a short term capacity adjustment policy for minimizing lateness in job shop poduction systems
DESCRIPTION
A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS. Henny P.G. van Ooijen J.Will M. Bertrand. Overview. Introduction Literature review Research question Policy for capacity adjustment Evaluation Future research. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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
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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
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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?
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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
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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?
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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
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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.
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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
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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
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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
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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