1212 / t 1 a short term capacity adjustment policy for minimizing lateness in job shop poduction...
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![Page 1: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/1.jpg)
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A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB
SHOP PODUCTION SYSTEMS
Henny P.G. van OoijenJ.Will M. Bertrand
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Overview
• Introduction• Literature review• Research question• Policy for capacity adjustment• Evaluation• Future research
![Page 3: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/3.jpg)
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Introduction• Job shop (functionally organized work centers)
– Dynamic, stochastic arrival pattern– Stochastic behaviour on the shop floor
Highly fluctuating throughput times => Poor performance
• Fixed lead times– “Adjust” demand – Adjust available capacity
• Small change of capacity => big impact on the performance
• Setting cost optimal due dates– Prediction of throughput times
![Page 4: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/4.jpg)
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Literature (I)
• Palaka et al.– Customers sensitive to quoted lead times (fixed
capacity/ marginal expansion)• So and Song
– Demands are sensitive to both price and delivery time (optimal setting of price/delivery time/capacity expansion)
• Ray and Jewkes– Demand is function of delivery time and price, and
price is a function of delivery time
![Page 5: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/5.jpg)
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Literature (II)
• Barut and Shridharan– Allocation (dynamically) of capacity to multiple product
classes
• Van Mieghem– Review strategic capacity management literature
Setting capacity levels on medium or long term for “average” orders, based on average lead times and/or average delivery reliability
![Page 6: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/6.jpg)
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Research question
Given fixed, realistic short, lead times, and given dynamic,
stochastic demand, then how can we obtain an (economically
justified) as high as possible delivery reliability?
![Page 7: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/7.jpg)
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Research question
Given fixed, realistic short, lead times, and given dynamic, stochastic demand, then how can we obtain an
(economicallyjustified) as high as possible delivery reliability?
ADJUST THE CAPACITIES AROUND A GIVEN LEVEL
![Page 8: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/8.jpg)
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Research question
Given fixed, realistic short, lead times, and given dynamic, stochastic demand, then how can we obtain an
(economicallyjustified) as high as possible delivery reliability?
ADJUST THE CAPACITIES AROUND A GIVEN LEVEL
HOW MUCH?
![Page 9: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/9.jpg)
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Research question
Given fixed, realistic short, lead times, and given dynamic, stochastic demand, what can we do to obtain a
(economicallyjustified) high delivery reliability?
ADJUST THE CAPACITIES AROUND A GIVEN LEVEL
HOW MUCH? Estimate the lateness given certain capacity levels
![Page 10: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/10.jpg)
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Forecasting throughput times (I)
• Empirically constructed routing normalized waiting time distribution functions Fg(.) per order category g
• Upon arrival an order with g operations and a required reliability of gets due date:
wloadactual
loadnormwN
1
)(1
operations
gj Floadnorm
loadactualptDD
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Forecasting throughput times (II)
In this research:
• Estimate of remaining waiting time of an order with g remaining operations, reliability :
gFloadnorm
loadactual 1
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Policy for capacity adjustment (I)
• If ntj is the actual load at a certain work center j at time t, then the total expected lateness is:
)))(((
; ;
.;.
xg
xordersreleased
joperationsremaining
joperremsWorkcentertj
xjx Floadnorm
n
ptDD
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Policy for capacity adjustment (II)
• Conjecture: the load at a certain work center can be interpreted as load in relation to the installed capacity
• “Adjusting” the load can be done by adjusting the capacity.
![Page 14: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/14.jpg)
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Policy for capacity adjustment (II)
• Conjecture: the load at a certain work center can be interpreted as load in relation to the installed capacity
• “Adjusting” the load can be done by adjusting the capacity.
)))(((
; ;
.;.
xg
xordersreleased
joperationsremaining
joperremsWorkcenter
tjj
xjx Floadnorm
n
ptDD
![Page 15: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/15.jpg)
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Policy for capacity adjustment (III)
• We assume : Capacity costs for adjusting the load with 1 unit is equal to c1; lateness costs is c2 per unit late.
))))((()1((min 2
; ;
.;.2
11
xg
xordersreleased
joperationsremaining
joperremsworkcenter
tjj
xjxti
m
ii F
loadnorm
n
ptDDcnc
![Page 16: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/16.jpg)
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Policy for capacity adjustment (IV)
• After some rewriting this leads to an equation of the form:
This is a Constrained Least Squares problem
)2
1(min
2
0aNcT
![Page 17: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/17.jpg)
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Evaluation
• Simulation study– Ideal job-shop; 5 work centers; 90%
utilization;First Come First Serve
– Capacities can be varied weekly or monthly– The same lead time for all orders/Different
lead times for orders of different categories
![Page 18: 1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand](https://reader033.vdocuments.site/reader033/viewer/2022052701/56649d5c5503460f94a3b30a/html5/thumbnails/18.jpg)
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Future research
• Evaluation study• How to determine capacity adjustment costs• How to find the empirical distribution functions• Other priority rules