Date post: | 31-Dec-2015 |
Category: |
Documents |
Upload: | lillian-schroeder |
View: | 19 times |
Download: | 1 times |
1
12
/ t
A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB
SHOP PODUCTION SYSTEMS
Henny P.G. van OoijenJ.Will M. Bertrand
2
12
/ t
Overview
• Introduction• Literature review• Research question• Policy for capacity adjustment• Evaluation• Future research
3
12
/ t
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
4
12
/ t
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
5
12
/ t
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
6
12
/ t
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?
7
12
/ t
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
8
12
/ t
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?
9
12
/ t
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
10
12
/ t
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
11
12
/ t
Forecasting throughput times (II)
In this research:
• Estimate of remaining waiting time of an order with g remaining operations, reliability :
gFloadnorm
loadactual 1
12
12
/ t
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
13
12
/ t
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.
14
12
/ t
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
15
12
/ t
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
16
12
/ t
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
17
12
/ t
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