conceptual shortcomings

• Simulation and empirical data are substantially different!

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 21

Data for Clearing function estimation 1/2

(Häussler/Missbauer 2014; see also Fine/Graves 1989) Scatter plot of ManNB machine ρ=57.5%, empirical data

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 22

Data for Clearing function estimation 2/2

(Häussler/Missbauer 2014) Scatter plot of PriNB machine ρ= 51.17%, simulation data

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 23

Clearing functions – conceptual shortcomings

• Simulation and empirical data are substantially different!
• OLS regression over empirical or simulation data:

Conditional expectation of output given deterministic load! Distinction between empirical clearing function and clearing function for planning purposes. => Conventional parameterization method estimates the wrong function!

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 24

Data for Clearing function estimation ½ (repeated)

(Häussler/Missbauer 2014; see also Fine/Graves 1989) Scatter plot of ManNB machine ρ=57.5%, empirical data

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 25

Clearing functions – conceptual shortcomings

• Simulation and empirical data are substantially different!
• OLS regression over empirical or simulation data:

Conditional expectation of output given deterministic load! Distinction between empirical clearing function and clearing function for planning purposes. => Conventional parameterization method estimates the wrong function!

• Expected output depends on composition of the load.

=> (at least) two-dimensional CF necessary!

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 26

Clearing functions for different deterministic initial WIP levels, measured in hours of work (Missbauer 2014)

1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 Expected load Expected output Initial WIP=0 Initial WIP=1 Initial WIP=2 Initial WIP=3 Initial WIP=4 Initial WIP=5 Ideal curve

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 27

Estimated function Xit = fi(Wi,t-1+Ait) on empirical data

(Häussler/Missbauer 2014a)

Xit = fi(Wi,t-1+Rit; Cit)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 28

R2 of bottleneck machines from simulation data - short period length (Häussler/Missbauer 2014a)

Simulation data Util. Nonl.1D Nonl.2D Missb. 2Dcf PriBNS 95.34% 0.743 0.939

k=68.61, C=359.99 k=23.06, C=352.31

PackBNS 71.95% 0.937 0.977

k=71.87, C=362.58 k=40.36, C=334.53

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 29

R2 of bottleneck machines from empirical data

(Häussler/Missbauer 2014a)

Empirical data Util. Lin. 1D Nonl.1D Nonl.2D Missb. simple 2Dcf simple ManBN 88.71% 0.435 0.664 0.664 0.687 0.681*,**

b=0.60 k=181.43, C=1550.09 β=0.89, C=1613.31, k=192.13

PriBN 82.77% 0.405 0.575 0.578 0.600 0.579*,**

b=0.52 k=768.16, C=1643.29 β=0.76, C=1521.47, k=601.22

PackBN 80.03% 0.471 0.655 0.656 0.702 0.721*,**

b=0.60 k=218.35, C=1574.57 β=0.63, C=1468.74, k=40.47

*autocorrelation, **multicollinearity

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 30

Clearing functions – conceptual shortcomings

• Simulation and empirical data are substantially different!
• OLS regression over empirical or simulation data yields

conditional expectation of output given deterministic load! Distinction between empirical clearing function and clearing function for planning purposes => Conventional parameterization method estimates the wrong function!

• Expected output depends on composition of the load (Wt-1 vs. Rt)

=> (at least) two-dimensional CF necessary!

• Expected output depends on accuracy of the load estimation (probability

distribution), which is time-dependent. => Stochastic programming problem, hardly tractable.

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 31

Iterative approach: generic mechanism

Fixed lead time order release model Lead time anticipation model

Simulation (Hung/Leachman 1996, Kim/Kim 2001) Transient queueing (Riaño 2003)

Released

• rders

Flow times (HL) Loading ratios (R) Loading ratios + utilizations (KK) Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 32

Model of a production unit with a single (bottleneck) work center: Pre-determined backward lead time (distribution)

(repeated)

• 1
• 1

,

Min! Subject to +

• 1, ...,

+ X - 1, ..., 1, ..., 1, ..., , , , 1, ...,

t t t t t t t t t t t t t t T b t t t t t t t t t

hW l I W W R X t T I I D t T R X w t T X C t T I R W X t T

τ τ τ τ − =

+ → = = = = = = ≤ = ≥ =

∑ ∑ ∑

Additional Symbol

, b t

w

τ

Fraction of the output in period t that must be released in period t τ − (in order to be finished in period t)

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |

Dagstuhl, Feb 7-12, 2016

Hubert Missbauer No. 33

• Order release function keeps system state under control and reduces scheduling

complexity.

• Order release planning models seem to be not very sensitive to limited accuracy of the

demand forecasts. But: different experimental setting might modify these results!

• Load-dependent lead time models outperform conventional fixed lead time models,

results for Input/Output control and rolling horizon are still inconclusive.

• Clearing functions (CFs) parameterized by OLS regressions are biased and overestimate
• utput.
• Conventional 1-dim. CFs are a major simplification and should be extended towards
• multiple explanatory variables (sample path of the process!)
• time-dependent parameters.

But: Implementing this in a tractable release model seems challenging!

• Modeling load-dependent flow times without referring to WIP evolution is problematic.
• Integrating simulation and optimization in order release planning is difficult, underlying

theory is largely unexplored.

• Consistency of master planning and order release models (-> Aggregation of queueing

networks) is a research topic.

Conclusions

Intro | Trad. ORR | FLT models | Clearing function models | CF shortcomings | Iterative | Conclusions |